Math k investigations in number, data, and space

Math Words and Ideas

Read Together

How Many? (0, 1, 2)
zero

0

zero balls

one

0
1

1

one ball

two

2

2

two balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. two), the numeral (e.g. 2) and the quantity (e.g. 2 dots, 2 balls,
2 pencils) to make sure they are the same amount.

4

four


Math Words and Ideas

Read Together

How Many? (3, 4)
three

3

3

three balls

four

4

4

four balls

Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. four), the numeral (e.g. 4) and the quantity (e.g. 4 dots, 4 balls,
4 pencils) to make sure they are the same amount.

five

5


Math Words and Ideas

Read Together

How Many? (5, 6)
five

5

5

five balls

six

6

6

six balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. six), the numeral (e.g. 6) and the quantity (e.g. 6 dots, 6 balls,
6 pencils) to make sure they are the same amount.

6

six


Math Words and Ideas

Read Together

How Many? (7)
seven

7

7

seven balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. seven), the numeral (e.g. 7) and the quantity (e.g. 7 dots, 7 balls,
7 pencils) to make sure they are the same amount.

seven

7


Math Words and Ideas

Read Together

How Many? (8)

eight

8

8

eight balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. eight), the numeral (e.g. 8) and the quantity (e.g. 8 dots, 8 balls,
8 pencils) to make sure they are the same amount.

8

eight


Math Words and Ideas

Read Together

How Many? (9)
nine

9

9

nine balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. nine), the numeral (e.g. 9) and the quantity (e.g. 9 dots, 9 balls,

9 pencils) to make sure they are the same amount.

nine

9


Math Words and Ideas

Read Together

How Many? (10)
ten

10

10

ten balls
Note to Teacher: Encourage students to count and compare multiple representations of the
same number: the word (e.g. ten), the numeral (e.g. 10) and the quantity (e.g. 10 dots, 10 balls,
10 pencils) to make sure they are the same amount.

10 ten


Math Words and Ideas

Read Together

Numbers: 0 to 10
0

zero

1

one

2

two

3

three

4

four

5

five

6

six

7

seven

8

eight

9

nine

10

ten

eleven

11


Math Words and Ideas

Read Together

Numbers: 11 to 19
11

eleven

12

twelve

13

thirteen

14

fourteen

15

fifteen

16

sixteen

17

seventeen

18

eighteen

19

nineteen

12 twelve


Math Words and Ideas

Read Together

Numbers: 20 to 25
20

twenty

21

twenty-one

22

twenty-two

23

twenty-three

24

twenty-four

25

twenty-five

thirteen

13


Math Words and Ideas

Read Together

Numbers: 26 to 30
26

twenty-six

27

twenty-seven

28

twenty-eight

29

twenty-nine

30

thirty

14 fourteen


Math Words and Ideas

Read Together

Calendar
A calendar is a tool for keeping track of time and events.
month

days of
the week
Sunday

September 2008
Monday

Tuesday

Wednesday

1

2

3

7

8

9

10

14

15

16

21

22

23

28

29

30

First
Day of Fall

Field
Trip to the Park

year

Thursday

4

Friday

Saturday

5

6

11

12

13

17

18

19

20

24

25

26

27

Family
Breakfast

First Day
of School

What will happen on Tuesday, September 16?
What day of the week is the first day of school?
When is the first day of fall?
Note to Teacher: Use this page to help students make sense of the calendar as tool for keeping
track of time and events.

fifteen

15


Math Words and Ideas

Read Together

Who is First? Who is Next?
ninth, 9th

tenth, 10th
eighth, 8th
seventh,
7th

first, 1st
sixth,
6th

second,
2nd

fifth, 5th

third, 3rd

fourth, 4th

Note to Teacher: When they line up, ask students to use ordinals to identify their position in line
(e.g. first, second, etc.).

16 sixteen


Math Words and Ideas

Read Together

Counting
People count every day. They count to find out how many.
How many balls?

1

4

2

5

3

6

7
10 balls

8

9

10

When do you count? What do you like to count?
Note to Teacher: Because counting is the foundation for much of the number work that
Kindergarteners do, encourage them to discuss why they count.

seventeen

17


Math Words and Ideas

Read Together

More Counting
How many students are here today?

20 students are here today.

How many students are in your class?

Note to Teacher: Who Is in School Today? Session 1.1. Use this page to show that we use
numbers both to count a set of objects (1, 2, 3, . . . 20) and to describe the quantity of those
objects (the total is 20).

18 eighteen


Math Words and Ideas

Read Together

Ways to Count
When you count, you say one number for each object.
You need to keep track of what you are counting.

The last number you say is the total. The total tells you
how many are in the group.
Look at how some children count.
Jack puts each button in a cup
as he counts it.

Three . . .

Abby moves each button as she
counts it.
Four . . .

Kiyo puts the buttons in a row
to count them.

Eight . . .

What do you do when you count?
Note to Teacher: Who Is in School Today? Session 2.5. Use these examples in your first
discussion about strategies for counting the objects in the Counting Jar and whenever you
discuss how students count.

nineteen

19


Math Words and Ideas

Read Together

Counting Jar
Step 1. Count how many.
Cubes

Step 2. Make the same amount.

