ASKM_Games_Intermediate_LG

Grades
3–6
leader’s guide
INTERMEDIATE
BORAH-GELLER, ROBERTSON, AND WEBER

leader’s guide
BORAH-GELLER, ROBERTSON, AND WEBER
Grades
3–6
INTERMEDIATE

Copyright © 2004 by Developmental Studies Center
All rights reserved. Except where otherwise noted, no part of this publication may be reproduced in
whole or in part, or stored in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without the written permission of the publisher. For
information regarding permissions, write to the Editorial Department at Developmental Studies Center.
Permission is granted to reproduce the blackline masters in this volume for classroom use only.
AfterSchool KidzMath is a trademark of Developmental Studies Center.
This project is based upon work supported by the National Science Foundation under grant
no. ESI-9705421. Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the authors and do not necessarily reflect the views of the National
Science Foundation.
This project was also supported by the Ewing Marion Kauffman Foundation under strategic
grant no. 20000853.
Developmental Studies Center
2000 Embarcadero, Suite 305
Oakland, CA 94606-5300
(800) 666-7270, fax: (510) 464-3670
www.devstu.org
ISBN-13: 978-1-57621-452-7
ISBN-10: 1-57621-452-4
Printed in China
3 4 5 6 7 8 9 10 PVN 11 10 09

Acknowledgments �� iv
From Us to You�� vii
Getting Started
Before You Begin�� viii
The Leader’s Role �� ix
Choose a Game�� ix
Collect the Materials�� x
Get Ready�� x
Before the Game�� xi
During the Game�� xi
After the Game�� xii
Materials in the Kits�� xiii
Helpful Information
Working Together�� xv
Tips for Playing Games Cooperatively �� xv
Social Skills�� xv
Making Decisions�� xv
Giving and Getting Help �� xvi
Playing Responsibly�� xvi
Math and Social Skills at a Glance�� xvii
Math Children Commonly Learn
in Grades 3–6 �� xix
Games
Introduction to Number Sense Games�� 1
Save $10.00 (Grades 3–5)�� 3
Spinning for Dollars (Grades 3–5) �� 9
Flick (Grades 3–6) �� 15
Bounce Back (Grades 3–6)�� 21
What’s My Rule? (Grades 3–6)�� 27
Number Detective (Grades 4–6)�� 33
Introduction to
Multiplication and Division Games�� 39
Ant Hill Picnic (Grades 3–4)�� 41
Rectango (Grades 3–5) �� 47
Lonely Aces (Grades 3–4)�� 53
Multiplication Basketball (Grades 3–6)�� 59
Multiplication Bowling (Grades 3–6)�� 65
Multiplication Uncovered (Grades 3–5)�� 71
Multiplication Baseball (Grades 3–6)�� 77
Multiple Moves (Grades 3–5) �� 83
Three Tac Toe (Grades 4–6)�� 89
Beach Ball Multiplier (Grades 4–6)�� 95
Forehead Factors (Grades 4–6)�� 101
The Leader Says Divide (Grades 3–5)�� 107
Spin Spot (Grades 4–6)�� 119
Target (Grades 3–6)�� 125
Disappearing Pyramid (Grades 3–6)�� 131
Stadium Tour, USA (Grades 3–6)�� 137
Equapardy (Grades 3–6) �� 143
Introduction to
Fraction, Decimal, and Percent Games�� 149
Flip Your Lid (Grades 3–6)�� 151
Wacky Cakes (Grades 3–4) �� 157
Fill ‘Em Up (Grades 5–6)�� 163
Picture This! (Grades 4–6)�� 169
Match Pass (Grades 5–6)�� 175
Three Hexagons (Grades 5–6)�� 181
Stick the Fraction on the Donkey (Grades 5–6)�� 187
Appendices
Correlation to National Mathematics Standards �� 195
Site Planning Tool�� 203
Leader’s Checklist�� 208
AfterSchool KidzMath Questionnaire �� 215
Dear Family Letter�� 218
Dear Family Letter in Spanish �� 219
Dear Teacher Letter �� 220
Additional Reading and Research�� 221
Math Glossary �� 222
contents

iv A F T E R S C H O O L K I D Z M AT H ™ G A M E Siv A F T E R S C H O O L K I D Z M AT H ™ G A M E S
Many people were involved in the development and production of the
AfterSchool KidzMath™ program. We are grateful for their time, valuable
suggestions, and encouragement.
We wish to express our deep appreciation to the National Science
Foundation and, in particular, to our program officers Sylvia M. James
and Julie I. Johnson for their support.
We also wish to thank the teachers, principals, mathematicians, and
youth development and education leaders who have served on our
Advisory Board:
Patrick Callahan
Sue Eldredge
Cheryl Green
Gilberto Guerrero, Jr.
Angela La Fleur
Hazel Lewis
Eddie McCord
Ginny Miller
Lisa Muntz
Pat Murphy
Barbara Roth
Erica Saxby
Belinda Thompson
Virginia Thompson
Gail Vessels
We wish to thank the following consultants who advised the developers
and contributed to the development of the program:
Donna Goldenstein
Camilla Schneider
Cecelia Wambach
Acknowledgments

I N T R O D U C T I O N vI N T R O D U C T I O N v
California
Berkwood Hedge School, Berkeley
Berkeley Unified School District
CampFire USA–Oakland East Bay Council
East Oakland Boxing Association
Ella Hill Hutch Community Center
Girls Incorporated of the Island City, Alameda
Indo Chinese Housing, San Francisco
Oakland Unified School District
San Bernardino City Unified School District–CAPS
(Creative After School Programs for Success)
San Francisco Boys Girls Club
San Francisco Unified School District
YMCA of the East Bay
Louisiana
Northwestern State University Child Family Network
Missouri/Kansas
Boys Girls Clubs of Greater Kansas City
Guadalupe Center, Inc., MO
Kidzone, KS
The Learning Exchange, MO
Linn County 21st Century Community
Learning Centers, KS
LINC (Local Investment Commission), MO
YMCA of Greater Kansas City
We would also like to give special thanks to Darlene Bell-Carson for her
invaluable input to the AfterSchool KidzMath Games program. Darlene devel-
oped many of the game ideas, provided constructive feedback on the games,
and field-tested the games with the authors.
Finally, the publication of this book would not have been possible without
the help of the AfterSchool KidzMath staff:
Muriel Christianson, Administrative Assistant
Richard Cossen, AfterSchool KidzMath Director
Ann House, Research Associate
Valerie Ruud, Editor
Jay Flom, Illustrator
Many after-school programs field-tested the materials, allowed the authors
into their sites to pilot and observe the activities, and provided us with
feedback that helped shape the content and format of the program.
We particularly wish to acknowledge the children and staff of the
following organizations:

I N T R O D U C T I O N viiI N T R O D U C T I O N vii
FTER-SCHOOL AND OUT-OF-SCHOOL PROGRAMS are
increasingly important to children’s learning and development.
They support children’s academic, artistic, social, health, and
recreational needs. Little curriculum, however, has been designed
specifically for these programs. To help in the area of mathematics,
we created the AfterSchool KidzMath™ Games program.
Developed with the assistance of staff and children in after-school
programs across the country, these games help children learn key
math skills while having fun. To meet the unique needs of after-
school programs, they are designed for large and small groups,
can be used with a range of ages, include opportunities for
movement, are easy to play, and require few materials. Thinking
about busy leaders, we designed a kit that includes most of the
needed materials and organized it in a way that is easy to use
with both large and small groups. The games can be used to help
children with skills needed for homework, as a free-choice activity,
as a structured activity for a group, in tutoring programs, or in
math or game clubs.
AfterSchool KidzMath Intermediate Games are 30 non-competitive
games that help children develop number skills. These games also
help children learn to make fair decisions, be responsible, and
help one another. Although certain grade levels are suggested for
each game, the games can easily be modified for younger and
older children.
We hope you have as much fun playing these games with children
as we have!
Lisa Borah-Geller, Laurel Robertson, Megan Weber
From us
to you

viii A F T E R S C H O O L K I D Z M AT H ™ G A M E S
getting started
before you begin
The AfterSchool KidzMath™ games help children
develop their understanding of and flexibility with
numbers. In particular, they help children develop
skills in three important areas: number sense;
multiplication and division; and fractions, decimals,
and percents. The games also help children learn
to be responsible, make decisions, and help each
other. Before you introduce AfterSchool KidzMath at
your site, think about ways you can incorporate it
into your existing activities. You may wish to use
the Site Planning Tool in the appendix (p. 203) to
help you. The form lists some of the characteristics
of sites that have most successfully implemented
the program. Also think about the following issues:
1 How will you fit the AfterSchool KidzMath
games into your site’s schedule?
• Start a weekly or biweekly math or game club
in which the children play the games.
• Use the games to build the children’s skills
during homework time. (For example, to
help children who are struggling with math
homework on division, use a game like
“Lonely Aces” to give them practice.)
• Play the games when there is extra time after
homework is done.
• After children know how to play the games,
have them available during free-choice time.
• Play the games during “buddy” time, pairing
older and younger children.
• Have a math camp during the summer.
• Have a math carnival. Set up several games in
a gym or outside and have groups of children
rotate from game to game.
2 What are your children’s specific needs
in mathematics?
• Talk to the children’s teachers about areas
where they need extra help. You can also
use the “Dear Teacher” letter on page 220 to
communicate with teachers.
• Ask the children what they are working on in
math at school and what they need help with.
• Use the “Math Children Commonly Learn in
Grades 3–6,” page xix, and “Correlation to
National Mathematics Standards,” page 195,
to help you learn more about the math skills
and concepts children typically study in
these grades.
3 How can you assess the children’s progress?
• The questionnaire that starts on page 215 will
help you identify the children’s strengths and
areas for improvement in meeting the three
AfterSchool KidzMath “Goals for Children”:
— Increase children’s enjoyment of
mathematics
— Increase children’s mathematical
understanding and skills
— Increase children’s ability to work
with others
• You can do assessments at the beginning,
middle, and/or end of the year.
4 What can you do to prepare your site,
staff members, and families to begin
AfterSchool KidzMath?
• Send home the “Dear Family” letter in English
or Spanish, pages 218 and 219, that explains
the AfterSchool KidzMath program to families.

I N T R O D U C T I O N ix
• Use the Site Planning Tool, page 203, to
assess your site and see what you can do to
make it a better place for children to do
AfterSchool KidzMath.
• Use the Leader’s Checklist, page 208, to
help you grow as you lead the games. The
checklist can be used for self-review or a
co-worker or administrator can use it as an
observation tool and provide feedback about
a game session. If you have a co-worker or
an administrator fill it out, be sure to schedule
time soon after the observation to talk about
what the observer noted. Discuss what worked
well and ideas for improvement.
• Talk to other staff members to see what is
needed to begin.
5 What are you going to do at your site to
keep AfterSchool KidzMath games alive?
• Work with another staff member to plan and
discuss the games.
• Take time at staff meetings for staff to plan,
play, and discuss the games.
6 If you are responsible for training other
staff, how will you introduce the program
and support staff members?
• Play games at a staff meeting.
• Have staff members watch you teach a
game to children and discuss it afterwards.
• Fill out the “Leader’s Checklist” as you watch
a staff member teach a game and discuss it
with the staff member afterwards.
• Schedule an AfterSchool KidzMath in-person
workshop through Developmental Studies
Center (DSC). Visit the website www.devstu.org
for more information.
The Leader’s Role
T
hese AfterSchool KidzMath games will be more
successful and have greater impact if you are well
prepared. The games are most effective if the leader
explains and demonstrates the game, asks mathematical
and social questions, and supports the children while they
play. (After the children have played a game several times
with your support, you may decide to let them play on
their own.) There are simple steps to take before, during,
and after each game that will support the children’s
learning and make the games fair and fun for all.
Choose a Game
Use the game summary on the first page of each game
to help you choose one. Ask yourself the following
questions as you choose a game.
 What math skills are the children learning?
Think about the children at your site. In what areas
do they need support as they learn new skills? Where
are they having trouble? Are they having trouble
with fractions? Do they need help understanding
decimals? Are they struggling with division? The
games are arranged from easiest to hardest in each
section. Review the games to find those that will help
the children develop the skills they are working on.
“Math and Social Skills at a Glance,” page xvii, lists the
math focus for each game and will help you choose a
game to meet your children’s math needs.
 What social skills are the children learning?
Are the children having difficulty helping one
another? Do they need help staying involved in a
game when it is not their turn? Do they know how
to give help without giving the answer? “Math and
Social Skills at a Glance” lists the social focus for each
game and will help you choose a game to meet your
children’s social needs.
 What type of activity do the children need?
Is it time for a noisy game with lots of movement or for
a quieter game? What will suit the children’s needs?
 What size group do you have?
Do you need a large-group game, one for several
small groups, or one for a pair to play? The suggested
group size is listed on the first page of each game.

x A F T E R S C H O O L K I D Z M AT H ™ G A M E S
Collect the Materials
Most of the materials needed to play each game are
found in the games kits, and are listed on the first page
of each game. Make sure you are familiar with the kits
and the materials in them. (See “Materials in the Kits,”
page xiii.) If additional materials are needed, they will
be listed in the “You’ll Need” section of each game.
Get Ready
 Read and play the game yourself.
Read and play each game yourself before introduc-
ing it to the children. The children are less likely to
enjoy the game if you are struggling to figure out
how to play while you are explaining the game to
them. Playing the game beforehand also will help
you see the challenges that may arise and plan a
way to deal with them.
 Understand the mathematics.
All math vocabulary words are italicized and
defined in the Math Glossary (pp. 222–223). You
can also find out more information about the
mathematics in each content area by reading the
introductions at the beginning of each section. To
find specific information about the mathematics in
each game, read the Math Skills paragraph on the
second page of each game.
 Think about whether to change the game.
Think about ways to modify the game to fit your
children’s needs. Some ideas are listed at the end
of each game in a section called “Changing the
Game.” Sometimes you will not know that you
need to modify a game until the children begin
playing. You can change the game on the spot.
 Think about where to play.
If possible, play the games where loud noises, lots
of movement, or other activities are not competing
for the children’s attention.
As you read through the game, think about the
size of the groups who will play and the kind of
game it is. Some games are played by small groups
of two, three, or four children on a table or small
game board. Some are played by large groups in
a setting where they have room to move. A few
require special preparation of the space — putting
up a game board or score sheet.
 Decide how to group the children.
Some of the games are played in groups of two to
four children. As you read through the game, think
about how you will form these groups. Be prepared
to explain to the children that they are expected to
be able to work with everyone, even if they are
not partnered with the person they were hoping
for. You can randomly assign children to play
together using any of the suggestions that follow.
To form pairs:
• Collect enough different small objects (like a
marking pen, toothpick, or large paper clip) for
half of the children. Cut a piece of string (or yarn
or paper) the length of each item. Randomly
distribute the objects and strings so that each
child has one or the other. Ask each child to find
the person whose object or string matches hers
in length.
• Write fractions on index cards for half of your
group and matching pictures of the fractions for
the other half. (For example, one card would
show 1
⁄2 and the matching card would show .)
Have each child pick a card and then find the
person with the matching card.
• Write four-digit numbers on index cards for half
of your group and the numbers expressed as
thousands, hundreds, tens, and ones for the
other half. (For example, 4,734 would be written
“four thousands, seven hundreds, three tens and
four ones.”) Ask the children to find the person
with a matching card.
To form small groups:
• Cut magazine pictures into as many pieces as
the number of children you want in each group.
Have each child choose a piece of the picture
and then find the other children with pieces of
the same picture.
• Write the children’s names on small pieces of
paper. Fold the papers and place them in a can
or bag. Randomly select three or four names at
a time to form a group.

I N T R O D U C T I O N xi
Before the Game
It is important that the children clearly understand a
game before they begin to play. Demonstrating is a
good way to communicate how to play. Use different
methods to demonstrate when playing small-group
games than when playing large-group games.
 To introduce a small-group game, explain the
game and demonstrate it for all the children at
once before you divide them into small groups to
play. Choose a child to demonstrate with you as
you explain the game, or choose a group of two to
four children to demonstrate as you explain. Invite
the children to ask questions about the game, or
use some of the “talk about” questions in the game
instructions to start a discussion.
Once all the children understand how to play,
divide them into groups of the suggested size.
Distribute the materials and have the groups play.
 To introduce a large-group game, have the whole
group practice playing. Once again, invite the
children to ask questions or use the “talk about”
questions to discuss the game. (For example, for
the game “Multiple Moves,” you might have all the
children practice an action and talk about why it is
important to be aware of their personal space to
play the game safely.)
During the Game
 Support the children as they play.
One of the most important roles of the leader is to
support the children while they play so that they
get the most out of the games and feel comfortable
and safe. Walk around while the children play to
make sure that all of the groups are working well
together, learning math, and having fun. Ask
questions — your own and the ones suggested in
the game instructions. Encourage the children to
figure out solutions for any problems that arise.
 Allow the children to choose who will go first.
There are many fair ways to decide who will go
first. If the children need help thinking of fair ways,
you might suggest one of the following ideas:
• order themselves alphabetically
• order themselves by height
• order themselves by birthdays
• choose someone who has not gone first lately
• play “rock, paper, scissors”
 Help children who are having difficulty.
In any group, some children will have difficulty with
parts of a game. Be aware of how you can support
children who need help. (For example, if a conflict
occurs, stop the game and ask the children to discuss
fair ways to resolve the conflict. If the children have
trouble shuffling cards the traditional way, suggest
an alternative, such as spreading the cards on the
table, mixing them up, and then making a new pile.)
 Help children of different ages and skill levels.
It is often a good idea to pair older or more-skilled
children with younger or less-skilled children
and encourage them to help each other. In such
groupings, the younger or less-skilled children feel
supported and listen to the mathematical thinking
of others, while the more-skilled or older children
build their own understanding by explaining their
thinking aloud.
Encourage all the children to use strategies that work
for them. (For example, in “Stadium Tour, USA” some
children may refer to the multiplication chart, while
others will rely on memorized multiplication facts.)
Be sensitive to older children who are having
difficulty with mathematical concepts. You may
have eleven-year-olds who are struggling with their
multiplication facts and eight-year-olds who know
them all. Children learn at different rates, so be
supportive and acknowledge everyone’s effort.
Encourage the children to help and support one
another.
 Encourage the children to decide some of the rules.
Children often think of ways to change a game as
they play. When this happens, have the children
talk about the change, whether it is fair to everyone
and whether all the group members can agree to it.
Then, allow them to change the game.
While playing, the children will occasionally need
to change the rules of the game to cover specific
situations. We intentionally included this option
because it keeps the children involved in the game

xii A F T E R S C H O O L K I D Z M AT H ™ G A M E S
and increases their ability to solve problems and
work together.
 Support children who are learning English
as a second language.
Explain the game in the child’s first language, if
possible. When you have two or more children who
speak the same language, have them play together.
Before playing, demonstrate a game until all the
children understand it. Explain and demonstrate the
meaning of difficult words in the game directions.
(For example, to explain stack, you might say,
“Stacking means putting one card on top of another,”
as you demonstrate how to stack the cards.)
After the Game
 Have Meaningful Discussions
An important part of your role is to ask questions
that will help the children think about the math
and social skills before, during, and after the game.
Use questions that require the children to explain
their thinking rather than answer in one or two
words. (For example, asking “How did you find that
number?” will give you more information about
children’s understanding than asking “What
number did you get?”) In each game, ideas for
questions or discussion topics to extend the
children’s learning are provided in the “talk about”
sections. You may decide to ask a question in a
different way or to ask different questions. You
need not ask every suggested question. When
asking questions choose appropriate words or
numbers that make sense for your group.
 Tips for Having a Discussion
• Ask questions that have more than one
correct answer.
• Help all the children have a chance to participate.
One way of doing this is to ask a question of the
group and then have each child turn to the per-
son sitting next to her to discuss their answers.
• Wait at least five seconds for the child to respond
to your question, to give her time to think after
hearing it.
• Use eye contact while asking the question and
stay interested while listening to the response.
• Encourage the children to practice good listening
skills (for example, look at the person who is
talking, wait for the person who is talking to
finish without interrupting).
• When a child gives a solution, ask him to
explain. (For example, you might ask “How did
you find that solution?” or “How did you figure
that out?” or “Please share your thinking with
us.”) This provides opportunities for the children
to learn strategies from one another.
• Acknowledge the children’s responses without
judging. (Nod and say, “hmm” or “thanks,”
or “okay.”)
• Repeat a child’s answer back, to make sure you
understand. (For example, you might say, “You said
that you count by fives 5 times to figure out that
five times five equals twenty-five. Is that right?”)
• If a child’s answer is incorrect, rather than telling
him he made a mistake, help him find his mistake
by asking a question. (For example, “You said six
times five is twenty-five. How did you find that
answer?” You might also say, “Try figuring that
out again and see what answer you get.”)

I N T R O D U C T I O N xiii
Materials in the Kits
Y
our set of game materials comes in six boxes,
one Leader’s Kit and five Kids’ Kits designed for
a total of 20 children. Use the holder to store the kits.
Most of the materials needed to play the games are
included in either the Leader’s Kit or Kids’ Kit. Some
games require other materials you probably have at
your site or can collect yourself. The first page of each
game tells you which game materials are in the kit
and what you will have to collect at your site.
The Kids’ Kit contains the materials for small-group
games. Each kit has enough materials for a group of
two to four children. The Leader’s Kit has the materials
for the large-group games and a book of instructions
for all the games, called the Leader’s Guide. The
“Players” information on the first page of each game
tells you whether the game is for large or small groups.
Before you begin to introduce the games at your site,
familiarize yourself with all the materials. The contents
of the boxes are listed on the back covers of the game
boards and Leader’s Guides.
The game boards in the Kids’ Kit come in a spiral-
bound book and can be used over and over again.
Two to four children share each game board. Some of
the game boards take up two pages. In this case the
game board book will need to be open flat so that
both halves show. Some of the games have blank
game boards you can use to make the game easier or
harder. There is also a blank dry-erase board in each
Kids’ Kit to keep score or provide a writing or drawing
space. On the back of each dry-erase board there is a
multiplication table that the children can use while
playing the multiplication and division games. The
game boards and dry-erase boards can be written on
using the dry-erase markers provided and erased with
a cloth, tissue, or paper towel. Do not use other types
of markers as they may not erase well.
One deck of playing cards is included in each Kids’ Kit.
Several games make use of these playing cards. Other
decks of cards are provided in perforated sheets. We
suggest that you punch them out yourself before using
the kits for the first time. You can assemble the deck
for each game by matching the designs on the back of
the cards. Put rubber bands around the decks of cards,
or store each in a small reclosable plastic bag.
Spinners are used for some games. To make a
spinner, slip the appropriate spinner card into the
plastic holder.
The illustrations on the game cards, spinner cards, and
game boards help you match the pieces of the game.
Before beginning to play with the children for the first
time, and as needed after that, talk about how to treat
the games materials responsibly and why this is impor-
tant. Talk specifically about making sure that materials
do not get lost. Older children can check what is in a
box using the checklist on the back of the game board
book. This helps the children develop responsibility for
taking care of materials, one of the social goals of
AfterSchool KidzMath.
10%10%

xiv A F T E R S C H O O L K I D Z M AT H ™ G A M E S
 The Leader’s Kit contains:
• A Leader’s Guide that gives the directions
for all the games
• 4 wall posters for “Stick the Fraction on
the Donkey”
• A wall poster for “Equapardy”
• 5 game boards for “Three Hexagons”
• A beach ball for “Beach Ball Multiplier”
• A permanent marker to write on the beach ball
• A dry-erase writing board with the multiplication
table on the back
• 3 dry-erase markers
• 10 dice
• 3 sheets of stickers to make different kinds
of dice
 Each Kids’ Kit contains:
• A spiral-bound book of game boards
• A plastic spinner holder
• 6 spinner cards to insert into the holder
• 100 plastic game markers
• A deck of playing cards
• 6 dice
• 11 sheets of perforated game cards
• A dry-erase board with the multiplication table
on the back
• 3 dry-erase markers
 Other materials you will need to play the games:
• Small reclosable plastic bags to store the decks
of cards
• 1 container for rolling dice (a paper or plastic
cup works well)
• 5 tennis balls
• 30 empty plastic bottles
• 20 small plastic lids (the ones on yogurt or
cottage cheese containers work well)
• 1 roll of masking tape
• 1 pad of self-stick notes
• 20 pencils
• Small pieces of paper
• Chart paper or several large pieces of paper
• 5 pieces of cloth, tissues, or paper towels to
erase dry-erase boards
Before playing a game, make sure you have gathered
and prepared all the materials. (For example, before
you play “Multiplication Uncovered,” you will need to
stick the round stickers on the dice and write numbers
on them.)
Before the children play a game, you will demonstrate
it as you explain the game directions. You may need
the materials in a Kids’ Kit or the Leader’s Kit to do
this. As the children get ready to play, make sure they
have located all the pieces they need to play the
game. After they play, make sure each group gets all
the pieces back in the Kids’ Kit.

