New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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Kindergarten
Counting and Cardinality
2012-11-20
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Table of Contents
Count
Sequence
Hundredth Day of School
Numbers 0-6
Numbers 6-10
Number Writing 0-10
Comparing Numbers
Click on a topic to
go to that section
Count Sequence
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to the table
of contents
Teacher Instructions
The following activities are suggestions for you to
work on as the year progresses. At this point
students are not expected to be able to count to 100
or skip count.
Teacher Instructions
Counting Sequence
Encourage children to count to 100 through daily
routines. (ex. Let's see where 100 steps will take us
down the hallway or around the playground.)
Ask children to finish the sequence when you start
counting with a random number such as 7. Use a stop
sign or hand signal for interrupted counting. Children
stop counting when sign is held up and then continue
when sign is put down.
Teacher Instructions
Counting By Tens, Fives, and Twos
Use bundles of tens (straws, sticks) to introduce
counting by tens. As you add a day to calendar
start adding one straw each day until you get to
ten. Wrap bundle with rubber band and then start a
new bundle... until you get to one hundred.
Use hands (five fingers) to count by fives.
Use shoes or socks to count by twos.
Counting By Tens
10
20
30
40
50
60
70
80
90
100
Counting by tens.
10
20
30
40
50
60
70
80
90
100
1
Counting by tens, what comes next?
A 10
B 31
C 40
10, 20, 30, ____
2
Counting by tens, what comes next?
A 41
B 50
C 100
10, 20, 30, 40, ____
Counting By Fives
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95 100
Counting By Fives
3
Counting by fives, what comes next?
A 16
B 20
C 25
5, 10,15, ____
4
Counting by fives, what comes next?
A 16
B 20
C 25
5, 10,15, ____
Counting by Twos
2
2
4
4
6
8
10
6
8
10
5
Counting by twos, what comes next?
A 5
B 7
C 8
2, 4, 6, ____
6
Counting by twos, what comes next?
A 9
B 10
C 11
2, 4, 6, 8, ____
Teacher Instructions
Count backward sometimes too.
• Count down to 0 like a rocket liftoff, a microwave, or a
timer ticking.
* Try counting down from a teen or higher number.
* Ready for blast-off story.
- Put on your astronaut suit.
- Up the elevator to the top of the space ship.
1 2 3 4 5 6 7 8 9 10 (squat and begin to stand as the
numbers go higher)
- Buckle yourself in safely.
- Count down for blast-off. (As they count down children
go from standing to squat position.)
- 10 9 8 7 6 5 4 3 2 1 Blast-off (Children jump )
10 9 8 7 6 5 4 3 2 1
20
19
18
17
16
15
14
13
12
11
Count Backwards
7
Counting backwards, what comes
next?
A 8
10, 9, 8, 7, ____
B 6
C 4
8
Counting backwards, what comes next?
A 13
B 15
C 10
20, 19, 18, 17, 16, 15, 14, ____
9
Counting backwards, what comes next?
A 14
B 9
C 0
13, 12, 11, 10, ____
Teacher Instructions
Ordinal Numbers
Ordinal numbers describe position.
Ask children, questions such as:
Who is first in line? Who is third from the end?
What number is the person at the end of the line?
Who is fifth in line?
Identify children by their position in line.
Then ask them to perform some sort of action.
1st
2nd
3rd
4th
5th
10 What position is the cat?
A
B
C
D
E
1st
2nd
3rd
4th
5th
11
Is the mouse third in line?
A
B
Yes
No
12 What position is the penguin?
A
B
C
D
E
1st
2nd
3rd
4th
5th
13 Is the baby 1st in line?
A
B
Yes
No
14
Is the X under the sixth horse?
A
B
Yes
No
X
15
Is the X under the 9th horse?
A
B
Yes
No
X
16 What position is the cow?
A
B
C
D
E
6th
7th
8th
9th
10th
X
Hundredth Day of School
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to the table
of contents
Teacher Instructions
The following activities are suggestions for you to
work on as you work towards the 100th day of
school. Refer back to these activities as you count
the number of days to get to 100.
Teacher Instructions
100th Day of School
Activities for the 100th day of school...
• Have each child bring a collection of 100 objects. (such as... cereal,
pennies, pasta, etc.)
