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
1 Explain the game as you play it with a child as your partner.
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
and pages 30–31 before
introducing the game to
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.)
 Give others time to think before
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.
more than two 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.

A n t H i l l P i c n i c 43
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

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