I N T R O D U C T I O N xv
helpful information
Working Together
T
he AfterSchool KidzMath games are cooperative
rather than competitive. At most after-school sites,
children of different ages and skill levels play together.
Competitive games put younger or less-skilled children
at a disadvantage. These children are more likely to
lose their turn or be “out.” As a result they have fewer
opportunities to practice math. Even more importantly,
consistently losing lowers children’s self-esteem, enjoy-
ment of math, and confidence in their mathematics
abilities. Cooperative games are fair and fun for all and
allow everyone to be successful and to learn.
Tips for Playing Games Cooperatively
 It takes time for children to learn to cooperate.
Playing games cooperatively may be quite a struggle
at first. Often, children are more familiar with compe-
tition than with cooperation. They need time to
adjust to this new way of playing games. (If many of
the activities at your site are competitive, it will be
even more difficult for the children to switch to play-
ing AfterSchool KidzMath games cooperatively.) The
children’s behavior will not change overnight. They
may need to play a game several times before they
can play it with success cooperatively. This is normal.
 Talk about the importance and benefits of
playing cooperatively.
Help the children understand that playing coopera-
tively makes the game fair for children of different
skills and ages. Working together gives everyone a
chance to learn math their own way at their own
speed and to experience helping and being helped.
 Seek support from other staff members and
your supervisor.
Talk about how to help the children learn to
cooperate. The more cooperative activities you do
at your site, the easier it will be for the children to
play the games cooperatively.
Social Skills
A
fterSchool KidzMath games help children learn
math and how to work together effectively. Just
like math skills, social skills are learned over time and
with repeated practice. AfterSchool KidzMath games
give children experience making decisions, giving and
getting help, and playing responsibly.
Making Decisions
The best way to learn to make good decisions is
to have many opportunities to talk about decision
making, to make decisions, and to think about the
results of these decisions. To help the children learn
to make decisions, you can:
 Provide lots of opportunities to make decisions.
Frequently involve the children, individually and in
groups, in making decisions about the games.
For example: When you begin playing these
games, you might have the children make simple
decisions, like who will go first. After they have
played the games for a while, you might have
them make more complicated decisions, for
example, how to change a game to make it
more or less challenging.
 Talk about what it takes to make a decision.
Help the children think about how to make a
decision and what to consider. When you need to
make a decision, talk with the children about your
decision-making process: identify the problem, find
several solutions, think about the outcome of each,
consider the needs and desires of all involved, and
come to agreement. (For example, when deciding
where to play a game, think aloud about the
reasons a certain area is appropriate to play in.)

xvi A F T E R S C H O O L K I D Z M AT H ™ G A M E S
 Discuss how the children made decisions.
When the children have made a decision, you
might ask:
– Do you all agree? How did you come to that
decision? Is your decision fair to everyone? How?
– What was your idea? Did it get included in the
decision? How did you decide to include it or
not include it?
– What do you think will happen as a result of
your decision?
Giving and Getting Help
Since children of different ages and skill levels play
the games together, it is important that the most-
skilled child does not take over the game, making it
difficult for a less-skilled child to take the time he
needs to do the math. Some children find it hard to
ask for help, because asking for help signals to others
that they don’t know something. It is important for
children to learn how to ask for help and to feel it is
safe to do so. They also need to learn how to give
help — how to support another person in figuring
something out for himself (rather than doing it for
him or telling the answer) and how to help in a way
that is respectful. To help children develop these skills:
 Involve the children in many cooperative activities.
When possible, provide cooperative activities in
addition to the AfterSchool KidzMath games. Each
time they work together to accomplish something,
the children develop social skills.
 Set an expectation that everyone helps others.
Children are more likely to help one another
before, during, and after the game if they believe
that they are expected to do so.
 Talk about how to ask for help and how to give help.
Before a game, talk about ways the children can
help one another. Role-play how to ask for help
and how to give help in ways that are respectful.
During and after the game, ask the children about
how they are helping each other and how to be
better at doing so. (For example, they could help
someone by asking a question or giving a hint
rather than telling him the answer.)
 Pay attention when the children make fun of one
another or are not helping one another.
Stop the game and discuss the consequences of
their behavior and the other ways they could
behave, or role-play more effective ways for the
children to play the game.
Playing Responsibly
We want children to learn to be responsible for their
learning and behavior. This includes such things as
being respectful to others, playing safely, taking turns,
and handling the materials responsibly. To help the
children develop these skills:
 Have a discussion before playing a game.
Discuss and role-play ways of respecting others
while playing a game. (For example, before playing
“Multiplication Uncovered,” page 71, discuss how it
feels to be laughed at if you say a wrong answer.
Have the children role-play how they will respond
if someone says the wrong answer.) The social
skills listed in the games can help you think about
the skills to discuss and role play with children.
 Have a discussion after playing a game.
Ask the children about how they played responsibly
and ways they could improve.

I N T R O D U C T I O N xvii
T
he AfterSchool KidzMath games help children
develop their understanding of and flexibility
with numbers. In particular, they help children
develop skills in three important areas: number
sense; multiplication and division; and fractions,
decimals, and percents. The games also help children
learn to be responsible, make decisions, and help
each other. This chart lists the math and social focus
for each game. Use this chart to help you pick games
that are appropriate for your children.
N U M B E R S E N S E GAM ES
Save $10.00, p. 3 • Add and subtract multiples of 25 • Stay involved while waiting for a turn 3–5
using money
Spinning for Dollars, p. 9 • Add multiples of 5 and 10 using money • Give others time to think before offering help 3–5
Flick, p. 15 • Add and subtract multiples of 10 • Consider all ideas before making a decision 3–6
• Be respectful when others make mistakes
Bounce Back, p. 21 • Subtract multiples of 100 • Encourage others 3–6
• Play safely
What’s My Rule?, p. 27 • Recognize number patterns • Stay involved while waiting for a turn 3–6
• Relate numbers to other numbers • Be persistent
Number Detective, p. 33 • Recognize that the position of a digit • Explain one’s thinking 4–6
determines its value • Be respectful when others make mistakes
M U LTI P LI CATI O N AN D D IVI S I O N GAM ES
Ant Hill Picnic, p. 41 • Divide by 12 or less with and • Give others time to think before offering help 3–4
without remainders
Rectango, p. 47 • Use a visual model of multiplication • Consider all ideas before making a decision 3–5
• Multiply by 6 or less
Lonely Aces, p. 53 • Divide by 7 or less • Give others time to think before offering help 3–4
• Stay involved while waiting for a turn
Multiplication Basketball, p. 59 • Multiply by 12 or less • Encourage others 3–6
• Add
Multiplication Bowling, p. 65 • Multiply by 10 or less • Make decisions together 3–6
• Add to 200 or less • Stay involved while waiting for a turn
Multiplication Uncovered, p. 71 • Multiply by 12 or less • Be respectful when others make mistakes 3–5
• Stay involved while waiting for a turn
Multiplication Baseball, p. 77 • Multiply by 6 or less • Be respectful when others make mistakes 3–6
• Give help respectfully when asked
Math and Social Skills at a Glance
GAME MATH SKILLS SOCIAL SKILLS GRADES
(continues)

xviii A F T E R S C H O O L K I D Z M AT H ™ G A M E S
Multiple Moves, p. 83 • Use multiples from 2 to 5 • Be respectful when others make mistakes 3–5
Three Tac Toe, p. 89 • Find multiples • Help without giving the answer 4–6
• Multiply by 12 or less
Beach Ball Multiplier, p. 95 • Multiply by 11 or less • Explain one’s thinking 4–6
Forehead Factors, p. 101 • Multiply or divide by 10 or less • Be respectful when others make mistakes 4–6
• Find factors • Help without giving the answer
The Leader Says Divide, p. 107 • Divide by 10 or less • Be respectful when others make mistakes 3–5
• Practice mental math
Spin Spot, p. 119 • Find factors • Help without giving the answer 4–6
Target, p. 125 • Add, subtract, multiply, and • Help without giving the answer 3–6
divide mentally • Give others time to think before offering help
Disappearing Pyramid, p. 131 • Add, subtract, multiply, and • Explain one’s thinking 3–6
divide mentally • Make decisions together
Stadium Tour, USA, p. 137 • Add, subtract, multiply, and • Give others time to think before offering help 3–6
divide mentally • Help without giving the answer
Equapardy, p. 143 • Add, subtract, multiply, and divide • Work as a group to solve a problem 3–6
F R ACTI O N, D EC I MAL, AN D P E R C E NT GAM ES
Flip Your Lid, p. 151 • Understand fractions of a group • Be respectful when others make mistakes 3–6
• Identify fractions and equivalent • Play safely
fractions
Wacky Cakes, p. 157 • Add fractions • Make decisions together 3–4
• Find equivalent fractions
Fill ‘Em Up, p. 163 • Understand meaning of tenths, • Consider all ideas before making a decision 5–6
hundredths, and one whole
• Add decimals
Picture This!, p. 169 • Understand meaning of percents • Stay involved while waiting for a turn 4–6
Match Pass, p. 175 • Recognize equivalent fractions • Stay involved when you’ve finished 5–6
and percents and others haven’t
• Add fractions and percents
Three Hexagons, p. 181 • Recognize equivalent fractions • Help without giving the answer 5–6
and percents • Stay involved while waiting for a turn
Stick the Fraction • Find fractions and percents mentally • Ask for help when needed 5–6
on the Donkey, p. 187 • Play safely
GAME MATH SKILLS SOCIAL SKILLS GRADES
Math and Social Skills at a Glance
continued

I N T R O D U C T I O N xix
Math Children Commonly Learn in Grades 3–6
K
nowing the math concepts and skills children are expected to learn in school will help you
assist your children with their homework, identify math areas they need to work on, and
choose appropriate math activities. The following list shows the grade in which children begin to
learn various number skills. Each grade includes and builds on what was taught in the previous
grades. The words in italics are defined in the “Math Glossary,” pages 222 and 223.
Grade 3
N U M B E R S
 Compare numbers to friendly numbers such as
500, 750, and 1000
 Understand the structure of our number system (for
example, that 613 is 6 × 100 plus 1 × 10 plus 3 × 1)
 Understand fractions as parts of unit wholes and
collections, as locations on number lines, and as
division of whole numbers
 Recognize and find equivalent forms of commonly
used fractions (for example, ½ = 2
⁄4 = 3
⁄6 = 4
⁄8)
O P E R ATI O N S (+, –, ×, ÷)
 Add and subtract multi-digit whole numbers
with ease
 Learn multiplication and division facts to 144
 Explore multiplication with two- and
three-digit numbers
 Explore addition and subtraction with fractions
and decimals
P R O B LE M S O LVI N G
 Choose and use tools and methods to solve word
problems involving
— addition, subtraction, multiplication, and division
with whole numbers
— addition and subtraction of decimals and fractions
 Develop and use strategies such as estimation,
mental calculation, and the ability to see if a
solution makes sense
Grade 4
 Understand and use large numbers
 Understand the meaning of decimals and their
place-value structure (for example, that tenths are
ten equal parts of 1)
 Recognize and write decimals to tenths
 Understand the relationship of decimals and
fractions (for example, ¾ = 0.75)
 Understand the meaning of percent and simple per-
centages such as 100%, 75%, 50%, 25%, and 10%
 Multiply multi-digit whole numbers with ease
 Explore division with two- and three-digit numbers
 Add and subtract fractions and decimals with ease
problems involving
with whole numbers
— addition and subtraction with fractions,
decimals, and percents
(continues)

xx A F T E R S C H O O L K I D Z M AT H ™ G A M E S
Grade 5
N U M B E R S
 Explore numbers less than 0
 Recognize and write decimals and percents
 Understand the relationship of fractions, decimals,
and percents (for example, 4
⁄5 = 80% = 0.8)
O P E R ATI O N S (+, –, ×, ÷)
 Divide multi-digit whole numbers with ease
 Explore factors and multiples
 Explore multiplication and division with fractions
and decimals
P R O B LE M S O LVI N G
problems involving
with whole numbers
— factors and multiples
— addition and subtraction with fractions, decimals,
and percents
— simple multiplication with fractions, decimals,
and percents
Grade 6
 Recognize, order, and write numbers less than 0
 Compare and order fractions, decimals, and percents
 Understand percentages greater than 100 and less
than 1
 Understand ratios
 Understand and use factors and multiples
 Multiply and divide fractions and decimals
with ease
problems involving
with whole numbers
— factors and multiples
with fractions, decimals, and percents
Math Children Commonly Learn in Grades 3–6
continued

n u m b e r s e n s e g a m e s 1
A
sound understanding of numbers is important to
children’s ability to do all mathematics. The most
important goal of elementary school mathematics is to
help children develop number sense — the ability to
understand and be flexible with numbers. To develop
number sense children need to understand the mean-
ing of numbers, how they relate to each other, how to
use them flexibly to solve problems, and how to apply
them to real-world situations.
In the number sense games, the children work with
place value and number relationships.
Place Value
The position of a digit (any one of the ten symbols 0–9)
in a number determines its value. (For example, in the
number 25 the “2” represents 20 because it is in the
tens place. In the number 32 the “2” is equal to 2
because it is in the ones place. Each place has ten
times the value of the place on its right.)
Although place-value concepts are introduced in the
early elementary grades, often it is not until fourth or
fifth grade that children fully understand them.
Number Relationships
Understanding number relationships — how numbers
relate to each other — helps children develop flexibility
with numbers. It also provides them with the back-
ground needed to calculate math problems mentally
and learn their addition, subtraction, multiplication,
and division facts. This includes:
 More than, less than, between, and equal to
These terms and their symbols ( , , = ) are used to
compare numbers. For example, four is less than five
(4 5), more than three (4 3), equal to half of eight
(8
⁄2 = 4), and between three and five (3 4 5).
 Number pattern
A number pattern is a sequence of numbers that
follow a rule that allows the next number in the
sequence to be predicted (for example, in the num-
ber pattern 3, 6, 9, 12, the next number is “15”
because the rule is “counting by threes”). Exploring
patterns helps children build an understanding of
the attributes of numbers (for example, whether the
number is even or odd) and how numbers relate to
one another.
 Friendly numbers
Learning how to add and subtract in their heads
with friendly numbers such as multiples of 10 (10,
20, 30, and so on) and multiples of 100 (100, 200,
300, and so on) helps children develop flexibility
with their mental calculations skills and understand
our number system. Numbers such as 5, 10, and
100; ¼, ½, and 3⁄4; and .25, .5, and .75 provide famil-
iar benchmarks that help children compare numbers
and compute. (For example, a child might compare
her answer to 100 to find out if it is more or less.)
 Number combinations
Numbers are made up of a combination of other
numbers. (For example, five can be made by com-
bining four and one, two and three, and five and
zero.) Number combinations do not change. (For
example, taking away a group of two from a group
of seven will always result in a group of five.)
Knowing the basic number combinations for addi-
tion, subtraction, multiplication, and division helps
children solve math problems in efficient ways.
introduction to
number sense
games

2 A F T E R S C H O O L K I D Z M AT H ™ G A M E S
Number Sense Games
Save $10.00, page 3
Spinning for Dollars, page 9
Flick, page 15
Bounce Back, page 21
What’s My Rule?, page 27
Number Detective, page 33

S a v e $ 1 0 . 0 0 3
Save $10.00©2004DevelopmentalStudiesCenter
For each group of players:
IN KIDS’ KIT
 Die
 Game marker
 Dry-erase marker
 “Save $10.00” spinner
 “Save $10.00” game board
The players move a marker on a game board accord-
ing to the roll of a die. If the marker lands on a “Spin”
square, the player spins to save or spend money. Play
continues until the group saves a total of $10.00 by
reaching the last space on the game board.
PLAYERS: Grades 3–5, small groups of two,
three, or four
GAME SUMMARY
YOU’LL NEED

 Add and subtract multiples of 25
using money
About the Math Skills
Adding and subtracting money are
important skills used every day. In
this game, the children use pictures
of quarters to add and subtract mul-
tiples of $0.25, such as $1.50, $0.75,
and $2.25. (A multiple of 25 is the
result of 25 multiplied by any whole
number.) With enough practice, the
children will learn how to add and
subtract money mentally.
 Stay involved while waiting
for a turn
About the Social Skills
When the children are waiting for
a turn, they need to stay involved
and continue following the action
of the game. They can stay involved
by helping other players count
the quarters.
 After you explain
and demonstrate
the game, ask
the children to
summarize the
game directions to
be sure that they
understand them.
Also ask them what
questions they have
before they start
to play.
Get ready
1 Read the game directions
and pages 6–7, and
play the game yourself
before introducing it to
the children.
2 If you are playing with
more than two children,
decide how you will divide
them into groups of two to
four to play the game.
MATH SKILLS SOCIAL SKILLS

S a v e $ 1 0 . 0 0 5
Game Directions
1 The players decide fairly who
goes first, second, and so on.
2 The players place the group’s
game marker on “Start” on the
“Save $10.00” game board.
3 The first player rolls the die
and moves the group’s marker
according to the roll. If the
space the marker lands on is
not marked “Spin,” that player’s
turn ends. If the square is
marked “Spin,” the player:
• spins the spinner.
• moves the group’s game
marker forward or backward
the number of spaces that
corresponds to the amount
the child spun. (For example,
if the player spins +$0.75,
she moves the marker three
spaces forward because $0.75
is equal to three quarters. If
the player spins –$1.25, she
moves the marker five spaces
back because $1.25 is equal
to five quarters.) This is the
end of the player’s turn.
4 The players take turns, mov-
ing the group’s game marker
until they “save $10.00” by
landing on the last space on
the game board. If they do not
land on the last space when
they get to the end of the
game board, the players can
decide how to end their game.
(For example, they could
decide that any amount that
gets the marker past $10.00
will end the game or they
could spin repeatedly until
they spin the amount that will
put them on the last space.)
GOAL: To save $10.00 together

Before the Game
1 Explain that the children will be playing a game where they
save and spend money, trying to save a total of $10.00. Ask the
children about their experiences saving and spending money.
2 Explain the game as you play it with a child as your partner.
• Have you ever saved money to buy something? How much did you
save? How did you earn or get your money? What did you buy?
• What is hard about saving money?
talk
about
• Look at this game board. How much money is on the entire
game board? How do you know? How much money is on half
the game board?
• If I spin +$1.25, how many spaces do I move forward? Why?
• If I spin –$0.75, how many spaces do I move backward? Why do you
think that?
talk
about
1 Help the children as they play. If appropriate, help them keep a
running total of the money saved and spent.
2 If a player or group suggests a change in the rules while they are
playing, allow them to discuss the change. Before changing the
rule, make sure the change is fair to all players, everyone in the
group agrees, and the math is still appropriate.
• How much have you saved so far?
• How much more do you need to save $10.00? How many quarters
is that?
talk
about
during the Game

S a v e $ 1 0 . 0 0 7
Help the children think about the math and how they played together.
after the Game
Changing the Game
1 To make the game more challenging:
• Have the children keep a running total, recording the money
they spend or save each turn and the new total saved.
2 To change the game:
• Have the children make up their own activities and amounts
spent or saved to put on the blank “Save $10.00” spinner. The
amounts should be between $0.50 and $2.00.
3 Ask the children how to play the game differently and try
their ideas.
• How did this game help you learn about money? Why is learning
about money important?
• What is the largest amount of money you spent on a turn?
The smallest?
• How did you stay involved while waiting for a turn?
• How many quarters are there in $10.00? How do you know?
talk
about

S p i n n i n g f o r D o l l a r s 9
S
p
inning for Dolla
r
s
©2004DevelopmentalStudiesCenter
IN KIDS’ KIT
 Die
 “Spinning for Dollars” spinner
 “Spinning for Dollars” game board
Players take turns rolling a die and spinning a
spinner to determine the amount of money they will
mark off on their game board. Players mark off the
money spaces and keep a running total until they
reach the specified dollar amount.
three, or four
GAME SUMMARY
YOU’LL NEED

 Add multiples of five and ten
using money
 Multiply using money
This game gives the children oppor-
tunities to practice multiplying and
adding money values mentally,
which is a necessary skill in everyday
life. The children multiply friendly
numbers like $0.05 and $0.10.
A multiple is the result of a whole
number multiplied by another whole
number. (For example, a multiple of
10 is 50 because 10 × 5 = 50.)
 Give others time to think before
offering help
When children of varying skill
levels play a game together, more
advanced children may want to say
the answer before other children
have had a chance to think. Each
child needs an opportunity to
ponder the problem for herself
in order to learn and grow.
 If you are playing with
children who are learn-
ing English as a second
language, be sure to
demonstrate the game
until all the children
understand it. And
explain difficult terms.
 Discussing the various
ways the children find
solutions provides
opportunities for the
children to learn strate-
gies from one another.
Get ready
the children.
more than four children,

Game Directions
1 The players decide fairly
who goes first, second, and
so on, and choose one of the
game boards to play on first.
The players all use the same
game board.
2 Taking turns, each player:
• rolls a die, saying the
number.
• spins the
“Spinning for
Dollars” spinner
to find an amount
of money.
• calculates a money total by
multiplying the number
rolled with the die by the
amount on the spinner.
• crosses out a space or
spaces that equal the money
total. (For example, if a
six is rolled and a $0.10 is
spun, the player crosses
out a $0.60 space because
6 × $0.10 = $0.60. If no
$0.60 space is available,
the player crosses out two
or more spaces that add up
to exactly $0.60, such as
$0.10 + $0.50.) If no space(s)
can be crossed out, the
player rolls and spins again
until she can cross out
a space.
• records the amount she
marked on the game
board and keeps track
of the total.
GOAL: To mark off a specified dollar amount
Dollars
52.0$
(continues)
$0.60
$0.50 + $0.10 = $0.60

Game Directions
3 The players play until they
reach or go over the dollar
amount specified for that
game board.
4 The players use a different
game board to play again.
(continued)

1 Help the children as they play.
Before the Game
Explain the game as you play it with a child as your partner.
• What amounts of money are shown on the spinner? How could you
make each amount using coins? Is there another way? What is it?
• How can you figure out how much money you need to cross out?
• What can you do if that amount is not written in one of the spaces?
• How can you work together to get to the total for the game?
• How can you keep track of the amount of money you have crossed
out so you know when you get to the total?
talk
about
• How are you working together?
• How much more do you need to get to the total?
• What is the largest amount of money you have crossed out on a turn?
talk
about
during the Game

after the Game
Changing the Game
1 To make the game less challenging:
• Write the money amounts $0.05, $0.10, $0.25, and $0.50 on
the spaces on the blank “Spinning for Dollars” game board. (You
will use each amount more than once.) Have the children spin
for a total of $2.50. The children spin the spinner and mark the
matching amount on their game board. They do not roll the die
or multiply in this version of the game.
• Write money amounts from $0.10 to $6.00 in the spaces on the
blank “Spinning for Dollars” game board. Have the children spin
for a total of $9.00. Have the children use two dice, add the
numbers rolled, and multiply the total by the amount spun.
their ideas.
• What did you like about this game? How can this game help you in
your everyday life?
• How did you work together?
• Did it get easier to figure how much to cross out as you played?
Why do you think that happened?
talk
about

FLI C K 15
IN KIDS’ KIT
 “Flick” score sheet
 “Flick” game board
OTHER MATERIALS
 Kids’ box
 Penny
Players take turns flicking a penny on a game board
to get points and keep a running total by adding
or subtracting tens. Players try to reach a total of
200 points after ten flicks.
three, or four
GAME SUMMARY
YOU’LL NEED
Fl ck

 Add and subtract multiples of ten
In this game the children add and
subtract multiples of ten mentally
(a multiple of ten is the result of ten
multiplied by any whole number).
As they get older, children often
rely too heavily on paper and pencil,
rather than working out problems in
their heads when appropriate. (For
example, encourage the children to
add 100 to 30 without writing the
problem down.)
 Consider all ideas before making
a decision
 Be respectful when others
make mistakes
After each flick of the penny, the
children decide whether to add or
subtract, and why. If they don’t
agree at first, they need to find
and discuss a fair way to decide
what to do. Modeling this behavior
before playing the game will help
the children learn how to make
decisions together.
 Playing games cooperatively
may be quite a struggle at
first. The children may need
to play a game several times
before they can play it with
success cooperatively.
 Two ways the children in a
group can decide who goes
first are to order themselves
alphabetically or by their
birthdays.
Get ready
the children.

