The document provides early math lesson plans for teaching preschoolers numbers and counting, left/right orientation, and geometry. It includes books, objectives, vocabulary, and activities for each topic. For example, one lesson teaches counting to 5 by using colored tiles and another has children grouping toy bugs into cages numbered 6-10. The reflection notes that the preschoolers needed more scaffolding than expected to use materials mathematically. Slowly introducing concepts over multiple days in different contexts helps children connect topics to play.

1. Math Files Part One Younger
Katherine A. Mileto
Math and Science for Young Children
January 31, 2013
Math Files Part One Younger
Champlain College
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Number Sense and Counting
Book
• Ten Black Dots by Donald Crews
Objective
Count forward from 0 to 5
And backward from 5 to 0.
Vocabulary
• One
• Two
• Three
• Four
• Five
• Zero
Skills
• Counting
• Using number words
• Recognizing numbers
NCTM (National Council of Teachers of
Mathematics) Expectations
• Count with understanding and recognize
“how many” in sets of objects.
• Develop understanding of the relative
position and magnitude of whole numbers
and of ordinal and cardinal numbers and
their connections.
• Connect number words and numerals to the
quantities they represent, using various
physical models and representation.
Counting to 5 and Back
Counting is the foundation for children’s early work with numbers. Your children can associate number
words with small collections of objects and gradually learn to count and keep track of objects in larger
groups. They can establish one-to-one correspondence by moving, touching, or pointing to objects as they
say number words. Children should learn that the next whole number in the counting sequence is one
more than the previous number, and that the last number named represents the last object as well as the
total number of objects.
Naturalistic Activity: Introduce the colored counting tiles at morning meeting. Show the students all the
ways they can be used, sorting, counting, stacking, etc. Place them in the math center. Observe the
children at planning time and see how many use the colored counting tiles. Take notes to document who
uses the tiles to count. Make comments like; I see you counted three tiles and laid them on the table in a
row.
Structured lesson:
Try It Here is a problem that involves counting to 5 and back.
Today is James’s day to put down and pick up the mats in the reading corner. There are 5 children in
James’s reading group. James will count forward as he puts the mates in the reading corner and count
backward as he picks up the mats. Can you help James count forward to 5 and back?
Introduce the problem. Then have children to the activity to solve the problem.
Give 5 Color Tiles to each pair of children. While displaying a tile, say: Let’s pretend that one of these
tiles is a mat for the reading corner. The sheet of paper is the reading corner. We will place one tile on the
sheet of paper for each child in James’s reading group.
1. To begin, ask children to make a circle shape with their hands. Tell children to say, “zero” to show that
there are no tiles on the paper.
2. Have children say “one” as they place a tile on the paper. Then have them place the other tiles on the
paper one at a time as they count: two…three…four…five. When children get to 5, tell them to stand
up, hold up their hands, and shout “Five!”
3. Now have children take the tiles off the paper one at a time as they count backward: five… four…
three…two… one… zero. When children get to 0, ask them to stand up, hold up their hands, and shout
“Blastoff!”
Lookout! Emphasize that zero means “empty” or “none.” But don’t expect children to understand zero
right away. Out of context, it is difficult for children to think of zero as a number, but as the initial or final
part of a counting-up or counting-down sequence, the idea of zero as a number makes more sense to
children.
Informal Activity:
• Have children talk about the process of counting from 0 to 5 and back.
• Say: Let’s count forward from 0 to 5. Ask: What number comes after 0? What number comes next?
Continue this line of questioning until all children have repeated the counting-forward sequence.
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One to One Correspondence
Book
• How Do Dinosaurs Count to Ten by
Jane Yolen and Mark Teague
Objective
Identify a number for a group
of 6 to 10 objects.
Vocabulary
• Six
• Seven
• Eight
• Nine
• Ten
Skills
• Counting
• Representing numbers
• Writing numbers
NCTM (National Council of Teachers of
Mathematics) Expectations
• Count with understanding and recognize
“how many” in sets of objects.
• Develop understanding of the relative
position and magnitude of whole numbers
and of ordinal and cardinal numbers and
their connections.
• Connect number words and numerals to the
quantities they represent, using various
physical models and representation.
• Develop a sense of whole numbers and
represent and use them in flexible ways,
including relating, composing and
decomposing numbers.
Groups of 6 to 10
A key to mathematical understanding for young children is making the link between the concrete and the
abstract – between physical models and written symbols. In this activity, children will represent numbers
6 to 10 by grouping objects and identifying the corresponding numerals.
Informal Activity: Introduce the backyard bugs and number cards during morning meeting. Show the
students that they can use the backyard bugs like the colored counting tiles. Show the students the number
cards. Discuss how the cards can be used to count items, as placemats to rest groups of bugs, etc. Place
them in the math center. Observe the children at planning time and see how many use the backyard bugs
and the number cards. Take notes to document who uses the bugs to make groups of 6-10. Also note who
uses the number cards and how they use them. Make comments like; I see you counted three bugs and laid
them on the number three card.
Structured Lesson:
Try It Here is a problem about identifying, reading, and representing numbers.
Tara’s class is putting Backyard Bugs in cages to make a Bug Zoo. Each cage has a number on it to tell
how many bugs to put in the cage. How will Tara know if she put the correct number of Bugs in each
cage?
Introduce the problem. Then have children do the activity to solve the problem.
Give Bugs, paper, crayons, and Number Cards 6-10 (BLM 1) to each group of children. Groups of 5.
1. Invite members of the group to create a “Bug Zoo” that has 5 “cages” (half-sheets of paper), containing
from 6 to 10 bugs. (One cage should have 6 Bugs, one cage should have 7 Bugs, and so on.)
2. Have group of members count the Bugs in each cage to verify that they contain only 6, 7, 8, 9, or 10
Bugs.