• Read stories about the number 100.
• Count by 1s, 5s, and 10s to 100.
• Bundle sticks in 10 groups of ten and create one bundle of 100.
• Write numbers on a 100 grid.
• Mix 100 snack items and eat a fantastic treat.
• Place in a bag the number cards for counting by tens from 10 to
100. Invite ten students to each take a card, identify its number, and
stand holding the card so the number faces outward. Then lead the
seated students in putting the numbers in order from least to
greatest.
More activities for the 100th day.
• Marshmallow numbers. Have the children make numerals 0
through 9 using toothpicks and miniature marshmallows. Have
the children place pairs of toothpick numerals side by side to
display two-digit numbers.
• Estimation Jars- Set up different size, clear jars filled with objects.
Fill one of the jars with exactly 100 pieces. Ask students to guess
which jar's contents are closet to 100 items.
• 100 -piece necklace. Give each student a piece of string, ten paper
squares, and a plastic bag of beads or pasta. Ask the children to
write the numerals 10, 20, 30 ... 100 on the separate paper
squares. Ask students to string 100 beads and to place the
appropriate number card on the necklace after every group of ten
beads.
• 100 Headbands. Give each student a headband and have them
write 100 in the center. Have the students decorate the strip with
100 stickers, stamps or drawings. Staple the headband to fit each
child's head.
More, more , more 100th day activities.
• Have the students use cotton swabs and paint to create an apple
tree with 100 apple dots. Or use the swab and paint to create their
own design using 100 paint dots.
• Divide the class into 10 groups and have each group compile a
list of ten words. Combine their lists to create a 100 word chart.
• 100 cents. Have the children collect 100 pennies, and then have
them exchange the pennies for nickels and dimes.
• Make a snake that measure 100 inches long. Have the students
decorate it with 100 designs.
• Make a banner that has 100 hand prints.
• Hang 100 balloons or streamers in the room.
• Ask the students to make a link with 10 chains. Combine the 10link chains to make a 100 link chain.
• 100 Drops of Water. Have the students predict how full a bowl
containing 100 spoonfuls of water will be. Use tape to mark where
they predict it will go. Count as you pour 100 spoonfuls into bowl.
100 Balloons and Cheers for the 100th day of School.
On the next page count by 5s and cheer for the 100th
day of school.
Numbers 0-6
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of contents
Teacher Instructions
Numbers 0-6
Encourage children to count the number of items in total. Count
squirrels outside, blocks at center time, cookies at snack time).
They may also count children who are present or objects at
discovery center.
When counting objects, say the number names in standard order,
pairing each object with one and only one name.
The children should understand that the last number said tells the
number of objects counted. The number of objects is the same
regardless of their arrangement or the order in which they were
counted.
The children should understand that each successive number
name refers to a quantity that is one larger.
Teacher Instructions
As you introduce each number in this unit the following activities
might be used.
• Drop objects in a container and have the children count how
many drops they hear.
• Read a favorite counting book to reinforce counting and
cardinality.
• Finger "Digits" ... Display a certain number of fingers. Have the
children select number card that matches number of digits.
• Show a number card and have the children hold up the correct
number of fingers.
• Number Search The children will search for specific number of
objects in the classroom. (ex. 3 pencils)
• Play "Simon Says".
Teacher Instructions
Individual Number Poster
Each child can make a number poster for each number.
1. Write number at top of paper.
2. Draw, use stickers, or glue objects that represent number.
3. When finished with unit compile number book.
This is the number one.
Count the object and trace the number 1.
This is the number 2.
Count the objects and
trace the number 2.
Count the objects.
Circle the correct number
1
2
1
2
1
1
2
2
Sort objects
1
2
This is the number three.
Count the animals and trace the number 3.
3
This is the number four.
Count the objects and then trace the number 4.
Count the objects.
Circle the correct number.
3
4
3
4
3
4
3
4
5
This is the number 5.
Count the objects and
trace the number 5.
Count the objects in the group and move
the correct number to the group.
Count the objects and trace the number 6.
Teacher Instructions
Play "I Have One, You Have Two"
Children take turns making number statements.
The first child might say, "I have one mouth."
The next child then replies, "I have two eyes".
The children keep taking turns adding one each
time until they get to six. Then start over again with
one.