FLI C K 17
1 The players choose fairly who
2 They put the top edge of the
game board against the side
of the children’s box to keep
the penny from flying across
the room and put the penny
anywhere behind the start line.
3 The first player flicks the penny
with her thumb and forefinger
on the game board, and says
the number the penny lands
on. The player writes that
number in the first space on
the score sheet. (The players
decide what to do if the penny
lands off the board.)
4 The players take turns flicking
a penny and saying the num-
ber it lands on. After each flick,
the players discuss whether to
add the number to or subtract
it from the previous total. They
record their the new total on
the score sheet.
5 The partners play until they
have flicked the penny ten
times. They record the final
total and compare it with 200.
6 The partners play again using
the game 2 column on the
score sheet.
GOAL: To reach the target total of 200
Game Directions
2 They put the top edge of the
game board against the side
of the kids’ box to keep the
penny from flying across the
room and put the penny any-
where behind the start line.
3 The first player flicks the penny
with her thumb and forefinger
on the game board, and says
the number the penny lands
on. The player writes that
number in the first space on
the score sheet. (The players
decide what to do if the penny
lands off the board.)
4 The players take turns flicking
a penny and saying the num-
ber it lands on. After each flick,
the players discuss whether to
add the number to or subtract
it from the previous total. They
record their new total on the
score sheet.
5 The partners play until they
have flicked the penny ten
times. They record the final
total and compare it with 200.
6 The partners play again using
the game 2 column on the
score sheet.
Kids’ Box
30
70
130
100
GOAL: To reach the target total of 200

2 Encourage the children to do the math in their heads rather than
with a pencil and paper.
Before the Game
2 While demonstrating, discuss how to play together.
• Should we add or subtract that number? Why? Does anyone think we
should do something else? Why?
• How can we decide what to do if one player thinks we should add
and the other player thinks we should subtract the number?
• What if your partner makes a mistake adding or subtracting the
numbers? How can you let him know without hurting his feelings?
talk
about
• How can you add/subtract those two numbers without using a pencil
and paper? What is another way?
• How are you making decisions together?
• Why did you decide to add/subtract that number?
• How many more points do you need to reach 200?
talk
about
during the Game

FLI C K 19
after the Game
Changing the Game
• Play to 100.
• Instead of flicking a penny on the game board, roll a die and
play ten rolls to get as close as you can to 20.
• Play with only five flicks to get to 200.
• Have the children make their own game boards.
their ideas.
• Did you get closer to 200 the first or the second game? How close did
you get to 200?
• Did you use a different strategy the second time you played? If so,
what did you do differently? Why?
• What did your partner do if you made a mistake? Did that work for
you? Why or why not?
• How did you make decisions? Did you both think that was fair? Why
or why not?
talk
about

B o u n c e B a ck 21
Bounce Back©2004DevelopmentalStudiesCenter
This is a subtraction game. Partners start with 1,000
points and try to reach zero points by taking turns
throwing and catching a tennis ball. Points are subtract-
ed from the total depending on the number of bounces
the ball makes before it is caught. To play this game,
you need a large space, like a gym or outdoor area.
PLAYERS: Grades 3–6, small groups of three or four
GAME SUMMARY
IN KIDS’ KIT
 Dry-erase writing board
OTHER MATERIALS
 Tennis ball or other small
ball that bounces well
 Large sheet of paper and
marker, or sidewalk chalk
 Tape
YOU’LL NEED

 Subtract multiples of 100
Multiples of 100 are the result of
100 multiplied by any whole
number. Subtracting with friendly
numbers such as 100, 200, and 300
helps children develop flexibility with
their mental subtraction skills and
understand our number system.
Children learn mental subtraction
skills best when using them in a real-
life situation such as calculating
points to keep score in a game.
 Encourage others
 Play safely
In this game, the children work
as a team to get to zero points. A
child may get upset with a partner
who does not catch the ball after
one bounce. Discuss how to encour-
age others and make all children
feel comfortable playing the game.
 When asking math
questions, collect
many ideas from the
children. You might
ask, “Who figured it
out a different way?”
 Before introducing a
game, decide on the
mathematical and
social questions you
might ask. Use a
highlighter pen or
pencil to mark the
“talk about” questions
you are going to use.
Get ready
and pages 24–25 before
introducing the game to
the children.
2 Choose a place to play
where the children have
room to throw and catch
a ball.
3 On the sheet of paper or
the ground, write the title
of the game and the point
system used to play it.
them into groups of three
or four to play the game.
Bounce Back
1 bounce = –300 points
2 bounces = –200 points
3 bounces = –100 points

Game Directions
1 The players decide who will
record first, who will throw first,
and who will catch first and how
far away from each other they
will stand.
2 The recorder writes the
starting total “1,000” on
the writing board.
3 The thrower stands with
her back toward the catcher.
The thrower throws the ball over
her head to the catcher.
4 If the catcher catches the ball on
one bounce, the players subtract
300 points from the total score.
If the catcher catches the ball
after two bounces, they subtract
200 points from the score. If the
catcher catches the ball after
three bounces, they subtract
100 points from the score.
(Catching the ball on the fly
or after more than three
bounces scores no points.)
5 The recorder reminds everyone
of the previous total. Players
calculate the new score and say
it aloud.
6 The recorder notes
the new score.
7 The players continue playing
until they reach zero points.
When they come to a total
near zero, they decide how
they will reach zero if a throw
puts them at less than zero.
(For example, they might add
instead of subtract points until
they reach zero.)
8 The players switch roles and
play again.
GOAL: To get from 1,000 points to zero points
1,000
– 300
700

1 Help the children as they play. Make sure the children are saying
the score after each throw.
2 Be sure all the children have a chance to be the scorekeeper so
that they can practice recording the math in the game.
Before the Game
1 Explain the game as two children demonstrate how to play it and
you record.
2 Have the rest of the group calculate the new score after each throw.
3 Discuss how to encourage each other and make everyone
feel comfortable.
• If you start with 1,000 points, and one partner catches the ball after two
bounces, how many points will you have? How did you figure it out?
• If you have 600 points and one partner catches the ball after three
bounces, how many points will you have? How did you figure it out?
talk
about
• What can you say to your partner to encourage him if he doesn’t
catch the ball on the first bounce?
• How do you want others to treat you during this game?
• How can you play this game safely?
talk
about
• How many points was this turn worth? What is your new score?
How did you figure it out?
• Do you want to reach zero points exactly or get as close as you can?
• Are you and your partners catching the ball on one bounce most of
the time? If you are, what could you do to make the game more
challenging for yourselves?
talk
about
during the Game

after the Game
Changing the Game
• Start out at zero and add points to reach a total of 1,000 points.
• Use a different point system. For example, for one bounce
subtract 100 points, for two bounces 50 points, and for three or
more bounces 25 points. Or start with 10,000 points and sub-
tract to zero with one bounce worth 1,000 points, two bounces
worth 500 points, and three or more bounces worth 250 points.
their ideas.
• How did you decide how far apart to stand?
• Was it difficult to subtract the points in your head? What helped you?
• Which group got less than zero points? If you decided you needed
exactly zero points, what did you do to get back to zero points?
• Did you play safely? Why do you think so?
• Was the game challenging enough for you and your partners? If not,
what could you do differently next time?
• Why is it important to be able to subtract numbers in your head?
talk
about

W h at ’ s M y R u l e ? 27
W
hat’s My Rule?
 Chalkboard and chalk or
several large sheets of paper
and a marker
The leader thinks of a number rule, for example,
numbers that are even (24, 232, and 1,320 follow
this number rule, but 21 and 75 do not). The leader
gives the players hints about her rule. The players try
to figure out the rule by guessing possible numbers to
see whether or not they follow the rule.
PLAYERS: Grades 3–6, large group of 10 or fewer
GAME SUMMARY
YOU’LL NEED

 Recognize number patterns
 Relate numbers to other numbers
“What’s My Rule?” gives the children
an opportunity to look for number
patterns in the numbers that follow
the rule. In doing so, the children
build an understanding of attributes
such as odd/even, multiples, and
digits. Number patterns are groups
of numbers that repeat or follow a
rule so that a person can predict
what comes next.
 Stay involved while waiting for
a turn
 Be persistent
The children need to stick with the
game until they figure out the rule.
They may need to make many
guesses before they come up with it.
 If possible, play the
game where loud noises,
lots of movement,
or other activities are
not competing for the
children’s attention.
Get ready
the children.
2 Decide on a number
rule that you will use to
demonstrate. Here are
some examples of rules
you might use:
• odd numbers (3, 27, 43)
• even numbers
(20; 2,000; 24)
• numbers with a zero
in the tens place
(104; 1,405; 607)
• numbers with a hundreds
digit that is even (204;
697; 1,890)

• numbers with digits that
when added together
equal 9 (27, 360, 342)
• two-digit numbers (57, 34,
12, 89)
• multiples of 3 (3; 6; 9; 36;
729; 2,187)
3 Draw a line down the
middle of the board or
paper. Label one column
“Yes” and the other “No.”
more than ten children,
them into groups and
which adult will lead each
group.

Game Directions
1 The leader thinks of a number
rule. The players take turns
guessing numbers and the
leader writes them in the “yes”
or “no” column depending on
whether or not they follow the
number rule. (For example, if
the rule is two-digit numbers
and a player guesses 300,
write 300 in the “no” column.)
2 When the players seem stuck,
the leader gives more exam-
ples of numbers that follow
the rule and those that don’t.
3 The players continue playing
until most of them seem to
know the rule. (Once some
players seem to know the
rule — they choose the num-
bers that fit the rule — you
can have these players give
the others clues.) Then the
leader calls on a player to
guess the rule.
4 If a player guesses at the rule
but is not correct, she can ask
another player to help. If they
don’t guess correctly, the
game resumes with players
taking turns suggesting
numbers. The game ends
when a player guesses the
rule correctly.
GOAL: Guess the leader’s number rule
yes
34
536
31
1,438
no
43
500
9
96
Sample Game
In this game, the rule is that the
number has a 3 in the tens place.

2 Once some of the children seem to know the rule (they are
choosing numbers that fit the rule), you can have those who
know it give the other children clues.
Before the Game
1 Start by discussing the meaning of a rule.
2 Explain the game as you demonstrate it with the group. Introduce
your rule by saying, “I am thinking of a number rule. One of the
numbers that follows my rule is ___.” (Write that number in the
“yes” column.) “One of the numbers that does not follow my rule
is ___.” (Write that number in the “no” column.)
• What is a rule? What does it mean to follow a rule?
• If I say that a number has to follow a rule, what do you think I mean?
For example, if the rule is that all the numbers are odd, what are
some of the numbers that follow this rule? What is another possible
rule? What numbers follow that rule?
talk
about
• Who would like to guess a number to find out more about my rule?
Why did you guess that number? What were you thinking my rule
might be?
• What can you do while you are waiting for your turn to guess?
talk
about
• If a child thinks he knows the rule and guesses a number that does
not follow the rule, ask, “What made you guess that number? What
did you think the rule was?”
• What kinds of patterns do you look for to help you guess the rule?
• How can you stay involved while you are waiting for your turn?
• Why is it important to be persistent in this game?
talk
about
during the Game

after the Game
• What kind of clues did you look for in the numbers to help you guess?
• Was it hard to keep guessing when you felt like you didn’t know
the rule? What kept you motivated to keep guessing until you figured
it out?
talk
about
Changing the Game
• Have the children play in pairs using a sheet of paper to record
the numbers.
their ideas.

n u m b e r D e t e c t i v e 33
n
umber Detective
NUMBER D ETE C TIVE 33
IN KIDS’ KIT
 “Number Detective Clues”
game board
OTHER MATERIALS
 Paper, self-stick notes, or
index cards
The first player writes a secret two-digit number,
which the other players — the number detectives — try
to guess. The first player provides clues to help the
number detectives guess the secret number.
three, or four
GAME SUMMARY
YOU’LL NEED

 Recognize that the position of a
digit determines value
In this game, the children learn
about and use digit and place value
concepts. A digit is any one of the
ten symbols 0–9. The place value is
the value of the position of a digit in
a number. (For example, in the num-
ber 21, the two is in the tens place
and represents 20, and the one is in
the ones place and represents one.)
 Explain their thinking
 Be respectful when others make
mistakes
The children may need encourage-
ment to be respectful when someone
needs help or guesses a number that
doesn’t fit the clues. Talk about how
to use appropriate body language
when someone makes a mistake
(for example, keeping a friendly
facial expression).
 When you group
the children to
play, explain that
they are expected
to work together,
even if their part-
ner is not the per-
son they were hop-
ing for.
Get ready
the children.
tens ones
2 1

Game Directions
writes the secret number and
who guesses first, second, and
so on. The guessers are called
“number detectives.”
2 The secret number writer writes
a two-digit number on a piece
of paper, self-stick note, or card,
taking care that the number
detectives do not see it. The
secret number must have a
different digit in each place
(22, 33, 44, and so on may
not be used).
3 The first number detective guess-
es a two-digit number. The secret
number writer writes the number
in the column marked “Guess,”
and then gives two clues, one
about the digits, and one about
place value. She writes a 0, 1, or 2
in the “Correct Digits” column to
show the number of correctly
guessed digits. (For example, if
the secret number is 23 and the
number guessed is 34, the num-
ber of correct digits is one — the
3.) For the second clue, she writes
a 0, 1, or 2 in the “Correct Places”
column to show the number of
correctly guessed digits that are
also in the correct place in the
secret number. (In this example,
the writer writes 0, because the 3
is not in the correct place. It is in
the ones, not the tens, place.)
4 The number detectives continue
taking turns guessing numbers.
After each turn, they discuss the
clues, talking about what they
know, what they might guess
next, and/or what the number
might be.
5 The number detectives continue
to take turns until they guess
the number.
GOAL: To guess a secret number
23
secret number

2 If a secret number writer is having trouble writing accurate clues,
partner with him, or pair him with another child to discuss the
clues to write.
Before the Game
1 Write a two-digit number such as 73 where everyone can see it.
Ask the children to name the digits in the number (7 and 3). Next
to the 73, write 34.
2 Take the role of the secret number writer, and demonstrate the game
with the entire group. Write a two-digit number on a card and hide it.
Have the children take turns guessing numbers. Write each guessed
number where everyone can see it. Then write each clue where
everyone can see it, and talk about the information the clue gives.
• Do the numbers have any digits in common? How many? (one) What
is that digit? (3)
• Is there a digit in the same place in both numbers? (no) What other
two-digit number has a 3 in the same place as in 73? (43, 23, 93, and
so on)
talk
about
• What does this clue tell us?
• What do we know about the number now?
• Why is it important to explain your thinking about the clues?
• If someone guesses a number that doesn’t fit the clues, what can you
do? Is that respectful? Why is this important?
talk
about
• What does this clue tell you?
• What might be a good number to guess next? Why?
talk
about
during the Game

after the Game
Changing the Game
• Limit the range for the secret number (for example, between
10 and 30 or between 50 and 70).
• Use three-digit numbers.
their ideas.
• If the secret number writer wrote a 2 as the clue in the “Correct
Digits” column, what would that tell you?
• If the secret number writer wrote a 1 as a clue in the “Correct Places”
column, what would that tell you?
• Did it get easier to guess the secret numbers as you played? Why?
• How did you act when someone made a mistake? Was that
respectful? Why?
talk
about

M u lt i p l i c at i o n a n d D i v i s i o n g a m e s 39
L
earning to multiply and divide is complex. Children
need many hands-on experiences exploring multi-
plication and division situations and lots of meaningful
practice. The multiplication and division games give chil-
dren experience with the following skills and concepts:
Meaning of Multiplication
Multiplication involves counting objects by equal
groups. (For example, three groups of four objects
equal twelve objects.)
Meaning of Division
There are two ways to think about division: the
number of equal groups in a number (for example,
there are two equal groups of three objects in the
number six) or the number of objects in each of the
equal groups in a number (for example, there are two
objects in each of three groups in the number six).
Multiplication and Division Terms
 Multiples
A multiple is the result of a whole number multiplied
by another whole number (for example, twelve is a
multiple of three because 3 × 4 = 12). Knowing how
to find multiples of a number helps children when
they learn about fractions.
 Factors
A factor is a number that divides evenly into
another (for example, four is a factor of both eight
and twelve). A factor can also be explained as one
of two or more numbers that are multiplied to get
an answer (for example, in 4 × 5 = 20, four and five
are factors).
 Remainders
A remainder is the amount left over when dividing
one number by another. (For example, when seven
objects are divided evenly into groups of two, there
is a remainder of one.)
 Other terms
Other terms in multiplication and division are
product, quotient, dividend, and divisor. The result
of a multiplication problem is called the product.
(For example, 20 is the product of 4 × 5. Factor ×
factor = product.) The result of a division problem is
called the quotient. (For example, 3 is the quotient
of 15 ÷ 5.) A dividend is the quantity to be divided
and the divisor is the quantity by which another
quantity is to be divided. (For example, in 24 ÷ 3 = 8,
24 is the dividend and 3 is the divisor. Dividend ÷
divisor = quotient.) You may want to introduce and
use these math terms with the children.
introduction to
Multiplication
and Division
games
6 ÷ 3 = 26 ÷ 3 = 2
remainder of one

Multiplication and Division Symbols
It is important for children to use symbols to represent
multiplication and division problems and understand
the meaning of each number and symbol in the prob-
lem. (For example, the children show that three stacks
of six pennies equals eighteen pennies with 3 × 6 = 18.)
Basic Multiplication and Division Facts
After children understand the meaning of multiplica-
tion and division, they can begin to memorize their
multiplication (up to 12 × 12 = 144) and division facts
(up to 144 ÷ 12 = 12) through exploration and practice.
Several tips can help them recall their facts. Children
should discuss strategies they use as they recall the
facts. Here are some multiplication tips:
 A number multiplied by zero is zero
 A number multiplied by two is doubled
 Count by fives to find a number times five
(for example, to solve 5 × 6 = 30, count by five six
times — five, ten, fifteen, twenty, twenty-five, thirty)
 A number multiplied by ten is the number with a
zero in the ones place (for example, 4 × 10 = 40)
 A number less than ten multiplied by eleven will
have an answer with both digits the same (for
example, 7 × 11 = 77)
Methods and Tools to Solve Problems
Children need to learn to select and use a variety
of methods and tools for multiplying and dividing
whole numbers, including paper and pencil, mental
calculation, and calculators. Encourage the children to
explore various ways to multiply and divide and to
share their methods with others.
Estimation
Estimating is finding a number that is close to an
exact amount or making an educated guess about
the amount. Children need to be able to estimate the
answers to multiplication and division problems. They
also need to determine whether their solutions make
sense. (For example, is it reasonable to get an answer
less than ten when multiplying 5 × 3?)
Multiplication and Division Games
Ant Hill Picnic, page 41
Rectango, page 47
Lonely Aces, page 53
Multiplication Basketball, page 59
Multiplication Bowling, page 65
Multiplication Uncovered, page 71
Multiplication Baseball, page 77
Multiple Moves, page 83
Three Tac Toe, page 89
Beach Ball Multiplier, page 95
Forehead Factors, page 101
The Leader Says Divide, page 107
Spin Spot, page 119
Target, page 125
Disappearing Pyramid, page 131
Stadium Tour, USA, page 137
Equapardy, page 143

A n t H i l l P i c n i c 41
IN KIDS’ KIT
 40 game markers to be
the crumbs
 “Ant Hill Picnic” spinner
 “Ant Hill Picnic” game board
The players spin a spinner to divide “crumbs” evenly
among ants making their way toward the picnic area.
Crumbs that cannot be distributed evenly are left
on spaces on the game board to form a path
leading to the picnic.
three, or four
GAME SUMMARY
YOU’LL NEED
Ant Hill Picnic

 Divide by 12 or less with and
without remainders
Children need opportunities to use
concrete objects to practice division.
Physically dividing crumbs (game
markers) evenly between ants helps
children make sense of division.
(For example, a child can divide
25 crumbs between 12 ants to see
that each ant gets two and one
crumb is left over. The leftover is
called the remainder.)
offering help
As partners play, one may solve the
problem faster than the other. Use
this game to help the children learn
to keep answers to themselves so
their partner has a chance to solve
the problem.
Get ready
the children.
 Encourage all the
children to work out
the answer in their
own way. Children
learn at different rates,
so be supportive of
everyone’s efforts.

Game Directions
1 The first player:
• spins the spinner to find the
number of ants and crumbs.
• divides the number of
crumbs evenly between
the number of ants. The
players can (but don’t have
to) use the ants on the
page opposite the game
board and put the game
markers on the ants to
divide the crumbs.
• finds the number of
crumbs each ant gets and
the number left over.
• puts any leftover crumbs
on the trail, one crumb per
space. (For example, if there
are five ants and 14 crumbs,
each ant gets two crumbs
and there are four left
over to place on the game
board trail.)
2 The players take turns until
they fill the game board path
with leftover crumbs and
reach the picnic area.
GOAL: To leave a trail of crumbs that reach the picnic area
ant
h
i
ll
picnic
6 crumbs
6 ants
14crum
bs
5ants
25crumbs
12ants
3
6
crumbs
5
ants
29crumbs 7ants
39crumbs
4ants
19
crum
bs
8ants
36crumbs
9ants
2
7
crumbs
1
1ants
23 crumbs10 ants

Before the Game
1 Set a context for the game by explaining that some hungry ants
are trying to make their way down a trail to the ant hill picnic.
During their travels, some ants leave and some new ants join.
Along the way, the ants find crumbs to keep them going. They
must divide the crumbs equally among them and place the leftover
crumbs on the trail that leads to the picnic. The trail of leftover
crumbs helps other ants find the picnic as well. Explain that the
children will use game markers to represent the crumbs.
3 Explain that some children will know the answer quickly while
others may need time to divide the crumbs between the ants.
Discuss how to give your partner time to think and work out the
answer for himself before offering help.
• How can you figure out the number of leftover crumbs (the remain-
der) if you have ten ants and 23 crumbs? What’s another way?
• How can you use game markers and the pictures of ants on the game
page to figure out how many crumbs you have left over?
talk
about
• Why is it important to give your partner a chance to figure it out for
himself before offering help?
• What can you do if you and your partner have different answers?
talk
about

after the Game
• What math did you use in this game?
• Did anyone help their partner? How? How did you know when your
partner had enough time to think and was ready for help?
• What did you like about this game? What didn’t you like?
talk
about
• How many more turns do you think you’ll need to get to the picnic?
Why do you think so?
• How many crumbs did each ant get?
• How many leftover crumbs are there? How did you figure it out?
talk
about
during the Game

Changing the Game
• Use the blank “Ant Hill Picnic Spinner” and write smaller numbers
for the crumbs.
• Use the blank “Ant Hill Picnic” spinner and write larger numbers
for the crumbs and the numbers 4 through 12 for the ants. You
may want to give the children extra game markers to use to find
the answers.
their ideas.
crumbs 5 5 6 4 6 10 10 8 9 11
ants 5 2 5 2 4 7 5 5 4 7

r e c ta n g o 47
rectango©2004DevelopmentalStudiesCenter
IN KIDS’ KIT
 2 dice
 Dry-erase markers
 “Rectango 1” game board
The players roll two dice to determine the length and
width of rectangles. They draw their rectangles on the
grid-like game board, trying to cover as much of the
game board as possible.
three, or four
GAME SUMMARY
YOU’LL NEED

 Use a visual model of
multiplication
 Multiply by six or less
In this activity, a grid with small
squares is a physical model that
helps children develop a mental pic-
ture of multiplication. (For example,
to picture 3 × 4 = 12, they can see
that a rectangle that is three squares
tall and four squares wide has a
total of twelve squares.) Having a
mental picture helps children solve
multiplication problems on paper.
a decision
In this game, the children make
decisions together about the best
place to draw each rectangle on
the game board. As they strategize
together, they learn to share
their ideas, compromise, and
reach agreement.
 Before introducing the
game, decide on the
mathematical and social
questions you might ask.
Use a highlighter pen or
a pencil to mark the “talk
about” questions you are
going to use.
 Use eye contact while
asking questions and
stay interested while lis-
tening to the response.
Get ready
the children.

r e c ta n g o 49
Game Directions
2 The first player throws two
dice to determine the length
and width of her rectangle.
(For example, if the player
rolls a four and a five, the
rectangle can be either four
squares long and five squares
wide or five squares long and
four squares wide. Either way
the rectangle will have a total
of twenty squares.)
3 The players decide together
where the first player will
draw the rectangle on the
game board.
4 The first player traces the
outline of the rectangle and
writes the multiplication fact
that describes the rectangle.
5 The players take turns until a
rectangle is rolled that does
not fit on the grid.
6 The players calculate the
number of squares they filled
in and write the total in the
scoring box.
7 They erase the board and
play again.
GOAL: Together fill in the largest possible number of squares on the game board
2 x 3 = 6
4 x 5 = 20

Before the Game
Explain the game as you play it with a child as your partner.
• What is a rectangle? (Note: If the children roll two of the same number,
such as a five and a five, they will make a square on the game board.
A square is a type of rectangle.)
• Where is a good place to draw the rectangle? Why?
• What can we do if we do not agree about where to draw a rectangle?
• How many squares did we fill in? What two numbers did we roll?
What multiplication fact do we write in the squares?
talk
about
• How can you find out the number of squares inside the rectangle?
What’s another way?
• How are you making sure that you both agree before one of you
draws a rectangle?
talk
about
during the Game

r e c ta n g o 51
after the Game
Changing the Game
• Have the children use one die. In this version, all rectangles will
be either one square long or one square wide.
• Have the children choose a number from one to six to be one
side of all the rectangles in a game. The children roll one die to
get the length of the other side.
• Use the “Rectango 2” game board.
• Include the option of using a rectangle that has the same area
as the rectangle rolled. (For example, if a three and four are
rolled, a child could make any of these three rectangles, whose
area is 12 squares: 1 × 12, 2 × 6, 3 × 4.)
• Have the children decide on different shapes to make for the
game board (for example, a pyramid or house).
4 Ask the children how to play the game differently and try their ideas.
• How did you figure out the best places to draw the rectangles? What
are some other ideas? (For example, draw small rectangles in the
corners so there is room in the middle of the grid for larger rectangles.)
• How does this game help you learn multiplication?
• What is the total number of squares you and your partner filled in out
of 144? Did you fill in half, more than half, or less than half of the
total number of squares? How do you know?
talk
about

l o n e ly a c e s 53
lonely aces©2004DevelopmentalStudiesCenter
The dealer lays out nine cards, face up in three rows of
three. The players take turns spinning for a number
and removing cards that the number can be divided
into without a remainder. After each round, the dealer
replaces the removed cards until all cards except the
aces have been removed.
three, or four
GAME SUMMARY
IN KIDS’ KIT
 Deck of playing cards,
with jacks, queens, and
kings removed (ace
equals one)
 “Lonely Aces” spinner
 10 game markers for
counting (optional)
YOU’LL NEED

 Divide by seven or less
Pictures and concrete objects like
game markers can help children
memorize division facts. In this
game, the children can use the
hearts, clubs, diamonds, or spades
on the playing cards to see if the
spun number can be divided evenly
into the number on the card. The
game also gives the children a
reason to practice dividing.
offering help
a turn
Some children will figure out a solu-
tion for their partner’s problem
before their partner does. They may
need help learning not to blurt out
the answer and how to give help
rather than just tell the solution.
Get ready
the children.
 Gather all the children
where they can see you
demonstrate the game
before they play. Then
demonstrate with a child
as your partner.
 Discussing the various
ways the children find
solutions provides
opportunities for the
children to learn strate-
gies from one another.