Hugo

Beth

Step 3. Show how many.

Note to Teacher: Who Is in School Today? Session 2.1. Encourage students to use this page
when they are working on the Counting Jar to help them remember the steps of the activity.

20 twenty


Math Words and Ideas

Read Together

More
Who has more?
Emma’s card

Jason’s card

3

6

Jason has more than Emma. 6 is more than 3.

Who has more?
Hugo’s cube tower

Lisa’s cube tower

Hugo has more than Lisa. 5 is more than 2.
Who has more? How do you know?
Rebecca’s cube train
Russell’s cube train
Note to Teachers: Counting and Comparing, Sessions 2.4 and 2.5. As you review this page
and the following two pages with students, ask them to find a card or create a cube tower that is
more, fewer, or equal to a given quantity.

twenty-one

21


Math Words and Ideas

Read Together

Fewer
Who has fewer?
Jae’s card

Kaitlyn’s card

4

8

Jae has fewer than Kaitlyn. 4 is less than 8.

Who has fewer?
Tammy’s cube tower

Mitchell’s cube tower

Mitchell has fewer than Tammy. 3 is less than 6.
Who has fewer?
Carmen’s cube train

Kyle’s cube train

Note to Teachers: Counting and Comparing, Sessions 2.4 and 2.5. As you review this page,
the previous page, and the following page with students, ask them to find a card or create a cube
tower that is more, fewer, or equal to a given quantity.

22 twenty-two


Math Words and Ideas

Read Together

Equal
Who has fewer?
Mia’s card

Victor’s card

5

5

Mia and Victor have the same amount.
5 is the same amount as 5. 5 is equal to 5.
Tammy’s cube tower

Mitchell’s cube tower

Sarah and Yoshio have equal amounts.
6 is the same amount as 6. 6 is equal to 6.
Can you show the same amount as Beth?
Beth’s cube train
Note to Teachers: Counting and Comparing, Sessions 2.4 and 2.5. As you review this page
and the previous two pages with students, ask them to find a card or create a cube tower that is
more, fewer, or equal to a given quantity.

twenty-three

23

Math Words and Ideas

Read Together

Ordering Fewest to Most
Brad grabbed four handfuls of cubes.

He built towers and counted the cubes.

7
4
5
3
He put the towers in order from fewest to most.
Green is the
smallest tower.
3 is the fewest.

3

4

5

7

Yellow is the
biggest tower.
7 is the most.

Build a tower that has more than 7 cubes. How many
cubes are in your tower?
Note to Teacher: Counting and Comparing, Sessions 2.10 and 2.11. Use this example to help
students think about ordering quantities from fewest to most.

24 twenty-four


Math Words and Ideas

Read Together

One More
Here are five stars.

1

2

3

4

5

4

5

One more is six.

1

2

3

Here are seven crayons.

1

2

3

4

5

6

6
One more is eight.

7

1

2

3

4

5

6

7

8

Here are 4 apples. If you
had 1 more, how many
apples would you have?
Note to Teacher: Measuring and Counting, Session 2.3. As students work on the concepts
of one more and one fewer, find and use other contexts, including the number line, that illustrate
what happens when you add one more or take one away.

25


Math Words and Ideas

Read Together

One Fewer
Here are five stars.

1

2

3

4

5

One fewer is four.

1

2

3

4

Here are seven crayons. One fewer is six.

1

2

3

4

5

6

7

1

2

3

4

5

6

Here are 4 apples. If you
had 1 fewer, how many
apples would you have?
1

2

3

4

Note to Teacher: Measuring and Counting, Session 2.3. As students work on the concepts
of one more and one fewer, find and use other contexts, including the number line, that illustrate

what happens when you add one more or take one away.

26


Math Words and Ideas

Read Together

Five Tiles
These students are looking at
this arrangement of 5 tiles.
Here’s how they know that
there are 5.
1
3
1
2

3

I counted
5 tiles.

4

1
1 and 3
and 1 is 5.

5

1

2

5
2

I saw 2,
2, and 1.

First I saw
3, then 4, 5.

4

2ϩ2ϩ1ϭ5

How do you know that there are 5?
Note to Teacher: Measuring and Counting, Sessions 4.1, 4.2, 4.4, 4.7, 4.9 and How Many
Do You Have?, Sessions 1.1, 1.2, 1.3, 1.4, 1.6, and 1.7. Use this page to discuss the fact that
there are different ways to arrange a certain quantity of tiles, and to show students that there
are different ways to see and describe the arrangements numerically.

twenty-seven

27

Math Words and Ideas

Read Together

Ways to Make 6
There are different ways to make a number.
Here are some ways to make 6.

Toss the Chips
These students tossed 6 two-color counters.
Some landed on the red side. Some landed on the
yellow side.

3 red and 3 yellow

2 red and 4 yellow

Six Tiles
These students arranged 6 tiles.

3 and 3

1 and 5

2 and 2 and 2

3 and 3

1 and 2 and 3

Can you think of another way to make 6?
Note to Teacher: How Many Do You Have?, Session 4.6. Use these pages to help students
see that there are certain combinations that make a number, no matter which material they are
using or what game they are playing. Encourage students to find combinations that appear more
than once.

28 twenty-eight