3. Have children find the Number Card that matches each cage.
Lookout! Watch for children who cannot create a group for a specific number. Have them count forward
from 1 as they touch each item.
Informal Activity: activity.
• Have groups talk about their Bug Zoos. Hold up a Number Card (BLM 1). Ask: How many Backyard
Bugs would you put in this cage? Say: Say the number. Now show me with your fingers. Repeat for
all numbers.
• Stress the words most and fewest. Say: Point to the cage with the most Bugs. Ask: How do you know
it has the most Bugs? Say: Point to the cage with the fewest Bugs. Ask: How do you know it has the
fewest Bugs?
• Point to the cage and hold up the Number card. Ask: What if I took one Bug out of this cage? How
many Bugs would be left? How many would there be if I put one more in this cage?
Solve It With children, reread the problem. Then have children draw a picture showing 5 Bug Zoos,
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Geometry; Spatial Sense
Book(s)
• Left or Right? By Karl Rehm
• Left Hand, Right Hand: A “Hands-
On” Book About Left and Right by
Janet Allison Brown
Objective
Identify left and right
Vocabulary
• Left
• Right
Skills
• Describing relative positions
• Classifying location
• Spatial reasoning
NCTM (National Council of Teachers of
Mathematics) Expectations
Geometry
• Describe, name, and interpret relative
positions in space and apply ideas about
relative position
Left and Right
The relative position of any object can be described using the words right and left. As with other ways of
determining location, such as inside and outside, right and left require a reference point. Without
something on the right, there is no left. Without something on the left there is no right. The ability to
describe location in terms of left and right is important in building geometric thinking and is especially
useful in real life. Using vocabulary of left and right will help children describe locations in space.
Naturalistic Activity: At morning meeting, introduce the sorting circles. Discus how the sorting circle can
be used to sort any of the items in the block/math center. Place the sorting circles in either center for the
children to use at planning time. Observe the children at planning time and see how many use the sorting
circles. Take notes to document who uses sorting circles to sort objects. Make comments like; I see you
put all the small blocks in the left circle and all the large blocks in the right circle.
Structured Lesson:
Try It Here is a problem demonstrating right and left.
After an art project, Mr. Lewis wants the paints to be put away. He wants the green and yellow paints to
be put on the left side of the drawer. He wants the red and blue paints to be put on the right side of the
drawer. Can you draw how Mr. Lewis wants the paints to be put away?
Introduce the problem. Then have children do the activity to solve the problem.
Distribute Color Tiles and Sorting Circles to groups of children.
1. Help children understand the concept of right and left by using the right and left sides of their bodies.
Say: Raise your right hand. Now touch your left knee with your left hand. Make sure children are able
to identify left and right correctly.
2. Say: We can use our right hand to help us know when something is on the right side. We can use our
left hand to help us know when something is on the left. Instruct children to place one circle in front of
the right of their group and one circle in front of the left of their group.
3. Invite children to place green and yellow tiles in the left circle. Remind children that this is the circle
to the left of their group. Have children place red and blue tiles in right circle. Remind them that this
is the circle to the right of their group.
Lookout! If children need extra help remembering right and left, spend some time discussing the
importance of right and left in children’s everyday life. Point out that we read from left to right, or that the
school bus driver sits on the left side of the bus. Look around the classroom and have children practice
identifying objects that are on their right or left. Also, point out to children that right/left position is
relative to their position.
Informal Activity:
• Ask: How do you know which is left and which is right? Discuss with students how they remember
left and right, for example by using their left and right hands.
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Reflection
First off, let me state that I am my center’s curriculum director and the above lessons were written, by me based off of
Learning Resources Hand-On Standards (2006) math lessons, for the preschool class, ages three to four years old. The above topics
were chosen because they are the foundations of mathematics. Students need to understand numbers, quantities, and directional words
in order to progress through the levels of mathematics (Charlesworth & Lind 2010). I was able to introduce each topic during
morning meeting. Then after snack I read the book(s), to the class before they began planning time. I was presently surprised to see
how the students played with items I put in the centers. Coming from the kindergarten class I expected more of a five and six year old
behavior, where when I introduce items and concepts the students tend to try out what was introduced on their own. The preschool
students, however, used the items for building or used the sorting hoops as pretend cars. I admired their creativity. It took more
teacher-scaffolding then expected to have the students use the materials in a mathematical way that pertained to the concept I was
introducing. It also took me a little longer to see that some of the things the students were doing were related to the math concepts.
For example, when the students were using the colored tiles for building I noticed that some of them were methodically stacking the
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tiles in piles of six. In order to connect these topics to play, I think that the teacher needs to slowly introduce the concepts over a few
days, in various ways. This way the students get the opportunity to see the topic in many contexts, so that they are comfortable
playing with the materials and using the vocabulary in everyday situations. Also, it might be important for the teacher to role model
the use of the materials pertaining to the lesson.
Reference
Charlesworth, R & Lind, K. (2010) Math and science for young children. Wadsworth, New York.
Learning Resources (publishers) (2006) Hands on standards: Photo-illustrated lessons for teaching math with manipulatives,
grades prek-k. Learning Resources Inc.
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tiles in piles of six. In order to connect these topics to play, I think that the teacher needs to slowly introduce the concepts over a few
days, in various ways. This way the students get the opportunity to see the topic in many contexts, so that they are comfortable
playing with the materials and using the vocabulary in everyday situations. Also, it might be important for the teacher to role model
the use of the materials pertaining to the lesson.
Reference
Charlesworth, R & Lind, K. (2010) Math and science for young children. Wadsworth, New York.
Learning Resources (publishers) (2006) Hands on standards: Photo-illustrated lessons for teaching math with manipulatives,
grades prek-k. Learning Resources Inc.
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