Game Directions
1 The players choose fairly who is
the dealer and who goes first,
second, and so on.
2 The dealer shuffles the cards and
places nine of them face up in
three rows of three.
3 The players take turns:
• spinning the spinner to get
a number.
• removing all of the cards
that the number spun can
be divided into without a
remainder. (For example, if
three is spun, the three, six,
and nine cards can be
removed because three divides
evenly into these numbers.)
A player who has trouble
knowing which cards to
remove can use the pictures
on the cards to help him. (For
example, if he wants to find
out if three divides evenly into
seven, he can see how many
groups of three and how many
are left over on the seven card
by counting the pictures on
the card by three.)
4 After each turn the dealer
replaces the used cards.
5 If the game gets stuck, the
players decide how to continue.
(For example, spin again or lay
out another row of cards.)
6 Play continues until only the
aces are left.
GOAL: To remove all cards except the aces
two groups of 3
one left over

2 If the children have difficulty dividing, encourage them to use the
hearts, diamonds, clubs, or spades on the cards, or give them
game markers, beans, or cubes that they can put into groups to
see if there is a remainder. (For example, if a child is trying to fig-
ure out if nine can be divided by three evenly, he can take nine
game markers and divide them into groups of three to see if there
is a remainder.)
Before the Game
2 If necessary, show how the number of hearts, diamonds, spades,
or clubs on the cards can be used to figure out which cards can
be removed. For example, if you roll a three, you can count the
pictures on the cards by three to see how many groups of three
there are and how many are left over.
• What are some ways to figure out which cards can be removed?
• How can you use the pictures on the cards?
• How will you know if your partner has had enough time to think and
needs help?
• What can you do while you are waiting for your turn?
• (Point to a seven card.) How many sets of four are there in seven? Is
there a remainder? What is it?
talk
about
• How are you figuring out which cards to remove?
• How are you staying involved while waiting for your turn?
• Which number on the spinner lets you remove the most cards in
one turn?
talk
about
during the Game

after the Game
Changing the Game
• Make your own cards with larger numbers, such as 50 through
80, and have the children play the game.
their ideas.
• How did you help your partner without giving the answer?
• What are the best numbers to spin? Why are they the best?
• (Point to a ten card.) How many sets of three are in ten? Is there a
remainder? What is it?
• How did this game help you learn to divide? What are some tips that
make certain numbers easy to divide? (For example, all even numbers
can be divided evenly by two; all numbers that end in zero or five can
be divided evenly by five.)
• Why do you think this game is called “Lonely Aces”?
talk
about
group agrees, and the math is still appropriate. (For example, if
none of the nine face-up cards can be removed, the group could
decide to add two cards together to make a number that can be
removed, remove the aces from the rows, start over, and so on.)

m u lt i p l i c at i o n b a s k e t b a l l 59
m
u
ltiplication basketba
ll
Before playing, the players decide on the point value
for the ball and the number of points to reach.
The players roll a die and multiply the point value of the
ball by the number rolled on the die to determine the
number of points the group will score if the ball makes
it through the basketball hoop. To play this game, you
need a large space, like a gym or outdoor area.
PLAYERS: Grades 3–6, large group of ten or fewer
GAME SUMMARY
IN LEADER’S KIT
 Multiplication table
(on the back of the
dry-erase writing board)
 Die
OTHER MATERIALS
 Basketball hoop (if you
don’t have a basketball
hoop see “Tips”)
 Basketball
 Plastic or paper cup to
roll the die in
YOU’LL NEED

 Multiply by 12 or less
 Add
Practicing multiplication facts in
many different ways, such as
through movement, helps children
memorize them. This game gives
the children a chance to practice
one set of multiplication facts at a
time — for example, the facts for
four (0 × 4, 1 × 4, 2 × 4, and so on).
 Encourage others
Before you start, discuss ways to
encourage one another while
playing this game. Playing together
to reach a final score and cheering
for other players help children feel
like part of a team. Before playing,
talk about how to be respectful
when a player misses the basket.
Get ready
the children.
more than one group,
explain and practice the
game with everyone first,
then divide the children to
play. Monitor each group
to make sure the game is
fun and fair for all.
 If you do not have a
basketball hoop, you
can use containers
such as boxes, bowls,
or small trash cans.
If you are using such
containers, use small
balls or crumpled pieces
of paper instead of
basketballs. Collect as
many containers and
balls as you need for
the children to play in
groups of four or five.
 You may want to
review multiplication
tips by reading “Basic
Multiplication and
Division Facts” on
page 40.
 Help the children build
on other people’s ideas.
You might say, “Did
anyone figure it out a
different way? If so,
would you explain it
to us?”

Game Directions
2 The players decide on the
point value of the ball for
the game (any number from
2 to 12) and the target num-
ber of points the team will
try to reach.
3 The players stand in line next
to the basketball court.
4 The first player shakes the
die in the cup, says the num-
ber, and multiplies it by the
point value of the ball. (For
example, if the ball is worth
three points and the die lands
on five, a basket will be worth
15 points because 3 × 5 = 15.)
5 If the first player makes
the basket on the first shot,
she writes the number of
points on the dry-erase board
and her turn is over. If she
doesn’t make it, she gets
one more try.
6 The players take turns trying
for baskets and recording the
new total on the dry-erase
board until the team reaches
the target number of points.
GOAL: To reach the target number of points
3 points × = 15 points

Before the Game
Explain how to play the game, and practice as a group.
• How many points should each basket be worth? How many points
should we play to? How can we decide in a fair way?
• What can you do if you need help figuring out how many points
your basket is worth?
• How can we cheer one another on and work as a team? Why is
this important?
• How should we act if someone misses a basket? Why is this important?
talk
about
• How many more points do we need to reach our goal? How do
you know?
• What can you do if you need help figuring out the number of points
your basket is worth?
talk
about
during the Game

after the Game
Changing the Game
• Make the game an addition, rather than a multiplication, game.
Add the number rolled on the die to the starting point value of
the ball to determine the value of the basket.
• Choose a point value for the ball. Use two dice. Roll the dice,
add the numbers rolled, and multiply the total by the point
value of the ball to determine how many points each basket
is worth.
• Assign a starting value of 12 points to the ball. Roll the die and
divide the number rolled into 12 to determine how many points
the basket is worth. (If the number rolled does not go evenly
into 12, the player rolls the die again.)
their ideas.
• How did you make everyone feel supported?
• How did this game help you learn the multiplication facts?
• What are some tips that make certain numbers easy to multiply? (For
example, to multiply a number by three, first double the number, then
add the answer to the number: 3 × 9 is nine doubled plus nine more.)
talk
about

m u lt i p l i c at i o n b o w l i n g 65
m
u
ltiplication bow
lin
g
Players bowl using plastic bottles and a tennis ball, adding
points toward a target score. Players multiply to find the
point value of the fallen bottles. To play this game, you
three, or four
GAME SUMMARY
IN LEADER’S KIT
 Multiplication table
(on the back of the
dry-erase writing board)
OTHER MATERIALS
 Tennis ball
 6 empty plastic bottles to
be the bowling pins
 One-foot-long piece of
masking tape to make the
shooting line
 Grocery bag with handles
(optional, see “Tips”)
YOU’LL NEED

 Multiply by ten or less
 Add to 200 or less
Learning all of the multiplication
facts at once can be overwhelming
for children. This game gives them
a chance to practice one set of
multiplication facts at a time —
for example, for six (0 × 6, 1 × 6,
2 × 6, 3 × 6, and so on) — by having
them choose a single point value for
the plastic bottles for several rounds
of bowling.
 Make decisions together
a turn
In this game, it may be challenging
for the children to stay involved
while waiting for a turn. It is
important to discuss things they
can do to remain involved: keeping
score, cheering on other players,
retrieving the ball, and setting up
the bottles or cans.
 To manage the mate-
rials, you may want
to put the masking
tape, tennis ball, and
bottles for each group
in a grocery bag with
handles. When it is
time to play, give
each group a bag.
 You may want to
Multiplication and
page 40.
 Walk around while
the children play to
make sure that all of
the groups are work-
ing well together,
learning math, and
having fun.
Get ready
the children.

Game Directions
1 The players:
• arrange the plastic bottles
in a triangle formation,
decide where the shooting
line will be, and place the
masking tape there.
• pick a single number from
one to ten to be the value of
each bottle.
• choose a target score from
100 to 200.
• decide fairly who goes first,
second, and so on.
2 The first player:
• rolls the tennis ball from
behind the shooting line to
knock down bottles.
• multiplies the chosen value
of the bottles by the number
of bottles knocked down to
find the score.
• records the score on the
group’s dry-erase board.
(For example, if each bottle
is worth six points and three
bottles are knocked over,
the score recorded is 18
because 6 × 3 = 18.) If the
player doesn’t knock any
bottles down, she gets
another turn.
3 The second
player takes
a turn, adding
his score to the
previous one
on the group’s
scoreboard.
they reach the target score.
GOAL: To work together to reach a target number of points
shooting line
18
+ 12
30

Before the Game
1 Explain that the children will play a bowling game. Discuss past
experiences with bowling.
• Who has bowled before? How do you play?
talk
about
• How much should each bottle be worth?
• What do you think would be a good target score to choose for this
game? Why do you think so?
• How can we decide where to place the shooting line? What can we
do if we cannot agree?
• If I knock down five bottles worth eight points each, how many
points will that be? How do you know?
talk
about
• How are you staying involved while waiting for your turn?
• How many more points do you need to reach your target score? How
did you figure that out?
talk
about
during the Game

after the Game
Changing the Game
• Assign greater values to the bottles (between 12 and 25), and
choose larger target numbers.
• Play with ten bottles and a larger target score.
• Give each bottle the value of 1
⁄6 of a point and have the children
add fraction scores to reach a total of five points. (For example,
if the first player knocks down two bottles, her score is 2
⁄6. If the
next player knocks down five bottles, her score is 5
⁄6 and she
adds her score to her partner’s score to get a total of 7
⁄6 or 11
⁄6.)
• How did you stay involved while waiting for your turn?
• What are some tips that can make certain numbers easy to multiply?
(For example, to multiply a number by nine, first multiply the number by
ten, and then subtract the number from the answer. See “Introduction to
Multiplication and Division Games,” pages 39–40, for more tips.)
• Was it difficult to reach your target score? Why or why not?
• How did you decide the point value for each bottle and for your tar-
get score? What did you do when you had different ideas?
talk
about

m u lt i p l i c at i o n u n c o v e r e d 71
m
u
ltiplication uncover
e
d
Players choose a group of multiplication facts on
a game board and cover the numbers with game
markers. They roll dice to determine a multiplication
problem, say the answer, and uncover a square on the
game board to see whether or not they are correct.
three, or four
GAME SUMMARY
IN KIDS’ KIT
 36 game markers
 “Multiplication Uncovered” game board
 2 dice covered with stickers
(see “Get Ready”)
YOU’LL NEED

The multiplication table is a valuable
tool in learning multiplication facts.
In this game, the players use a multi-
plication table as a game board.
When they see all of the facts in a
chart, children begin to recognize
patterns in them. This enables them
to visualize the answers to multipli-
cation problems when they do not
have the chart.
make mistakes
a turn
When children of different skill
levels are playing together, children
who figure out the answers quickly
often have trouble staying involved
while the others are working out the
answers. While demonstrating the
game, discuss what the children can
be doing while they are waiting for
their turn (figure out the math in
their head, help their partner if
needed, and so on).
 The game board for this
game is a multiplication
table. Familiarize your-
self with the table and
how to use it. (For
example, if you want
to find the answer to
3 × 6, put a finger of
your right hand on the
three at the top of the
chart and a finger of
your left hand on the
six at the left side of the
chart. Slide your fingers
in straight lines across
the chart until they
meet at 18.)
 You may want to
Multiplication and
page 40.
Get ready
1 Read the game directions and
pages 75–76, and play the
game yourself before intro-
ducing it to the children.
2 Prepare two dice for each
group of players. Cover the
dice faces with round stickers
from the kit. On the first die,
write 1, 2, 3, 4, 5, 6 on the
faces. On the second die, write
7, 8, 9, 10, 11, 12 on the faces.
3 If you are playing with more
than four children, decide
how you will divide them into
groups of two to four to play
the game.

Game Directions
goes first, second, and so on
and which section of the
board they will play in first.
They cover each number in
the chosen section with a
game marker.
2 The players figure out
which dice they will use for
the section they choose. The
children use the dice that
correspond to the numbers
on the rows and columns of
the part of the game board
they are using. (Refer to
the illustration.)
GOAL: To remove three game markers
in a row from one section of a game board
1
2 3
1
2 3
OPTION A
8 9
7
1
2 3
OPTION C
8 9
7
8 9
7
OPTION D
1
2 3
8 9
7
OPTION B
(continues)

Game Directions
3 The first player rolls the dice
that match the chosen section
to determine a multiplication
problem.
4 The player says the problem
and the answer, and uses the
game board to check her
answer by removing the game
marker from the square that
corresponds to the problem.
(For example, if the child rolls
a four and a three, she says,
“Four groups of three equal
twelve.” She finds the corre-
sponding space on the game
board and removes the game
marker to see if she is correct.)
5 If the player is incorrect, she
returns the game marker. If
she is correct, she removes
the game marker. The player
may also state other multi-
plication problems with the
same answer and uncover the
squares for those problems.
(For example, if the child
rolls four and three, she can
also uncover the squares for
the problem two groups of
six. In both cases, the answer
is twelve.) Play passes to
the next player.
6 Play continues until three
game markers in a row have
been removed from the target
section. (Emphasize that the
players are working together
to remove the game markers,
not individually collecting the
game markers they remove.)
7 The players choose another
section of the game board
and play again.
(continued)

Before the Game
2 Discuss how to use the game board and how to play together.
• What does this game board look like? (You may need to explain that
it is a multiplication table and show the children how to use it.) How
can you use it to help you learn the multiplication facts?
• How can we decide which section of the game board to play on first?
• How do we know which dice to use?
• How can you stay involved when you are waiting for your turn?
• What should you do if your partner makes a mistake?
talk
about
• How is this game helping you learn the multiplication facts?
• How are you staying involved when it is not your turn?
• Which are the hardest facts to learn? The easiest? Why?
talk
about
during the Game

after the Game
Changing the Game
Ask the children how to play the game differently and try their ideas.
• What has helped you learn the multiplication facts?
• What are some tips that make certain numbers easy to multiply?
(See “Introduction to Multiplication and Division Games,” pages 39–40,
for tips.)
• Was it hard or easy to stay involved while waiting for your turn?
What helped you?
talk
about

m u lt i p l i c at i o n b a s e b a l l 77
m
u
ltiplication baseba
ll
The players form a baseball team, trying to beat the
score of a made-up team (called Team 1). They roll two
dice, multiply the rolled numbers, find the baseball play
that corresponds to the answer, and move markers on
the game board to complete baseball plays.
three, or four
GAME SUMMARY
IN KIDS’ KIT
 9 game markers to represent the
nine players on a baseball team
 2 dice
 “Multiplication Baseball” game board
 “Baseball Play Sheet”
YOU’LL NEED

 Multiply by six or less
Children need many experiences
with multiplication facts before
they recall them easily. Knowing the
multiplication facts helps children
solve multiplication and division
problems with larger numbers.
make mistakes
 Give help respectfully when asked
In this game, the children may make
mistakes multiplying or following
the baseball rules. Children often
worry that others will tease them
if they give an incorrect answer.
Discussing how they want to be
treated when they make mistakes
helps the children create a caring
community where they can help
each other and take risks.
Get ready
the children.
them into groups of two
to four to play the game.
 You may want to review
multiplication tips by read-
ing “Basic Multiplication and
Division Facts” on page 40.
 You may want to put
children familiar with
baseball in a group with
children who aren’t.
 Encourage all the children
to use math strategies
that work for them. Some
children may refer to the
multiplication chart on
the back of the dry-erase
writing board, while others
will rely on memorized
multiplication facts.

Game Directions
2 Team 1 is a made-up team that
the players will try to beat. To
determine the score for inning 1
for Team 1, the players roll a die
and record the number rolled in
the inning 1 box on the “Baseball
Play Sheet.”
3 The players are Team 2. They
place nine game markers to
represent Team 2 in a line
behind home plate on the
game board.
4 The first player:
• rolls two dice.
• multiplies the numbers.
• uses the “Baseball Play
Sheet” to find the play that
corresponds to the answer.
• completes the play by moving
her game marker and record-
ing any runs or outs on the
play sheet. (For example, if
she rolls a six and a two,
6 × 2 = 12, and 12 is a “single.”
She moves the game marker
from home plate to first base.)
GOAL: Together beat Team 1’s score
TEAM 1 SCORE
TEAM 2 SCORE
TEAM 2 OUTSTS
I N N I N G
1
I N N I N G
2
I N N I N G
3
TOTAL
SCORE
2
13
2
Home
Plate
(continues)
12–18 SINGLE

Game Directions
5 The players take turns, moving
game marker runners and
recording runs and outs.
6 After each inning for Team 2,
the players roll the die again to
determine the score for Team 1
for the next inning.
7 The players play three innings,
clearing all the game marker
“runners” from the bases
between innings.
8 Play continues until Team 2 has
completed three innings. The
players total their score and
Team 1’s score and compare
the scores.
(continued)

Before the Game
1 Explain that the children will play a baseball multiplication game with
dice, and talk about some of the baseball vocabulary they will use.
• What is an inning in baseball? How many outs are there per inning?
• What is a strike in baseball?
• What is a walk in baseball?
talk
about
• If you roll a six and a five and multiply them what is the answer?
What is the play on the “Baseball Play Sheet” for 30? What would you
do with the game marker? Do you need to record anything?
• How do you record a strike? A run?
• How do you know when an inning is over and you need to go to the
next inning? (Each inning has three outs.)
• If your partner makes a mistake during the game, what is a respect-
ful way to act?
talk
about
• Do you think you will be able to beat Team 1’s score? Why or why not?
• How are you and your group helping each other?
talk
about
during the Game

after the Game
Changing the Game
• Play the game outside. Set up a small baseball diamond and have
the children themselves move around the bases according to the
instructions on the “Baseball Play Sheet.” (Use a paper or plastic
cup to roll the dice, and have one player act as scorekeeper.)
their ideas.
• How did your score compare to Team 1’s score? How many runs
apart were your scores?
• How did this game help you learn multiplication? Why is learning
multiplication important?
• What were the easiest multiplication facts for you in this game?
Which were the hardest? What are some tips that make certain
numbers easy to multiply? (For example, any number times four
is the number doubled twice. For more tips, see “Introduction to
Multiplication and Division Games,” pages 39–40.)
• How did you help each other?
talk
about

m u lt i p l e m o v e s 83
multiple moves
NO MATERIALS NEEDED
The players stand in a circle. One player chooses a
number and a corresponding number of actions (for
example, three and clap, hop, snap). The players count
until they get to a multiple of the chosen number and
do the actions. To play this game, you need a large
space, like a gym or outdoor area.
PLAYERS: Grades 3–5, large group of ten or fewer
GAME SUMMARY
YOU’LL NEED

 Use multiples of the numbers
from two to five
This game helps the children use
multiples in a concrete way that will
help them remember multiplication
facts. A multiple is the result of any
whole number multiplied by another
whole number. (For example, some
multiples of three are 3, 6, 9, and
12 because 3 × 1 = 3, 3 × 2 = 6,
3 × 3 = 9, 3 × 4 = 12.)
make mistakes
In this game, the children may feel
like they’re in the spotlight on their
turn. Some children will find the con-
cept of multiples easy and will enjoy
the action of the game. Others may
find multiples challenging. To allow
everyone to feel safe to play, discuss
how to be respectful of players who
make mistakes or need help.
 Before playing, make
sure that you understand
what a multiple is. You
may want to brush up
on your own under-
standing of multiples
by reading “Introduc-
tion to Multiplication
and Division” on
pages 39–40.
 To introduce this large-
group game, have the
whole group practice
playing safely. (For
example, you might
have all the children
practice a physical
action and talk about
why it is important to
be aware of their per-
sonal space to play
the game safely.)
Get ready
and pages 87–88 yourself
before introducing the
game to the children.
where the children can
stand in a large circle.

Game Directions
1 The players stand in a circle.
2 One player chooses a number
from two to five and a series
of actions. (For example, if
three is chosen, the player
makes up a series of three
actions, such as clapping,
finger snapping, and jumping.)
The player stands in the
middle of the circle to lead
the actions.
3 One player in the circle
begins the counting by
whispering “one.”
4 The next player whispers
“two” and the players continue
to count in turn until they
reach the chosen number. The
whole group says the number
and does the actions. (In the
example, the first player whis-
pers “one,” the second player
whispers “two,” and everyone
says “three” and claps, snaps,
and jumps.)
GOAL: To count around the circle twice
(continues)
3-- CLAPPING,
FINGER SNAPPING,
AND JUMPING
3

Game Directions
5 The players continue counting
in turn until they reach a
multiple of the chosen num-
ber. All the players say the
multiple and do the series of
actions. (For example, if the
number is three and they
reach nine, they would all
say, “nine” and do the three
chosen actions.)
6 Play continues until the play-
ers have counted around the
circle twice.
7 A different player chooses
another number from two to
five and a different series of
actions, and the players play
another round.
8 The players take turns as
long as the game holds the
group’s interest.
(continued)

Before the Game
1 Explain how to play the game, and practice as a group. Explain
that the larger the multiple, the more challenging the game,
because the children will need to remember more actions.
• What is a multiple? What is another way to explain it?
• What are some multiples of three? How do you know?
• What are some appropriate actions we could choose?
• How do you want others to act if you make a mistake?
talk
about
• How are we acting when people make mistakes? Is that respectful?
What, if anything, do we want to do differently?
• How does it feel to be laughed at when you make a mistake? Why is
it important to treat others with respect?
talk
about
during the Game

after the Game
Changing the Game
• In addition to doing the actions for multiples, do them for
numbers that have the chosen number as one digit. (For
example, if the chosen number is four, say and do the actions
for multiples of four, such as 4, 8, 12, and for numbers that
have 4 as a digit, such as 14, 24, and so on.)
• Use multiples of six.
• Use two separate actions, rather than a series of actions, one for
multiples of the chosen number and one for numbers that have
the chosen number as a digit. (For example, the children could
clap on the multiples and snap on the digits. If a number both is
a multiple and has the chosen number as one of its digits, the
children do both actions.)
their ideas.
• How did we act respectfully?
• How does this game help you with your multiplication facts?
talk
about

t h r e e ta c t o e 89
three tac toe
IN KIDS’ KIT
 2 dice
 “Three Tac Toe” game board
Players take turns rolling and adding two dice and
crossing out a number that is a multiple of the total on
a game board. Players try to cross out three numbers
in a row as many times as possible.
three, or four
GAME SUMMARY
YOU’LL NEED

 Find multiples
Children with different levels of
multiplication skill can play together
using different strategies. Some will
have memorized the multiplication
facts, some will skip count (count by
units other than one), and others
may use the game board itself. In
this game the children work on
finding multiples, which helps them
learn multiplication. A multiple is
the result of any whole number
multiplied by another whole number.
(For example, multiples of 4 are 4, 8,
12, and so on because 4 × 1 = 4,
4 × 2 = 8, and 4 × 3 = 12.)
 Help without giving the answer
It is important to teach children
how to give help without telling the
answer. This way, the child who
needs help can learn to rely on him-
self for answers to difficult problems.
Show the children how to help by
giving a clue or asking a question.
Get ready
the children.
sure that you under-
stand what a multiple
is. You may want to
brush up on your
own understanding
of multiples by reading
“Introduction to
Multiplication and
Division Games” on
pages 39–40.
 Before introducing
the game, practice
explaining the game
directions out loud.