Click for interactive
dice on the web.
Click for interactive
dice on the web.
Each number represents a set of objects.
Draw objects for each number.
1
2
3
Each number represents a set of objects.
Draw objects for each number.
5
6
Click for interactive spinner on web.
Click on change spinner and rename
sections with numbers and add a 6th
section.
17 How many bears can you count?
A
B
C
D
2
3
4
5
18 How many elephants can you count?
A
B
C
D
1
2
3
4
19 How many monkeys can you count?
A
B
C
D
3
1
6
4
20 How many alligators can you count?
A
B
C
D
5
2
6
3
To sequence numbers we must put them in the correct
order, each time adding the number that represents one
more.
Sequence the numbers in correct order.
Numbers follow a sequence .
In this sequence the next number represents one more.
What number should come next?
What number is missing?
12 3 4 5 6
21 Are these numbers in correct sequence?
A
B
Yes
No
22 Are these numbers in correct sequence?
A
B
Yes
No
23 What number comes next in the
sequence?
A 4
B 3
C 5
24 What number comes next in the sequence?
A
B
C
4
3
6
25 What number is missing?
A
B
C
D
E
2
3
4
5
6
1
2
3
4
6
zero
Count the animals and circle the correct number.
26 Are there zero hippos?
A
B
Yes
No
27 Are there zero lions?
A
B
Yes
No
Numbers 6-10
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of contents
Numeral
Definition: A word, symbol or figure that represents a number.
For example, seven, VII, llll ll , and 7 are all numerals that represent
the same number.
Counting Objects
When counting objects, say the number names in the standard
order, pairing each object with one and only one number name.
Understand that the last number said tells the number of objects
counted. The number of objects is the same regardless of their
arrangement or the order in which they were counted.
Understand that each successive number name refers to quantity
that is one larger.
six
Build and Identify 6
Draw more to make a group of 6.
seven
Build and Identify 7
Draw more windows to make a group of 7.
Start
Click for interactive spinner on
web.
Click on change spinner
and rename sections with
numbers and add a 6th
section.
eight
Build and Identify 8
Draw more to make a group of 8.
nine
Build and Identify 9
Draw more to make a group of 9.
Doughnut Number Roll
Click for link.
ten
Build and Identify 10
Draw more to make a group of 10.
How many?
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
Working with Numbers 0-10
Number Clap- Each student has number cards labeled
0-10. The teacher claps her/his hands. The students
count silently. The children find the number card that
corresponds to claps and hold up the card. They then
find the correct number of objects from pile in center
of table.
Number Sequence- Use number cards and place in
correct sequence against timer.
Number Trace- Trace number cards with finger. The
cards should have raised numbers or sand paper.
Next page - match number of objects to numeral.
1
2
3
4
5
6
7
8
9
10
High - Low Game
You need two players. Each
player has playing cards numbered 1 - 10.
Each player flips one card.
They must decide which number
is higher or lower. Then continue
choosing cards.
Domino Number Match
1
2
3
4
5
6
7
8
9
10
What's My Number?
Hand out dominoes. The
students will count the dots.
Ask one student to write the
number.
** Skip eleven and twelve
dots at this point.
28 How many ducks ?
A
B
C
D
7
8
9
10
29 How many pigs?
A
B
C
D
7
8
9
10
30 Are there 10 parrots?
A
B
Yes
No
31 How many birds?
A
B
C
D
7
8
9
10
Tally Marks
Tally marks are another way to represent a number of objects.
You might want to introduce tally marks with this story or another
of your own.
Once there were five caterpillars. They decided to take a nap on a
beautiful green leaf. Each caterpillar crawled onto the leaf.
1...2...3...4... When it was number 5's turn there was no room for
him. So he decided to lay across the other four.
1
2
3
4
5
6
7
8
9
10
32 Are there 5 tally marks?
A
B
Yes
No
33 How many tally marks?
A
B
C
D
6
7
8
9
34 How many tally marks?
A
B
C
D
5
8
9
10
Number Sequence
Put numbers in order... Identify one number.
Ask the students to find number before or after.
Students may work with own cards.
3
1
5
2
7
4
8
10
6
9
What's Missing?