Game Directions
2 The first player rolls the
dice, adds the rolled numbers
together, and chooses a
multiple of that number to
cross out on the game board.
(For example, if a two and a
four are rolled, the total is six.
Multiples of six are the result
of six times any whole num-
ber. Six, 12, and 18 are multi-
ples of six because 6 × 1 = 6,
6 × 2 = 12, 6 × 3 = 18.)
3 The players take turns rolling
the dice and crossing out num-
bers, trying to get three num-
bers in a row. The rows can be
vertical, horizontal, or diago-
nal. Players work together, not
against each other, to cross
out three in a row.
4 The players earn points each
time they complete a row of
three. They record the points
on the game board — one
point for each row of three
numbers less than 71 and two
points for each row of three
numbers more than 71 (green
area on the game board).
5 Play continues as long as
the game holds the group’s
interest or for a set time.
GOAL: To get three numbers in a row as many times as possible

2 If a player is having difficulty figuring out a number’s multiples,
help by demonstrating how to “skip count” by that number on the
game board. (Skip counting is counting by a unit other than one, for
example by two: 2, 4, 6, 8, 10, 12.)
group agrees, and the math is still appropriate. (For example, the
children might make up a rule that you must use numbers that are
not already part of a row of three when counting three numbers in
a row.)
Before the Game
• What is a multiple? (For example, a multiple of three is the result of three
times a whole number [for example, 3 × 1 = 3 , 3 × 2 = 6 , 3 × 3 = 9 ],
so some of the multiples of three are three, six, and nine.)
• What are ways to find multiples if you don’t know the multiplication
facts? (See “About the Math Skills.”)
• How can you help your partner without telling the answer?
talk
about
• What are some of the multiples of nine? How do you know?
• How are you helping each other without telling the answer?
• How many numbers larger than 70 have you crossed out?
talk
about
during the Game

after the Game
Changing the Game
• Use only one die.
• Use three dice.
• Allow the players to add one or two to a multiple of the number
rolled to get the number to cross out. This provides a way
for players to be strategic about the numbers they get. (For
example, a player who rolls a three and wants to cross out
ten, may do so because ten is one more than nine, which is
a multiple of three.)
their ideas.
• What are the benefits of playing the game together instead of against
each other?
• What were the hardest multiples to figure out? The easiest?
• What strategies did you use to get three in a row?
• How does learning multiples help you in math?
talk
about

b e a c h b a l l m u lt i p l i e r 95
b
each ball multiplie
r
Players throw and catch a beach ball with the numbers
from zero to eleven written on it. When a player
catches the ball, he says the number under each hand
and then all the players multiply the two numbers
together and say the answer. To play this game, you
PLAYERS: Grade 4–6, large group of ten or fewer
GAME SUMMARY
YOU’LL NEED
IN LEADER’S KIT
 Inflatable beach ball
 Permanent marker

 Multiply by eleven or less
Children need many different ways
to practice their multiplication facts
before and after they memorize
them. Some children learn best
when they connect physical
movement to learning.
In this game, the children may come
up with different answers. Ask the
children to explain their thinking so
they can learn from one another
and determine the correct answer.
 You may want to
Multiplication and
page 40.
 As you are planning,
think about the ques-
tions your children
might have about the
game and how you will
answer the questions.
Get ready
and pages 98–99 yourself
before introducing the
game to the children.
2 Blow up the beach ball.
Decide how you will
divide it into 12 sections
(for example, on a six-
paneled ball, you can
divide each panel in two)
and write the numbers
0–11 on the ball, one
number on each section.
where the children can
stand in a large circle.
8
2
11 5
9
3

Game Directions
1 The players stand in a circle.
2 The leader says a player’s
name and throws the ball
to her.
3 The player who catches the
ball says the number under
each hand, or closest to each
hand, in a multiplication
sentence such as “five groups
of three equal…” or “five times
three equals….”

4 All the players then say the
answer together. If they don’t
agree, they discuss which
answer is correct and why
they think so.
5 The player with the ball then
says another player’s name
and throws it to him.
6 The players take turns throw-
ing and catching the ball until
everyone has had a turn.
GOAL: To throw the ball to each player in the circle
82
11 5
9
3
MARIANA!
FIVE GROUPS OF
THREE EQUAL . . . .

Before the Game
Explain how to play the game, and practice as a group.
• What can you do if you do not know the answer?
• How can we make sure that everyone gets a turn to catch the ball?
• How did you figure out the answer? What’s another way?
talk
about
• How did you find the answer? What’s another way?
• What are some tips that make certain numbers easy to multiply?
(For example, a number multiplied by zero is zero, a number multiplied
by two is doubled, a number multiplied by ten is the number with a
zero added. See “Introduction to Multiplication and Division Games,”
pages 39–40, for more tips.)
talk
about
during the Game

after the Game
Changing the Game
• Have the children say which of the numbers under their hands
is greater.
• Write the numbers 0–6 on the ball. (You will need to write some
numbers twice.)
• Write larger numbers (10–20) on the ball and have the children
add rather than multiply the numbers.
• Write the numbers 6–12 on the ball. (You will need to write
some numbers twice.) Multiply them.
• Add division to the game. Before beginning each round,
choose a number from two to six. Have the children multiply
the numbers under their hands and divide the answer by the
chosen number.
• Have the players pass the ball from one to the next until the
leader says, “Stop!” The player holding the ball multiplies the two
numbers his hands are covering.
• If you are playing with children of various grades from grades
K–6, give the children a choice between adding or multiplying
when it is their turn.
their ideas.
• Which are the easiest numbers to multiply? Why? Which are the
hardest? Why?
• What could we do differently next time we play?
talk
about

f o r e h e a d f a c t o r s 101
forehead factors
IN KIDS’ KIT
 Deck of playing cards, with
jacks, queens, and kings
removed (ace equals one)
 Multiplication table (on the back
of the dry-erase writing board)
The dealer (called the “foreheader”) deals a playing card
to each of the other two players and says, “Foreheads!”
Each player puts the card face up on their forehead
without looking at their number. The “foreheader” mul-
tiplies the numbers on the two cards and says only the
answer. The players with the cards on their foreheads
try to guess the number of the card they are holding.
PLAYERS: Grades 4–6, small groups of
three or four
GAME SUMMARY
YOU’LL NEED

 Multiply or divide by ten or less
 Find factors
Children often find division more
challenging than multiplication.
In this game, they can use their
multiplication knowledge as a
strategy to figure out the answers
to division problems. (For example,
if the “foreheader” says 30 and the
other player’s card is a six, a child
can think about the problem as
“What number times six equals 30?”
or “How many groups of six in 30?”)
This game also uses factors (numbers
that divide evenly into another num-
ber.) (For example, three is a factor
of 12 because there are four groups
of three in 12 with no leftovers.)
make mistakes
In this game, some children may easi-
ly figure out the number on their card
on their first guess, while others may
need several guesses. Encourage the
children to help each other by giving
hints or asking questions rather than
telling the answer.
stand what a factor is.
You may want to brush
up on your own under-
standing of factors by
reading “Introduction
to Multiplication and
pages 39–40.
 Familiarize yourself
with how to use the
multiplication table.
(For example, to find
the answer to 3 × 6,
put a finger of your
right hand on three at
the top of the chart.
Put a finger of your left
hand on six at the left
side of the chart and
slide your fingers
straight across the
chart until they meet
at 18.)
Get ready
the children.
them into groups of three
or four to play the game.

Game Directions
1 The players stand or sit facing
each other.
will be the “foreheader” first,
second, and so on.
3 The “foreheader” gives two
of the other players one card
each. The players do not look
at their cards.
4 When the “foreheader” says,
“Foreheads!” the players put
their cards face up on their
foreheads without looking at
their own cards.
5 The “foreheader” multiplies the
two cards together and says
the answer. (The “foreheader”
should say only the answer,
not the two numbers that
were multiplied.) If there is a
fourth player, she can help the
foreheader make sure he has
the correct answer.
6 The two players look at each
other’s cards and each says
what he thinks the number on
his card is.
7 The “foreheader” and the
fourth player say whether or
not the number is correct. If
the number is correct, the
player can look at his card. If
the number is incorrect, the
“foreheader” or fourth player
can give hints or ask ques-
tions until the player guesses
the correct answer. (A hint
might be, “How many groups
of six are in 18?”)
8 The players switch roles until
everyone has had a chance to
be the “foreheader,” or as long
as the game holds their interest.
GOAL: To guess the number of the card on their forehead
18
foreheader

Before the Game
Explain the game as you play it with two children as your partners.
• How can the “foreheader” use the multiplication table without the
other players seeing, if she does not know how to multiply the two
numbers on the cards?
• If a player has a six card and does not guess her number correctly,
what are some hints the “foreheader” could give her? (For example,
“Your number is between five and ten. Your number is an even number.”)
• How do you want to be treated if you guess an incorrect answer?
talk
about
• After a child guesses her number correctly ask: How did you figure
out your number?
• If a child did not guess correctly, ask the foreheader: What hints could
you give to help him guess his number? (For example, one hint might
be “How many groups of six equal 30?”)
talk
about
during the Game

after the Game
Changing the Game
• Have the “foreheader” add the two cards instead of
multiply them.
• Use only the cards from ace to five.
• Choose a target number greater than 20. The “foreheader” adds
the cards mentally and states their difference from the target
number. The other players guess the numbers on their cards.
(For example, if the target number is 25 and the cards are six
and eight, the “foreheader” says eleven because six plus eight
equals 14 which is eleven less than 25.)
their ideas.
• What are some hints or questions you used to help your partner
guess her number? How helpful were the hints or questions?
• What math did you use to play this game?
• How did you treat each other when you guessed the wrong number?
What will you do the same way or differently the next time you play?
• Why is this game called “Forehead Factors”? What is a factor? (A factor
is a number that divides evenly into another. For example, one, two,
three, and six are all factors of six. A factor can also be explained as
one of two or more numbers that are multiplied to get a result.)
talk
about

t h e l e a d e r s ay s d i v i d e 107
t
h
e
leader says divid
e
 “How Many Times? Division,”
pages 112–116
This game is based on “Simon Says.” The players
choose an action and figure out how many times
to do that action according to instructions from the
leader. No player is ever out, so that all the players
practice division. To play this game, you need a large
space, like a gym or outdoor area.
PLAYERS: Grades 3–5, large group
of twenty or fewer
GAME SUMMARY
YOU’LL NEED

 Divide by 10 or less
 Practice mental math
Dividing numbers in our heads
without a pencil and paper is a skill
needed in everyday life. In this
game, the children practice dividing
numbers mentally in a fun way.
They combine division with physical
movements such as jumping or
clapping. Learning all of the division
facts at once can be overwhelming
for children. This game gives them
a chance to practice one set of
division facts at a time — for exam-
ple, the threes table — dividing by 3
(0 ÷ 3, 3 ÷ 3, 6 ÷ 3, 9 ÷ 3, and so on).
make mistakes
Children often worry that others will
tease them if they give an incorrect
answer. Discussing how the children
want to be treated when they make
mistakes helps create a caring
community where children feel
comfortable taking risks.
 Be sensitive to older
children who are
having difficulty
with math concepts.
Children learn at
different rates, so
acknowledge every-
one’s effort and
encourage the
children to help
one another.
Get ready
the children.
2 Decide which division
table the children will
work on first (for example,
dividing by 4, dividing by 7,
or dividing by 9), see “How
Many Times? Division,”
pages 112–116.

Game Directions
1 The players stand facing the
leader with enough space
between them to move freely.
2 The players take turns choosing
an action for the group to do
(for example, clap, jump, roll
shoulders backward).
3 Once an action is chosen,
the leader restates the action,
gives a division problem, and
gives the children time to
think. The leader then says,
“Go!” and the children count
the answer as they do the
action. (For example,
the leader says, “The
leader says touch the
floor 25 divided by 5
times,” gives the children time
to think, and says, “Go!” The
children say, “One, two, three,
four, five” as they touch the
floor five times.) The leader
uses the “How Many Times?
Division” lists for division prob-
lems. The players follow the
directions only if the leader
says, “the leader says” before
giving the direction.
4 Play for as long as the game
holds the group’s interest or
until each player has had a
chance to choose an action.
GOAL: Do an action when the directions include “the leader says”
THE LEADER SAYS
TOUCH THE FLOOR
25 DIVIDED BY 5 TIMES
. . . GO!
ONE, TWO,
. . . FIVE!

2 Talk about strategies for finding the number of times to do
an action.
Before the Game
Explain how to play the game, and practice it as a group.
• What kinds of actions can we do?
• What are some ways to find the answer to 45 divided by 9?
• What is 49 divided by 7? How do you know?
• What can you do if you don’t know how many times to do an action?
• What should we do if someone makes a mistake? Why?
talk
about
• How did you figure out the number of times to do that action? Did
anyone figure it out a different way? How?
talk
about
during the Game

after the Game
Changing the Game
• Use “The Leader Says” from AfterSchool KidzMath™
Primary Games.
• Have the children add and subtract with three numbers to
arrive at a total. (For example, “The leader says hop on one
foot 8 – 3 + 6 times.”)
• Use the “How Many Times? Mixed Division” list (p. 117).
• Use the “How Many Times? Fractions and Percents” list
(p. 118).
• Use division facts for 11 and 12. (Prepare a list of facts before
starting to play so that the game will go smoothly.)
• Which were some of the easier problems to figure out? Why?
• Which were some of the more difficult problems to figure out? Why?
• Did we make it comfortable to make a mistake? If so, how? If not,
what could we do differently the next time we play? Why is it impor-
tant to make it comfortable for others if they make a mistake?
• When do you use division in everyday life?
talk
about

how many times?
DIVISION
Use this sheet to give you ideas for how many times to ask players to
do an action. Choose one set of division facts to work on at a time
(for example, “Dividing by 6”). The answers are in parentheses.
DIVIDING BY 1
3 divided by 1 times (3)
DIVIDING BY 2
The leader says,…

how many times?
DIVISION
DIVIDING BY 3
DIVIDING BY 4
The leader says,…

how many times?
DIVISION
DIVIDING BY 5
DIVIDING BY 6
The leader says,…

how many times?
DIVISION
DIVIDING BY 7
DIVIDING BY 8
The leader says,…

how many times?
DIVISION
DIVIDING BY 9
DIVIDING BY 10
The leader says,…

how many times?
MIXED DIVISION
If you want to make the game more challenging, use this page to give
you ideas for how many times to ask players to do an action.
This page contains division facts that are from all the division tables.
The answers are in parentheses.
The leader says,…

how many times?
FRACTIONS AND PERCENTS
Use this sheet to give you ideas for how many times
to ask players to do an action.
1
⁄2 of 10 times (5)
100% of 15 times (15)
7
⁄8 of 8 times (7)
25% of 4 times (1)
1
⁄2 of 22 times (11)
1
⁄4 of 16 times (4)
50% of 18 times (9)
10
⁄20 of 20 times (10)
25% of 100 times (25)
7
⁄12 of 12 times (7)
1
⁄4 of 12 times (3)
50% of 16 times (8)
10
⁄10 of 10 times (10)
4
⁄4 of 5 times (5)
50% of 30 times (15)
6
⁄10 of 10 times (6)
1
⁄2 of 2 times (1)
1
⁄4 of 4 times (1)
100% of 16 times (16)
1
⁄2 of 30 times (15)
The leader says,…

s p i n s p o t 119
GAME SUMMARY
IN KIDS’ KIT
 2 different-colored game markers
 “Spin Spot” spinner 1
 “Spin Spot” game board
Players choose a target space on the game board.
They spin a spinner to get numbers and move their
game markers across the game board, trying to reach
the target space at the same time.
three, or four
YOU’LL NEED
spin spot

stand what a factor is.
You may want to brush
standing of factors by
to Multiplication and
pages 39–40.
 When a child gives a
solution, ask him to
explain. You might ask,
“How do you know
that is the answer?” or
“How did you figure
that out?”
Get ready
 Find factors
In this game, the children find
possible factors for numbers on a
spinner. A factor is a number that
divides evenly into another. (For
example, three is a factor of 12
because there are four groups of
three in 12 with no leftovers.)
Multiplication facts can often be
used to help children figure out the
factors of a number. (For example,
1 × 6 = 6 and 2 × 3 = 6 so one, two,
three, and six are factors of six.)
In this game, some children may
need help finding factors of the
number spun. Encourage partners
to help by asking questions such
as “What numbers can you multiply
to make ten?” rather than telling
the answer.
the children.

s p i n s p o t 121
Game Directions
1 If more than two children are
playing a game, have them
divide into two groups to play.
2 The players sit across from
each other and choose a tar-
get space on the game board,
marking it with an “x.”
3 Each player or pair of players:
• selects a game marker.
• places the game marker at
the start line closest to her.
4 The first player or pair spins
the spinner.
5 Both players or pairs move the
game markers into any space
in their first row that has a
number that is a factor of the
number spun. (For example, if
18 is spun, the player can
move the game marker to a
square containing 1, 2, 3, 6, or
9, because all these numbers
divide evenly into 18 and are
factors of 18.) If one of the
players can’t use the number to
move, the other player moves
and they decide together who
will spin next. If neither of them
can use the number, the player
spins again.
GOAL: To reach the target space at the same time
sp
in
spot • 1
6
16
22
27 12
18
13
10
2430
start
start
(continues)

Game Directions
6 The second player or pair
spins. This time both players
or pairs move their game
markers into an adjoining
space with a number that is
a factor of the number spun.
(Any adjoining space touches
the space with the game
marker at one of its sides
or points.)
7 The players or pairs continue
until both game markers reach
the target space at the same
time. One player or pair can-
not arrive at the target space
unless the other player or pair
can do so on the same turn.
(continued)
sp
in
spot • 1
6
16
22
27 12
18
13
10
2430
start
start
target
space
All of these spaces are
adjoining or touching the
space with the six.

s p i n s p o t 123
Before the Game
2 Explain that if there are two children per game board, each child
will get his own game marker. Explain that if there are three chil-
dren per game board, one child will get her own game marker and
the other two will share. Explain that if there are four children per
game board, two children will share each game marker.
• If one player or pair is having trouble finding the factors of a number,
ask the other players: How can you help without giving the answer?
• What numbers divide evenly into the number spun? How do you know?
talk
about
during the Game
• In this game you will find factors of the number spun. What is a factor?
• How can you figure out which spaces you can move to?
• How many turns do you think it might take to reach the target space?
• How can you plan to reach the target space at the same time?
talk
about

Changing the Game
• Use the “Spin Spot” spinner 2.
their ideas.
• Did you help another player? How?
• Which numbers were the best to spin? Why?
• Which numbers were the worst to spin? Why?
• What strategy did you use to reach the target space at the same time?
talk
about
after the Game

ta r g e t 125
GAME SUMMARY
IN KIDS’ KIT
Three rows of three cards are placed face up.
Another card is turned face up to be the target
number. The players take turns combining cards using
addition, subtraction, multiplication, and division to
make the target number. Once all possible combina-
tions are removed from the face-up cards, the cards
are replaced and partners continue to find equations
that equal the target number.
three, or four
YOU’LL NEED
target

 Rather than telling a
child who makes an
error that he made a
mistake, help him find
his mistake by asking
questions. (For exam-
ple, “You said that 6
times 5 is 25. How did
you find that answer?”) Get ready
 Add, subtract, multiply, and
divide mentally
In this game, the children use
addition, subtraction, multiplication,
and division to make a target
number. This helps them learn to
think about numbers flexibly and
do mental math.
offering help
Learning to give help, not the answer,
is an important skill that benefits
both the child needing help and the
one giving it. The child giving the
help deepens her understanding
of the math by thinking of clues
to support the other child. The
child receiving the help has the
opportunity to see the problem in
a different way and still have the
satisfaction of figuring out the
answer herself.
the children.
2 Think about the math
skills of the children to
determine whether they
are ready for multiplication
and division or need more
practice with addition and
subtraction. Change the
game accordingly.

ta r g e t 127
Game Directions
1 The players choose fairly
who deals and who goes first,
second, and so on.
2 The dealer places ten cards
face up: three rows of three
cards with one card on the
side to be the target number.
The target number stays the
same for the entire game.
3 The first player removes cards
that can be combined using
multiplication, division, addi-
tion, and subtraction to equal
the target number. (Ace equals
one.) At least two cards must
be removed at a time. (For
example, if the target number
is five, as in the illustration,
there are several possible
equations. A player could
remove the two and three,
because 2 + 3 = 5; the six
and ace, because 6 – 1 = 5; or
the two, three, two, and four,
because two times three is six,
plus four more is ten, divided
by two equals five.)
4 When all possible combinations
have been removed, the dealer
fills the empty spaces, and the
next player finds equations for
the target number.
5 The partners take turns until
they have used all of the
cards or all cards are dealt
out and no more equations
that equal the target number
can be made.
GOAL: To remove all the cards by finding combinations
of cards that equal the target number
target
number

Before the Game
2 If a child is having difficulty seeing combinations, help by
asking questions.
3 If a player or group suggests a change in the rules while they
are playing the game, allow them to discuss the change. Before
changing the rule, make sure the change is fair to all players,
everyone in the group agrees, and the math is still appropriate.
(For example, if all nine cards have been dealt out and there are
no ways to make the target number, a group might decide to
either keep playing by adding another row of cards or start over.)
2 If the children are ready, use examples of multiplication and divi-
sion to encourage them to move beyond addition and subtraction.
Also demonstrate giving help without giving the answer.
• Do you see a way you could combine some of the cards to equal the
target number? What is another way? Is there a way we could make
the target number using more cards?
• How could you use multiplication and/or division to equal the
target number?
• How could you use these two cards to make the target number?
• How do I know when I should help my partner?
talk
about
• How did you use those cards to make the target number?
• How are you helping each other without giving the answer?
talk
about
• How could you use these three cards to make the target number?
• How could you use division to make the target number?
Multiplication? Addition? Subtraction?
talk
about
during the Game

ta r g e t 129
Changing the Game
• Use ace to five from two decks of cards (40 cards).
• Choose one “wild card” that can be used as any number.
• Use a full deck of cards, including face cards. Make the
jack equal eleven, the queen equal twelve, and the king
equal thirteen.
their ideas.
• What target numbers were the easiest to get? The hardest?
• How did it work to give help instead of just giving the answer?
• How did you know when to offer help?
talk
about
after the Game

d i s a p p e a r i n g p y r a m i d 131
GAME SUMMARY
IN KIDS’ KIT
This game is a variation of the card game “Solitaire.”
Cards are laid out in a pyramid shape with one card
at the top and a row of seven cards at the bottom.
Players take turns finding two or more cards that equal
ten and removing them from the pyramid. The goal
is to make the pyramid disappear or to remove as
many cards as possible.
three, or four
YOU’LL NEED
d
isappearing pyram
i
d

 If necessary, teach the
children to shuffle cards or
show them an alternative,
such as spreading the
cards on the table, mixing
them up, and then making
a new pile.
 Talk about the importance
and benefits of playing
cooperatively. Help the
children see that playing
cooperatively makes the
game fair for children of
different skills and ages.
Get ready
divide mentally
This game helps children move
easily among addition, subtraction,
multiplication, and division. At first,
some children may use only addi-
tion. As they hear other children’s
strategies for making ten, they will
begin to use subtraction, multiplica-
tion, and division.
To get the most from the game, each
player should explain her strategy
and make sure her partner agrees
before she removes cards. The
children will need to be reminded
to slow down and do this.
the children.
decide how you will
divide the children into
groups of two to four
to play the game.

Game Directions
lays out the pyramid and who
removes cards first, second,
and so on.
2 The dealer shuffles the cards
and lays them face up in a
pyramid shape, laying out one
card to be the first row, and
building the pyramid by add-
ing rows, each one slightly
overlapping the previous one.
All the remaining cards are
put in a pile face down.
3 The first player looks for
cards that can be used to
make equations that equal
ten. Multiplication, division,
addition, and/or subtraction
may be used. (For example, a
ten card by itself; a ten card
and an ace [10 × 1 = 10]; or a
nine, a three, and a two card
[9 + 3 – 2 = 10].)
Only cards that have no cards
on top of them may be used.
If no equation can be made
with the available cards, the
player turns over a card
from the face-down pile and
looks for equations using the
new card. If no equation is
possible, cards are turned over
from the face-down pile until
the player is able to make ten.
GOAL: To make the card pyramid disappear by removing all the cards
(continues)

Game Directions
4 The player says the equation
(for example, “Eight times two
equals sixteen, minus six
equals ten”). Both players
must agree that the equation
equals ten before the cards
can be removed. The removed
cards are placed face up in a
“tens pile.”
5 The second player takes
a turn.
6 The players continue
taking turns.
7 If they have exhausted
the face-down pile and no
equations that equal ten are
possible, the players may
choose to continue to play
with a new rule. They might
turn over two cards at a
time from the face-down
pile, or they might decide
on their own rule about how
to continue.
8 Play continues until all the
cards are removed from the
pyramid or no more moves
are possible.
(continued)

1 Start by discussing ways to make ten.
Carefully lay out a pyramid of cards, showing the children how to
make each row.
• What are two or more numbers that equal ten?
• Can anyone think of a way to make ten that uses subtraction?
Multiplication? Division?
talk
about
• How could you make ten using these cards? What’s another way?
• How can you let your partner know why you are taking those cards?
What can you do if she doesn’t agree that those cards equal ten?
• How will you know when your partner needs help?
• What can you do if no moves seem possible?
talk
about
during the Game
• Is there any way to use these cards to make ten?
• Could subtraction help you to make ten with these cards?
• If you can’t find an equation, what can you do?
• How do you know that your partner agrees before you remove
the cards?
talk
about
Before the Game

after the Game
Changing the Game
• Use only addition or only addition and subtraction to make ten.
• Have the children make equations that equal 13, 15, 20, or 30.
• Add the face cards to the deck. Have the children make
equations for 20 or 30, using the jack to represent eleven, the
queen to represent twelve, and the king to represent thirteen.
their ideas.
• What are some equations that equal ten using two cards?
Three cards?
• What are some equations that make ten using multiplication
or division?
talk
about

s ta d i u m t o u r , u s a 137
GAME SUMMARY
Players make a basketball “stadium tour” across the
country — adding, subtracting, multiplying, or dividing
numbers on three dice.
PLAYERS: Grades 3–6, small groups
of two, three, or four
s
tadium tour, usa
IN KIDS’ KIT
 3 dice
 2 different-colored game markers
 Multiplication table (on the back
of the dry-erase writing board)
 “Stadium Tour, USA” game board
YOU’LL NEED

 Repeat a child’s answer
back to her to make
sure you understand.
(For example, you might
say, “You said that you
count by fives 5 times
to figure out that five
times five equals 25. Is
that right?”)
 Familiarize yourself
with how to use the
multiplication table.
(For example, if you
want to find the answer
to 3 × 6, put a finger of
your right hand on the
three at the top of the
chart. Put a finger of
your left hand on the
six at the left side of the
chart. Slide each of your
fingers in a straight line
across the chart until
they meet at the 18.)
Get ready
divide mentally
Playing this game, which requires
that children use addition, subtrac-
tion, multiplication, and division,
helps them learn to think flexibly
and solve problems mentally.
offering help
Learning when and how to offer
help takes time and experience.
Children must learn to determine
whether or not their partners have
had enough time to think and would
welcome help and how to ask if
their partner would like help.
They also need to learn how to
help by asking questions rather
than by telling the answers.
the children.