1
2
3
4
5
6
7
8
9
10
To sequence numbers we must put them in the correct
order, each time adding the number that represents one
more.
1
2
3
5
4
6
7
8
5
6
7
8
8
9
9
6
7
10
Numbers follow a sequence .
In this sequence the next number represents one more.
What number should come next?
What number came first?
5 6 ____
____
6
___
5
7
8
6
_____
7
8
9
____
____ 8
9
7
____
8
____
9
10
35 Are these numbers in correct sequence?
A
B
Yes
No
5 6 7 8 9 10
36 What number comes next?
A
B
C
D
7
8
9
10
6
7
_____
37 What number comes first?
A
B
C
D
1
6
7
10
_____
8
9
38 Are these numbers in correct sequence?
A
B
4
Yes
No
6
5
7
8
9
10
Number Writing 0-10
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of contents
The following stroke- formations will
lay the groundwork for number writing.
Circular
O O
O
Curved
Vertical
l
l
l
l
l
l
Horizontal
-- - - -
Diagonal
/ / / / /
Figure 8's
8 8 8
Let's go to the circus and practice our strokes.
Use your straight arm to write in the sky.
Then practice on your smart board, dry erase
board, or paper.
Strokes start on the next page.
Circular - Draw the balloons at the circus.
Horizontal - Walk across the tightrope.
Draw the steps you take as you move.
__ __ __ __ __ __ __ __ __ __
Curved - Draw the cotton candy.
Make the curved shapes.
Diagonal - Slide down the elephant's trunk.
Draw the movement as you slide down.
Vertical - See the monkey on the pole.
Down the pole he goes.
Draw the monkey's pole.
Figure 8 - Watch the skateboarder follow the path.
Draw the 8s he will follow.
Roll the dice, count the
dots, and then write
the corresponding
numeral.
Click for interactive
dice on the web.
Count the objects in each group. Write the number.
Spin. How many? Write the number on the board.
Click for interactive web site.
Click change spinner to
set it up for 10 regions.
Read the numbers in sequence.
Cover the numbers with the screen
then write the numbers below the screen.
Write the number that comes next.
Comparing Numbers
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of contents
Give the students opportunities to determine which group is
larger, smaller or the same as another group. The children should
identify whether the number of objects in one group is greater
than, less than, or equal to the number of objects in another group
by using matching and counting strategies.
Extend this skill by having the students create groups with one
more or one less object.
Exploring Same Number
Draw the same number of buttons as button holes.
Exploring Same Number
Place one dog on each stool.
We need the same number of dogs
as stools.
Exploring More and Fewer (Less)
Exploring More and Fewer (Less)
Exploring More and Fewer (Less)
Same, More, Fewer
Draw the same
Number of
flowers.
Draw more
flowers.
Draw fewer
flowers.
Exploring Same, More, Fewer
Make a group of the
same number of
peanuts as elephants.
Make a group of more
peanuts than
elephants.
Make a group of less
peanuts than
elephants.
One More, One Fewer
one less
one more
One More. One Fewer
Draw a group with
one less.
Draw a group
with one more.
Problem Solving
Problem Solving
Color one square
for each animal.
Which group has
more? Which
group has less?
Using Graphs to Compare
Color each graph
to show how many
dogs and bears.
Use same, more,
or less to tell about
the graphs.
39 Are there more peanuts than elephants?
A
B
Yes
No
40 Are there fewer balls than cats?
A
B
Yes
No
41 Which group has less?
42 Which group has more?
Comparing Written Numerals
Ask children to distinguish the quantity of a written
numeral compared to another written numeral. Display
written numerals from 1 to 10 and have the children
compare the two numbers. Use the terms more and less
as you compare the numbers.
You have five green buttons and I have seven.
Which number is more?
Compare Numbers
More and Less
Number Squeeze Game
Greater Than or Less Than
0
1
2
3
4
5
6
7
8
9
10
43 Which number is more?
A
B
44 Which number is less?
A
B
45 Is 4 greater than 3?
A
Yes
4
B
No
3
46 Is 8 less than 6?
A
Yes
8
B
No
6
New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative (PMI)
For additional NJCTL Math content, visit
http://njctl.org/courses/math/.
Progressive Science Initiative (PSI)
For NJCTL Science content, visit http://njctl.org/courses/science/.
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