Game Directions
1 The first player:
• rolls three dice.
• adds, subtracts, multiplies,
and/or divides the rolled
numbers to get an answer
that equals one of the seat
numbers in the first stadium.
• explains the answer to
his partner.
• places the marker on the
game board on the first
stadium (Oakland, California).

For example, if the player rolls a five,
three, and two, some of the possible
solutions are:
• “Five plus three equals eight. Eight
minus two equals six.”
• “Five times two equals ten. Ten minus
three equals seven.”
2 If a player is not sure how to
combine the numbers to make
an equation that works, the
other partner may offer help.
3 If all the players agree that the
rolled numbers cannot be used,
the player keeps rolling the dice
until he can use the numbers he
rolls to get an empty seat.
4 The dice pass to the second
player, who rolls the dice
until she can use the numbers
she rolls to make one of the
available seat numbers in the
first stadium. The second player
cannot sit in the first player’s
seat (use the same answer as
the first player).
5 The players follow the arrows to
the next stadium on the game
board. Neither player can move
on to the next stadium until
both players are seated in the
current one.
they are both seated in the last
stadium on the game board.
GOAL: To get seats for a game in each stadium

Before the Game
1 Talk about a stadium.
2 Explain that in this game the players are two friends taking a trip
to see basketball games in various stadiums across the country. In
each stadium, there are only a few seats available. The players will
roll three dice, then add, subtract, multiply, or divide the rolled
numbers to find a combination that equals one of the available
seat numbers. Explain that if there are four people in the group,
each pair will share a game marker. If there are three people in a
group, two of them will play as a pair.
4 Talk about how students who are still learning multiplication facts
can use the table on the back of the writing board to multiply.
• What is a stadium? How many of you have been to a stadium?
What did you see at the stadium?
talk
about
• (Show the game board.) What does this game board show? Which
team plays at each stadium? (Warriors–Oakland, CA; Suns–Phoenix,
AZ; Mavericks—Dallas, TX; Bulls—Chicago, IL; Knicks—New York, N.Y;
Hawks—Atlanta, GA; and Heat—Miami, FL)
• Look at the numbers my partner just rolled. Can anyone find a way
to use the numbers to equal one of the Oakland seat numbers?
talk
about
• What is a multiplication table? How can you use it to help you play
this game?
• What are some things that might tell you that other players have had
time to think and might welcome help? What could you say to find out?
talk
about

after the Game
• Which stadiums are the most difficult to get seats in? Why do you
think they are difficult to get?
• Which stadiums had the easiest seats to get? Why do you think they
were easy to get?
• How did you know when someone had enough time to think and
was ready for help?
talk
about
2 If a player is stuck, but a move is possible, allow time for him to
think, then ask if he wants help. If he does, you or the child’s
partner can give help by asking a question, such as “Since you
need to make a very large number, which do you think would
work best: addition, subtraction, multiplication, or division?”
during the Game
• How could you use the numbers that you rolled to help you get one
of the seat numbers in the next stadium? Can they be used to make
any other of the seat numbers?
talk
about

Changing the Game
• Fill in the blank “Stadium Tour, USA” game board using only the
numbers 1–12. Have players use only addition and subtraction
to play the game.
• Once the two players are in the same stadium, have them take
turns rolling the dice until they are seated next to each other
before moving on to the next stadium.
• Fill in the blank “Stadium Tour, USA” game board using seat
numbers 1–40. Have the players roll four dice to play the game.
• Add stadiums from more cities to the game board.
• Have the children decide on a different sport (for example,
baseball, soccer, or football) or event (for example, concert)
and illustrate the blank “Stadium Tour, USA” game board with
drawings of their chosen sport.
their ideas.

e q u a p a r d y 143
GAME SUMMARY
This game is similar to “Jeopardy.” The leader takes
an answer card from a category like “addition” or
“division,” turns the card over, and announces the
number. Each group works together to come up with
a different equation for that answer. The groups work
together to score 5,000 points.
PLAYERS: Grades 3–6, large group of 20 or fewer,
divided into small groups of four players each
equapardy
YOU’LL NEED
IN LEADER’S KIT
 “Equapardy” poster
OTHER MATERIALS
 Small self-stick notes

 Show enthusiasm for the
game and help keep the
game cooperative.
 Encourage the children
to use mathematics
strategies that work for
them and discuss the
various ways the children
find solutions. This
provides opportunities
for the children to
learn strategies from
one another.
 Add, subtract, multiply,
and divide
In this game, the children see that
there are several ways to get a
given number. This game gives the
children experience finding equations
instead of answers. (An equation is
two equal quantities separated by
an equals sign, e.g., 52 + 23 = 75.)
The children practice using addition,
subtraction, multiplication, and
division to equal a number.
 Work as a group to solve
a problem
This game requires a lot of team
work. Each group decides the
category and difficulty of the
answers to choose, and finds an
equation. Before playing the game,
discuss ways of working together
that allow everyone to contribute.
Get ready
the children.
2 Make a game board using
the “Equapardy” poster in
the Leader’s Kit and small
self-stick notes. You will
make answer cards for
each of the categories and
adhere them to the poster.
Write an addition sign on
the front of six notes.
Then write a number
on the sticky side of
each note (use 14, 37,
73, 114, 345, 1250) and
stick the numbers to the
poster in order in the
addition column. Write
a subtraction sign on the
front of six more notes.
Then write a number on
the sticky side of each of
these (use 12, 60, 85, 124,
459, 2990) and stick these
to the poster in order under
the subtraction sign. Repeat
this process for multiplica-
tion, using the numbers 20,
40, 50, 100, 400, 500; divi-
sion, using the numbers 1,
2, 4, 3, 5, 8; and mix, using
the numbers 12, 20, 25, 30,
36, 40.
14
Sticky side
+

3 Decide how you will divide
the children into groups of
100
200
300
400
500
600
points
mix
+
+
+
+
+
+ – .–.
.–.
.–.
.–.
.–.
.–.
x MIX
MIX
MIX
MIX
MIX
MIX
x
x
x
x
x
–
–
–
–
–

Game Directions
which group goes first,
second, and so on.
2 The first group decides on
a category and point value
(for example, addition for
300 points).
3 The leader turns over the
self-stick note in that space
and tells the whole group
the answer.
4 Each small group works
together to find an equation
that uses the chosen opera-
tion and equals the number
on the card. (For example,
if the number is 50, and the
category is multiplication,
the equation can be 5 × 10,
5 × 5 × 2, 25 × 2, or 50 × 1.)
5 Each small group shares its
equation. If the equation is
correct and hasn’t already
been said, the whole group
gets the points. (For example,
if three of four small groups
playing a 300-point card say a
different correct equation, the
large group scores 900 points.)
Record the points.
Note: There is one score
for the large group; each
small group does not have
a separate score.
6 Play continues with the next
small group choosing an
answer card until the total
score equals 5,000 points.
(Make sure that a different
small group gives its equation
first each round.)
GOAL: The large group earns 5,000 points together

2 If a player or small group suggests a change in the rules while they
are playing, allow them to discuss the change. Before changing the
1 Explain the game as you demonstrate it with a small group
of three or four children. Explain that there are five categories,
“addition,” “subtraction,” “multiplication,” “division,” and “mix.” “Mix”
means that the groups can use any operation or combination of
operations in their equation.
2 Explain that the more difficult answers have higher point values.
3 Discuss how to work together to play the game.
• How can your small group work together to decide which card
to choose?
• How can you work in your small group so that everyone contributes
to your equation?
• If the answer is 50 and the operation is multiplication, what equa-
tions will work? What is another idea?
talk
about
• How are you working together to find the equation?
• How are you making sure that everyone in your group contributes?
talk
about
during the Game
Before the Game

after the Game
Changing the Game
• Make a new category “fractions, decimals, and percents” with
the answers 1, 2, ½, 50%, 1.5.
their ideas.
• What made an equation difficult to find?
• What challenges did you face working in a group? What was success-
ful about your small group?
talk
about

F r a c t i o n , D e c i m a l , a n d P e r c e n t g a m e s 149
F
ractions, decimals, and percents are often difficult
for children to grasp. When helping the children
develop these concepts, use objects and pictures
before introducing numbers and symbols. Encourage
them to make connections between fraction, decimal,
and percent concepts.
By playing the fraction, decimal, and percent games,
children build the following important understandings:
 Fractions
Children need to understand that a whole (an
area or a set of objects) can be divided into equal
parts and that a fraction names a specific number
of those parts.
 Decimals
Decimals (sometimes called decimal fractions) are
another way to write fractions for tenths, hundredths,
thousandths, and so on. Before they work with
decimals, be sure the children understand that a
whole can be divided into 10 equal parts. Likewise,
before they work with hundredths, be sure that they
understand that a hundredth is one-tenth of a tenth
and 10 hundredths is one-tenth.
Children also need to understand the place-value
meaning of decimals. Begin with a whole of 1. Help
the children understand that we take one-tenth of
this whole to form the new unit, tenths. To show
this new unit, our place-value system uses a decimal
point after the ones place. The decimal point sepa-
rates values of a whole or greater from values that
are less than a whole. When reading a number
such as 1.2, the word and is said for the decimal
point — one and two-tenths, rather than one point
two. Using the terms tenths and hundredths helps the
children continue to link fractions and decimals.
 Percents
A percent is a number expressed as a fraction of
100. The word percent comes from the Latin words
per centum, which means “out of a hundred” or “for
every hundred.” It is critical that children understand
100 as the base for percents. Eleven percent, for
example, means eleven out of every hundred or
11
⁄100. Any fraction or decimal can be expressed as
a percent by multiplying it by 100. For example,
0.48 x 100 = 48% or 3
⁄4 x 100 = 75%.
introduction to
Fraction, Decimal,
and Percent games
¾ ¾
10 tenths = 1 whole
one tenth (0.1)
100 hundredths = 1 whole
one hundredth (0.01)
or

Language and Symbols
Help the children connect a model for rational numbers
(a picture or set of concrete objects) with the word
name and symbols that identify it. For example,
Ordering and Comparing
Fractions, decimals, and percents are numbers that
can be ordered and compared. The children explore
these concepts with real objects and pictures before
using symbols. When helping them learn to order and
compare, encourage the children to use benchmarks
such as 0, 1, ½, 0.5, 50%. For example, they might
compare fractions such as 5
⁄12 and 6
⁄10 by comparing
each to ½ and discovering that 5
⁄12 is a bit less than ½
and 6
⁄10 is a bit more. They might compare decimals
such as 0.18 and 0.8 to find which is closer to 1.
Equivalence
Two aspects of equivalence are important for children
in grades 3–6. First is understanding equivalent frac-
tions (fractions that name the same part of a whole)
and decimal equivalents (decimals that name the same
part of a whole). For example, the children need to
understand that 1
⁄2 has many equivalent fractions,
such as 2
⁄4, 4
⁄8, and 5
⁄10.
Second, the children should be able to identify
equivalent forms of fractions, decimals, and percents.
Introducing fractions, decimals, and percents simulta-
neously will help the children understand that ½ is
equal to 5
⁄10, which can be stated as 0.5 and is equal
to 50%, or that 0.40, 40
⁄100, and 40% are equivalent.
Fraction, Decimal, and Percent Games
Flip Your Lid, page 151
Wacky Cakes, page 157
Fill ’Em Up, page 163
Picture This!, page 169
Match Pass, page 175
Three Hexagons, page 181
Stick the Fraction on the Donkey, page 187
FRACTIONS
DECIMALS
PERCENTS

f l i p y o u r l i d 151
flip your lid©2004DevelopmentalStudiesCenter
The players stand around a circular target, such as a hula hoop,
with each player holding a plastic lid. They all toss the lids at the
same time, trying to get them into the hoop. Once the lids have
been tossed, the group discusses the fraction of the lids that landed
in the target and equivalent fractions for that fraction. The group
earns points by landing more lids in the hoop than out. To play this
game, you need a large space, like a gym or outdoor area.
PLAYERS: Grades 3–6, large group of 14 or fewer
GAME SUMMARY
IN LEADER’S KIT
OTHER MATERIALS
 Plastic lids, like the ones on
yogurt or cottage cheese con-
tainers, one for each child
 Circular target (such as a hula
hoop, six-foot piece of rope,
large container, or a circle
drawn with sidewalk chalk)
YOU’LL NEED

 Understand fractions of a group
of items
 Identify fractions and equivalent
fractions
This game gives children active
experiences creating fractions with a
group of objects. Fractions show part
of a whole or part of a group by
telling the number of equal parts in
the whole and the number of parts
you are describing. The lids inside
and outside the target are a visual
model of a fraction. (For example,
the children can connect five lids
out of a total of fifteen lids in the
target to the fraction 5
⁄15.) Equivalent
fractions are fractions that name the
same part of a whole (for example,
2
⁄4 and ½).
make mistakes
 Play safely
Children have various levels of famil-
iarity with fractions. To take risks
and share their thinking, children
must feel comfortable making mis-
takes. Before playing, have a discus-
sion about ways to be respectful of
players who make mistakes.
 Before playing, you
may want to brush up
on your own under-
standing of fractions by
reading “Introduction to
Fraction, Decimal, and
Percent Games” on
pages 149–150.
 Make sure all children
have a chance to par-
ticipate in discussions.
One way to do this is
to ask a question of the
group and then have
each child turn to the
person next to her to
discuss their answers.
Get ready
the children.
where the children have
room to toss the lids.
3 If you are using a piece
of rope, form it into a
circle on the ground where
the children are going to
play. If you are using side-
walk chalk, make a circle
that is about 22 inches
in diameter.

Game Directions
1 The players stand in a circle
around a circular target.
2 The leader gives each player
a lid.
3 The leader says, “Flip your lid!”
(or another signal the group
decides on) and the players
toss their lids, trying to get
them into the target.
4 Once all of the lids have
landed, the players stand back
and discuss the fraction of lids
that landed in the target and
any equivalent fractions for
that fraction. (For example, if
twelve lids are thrown, and six
land in the target and six land
outside the target, the fraction
is 6
⁄12. An equivalent fraction
for 6
⁄12 is ½.)
5 The players determine whether
or not they earned a point.
(A point is earned if half the
lids or more land in the target.
Two points are earned if all of
the lids land inside the target.)
One player records the score.
6 Each player picks up the
closest lid and takes another
turn. For each turn, have the
children take one step back
from the target before they
toss. Add some variety in
how they toss the lids. (For
example, you might ask them
to face backward and toss
the lid, toss the lid under their
leg, or stand sideways.)
7 Players continue tossing lids
until the group has five points.
GOAL: To get five points
6
12
or
1
2
target
3
10

2 If you notice that some children are having trouble understanding
how to figure out the fractions, ask a player who understands to
explain the fraction to the group.
Before the Game
1 Explain the game and practice as a group. It is important to give
the children time to practice tossing the lids into the target before
they play.
2 While practicing the game, discuss how to play safely and why it is
important to follow directions.
• How can we play this game safely?
• What would happen if we all ran into the middle of the target to try
to get our lids?
• What signal will we use to let everyone know when to toss the lids?
• What should we do if someone makes a mistake when figuring out the
fraction? Why is it important that we all feel safe to make mistakes?
talk
about
• How will we count the lids that land in the target?
• How many lids are there in all? How many are inside the target?
How can we say that as a fraction?
• What is another name for that fraction? (For example, 1
⁄2, 2
⁄4, 4
⁄8 are
some of the equivalent fractions for 8
⁄16.)
• Do we get a point? How do you know if we get one?
talk
about
during the Game

Help the children think about the math and how they played together
after the Game
Changing the Game
• Record the fraction from each round. When the game is
over, have the children arrange the fractions in order from
smallest to largest.
their ideas.
• What did we do to play this game safely?
• How did we help all players feel comfortable if they made mistakes?
• What math were we learning while playing this game?
talk
about

w a c k y c a k e s 157
wacky cakes©2004DevelopmentalStudiesCenter
IN KIDS’ KIT
 “Wacky Cakes Pans”
game board
 “Wacky Cakes Pieces:
Thirds, Sixths, and Twelfths”
 “Wacky Cakes Spinner:
Thirds, Sixths, and Twelfths”
Players spin a spinner to determine which size paper
cake pieces to take (such as 1
⁄3 or 2
⁄12 of a cake). They
place the cake pieces on a game board to make a total
of three whole “wacky cakes.” Each wacky cake is
made up of several fun flavors, like vanilla-spinach-
cream and strawberry-pickle.
three, or four
GAME SUMMARY
YOU’LL NEED

 Add fractions
 Find equivalent fractions
A visual model is helpful in under-
standing fraction concepts. Fractions
show part of a whole by telling the
number of equal parts in the whole
and the number of parts you are
describing. In this game, cards allow
the children to recognize different
fractions that represent the same
quantity (are equivalent fractions)
and ways that fractions can be
combined to make a whole.
When children make decisions
together they learn how to listen,
compromise, and reach agreement.
Children also will be more involved
in a game if they are able to make
decisions while playing.
 Before playing, you
may want to brush
up on your own
understanding of
fractions by reading
“Introduction to
Fraction, Decimal,
and Percent Games,”
pages 149–150.
 Ask the “talk about”
questions you chose
when you prepared
for the game. Ask
other questions you
think of while the
children are playing.
Get ready
1 Punch out the cake pieces
from one sheet of “Wacky
Cakes Pieces” to use to
show the children how to
play. (It is helpful to do this
ahead of time, so that the
children don’t have to wait
for you.)

the children.

Game Directions
1 The players:
• sort their cake pieces so that
all the thirds are together, all
the sixths are together, and
all the twelfths are together.
• decide fairly who goes first,
second, and so on.
2 The first player:
• spins the spinner to get
a fraction.
• takes the appropriate cake
piece(s) to match the fraction
spun and names them (for
example, “three-twelfths
vanilla-spinach-cream”).
• decides with the other
players where to
place the piece(s) on
one or more of the
game-board cake
pans. (For example,
if 3
⁄12 is spun, the
player can put 2
⁄12
on the first cake
pan and 1
⁄12 on a
different cake pan.)
3 The second player takes
a turn. A player who spins a
fractional cake piece that is
not available or does not fit
on any of the cake pans can
trade cake pieces for equiva-
lent fractions. (For example,
if 1
⁄3 is spun, the player can
take a 1
⁄3 piece, two 1
⁄6 pieces,
or four 1
⁄12 pieces.) Trading
available pieces or pieces
already on cakes is permitted.
4 Players take turns until all three
wacky cakes are complete.
GOAL: To make three whole wacky cakes
1
12
1
12
vanilla-spinach-cream
1
12
1
12
1
12
1
12
1
3
1
3 bubble-gum-
chocolate
1
12
1
12
1
12
1
12
1
12
1
12
1
12
1
12

Before the Game
1 Explain that the children will play a game in which three cakes are
divided into pieces.
2 Discuss the children’s experiences sharing food.
3 Put all the vanilla-spinach-cream cake pieces on one pan, all
the strawberry-pickle pieces on another, and all the bubble-gum-
chocolate pieces on the last pan. Using the game board, show how
the three cakes are cut into pieces. Explain that in this game, the
children will mix the flavors together to make three wacky cakes.
• Have you ever shared a cake, pizza, or cookie with someone? Did you
divide it fairly? How did you do that? How much did each person get?
talk
about
• How many pieces does the bubble-gum-chocolate cake have?
Are they equal? How do you know? Why is one piece of the bubble-
gum-chocolate cake labeled 1
⁄3? How much is two pieces of bubble-
gum-chocolate cake? How much is three pieces of bubble-gum-
chocolate cake?
talk
about
• What are some fair ways we could decide who will go first?
• If I spin 3
⁄12, what are some of the things we could do with the
cake pieces?
• If I spin 1
⁄3, but we don’t have any 1
⁄3 cake pieces left, what could
we do?
• What can my partners and I do if we don’t agree? Is that fair?
talk
about

during the Game
after the Game
• Is 2
⁄6 of the strawberry-pickle cake equal to 3
⁄12 of the vanilla-spinach-
cream cake? How do you know?
• Which fraction do you hope to spin next? Why?
• Which is smaller, 1
⁄12 or 1
⁄3? How do you know?
• Which is larger, 2
⁄6 or 11
⁄12? How do you know?
• How are you and your partners deciding which pieces to pick and
where to put them? Is this fair? Why do you think so?
talk
about
• What happened during your game? How difficult was it to make the
three wacky cakes? Why?
• How did you work together to make decisions? Was that fair? Why or
why not?
• Which fractions were best to spin? Why?
• How many twelfths are in 1
⁄3? How do you know? (Have the children
use the cake pieces to figure this out if necessary.)
talk
about

Changing the Game
• Have the children draw the wacky cakes they’ve completed
and write a number sentence to describe each wacky cake.
(For example, 1
⁄3 bubble-gum-chocolate + 1
⁄6 strawberry-pickle +
6
⁄12 vanilla-spinach-cream = one whole wacky cake.) You might
staple the children’s work together to make a book for the
group to read.
• Use the “Wacky Cakes Pieces: Halves, Fourths, and Eighths”
and the “Wacky Cakes Spinner: Halves, Fourths, and Eighths.”
• Have the children make three wacky cakes by placing the
cake pieces on the game board. Have the children take turns
spinning the spinner and exchanging equivalent cake pieces to
try to make each cake have a single flavor. (For example, trade
1
⁄6 strawberry-pickle from one cake with 2
⁄12 vanilla-spinach-cream
from another cake.)
their ideas.

f i l l ‘ e m u p 163
fill ‘em up©2004DevelopmentalStudiesCenter
Players take turns choosing decimal cards and coloring
in the matching decimal values on a game board,
trying to make a total of exactly two wholes.
three, or four
GAME SUMMARY
IN KIDS’ KIT
 “Fill ‘Em Up” game board
 “Decimal Cards”
YOU’LL NEED

 Understand the meaning of
tenths, hundredths, and one whole
 Add decimals
A visual model helps children
understand the meaning and value
of decimal numbers. In this game,
the children color in tenths and
hundredths on a ten-by-ten grid of
squares to make two wholes. Each
square on the grid is worth 0.01or
1
⁄100 (said one one-hundredth).
a decision
When children make decisions
together they learn how to listen,
compromise, and reach agreement.
Children who have the opportunity
to make decisions during a game
will also be more involved in it.
 If needed, brush up on
your own understand-
ing of decimals by
to Fraction, Decimal,
and Percent Games”
on pages 149–150.
 Make sure all children
are getting a turn and
that all voices are heard.
Get ready
1 Punch out the decimal
cards from a sheet of
“Decimal Cards” for
demonstrating the game.
the children.
3 Decide which of the chil-
dren are ready to play the
game. (Players need to
understand the meaning of
decimals to be successful.)
one-tenth (0.1)
10 tenths = 1 whole
one-hundredth (0.01)
100 hundredths = 1 whole

f i l l ‘ e m u p 165
Game Directions
1 If they have not already
prepared the decimal cards,
the players punch out the
“Decimal Cards.”
3 The first player:
• mixes up the cards and
places the deck face down.
• turns over the first three
cards and places them face
up in a row.
4 Together the players:
• decide which card to choose,
and name the decimal (for
example, 0.75 is said seventy-
five hundredths and 0.2 is said
two-tenths).
• decide where to color in the
corresponding amount on
one of the grids. The players
cannot use an amount that
would more than fill the
grid. In addition, the players
cannot split a decimal
amount in order to color in
parts of two grids. (For
example, if the players
choose 0.9, they cannot
place 0.5 on one grid and
0.4 on the other.)
5 The first player:
• writes the decimal below the
grid (each grid is equal to
one whole).
• puts the used card at the
bottom of the pile.
• turns over the top card in
the pile to replace the
used card.
GOAL: To make two wholes on a game board
0.3
(continues)

Game Directions
6 The players decide on a new
card, and the second player
takes a turn writing the
decimal below the grid. The
players use a new color for
each turn.
both grids are completely
filled or until all the cards
showing have values greater
than the amounts left uncol-
ored on the grids.
8 The players then add up the
amounts colored in on the
grids, using the decimals they
have recorded below the grids.
The goal is to get as close as
possible to two by filling in
both the grids.
9 The players play again, trying
to beat their score or to match
it if they scored exactly two.
(continued)
0.3 0.2 0.45 0.05+ + + += 1 = 0.90.5 0.4
Total = 1.9

f i l l ‘ e m u p 167
Before the Game
1 Discuss numbers that come between zero and one. If necessary,
explain that whole numbers and zero are the counting numbers
and decimals and decimal fractions are numbers that come
between whole numbers.
2 Explain the game as you play it with a child as your partner. Show
the decimal grids as you talk about tenths and hundredths.
• What types of numbers come between zero and one? What are some
of the numbers that come between zero and one?
• What are some examples of decimal numbers? Are these numbers
between zero and one? How do you know?
• What are tenths? How many tenths in one whole?
• What are hundredths? How many hundredths in one whole?
talk
about
• (Point to one of the grids on the game board.) How many columns
are in this grid? How many squares are in this grid? (Explain that each
grid represents one whole.)
• How many tenths are in one whole grid? What does a tenth look like
on the grid?
• How many hundredths are in one whole grid? What does a hun-
dredth look like on the grid?
• Show a decimal card. How do you read this number?
• What are some fair ways we could decide who will go first?
• How can you decide with your partner which card is the best one to
pick? What will you do if you cannot agree?
talk
about

after the Game
Changing the Game
• Use only the decimal cards with values in the tenths.
(Remove the decimal cards with values in the hundredths.)
their ideas.
• How did you decide which card to choose? Was that fair? Why or
why not?
• How much did you score in your first game? How did you figure out
your score?
• Did you score more or less in your first game? How do you know?
• Why do we need decimal numbers? When do we use them in every-
day life? (money, batting averages, swim race times, weights of foods)
talk
about
1 Help the children as they play. Make sure they say the decimal
names correctly (for example, 0.85 is said “eighty-five hundredths”
and 0.2 is said “two-tenths”).
• Where can you color in the decimal amount for that card?
• (Point to one of the grids.) How much is this whole grid worth?
• Which of the three decimal cards showing is worth the most? The
least? How do you know?
talk
about
during the Game

p i c t u r e t h i s ! 169
picture this!
IN KIDS’ KIT
 “Picture This!” game board
 “Picture This!” spinner
 “Picture This!” cards
The players turn over a card to find a percentage and
spin to find a symbol. On a game board grid with 100
squares, the players draw the symbol in the number of
squares that match the percentage. They try to fill in as
many squares as possible without having any of the
same symbol next to each other.
three, or four
GAME SUMMARY
YOU’LL NEED

 Understand the meaning
of percents
A percent is the amount out of
each hundred (for example, eleven
percent means eleven out of every
hundred or 11
⁄100). In this game, the
children draw pictures to fill in a grid
of 100 squares. Each square on the
grid is worth one percent. A visual
model (the grid of squares) helps the
children understand the meaning
and value of percents.
for a turn
In this game, the children stay
involved by making sure that the
child who is drawing does not draw
the same design in two squares that
are next to each other.
 If needed, brush up
on your own under-
standing of percents
by reading “Introduction
on pages 149–150.
 Discuss ways to make
the environment com-
fortable for learning
and risk-taking (for
example, no teasing
when others make
mistakes, treating
others respectfully,
waiting for a turn,
and so on).
Get ready
the children.
2 Punch out a set of “Picture
This!” cards to use for
demonstrating.
10%10% 14%14%
13%13%

Game Directions
1 Decide fairly who goes first,
second, and so on.
2 The first player:
• shuffles the “Picture This!”
cards and places them face
down on the table in a pile.
• takes the top card to find
the percentage of the game
board to fill in.
• spins the picture spinner to
find the symbol to draw.
• on the game board, draws
the symbol in the number
of squares that represent
the percentage on the
card. The player must
not draw symbols
in squares that are
touching each other.
(For example, if the
player gets “8%” and
“stars” are spun, then
the player draws a
star in eight squares that are
not touching each other
on the game board.)
they can no longer fill in
squares without having the
same symbol in touching
squares.
In this example, no
more stars can be
drawn because the
only squares left
already have a star
next to them.
4 The players calculate the
percentage of the squares
that contain symbols and
write the total percent at the
bottom of the game board.
GOAL: Fill in as many squares as possible without drawing
two of the same symbol next to each other
8%8%
pictu
r
e
this!

Before the Game
1 Start by discussing percents.
2 Show the game board and have the children find the total
number of squares on the game board. Explain that the
100 squares represent 100% or one whole.
• What are percentages? When do you use percentages? What does
it mean when a price tag says “50% off”?
• Explain that a percentage is the amount out of each 100. (For exam-
ple, 11% means eleven out of every hundred or 11
⁄100. For example,
11% of $1.00 is 11cents.)
talk
about
• Do you think it is possible to fill 100% of the game board? Why do
you think that?
• What percentage of the game board is filled? How do you know?
• How can partners stay involved while waiting for a turn?
(For example, they can make sure that the symbols are being drawn
in the correct squares.)
talk
about
• What percentage of the game board is filled in? How do you know?
• What is the best strategy to use when deciding where to put the
symbols? Why?
talk
about
during the Game

after the Game
Changing the Game
• Have the children use the blank spinner and make up their
own symbols for the game.
their ideas.
• What percentage of the game board did your group fill in? How
many groups filled in a higher percentage? A lower percentage?
• What percentage of the game board is filled with stars? Swirls?
• What is the best strategy to use when deciding where to put the
symbols? Why?
• How did you stay involved while waiting for your turn?
talk
about

m at c h p a s s 175
match pass©2004DevelopmentalStudiesCenter
IN KIDS’ KIT
 “Match Pass” cards
This game uses cards showing equivalent fractions and
percents. Players take turns discarding and picking up
cards until each has four cards with the same value (for
example, 1
⁄2, one-half, 50%, and ). Because the deck
includes a wild card, one card will be left over. The
value of this card is the score for the game. The chil-
dren play several rounds until their total score is
at least two.
PLAYERS: Grades 5–6, small groups of four
(This game works only for groups of four.)
GAME SUMMARY
YOU’LL NEED

 Recognize equivalent fractions
and percents
 Add fractions and percents
This game gives the children
practice with equivalent fractions
(fractions that name the same part
of a whole quantity, like ½ = 2
⁄4). It
also helps them match equivalent
fractions and percents. In playing
this game, the children see that 1
⁄4,
25%, one-fourth, and are
equivalent (different names for the
same number).
 Stay involved when you’ve
finished and others haven’t
In this game, some children will
finish before others. Children who
finish early can remain involved by
helping other players decide which
cards to discard.
 You may want to brush
standing of fractions
and percents by reading
“Introduction to Fraction,
Decimal, and Percent
Games” on pages 149–150.
 After asking a question,
wait five seconds to give
the children a chance to
think before calling on
anyone to respond.
Get ready
1 Punch out a set of “Match
Pass” cards to demonstrate
the game.
the children.
3 Decide how you will divide
the children into groups of
four to play the game. This
game must be played in
groups of four.

Game Directions
1 If they have not already
prepared the cards, the
players punch out the
“Match Pass” cards.
who deals, who keeps score,
and who goes first, second,
and so on. This will change
for each round.
3 The dealer mixes the cards,
deals four cards face down to
each player, and places the
final card face down in the
middle. The players look at
their cards, holding them so
that they are hidden from the
other players.
4 The first player picks up the
card on the table.
He chooses a card to discard
and places it face down on
the table in front of the
person to his left.
5 The second player picks up
that card and discards a card
to the player to her left.
6 When a player has four cards
with the same value (for
example, 11
⁄2, 150%, one and
one-half, ) the player
places his cards face up on
the table and discards his
final card to the person on
his left. Players who have laid
their cards on the table can
help others. The wild card
can be used as any value.
GOAL: To get two points
(continues)
onew
hole
onew
hole
1
2
1
2
1
4
1
4
25%25%
onew
hole
onew
hole
1
2
1
2
1
4
1
425%25%

Game Directions
7 Play continues until each
player has laid four equivalent
cards face up on the table. The
value of the remaining card is
the point score for that round.
8 The scorekeeper records
the score.
9 For the next round, the
players decide who will deal,
and so on, and play again.
At the end of the round, the
round’s score is added to the
previous round’s score. Play
continues until the total score
is at least two.
(continued)

Before the Game
1 Discuss percents and fractions using a set of cards. Lay a set of
cards face up on the table.
2 Organize the cards into four rows of four cards with the
same value.
3 Explain the game as four children demonstrate how to play it.
• What kinds of numbers are on these cards?
• Are any of the numbers on these cards equivalent? Which ones? How
do you know?
talk
about
• (Point to 1
⁄2.) What kind of number is this? (fraction) What does that
mean? What are some other ways of showing 1
⁄2?
• (Point to 150%.) What kind of number is this? (percentage) What does
that mean? What are some other ways of showing 150%?
• (Point to .) What fraction does this picture show? (1
⁄4) What does
that mean? What are some other ways of showing 1
⁄4?
• (Point to 1.) What kind of number is this? (whole number) How is that
number different from the other numbers? What are some other
ways of showing 1?
talk
about
• What will you do if you don’t know the value of one of your cards?
How can you ask for help?
• What can you do to stay involved while waiting for your turn?
talk
about

during the Game
• How are you staying involved once you have laid your cards on
the table?
• How many points do you have so far? How do you know? How many
points do you need to get to two? How do you know?
talk
about
after the Game
Changing the Game
1 To make the game less challenging, use the cards to play
“Concentration.” Remove the wild card. Have the students
shuffle the cards, lay them out in four rows of four, and take
turns finding equivalent pairs.
their ideas.
• What mathematics did you learn while playing this game? How is it
used in the real world?
• What did people do to stay involved in the game even after they had
put their cards down on the table?
talk
about

t h r e e h e x a g o n s 181
three hexagons
IN KIDS’ KIT
 “Three Hexagons” cards
IN LEADER’S KIT
 “Three Hexagons” game board
This game is similar to dominoes. Players take turns
matching sides of triangle cards that show equivalent
numbers. They try to make three touching hexagons
(a closed shape with six sides and six angles ).
three, or four
GAME SUMMARY
YOU’LL NEED

 Recognize equivalent fractions
and percents
Equivalents are different ways
of naming the same quantity.
(For example, 1
⁄2 can also be
said as 50% or .)
for a turn
This game will be challenging for
some and easier for others. The
children who find it easy will want
to tell the others the answers. When
demonstrating the game, discuss
ways the children can help each
other without giving the answer.
(For example, the children can ask
questions like “What is another way
of showing 1
⁄4?” or “What is the
equivalent percentage for 1
⁄4?”) Before playing, you may
want to brush up on
your own understanding
of fractions and percents
on pages 149–150.
 Rather than tell the
children the answers,
help them figure out
solutions for themselves.
Get ready
1 Punch out a set of “Three
Hexagons” cards to demon-
strate the game.
the children.
© 2004 Developmental Studies Center

Game Directions
1 If they have not already pre-
pared them, the players punch
out the “Three Hexagons” cards.
2 The players prepare to play by:
• placing all the cards face down
in the middle of the group.
• selecting their playing cards
and laying them face up on
the table. (In groups of two or
three children, each child takes
seven cards. In groups of four,
each child takes five cards.)
The extra cards are placed face
down to be the pool.
4 The first player places one of
her cards face up on the game
board so that all the players
can see it. The triangle is placed
so that it aligns with one side of
a hexagon.
5 The players take turns matching
one side of their card with one
side of a card that is already on
the game board. The sides must
be equivalent, but not exactly the
same (for example, you can
place a 50% or a next to 1
⁄2,
but you cannot place two 1
⁄2’s
next to each other).

If a player is unable to play, the
next player has a chance to lay
down a game card. If no player
is able to play a game card, the
original player selects a card
from the pool and looks for a
place to lay it down. If necessary,
the players take turns selecting
cards from the pool until one of
them is able to play.
6 Play continues until three touch-
ing hexagons are complete or
until no more plays are possible.
7 The players play the game again.
GOAL: To make three touching hexagons
1
150%
1
4
1
1
2
50%

Before the Game
1 Place the game cards face up in front of you. Explain that the
players will use these cards like dominoes, putting down cards
that show equivalent numbers.
• What kinds of numbers do you see on these cards?
• Do any of these show equivalent numbers (different ways of naming
the same quantity)? Which ones?
• (Show the children a 1
⁄2 card.) What other card is equivalent to 1
⁄2?
(If necessary, explain again that the sides next to each other must
be equivalent.)
talk
about
• What does a hexagon look like? How could we use these triangles to
make a hexagon?
• Which one of your cards could you lay down to touch this card? Why?
• How can you help another player without giving the answer? Why is
it important to not give the answer when you are giving help?
• How can you stay involved while you are waiting for your turn?
(Point out that the children can check their own cards for places to
play while their partners are playing.)
talk
about
• (Point to a fraction or a picture on a card.) What is the equivalent percent?
• What is the equivalent fraction for 25%? 50%? 150%?
• Will placing that card there make a hexagon? How do you know?
• What are you doing while you are waiting for your turn?
talk
about
during the Game

after the Game
Changing the Game
• Keep a running total of the fractions and decimals played.
• Have the children use six triangles to make a parallelogram or
five triangles to make a trapezoid. The children try to make three
parallelograms or three trapezoids.
their ideas.
• Did you help someone without giving the answer? How?
• What was the hardest part of the game? Why? Did it get easier?
• What math were we learning in this game?
• What other shapes could you make using the triangles?
talk
about
parallelogram trapezoid

STICK THE F RACTION ON THE D ONKEY 187
s
tick the fractio
n
on the donkey
This game is based on the game “Pin the Tail on
the Donkey.” The players take turns putting on
a blindfold, spinning around three times, choosing
a fraction or percent, sticking it on the donkey,
and figuring out their points.
PLAYERS: Grades 5–6, small groups of five
or fewer
GAME SUMMARY
88
88
88
88
1212
1212
1212
44
44
44
44
IN LEADER’S KIT
 “Stick the Fraction on the
Donkey” poster
IN KIDS’ KIT
OTHER MATERIALS
 Tape to attach the donkey
poster to the wall
 20 small self-stick notes
on a large piece of paper
(see “Get Ready”)
 Blindfold (optional)
YOU’LL NEED

 Find fractions and percents mentally
Fractions are a way to show part
of a whole or group by telling the
number of equal parts in the whole
and the number of those parts you
are describing. Percents are the
amount out of each one hundred.
(For example, eleven percent means
eleven out of every 100.) We often
need to find a fraction or percentage
in our head (for example, to figure
out a sale price, a tip, or how to split
an item between several people).
In this game, the children practice
calculating fractions and percents
in a fun way.
 Ask for help when it is needed
 Play safely
Some children will know right away
what one-twelfth of twelve is, others
will need time to figure it out. When
practicing this game, discuss how a
child can ask for help and how the
other children can respond in a
respectful way.
Get ready
the children.
2 Think about how many
children will be playing and
how many groups there
will be. Choose a place
to play where the groups
will have room to move
around freely.
3 For each set of 20 self-stick
notes, write 1
⁄2 on four,
50% on four, 1
⁄4 on four,
25% on four, and 100% on
four, and place them
on a piece of paper. (See
illustration below.)
more than five children,
them into groups of five or
fewer to play the game.
1
⁄2
1
⁄2
1
⁄2
1
⁄2
100% 100% 100% 100%
50% 50% 50% 50%
25% 25% 25% 25%
1
⁄4
1
⁄4
1
⁄4
1
⁄4
 Before playing, you may
want to brush up on
your own understanding
of fractions and percents
on pages 149–150.
 Children may have par-
ticular difficulty figuring
out ¼ or 25% of a
number. One strategy
is to find ½ or 50% of
a number and then take
½ or 50% of that to find
the solution. (For exam-
ple, to find ¼ or 25% of
8, take ½ or 50% of 8
which is 4. Then take ½
or 50% of 4 which is 2.
Two is ¼ or 25% of 8.)

goes first, second, and so on,
and who is the scorekeeper.
2 The first player puts on the
blindfold or closes her eyes.
The next player spins her
around three times and holds
up the paper with the small
self-stick notes for the first
player to choose one. The first
player takes one self-stick note
off the paper.
3 The player who is helping
directs the blindfolded player
towards the donkey.
4 The blindfolded player
walks to the donkey,
sticks the fraction or
percent self-stick note on
the donkey, takes off
the blindfold or opens
her eyes, and figures out
the score. (For example,
if the self-stick note
shows “1
⁄2” and is stuck
to a 12 on the poster, six
points are added to the
group’s score because 1
⁄2
of 12 equals six.)
5 The scorekeeper adds the
points to the group’s score.
6 Play continues until the group
reaches 50 points. If neces-
sary, remove the self-stick
notes from the donkey and
use them again.
GOAL: To get 50 points
Game Directions
stick the fraction
on
the donkey
stick the fraction
on
the donkey
88
88
88
88
88
1212
1212
1212 1212
1212
44
44
44
44
44
44
44
44
1
2
6
+6
12
previous score
new points
new score

2 If some children are having trouble figuring out how many
points they received, have children who understand explain
their thinking.
3 If a player suggests a change in the rules while they are playing,
allow them to discuss the change. Before changing the rule, make
sure the change is fair to all players, everyone in the group agrees,
and the math is still appropriate.
Before the Game
Explain how to play the game and practice as a group.
• What can you do if you don’t know how to figure out the number
of points?
• What is 50% of 12? 1
⁄2 of 4? 25% of 12? How do you know? Did
anyone figure it out a different way?
• How can you make sure the blindfolded player or player with her
eyes closed remains safe?
• What should we do if someone makes a mistake? Why?
talk
about
• How did you figure out 1
⁄4 of 12? Did anyone figure it out a different
way? How?
• How are you asking for help when you need it?
talk
about
during the Game

after the Game
Changing the Game
• Have the children draw their own animal for the game.
their ideas.
• What were some of the easier point scores to figure out? Why? Which
fractions or percentages were more difficult to figure out? Why?
• Which fraction is the same as 25%? How do you know?
• How did you make sure the player with his eyes closed or blindfolded
was safe?
talk
about

A P P E N D I C E S 195
T
he National Council of Teachers of Mathematics
(NCTM) has created a set of standards to guide
the teaching of mathematics and help teachers and
after-school staff understand the skills and concepts
children should learn. The standard for Number and
Operations is:
To meet this standard, the NCTM specifies expectations
for children’s learning in grades K–12. The chart on
the following pages lists the NCTM expectations for
grades 3–5 and grades 6–8 and identifies the
AfterSchool KidzMath games that will help children
meet these expectations. Please note that this is not
a comprehensive list of all the NCTM standards and
expectations for these grade levels.
The AfterSchool KidzMath Games program also helps
children work toward NCTM’s Problem Solving,
Reasoning and Proof, Communication, Connections,
and Representation Standards. 
“ Instructional programs from
pre-kindergarten through grade 12
should enable all students to—
• understand numbers, ways
of representing numbers,
relationships among numbers,
and number systems;
• understand meanings of
operations and how they relate
to one another;
• compute fluently and make
reasonable estimates.”
(Principles and Standards for School
Mathematics, National Council of
Teachers of Mathematics, 2000, p. 32)
nctm standards

Grades3–5
CorrelationtoNCTM
NumberandOperationsStandard
Expectations:
Understandtheplace-valuestructureofthe
base-tennumbersystemandbeabletorepre-
sentandcomparewholenumbersanddecimals
Recognizeequivalentrepresentationsforthe
samenumberandgeneratethembydecompos-
ingandcomposingnumbers
Developunderstandingoffractionsasparts
ofunitwholes,aspartsofacollection,as
locationsonnumberlines,andasdivisionsof
wholenumbers
Usemodels,benchmarks,andequivalentforms
tojudgethesizeoffractions
Recognizeandgenerateequivalentformsof
commonlyusedfractions,decimalsandpercents
Explorenumberslessthan0byextendingthe
numberlinethroughfamiliarapplications
Describeclassesofnumbersaccordingtocharac-
teristicssuchasthenatureoftheirfactors
Expectations:
Understandvariousmeaningsofmultiplication
anddivision
Understandtheeffectsofmultiplyingand
dividingwholenumbers
Identifyanduserelationshipsbetween
operations,suchasdivisionastheinverseof
multiplicationtosolveproblems
Understandandusepropertiesofoperations,
suchasthedistributivityofmultiplicationover
addition
Understandnumbers,waysofrepresentingnumbers,relationshipsamongnumbers,andnumbersystems
Understandmeaningsofoperationsandhowtheyrelatetooneanother
AntHill
Picnic
BeachBall
Multiplier
Bounce
Back
Disappearing
PyramidEquapardy
Fill’Em
UpFlick
Flip
YourLid
Forehead
Factors
Lonely
Aces
✔
✔
✔
✔
✔
✔
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✔
✔
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✔

Grades3–5
CorrelationtoNCTM
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✔
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Match
Pass
Multiple
Moves
Multiplication
Baseball
Multiplication
Basketball
Multiplication
Bowling
Multiplication
Uncovered
Number
Detective
Picture
This!Rectango
Save
$10.00
Expectations:
wholenumbers
Expectations:
anddivision
addition

Grades3–5
CorrelationtoNCTM
Expectations:
wholenumbers
Expectations:
anddivision
addition
Spin
Spot
Spinning
forDollars
StadiumTour,
USA
Stickthe
Fractionon
theDonkeyTarget
TheLeader
SaysDivide
Three
Hexagons
Three
TacToe
Wacky
Cakes
What’sMy
Rule?
✔
✔
✔
✔
✔
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✔
✔
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✔
✔
✔
✔
✔

Grades3–5
CorrelationtoNCTM
Expectations:
Developfluencywithbasicnumbercombinations
formultiplicationanddivisionandusethese
combinationstomentallycomputerelatedprob-
lems,suchas30×50
Developfluencyinadding,subtracting,multiply-
ing,anddividingwholenumbers
Developuseofstrategiestoestimatetheresults
ofwhole-numbercomputationsandtojudgethe
reasonablenessofsuchresults
Developandusestrategiestoestimatecomputa-
tionsinvolvingfractionsanddecimalsinsitua-
tionsrelevanttostudents’experience
Usevisualmodels,benchmarks,andequivalent
formstoaddandsubtractcommonlyusedfrac-
tionsanddecimals
Selectappropriatemethodsandtoolsforcom-
putingwithwholenumbersfromamongmental
computation,estimation,calculators,andpaper
andpencilaccordingtothecontextandnature
ofthecomputationandusetheselectedmethod
ortool
Computefluentlyandmakereasonableestimates
AntHill
Picnic
BeachBall
Multiplier
Bounce
Back
Disappearing
PyramidEquapardy
Fill’Em
UpFlick
Flip
YourLid
Forehead
Factors
Lonely
Aces
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔✔
✔
✔
✔
✔
✔
✔
✔

Grades3–5
CorrelationtoNCTM
Expectations:
lems,suchas30×50
tionsanddecimals
ortool
Match
Pass
Multiple
Moves
Multiplication
Baseball
Multiplication
Basketball
Multiplication
Bowling
Multiplication
Uncovered
Number
Detective
Picture
This!Rectango
Save
$10.00
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔

Grades3–5
CorrelationtoNCTM
Expectations:
lems,suchas30×50
tionsanddecimals
ortool
Spin
Spot
Spinning
forDollars
StadiumTour,
USA
Stickthe
Fractionon
theDonkeyTarget
TheLeader
SaysDivide
Three
Hexagons
Three
TacToe
Wacky
Cakes
What’sMy
Rule?
✔
✔
✔
✔
✔
✔
✔
✔✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔

Grades6–8
CorrelationtoNCTM
Fill
‘EmUp
Flip
YourLid
Forehead
Factors
Match
Pass
Multiple
Moves
Picture
This!
Spin
Spot
Stickthe
Fractionon
theDonkey
Three
Hexagons
ThreeTac
Toe
Wacky
Cakes
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
✔
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✔
Expectations:
Workflexiblywithfractions,decimals,and
percentstosolveproblems
Developmeaningforpercentsgreaterthan100
andlessthan1
Usefactors,multiples,primefactorization,and
relativelyprimenumberstosolveproblems*†
Expectations:
Understandthemeaningandeffectsof
arithmeticoperationswithfractions,decimals,
andintegers
*AfterSchoolKidzMathcoversonlyfactorsandmultiples.
†
Alltheothermultiplicationanddivisiongamesalsohelpchildren
withfactorsandmultiples,butlessdirectly.

siteplanningtool:AfterSchoolKidzMath™
SiteCharacteristics
Herearesomecharacteristicsofafter-schoolsiteswhereAfterSchoolKidzMathhasbeenmostsuccessful.Althoughrecommended,theydon’tall
havetobeinplacetogetstarted.Usethischarttolaunchanddevelopyourprogramandtoidentifyitsneeds.Markandfillintheappropriate
columnforeachsitecharacteristic.Youmaywanttocopythechartandworkonitatastaffmeeting.
SITE We’vegot Wecanmakethathappensoon. Weneedtoworkonthis.
CHARACTERISTIC thatnow. Here’show: Nextstepsare:
Space
Spaceisbigenoughforactivities,
yetsmallenoughtobecozy—
Spacecanbemadecomfortable
forplayinggames—
Chairsandtablesareavailable
forplayinggames—
Spaceisquietenoughforthe
childrentoconcentrateon
playinggames—
©2004 Developmental Studies Center

Scheduling
Sessionsoccurregularly,twoor
threetimeseachweek,witha
consistentgroupofchildren—
Sessionsfollowsnackor
recreationaltime—
Sessionsareatatimethat
doesnotconflictwithsportsor
recreationactivities—

Staffing
Staffdevelopspositive
relationshipswithchildren
overtime—
Staffistrainedinthe
AfterSchoolKidzMath™
program
andgroupmanagement—
Stafftakestimetoplan
gamesbeforedoingthemwith
thechildren—

Attitudes
Staffandleadershipareexcited
aboutworkingwithchildren—
Staffandleadership
areenthusiasticaboutthe
program—
Staffandleadershipare
committedtobuildingmath
andsocialskills—
Valuesatthesiteare
consistentwiththoseofthe
program
andincluderesponsibility,respect,
andcooperation—

Programming
Approachtoprogramming
iscreativeandimaginative—
Childrenhavechoicesabout
howtheyspendtheirtime—
Activitiesareappropriate
forthechildrenparticipating—

Effective leadership makes a difference in the success of after-school programs, including
AfterSchool KidzMath.™
This checklist can help you think about and improve the way you
use the program to
 support children’s math learning,
 support children’s social learning, and
 make the activities fair and fun for all.
The Leader’s Checklist has three main sections: Before the Game, During the Game, and
After the Game. Each section has a set of questions for you to consider and examples of
what works best.
Ways to Use the Leader’s Checklist
You can use the Leader’s Checklist in a variety of ways. Here are some ideas:
 You can review this checklist when planning games sessions.
 You can do a self-review and reflection after a game session.
 A group of leaders can review and discuss this checklist every once in a while as a
“refresher course” on AfterSchool KidzMath.
 You can ask a co-worker or administrator to observe
a game and use this checklist to give feedback about
the game session. Make time soon after the game
session to meet with the observer and talk about what
she noticed, focusing on what worked well and
ideas for improvement.
leader’s checklist

leader’s checklist
 Set aside time to prepare:
• Allow yourself at least 20 minutes to prepare the
game before you meet with the children.
• Discuss any questions you have with another
staff person or your supervisor, or bring them up
at a staff meeting.
 Did you set aside time to prepare?
Comments/Ideas:
 Read the game:
• Imagine playing the game while reading
the instructions.
• Consider what resources (time, materials, space)
would be needed to play this game.
• Be sure that you understand all of the math
words used in the game. The math skills
section in the game and the math glossary in
the appendix can help you.
 Did you read the game carefully?
Comments/Ideas:
 Practice the game:
• Practice playing the game yourself or with
someone else.
• Make sure you can easily explain the directions,
and practice explaining them out loud.
• Think about the questions your children might
have about the game and how you will answer
the questions.
 Did you play the game ahead of time?
Comments/Ideas:
planning reflection
Name of the Game __________________________________________________ Date��
Name of the Leader___________________________ Name of Observer��
This checklist can help you think about how to improve your practice of AfterSchool KidzMath.™
The checklist has
three main sections: “Before the Game,” “During the Game,” and “After the Game.” In each of these sections, there is
a checklist of items to help you plan (the column labeled “Planning”) and some questions to help you think about
how the game worked and how to make improvements (the column labeled “Reflection”).
before the game
Yes
Yes, but
needed to spend
more time No
Yes
Yes, but could
be improved No
Yes
Yes, but could
be improved No

 Prepare the space and materials:
• Make the setting appropriate for activity (tables
are arranged, area is set up).
• Have needed materials ready and available
(cards are punched out, number tags have num-
bers written on them).
 Did you prepare the space and materials?
Comments/Ideas:
planning reflection
Yes
Yes, but could
be improved No
 Make decisions:
• Decide how to make the game meet children’s
needs by referring to the “Changing the Game”
section on the last page of the game if needed.
• Decide how to group the children.
— Be prepared to explain that children are
expected to work with everyone even if they
are not partnered with the person they were
hoping for.
— You can randomly assign pairs or groups.
(For example, cut magazine pictures into the
number of pieces equal to the number of
children you want in each group. Have each
child choose a piece of the picture and then
find the other children with pieces of the
same picture.)
• Decide the mathematical and social questions
you might ask.
— Read the game and mark the “talk about”
questions you might ask. (You do not need to
ask all the suggested questions.)
— On a piece of paper, write the questions you
have chosen and any of your own so you
have them ready when you teach the game.
 Did you make the decisions needed before playing
the game?
Comments/Ideas:
Yes
Yes, but could
be improved No

 Explain the game:
• Gather the children in a circle to demonstrate or
practice the game.
• Discuss ways to make the environment comfort-
able for learning and risk-taking (for example, no
teasing when others make mistakes, treating oth-
ers respectfully, waiting for a turn, and so on).
• Role-play and talk about how to ask for help and
give help.
• For small group games: Choose a child to be
your partner(s) as you explain the game or
choose a group of two to four children to dem-
onstrate as you explain.
• For large group games: Explain the game and
have the whole group practice playing.
• Use “talk about” questions to discuss the game.
 Did you explain the game and demonstrate or
practice it?
Comments/Ideas:
planning reflection
Yes
Yes, but could
be improved No
 Check for understanding:
• Ask children to summarize the game directions
before they start to play.
• Before getting started, ask the children what
questions they have about the game.
 Did you check for understanding?
Comments/Ideas:
Yes
Yes, but could
be improved No
 Have children make decisions:
• Have the children decide who will go first (for
example, choose someone who has not gone
first lately, order themselves by birthday, and
so on).
• Have the children decide a new game rule if
it comes up. Be sure the children talk about
the change, whether it is fair to everyone and
whether all the group members agree to it.
 Did you allow the children to make decisions?
planning reflection
during the game
Yes
Yes, but needed
to provide more
opportunities No
Comments/Ideas:

 Support children as they play:
• Walk around while children play to make sure
that all of the groups are working well together
and learning math.
• Make sure all children are getting a turn and that
all voices are heard.
• Show enthusiasm for the game.
• Help keep the game cooperative.
• Encourage children to use mathematics strategies
that work for them.
• Give help to children without giving them
the answers.
• Encourage and assist children to figure out
solutions for themselves.
 Did you support the children as they played?
Comments/Ideas:
planning reflection
Yes
Yes, but needed
to provide more
support No
 Encourage children to help each other:
• Set an expectation that everyone helps each
other in a respectful way.
• Intervene when children make fun of one
another or are not helping one another.
 Did you encourage the children to help
each other?
Comments/Ideas:
Yes
Yes, but could be
improved No
 Ask mathematical and social questions to promote
learning and conversation:
• Ask the “talk about” questions you chose when
you prepared for the game. Ask other questions
you think of while the children are playing.
• Ask open-ended questions with more than one
correct answer (for example, “How did you figure
out your answer? What’s another way?”).
• Ask mathematics questions (for example, “Why
did you decide to subtract that number?”).
• Ask questions about social skills (for example,
“How can we play this game safely?”).
 Did you ask mathematical and social questions?
Comments/Ideas:
Yes
Yes, but could be
improved No

 Ask children questions about the game:
• Talk about how the game went or what could
be improved for next time.
• Discuss ways to play the game differently
next time.
 Did you ask questions about the game?
Comments/Ideas:
planning reflection
after the game
Yes
Yes, but could be
improved No
 Think about how you asked questions:
• After asking a question, wait five seconds to
give children a chance to think before calling
on someone.
• Collect many ideas from the group (for example,
“Who figured it out a different way?”).
• Ask follow-up questions (for example, “Daniel
says his group needed 10 more points to
reach 0. How many more turns do you think
it took to reach 0?”).
 Did you wait after asking a question to give children
a chance to think before you called on someone?
 Did you ask for different ideas (for example, asking
who found the answer in a different way)?
 Did you ask follow-up questions?
Comments/Ideas:
Yes
Yes, but
could have
waited longer No
Yes
Yes, but
could have asked
for more No
Yes
Yes, but
could have asked
for more No

Comments and ideas for leading AfterSchool KidzMath™
games:
What went well?
What could I improve for next time?
What are your other comments, ideas, or questions?

afterSchool KidzMath™
Questionnaire
AfterSchool KidzMath has three goals:
 Increase children’s enjoyment of mathematics
 Increase children’s mathematical understanding
and skills
 Increase children’s ability to work with others
Use the this questionnaire to help you identify how
the children in your group see themselves in relation
to the goals.
When to Use this Questionnaire
You can use this questionnaire at any time during the
year. If you want a record of how your children have
changed, you may want to give the questionnaire at
the beginning, middle, and end of the year. After you
give the questionnaire the first time, play AfterSchool
KidzMath games at least twice a week for three to four
months with same group of children before giving
the questionnaire a second time. If you do decide to
compare the results, be sure that you assessed the
same children both times.
Ways to Use this Questionnaire
This tool can be used in a variety of ways. Here are
some ideas:
• You, the leader, can use the questionnaire with a
group of children. Gather the children together,
read a question, read the responses, and have the
children raise their hand to choose one of the
responses. When doing this with the group, think
about how the majority of the group feels. (For
example, if there are ten children in the group
and eight say they enjoy math, you would mark
the response “a lot” for the first question.)
• Have each child complete the questionnaire to
learn about how each one views her skills. Fluent
readers (usually in grades 4–6) can fill out the
questionnaire on their own. For less fluent readers
(usually grade 3 and below), read the questions
and responses aloud as the children follow along
with you and mark their choices. Have very young
children or children with special needs answer
verbally or point to the picture that shows their
responses. In this case, you may need to work
with only one child or two children at a time.
• You can use the questionnaire with just some
of the children. You may want to know how
a particular group of children see themselves.
Or, you may want an overview of the group.
To get a balanced view, pick some children who
work well with others, some doing well in math,
some with average skills, and some children who
are struggling.
In any case, after giving the questionnaire talk about it
with the children. Use questions like:
 What did you learn about yourself from
this questionnaire?
 What does this questionnaire tell you that
you might work on?
 How can we help one another work even
better together?
How to Explain this
Questionnaire to Children
Explain that this questionnaire is a tool to help the
children and you understand what they think about
mathematics and about how they work with others.
Let them know that you will use this information to
choose games and activities and to pick questions for
them to discuss.

Date ________________ Grade Level(s)��
Child’s/Children’s Name(s)��
Leader’s Name ��
These questions will help us understand how you think and feel about
mathematics and about working with others. Read each question.
Mark the picture that shows your answer. If you are not sure of which
answer to pick, choose the one that is closest to how you think or feel.
Not at all A little A lot
How much do you enjoy math?
Not very good So-so Very good
How good are you at math?
How good are you at multiplication?
How good are you at division?
afterSchool KidzMath™
Questionnaire

Not very well So-so Very well
How well do you understand fractions?
Not very well So-so Very well
How well do you work in a group?
When you work in a group, how good are you at asking others what
they think before making a decision?
How good are you at helping others without just telling them the answer?
How good are you at taking care of the materials (like games and balls)
at our site?
Not very comfortable So-so Very comfortable
How comfortable do you feel asking other children to help you
if you need help?

Dear Family,
This year we are doing an exciting after-school math program called
AfterSchool KidzMath™
Games at our site. The program’s goals are to
increase children’s interest in math, understanding of math, and
ability to work with others.
Together, we will learn new games that will build children’s
confidence in mathematics while they have fun. The AfterSchool
KidzMath games help children learn important number skills and
concepts that aid them as they become successful math learners.
Please feel free to come by and ask us more about the program.
Sincerely,

apreciada familia,
Este año tenemos un programa muy estimulante de matemáticas
al cual llamamos “AfterSchool KidzMath.™
” El programa se lleva a
cabo en nuestro local durante las horas después de la escuela.
La meta que tenemos es aumentar el interés y entendimiento de
las matemáticas en los niños, lo mismo que la destreza de poder
trabajar con otros.
Juntos vamos a aprender nuevos juegos que van a edificar la
confianza de los niños en las matemáticas mientras que se divi-
erten. Los juegos del programa “AfterSchool KidzMath” ayudan
a que los niños aprendan conceptos y destrezas importantes con
los números lo que les va a ayudar a medida que van aprendiendo
las matemáticas con éxito.
Si desea saber más acerca del programa, puede venir y hablar
con nosotros.
Atentamente,

Dear Teacher,
This year we are doing an exciting after-school math program called
AfterSchool KidzMath™
Games at our site. The program’s goals are to
increase children’s interest in math, understanding of math, and
ability to work with others.
Together, we will learn new games that will build children’s confi-
dence in mathematics while they have fun. The AfterSchool KidzMath
games help children learn important number skills and concepts in
number sense, multiplication, fractions, decimals, and percents.
We will be more effective in helping our children if we know areas
where they might need some extra time or help. Please contact me
at ___________________, so that we can talk about how we can help
specific children.
Please feel free to come by and ask me more about the program.
Sincerely,
AfterSchool KidzMath is a program of Developmental Studies Center, Oakland, CA.

additional reading
and research
Mathematics
Mokros, Jan, Susan Jo Russell, and Karen Economopoulos. Beyond Arithmetic: Changing Mathematics in the Elementary
Classroom. Menlo Park, CA: Dale Seymour Publications, 1995.
National Council of Teachers of Mathematics. Principles and Standards for School Mathematics: Reston, VA: National
Council of Teachers of Mathematics, 2000.
Owens, Douglas T., ed. Research Ideas for the Classroom: Middle Grades Mathematics. National Council of Teachers of
Mathematics Research Interpretation Project. New York: Macmillian Publishing Company, 1993.
TIMSS. Third International Mathematics and Science Study Sourcebook of 4th-Grade Findings. Philadelphia: Mid-Atlantic
Consortium for Mathematics and Science Education, 1997.
Zaslavsky, Claudia. The Multicultural Math Classroom: Bringing in the World. Portsmouth, NH: Heinemann, 1996.
Social Development/Cooperative Learning
Aycox, Frank. Games We Should Play in School: A Revealing Analysis of the Social Forces in the Classroom and What to Do
about Them. Discovery Bay, CA: Front Row Experience, 1997.
Gibbs, Jeanne. Tribes: A New Way of Learning and Being Together. San Rosa, CA: Center Source Publications, 2001.
Kagan, Spencer. Cooperative Learning. San Juan Capistrano, CA: Kagan, 1997.
Noddings, Nel. Philosophy of Education. Boulder, CO: Westview Press, 1995.
Nettell, Dave. Cooperative Adventures Teacher’s Handbook. Available from the author at
http://www.cooperativeadventures.com/book.htm
After-School
LA’s BEST and the UCLA Center for the Study of Evaluation. A Decade of Results: The Impact of the LA’s BEST
After School Enrichment Program on Subsequent Student Achievement and Performance. June 2000.
www.lasbest.org/learn/uclaeval.pdf
Román, Janette. NSACA Standards for Quality School-Age Care. Dorchester, MA: National School-Age Care
Alliance, 1998.
U.S. Dept of Education. Bringing Education to After-School Programs, Office of Educational Research and Improvement.
(Summer 1999). http://www.ed.gov/pubs/studies.html
Hall, George and Brooke Harvey. Building and Sustaining Citywide Afterschool Initiatives: Experiences of the Cross-Cities
Network Citywide Afterschool Initiatives. Wellesley, MA: National Institute on Out-of-School Time, 2002.
http://www.niost.org/publications/index.html
*The School-Age Notes Catalog is also an excellent resource for books on school-age care. See their website at:
http://www.schoolagenotes.com

decimal place: the position of a digit to the right
of a decimal point, such as the tenths place or the
hundredths place
decimal: (sometimes called a decimal fraction) a way to
write fractions for tenths, hundredths, thousandths, and
so on (e.g., 23.5, twenty-three and five-tenths; or 0.756,
seven-hundred fifty-six thousandths)
decimal point: a dot placed to the
left of a decimal. A number with a
decimal point, such as 23.5, is read
“twenty-three and five tenths,” not
“twenty-three point five.”
digit: any one of the ten symbols 0–9
dividend: the quantity to be divided
(e.g., in 24 ÷ 3 = 8, 24 is the dividend)
divisor: the quantity by which another quantity is to be
divided (e.g., in 24 ÷ 3 = 8, 3 is the divisor)
equation: two equal quantities separated by an equal
sign (e.g., 52 + 23 = 75)
equivalent: different ways of naming the same quantity
(e.g., 0.5 = 50% = 1
⁄2)
estimate: find a number close to the exact amount —
an educated guess
even number: a number divisible by 2 with no
remainder (leftover) (e.g., 2, 14, and 634)
factor: a number that divides evenly into another
(e.g., 6 ÷ 2 = 3; so 2 and 3 are factors of 6). A factor
can also be explained as one of two or more numbers
that are multiplied to get a result (e.g., in 4 × 5 = 20,
4 and 5 are both factors).
fraction: a way to show part of a whole or part of
a group by showing the number of equal parts in
the whole and the number of those parts you are
describing (e.g., in 3
⁄7 the 3 shows the parts and
the 7 shows the number of parts in the whole)
geometry pattern: a group of shapes or figures that
repeat or follow a rule so that a person can predict
what comes next
grid: a pattern of lines that cross to
form squares
hexagon: a closed shape with six
sides and six angles
hundreds (place): The third place to the left of the
decimal point in a number. The value is one-hundred
times the digit in that place (e.g., a 4 is in the hundreds
place in 459 and is worth 400).
hundredths (place): The second place to the right
of the decimal point in a number. The value is one-
hundredth of the digit in that place (e.g., the 7 is
in the hundredths place in 0.87 and is worth seven-
hundredths of one-whole).
multiple: the result of a whole number multiplied by
another whole number (e.g., a multiple of 4 is 20
because 4 × 5 = 20)
math Glossary
This glossary gives definitions for the math words that may be unfamiliar but are important to understanding the
games. The math words are italicized in the games to show that they are defined here.
23.5
decimal point

number pattern: a group of numbers that repeat
or follow a rule so that a person can predict what
comes next
number relationships: how numbers relate to each
other (for example, four is less than five, more than
three, and half of eight)
number sense: understanding and being flexible with
numbers — what numbers mean; how they relate to
each other; the effects of adding, subtracting, multiplying,
and dividing; ways to use numbers flexibly to solve prob-
lems; and ways to apply numbers to real-world situations
odd number: a number that has a remainder of 1 when
divided by 2 (numbers ending in 1, 3, 5, 7, or 9; e.g., 29,
33, and 845)
ones (place): the first place to the left of the decimal
point in a number. The value is equal to the digit in
that place (e.g., the 9 is in the ones place in 459 and
is worth 9).
operations: addition, subtraction, multiplication,
and division
percent: a number expressed as a fraction of 100 (e.g.,
11 percent means 11 out of every hundred or 11
⁄100)
place value: includes three main ideas:
1) grouping by 10 (e.g, you can trade one ten for ten
ones or ten ones for one ten)
2) a structure based on multiplication (e.g., 982 is
9 × 100 plus 8 × 10 plus 2 × 1 as well as a collection
of 982 objects)
3) the position of the digit: The position of the digit (any
one of the ten symbols 0–9) in a number determines
its value. (In the number 25, the “2” is equal to 20
because it is in the tens place. In the number 32, the
“2” is equal to 2 because it is in the ones place.) Each
place has ten times the value of the place to its right.
product: the result of a multiplication problem
(e.g., 20 is the product of 4 × 5)
quotient: the result of a division problem (e.g., 3 is the
quotient of 15 ÷ 5)
ratio: a way to show the relationship of two quantities
(e.g., if there are 10 boys and 16 girls, the ratio of boys
to girls is 10
⁄16 or 5
⁄8)
rational number: any number that can be written
as a fraction. All common fractions and terminating
decimals (a decimal that contains a limited number of
digits) are rational.
remainder: the amount left over when dividing one
number by another (e.g., 16 divided by 3 equals 5,
remainder 1)
tens (place): the second place to the left of the decimal
point in a number. The value is ten times the digit in
that place (e.g., the 5 is in the tens place in 459 and is
worth 50).
tenths (place): the first place to the right of the decimal
point in a number. The value is one-tenth the value of
the digit in that place (e.g., the 8 is in the tenths place
in 0.8 and is worth eight-tenths of one-whole).
whole numbers: include zero and the counting
numbers 1, 2, 3, 4, 5, 6, and so on. If a number has
a negative sign, a decimal point, or a part that’s a
fraction, it’s not a whole number.

The Annenberg Foundation, Inc.
The Atlantic Philanthropies (USA) Inc.
Booth Ferris Foundation
The Robert Bowne Foundation, Inc.
The Annie E. Casey Foundation
Center for Substance Abuse Prevention
U.S. Department of Health and Human Services
The Danforth Foundation
The DuBarry Foundation
The Ford Foundation
William T. Grant Foundation
Evelyn and Walter Haas, Jr. Fund
Walter and Elise Haas Fund
The Horace Hagedorn Foundation
J. David and Pamela Hakman Family Foundation
Hasbro Children’s Foundation
Charles Hayden Foundation
The William Randolph Hearst Foundations
Clarence E. Heller Charitable Foundation
The William and Flora Hewlett Foundation
The James Irvine Foundation
The Robert Wood Johnson Foundation
Walter S. Johnson Foundation
Ewing Marion Kauffman Foundation
W.K. Kellogg Foundation
John S. and James L. Knight Foundation
Lilly Endowment, Inc.
Longview Foundation
Louis R. Lurie Foundation
The MBK Foundation
The John D. and Catherine T. MacArthur Foundation
A.L. Mailman Family Foundation, Inc.
Mr. and Mrs. Sanford N. McDonnell
Charles Stewart Mott Foundation
National Institute on Drug Abuse,
National Institutes of Health
National Science Foundation
New York Life Foundation
Nippon Life Insurance Foundation
Karen and Christopher Payne Foundation
The Pew Charitable Trusts
The Pinkerton Foundation
The Rockefeller Foundation
Louise and Claude Rosenberg Jr. Family Foundation
The San Francisco Foundation
Shinnyo-en Foundation
Silver Giving Foundation
The Spencer Foundation
Spunk Fund, Inc.
W. Clement Jessie V. Stone Foundation
Stuart Foundation
The Stupski Family Foundation
The Sulzberger Foundation, Inc.
Surdna Foundation, Inc.
John Templeton Foundation
U.S. Department of Education
The Wallace Foundation
Wells Fargo Bank
Funding for Developmental Studies Center has been generously provided by:

Reorder Information
AfterSchool KidzMath
Primary Games Package (K–2) KM-GP
Program contains 1 Leader’s Kit and 5 identical Kids’ Kits.
Primary Story Guides Kit (K–2) KM-SGCPP
Program contains 1 Leader’s Guide, 10 Story Guides,
10 children’s books, plus game accessories.
Available separately
Primary Set without Story Books KM-SGLPP
Primary Story Books KM-TBSP
Individual titles can be ordered by calling our
customer service department.
Title Author
100th Day Worries Cuyler
The Doorbell Rang* Hutchins
Grandfather Tang’s Story Tompert
How Big Is a Foot? Myller
Inch by Inch Lionni
My Rows and Piles of Coins Mollel
Math Counts: Numbers Pluckrose
Seven Blind Mice Young
Ten, Nine, Eight* Bang
Under the Lemon Moon* Fine
*Book available in Spanish
Intermediate Games Package (3–6) KM-GI
Program contains 1 Leader’s Kit and 5 identical Kids’ Kits.
Intermediate Story Guides Kit (3–6) KM-SGCPI
Program contains 1 Leader’s Guide, 10 Story Guides,
10 children’s books, plus game accessories.
Available separately
Intermediate Set without Story Books KM-SGLPI
Intermediate Story Books KM-TBSI
Individual titles can be ordered by calling our
customer service department.
Title Author
Can You Count to a Googol? Wells
Cut Down to Size at High Noon Sundby
First Day in Grapes Pérez
Fly High!
The Story of Bessie Coleman
Borden
Kroeger
The King’s Chessboard Birch
Marvelous Math:
A Book of Poems
Hopkins
My Very Own Room/
Mi propio cuartito
Pérez
Once Upon a Dime Allen
Shota and the Star Quilt Bateson-Hill
The Warlord’s Puzzle Pilegard
Ordering Information:
To order call 800.666.7270 * fax 510.842.0348 * log on to www.devstu.org * e-mail pubs@devstu.org
Or Mail Your Order to:
Developmental Studies Center * Publications Department * 2000 Embarcadero, Suite 305 * Oakland, CA 94606
AfterSchool KidzMath™ Complete K–6 Program KM-GSGPI
The complete program includes four packages: Primary Games (K–2), Intermediate Games (3–6),
Primary Story Guides (K–2), and Intermediate Story Guides (3–6). The games, books, and activities
increase children’s enjoyment of mathematics.

KM-LGI
ISBN 978-1-57621-452-7
y(7IB5H6*MLOPMR(+;!z!!z!
IllustrationsbyJayFlom
The Leader’s Kit contains:
 A Leader’s Guide that gives the
directions for all the games
 4 wall posters for “Stick the
Fraction on the Donkey”
 A wall poster for “Equapardy”
 5 game boards for “Three Hexagons”
 A beach ball
 A permanent marker to write
on the beach ball
 A dry-erase writing board
with the multiplication table
on the back
 3 dry-erase markers
 10 dice
 3 sheets of stickers to make
different kinds of dice
The Kids’ Kit contains:
 A spiral-bound book of
game boards
 A plastic spinner holder
 6 spinner cards to insert
into the holder
 100 plastic game markers
 A deck of playing cards
 6 dice
 5 decks of game cards
 A dry-erase board with
the multiplication table
on the back
 3 dry-erase markers

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