Math k investigations in number, data, and space

Note to Teacher: Encourage students to count and compare multiple representations of the same number: the word e.g.. Note to Teacher: Encourage students to count and compare multiple rep

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

four

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

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

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

8 eight

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

How Many? (8)

eight

eight 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

10 ten

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

How Many? (10)

ten

ten balls

Calendar

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

September 2008 Sunday Monday Tuesday Wednesday Thursday Friday Saturday

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

days of

month

seventh, 7th

eighth, 8th

ninth, 9th tenth, 10th

Note to Teacher: When they line up, ask students to use ordinals to identify their position in line

(e.g first, second, etc.)

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Counting

People count every day They count to find out how many.

How many balls?

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

10 balls

18 eighteen

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)

How many students are in your class?

More Counting

How many students are here today?

20 students are here today.

nineteen

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

What do you do when you count?

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

20 twenty

Counting Jar

Cubes

Step 1 Count how many.

Step 2 Make the same amount.

Beth Hugo

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

Jason’s card 6

Jason has more than Emma 6 is more than 3.

Who has more?

Hugo has more than Lisa 5 is more than 2.

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.

Who has more? How do you know?

Rebecca’s cube train Russell’s cube train

Fewer

Who has fewer?

Jae’s card 4

Kaitlyn’s card 8

Jae has fewer than Kaitlyn 4 is less than 8.

Who has fewer?

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.

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Can you show the same amount as Beth?

Beth’s cube train

Equal

Who has fewer?

Mia’s card 5

Victor’s card 5

Mia and Victor have the same amount.

5 is the same amount as 5 5 is equal to 5.

Sarah and Yoshio have equal amounts.

6 is the same amount as 6 6 is equal to 6.

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.

24 twenty-four

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.

3 4 5 7

Green is the smallest tower

3 is the fewest.

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.

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

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

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

First I saw

3, then 4, 5.

1 and 3 and 1 is 5.

1

3 1

27

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

How do you know that there are 5?

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Five Tiles

These students are looking at

this arrangement of 5 tiles.

Here’s how they know that

there are 5.

2
2
1  5

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

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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.

Six Tiles

These students arranged 6 tiles.

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

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More Ways to Make Six

Here are some more ways to make 6.

Six Crayons in All

These students made 6 with red and blue crayons.

Note to Teacher: How Many Do You Have?, Session 2.5 Encourage students to use this

page in order to remember the steps for solving story problems

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Solving Story Problems

1 Listen to the story 2 Tell the story in your own words.

3 Solve the problem You can:

4 Show your solution.

Note to Teacher: How Many Do You Have?, Sessions 3.3 and 3.5 After reviewing this

page and the following three pages, ask students to visualize, act out, and solve these story

problems, as well as the others you create

Was this story about putting groups together or about taking away part of a group?

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A Library Story Problem

Here is a story about children at a library.

Three children were reading books at the library.

Then two more children came to the library to read.

What happened in this story?

Note to Teacher: How Many Do You Have?, Sessions 3.3 and 3.5 After reviewing this page,

the previous page, and the following two pages, ask students to visualize, act out, and solve these story problems, as well as others you create

How would you solve the problem?

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Solving a Library Story Problem Here’s the story.

There were 3 children reading books at the library

Then 2 more children came to the library to read

How many children in all were reading at the library?

Here are some ways students solved this problem.

These students acted

out the story.

Jack drew a picture.

I took 3 cubes Then

I took 2 more cubes

Then I counted them.

I drew the kids

3 and 2 is 5.

Note to Teacher: How Many Do You Have?, Sessions 3.3 and 3.5 After reviewing this

page, the previous two pages, and the following page, ask students to visualize, act out,

and solve these story problems, as well as others you create

Was this story about putting groups together or about taking away part of a group?

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A Story Problem

About Books

Here is a story about books.

Corey was looking for books in the library

She saw 5 books on the table.

Corey took 2 of the books from the table to read.

What happened in this story?

How would you solve the problem?

Note to Teacher: How Many Do You Have?, Sessions 3.3 and 3.5 After reviewing this page

and the previous three pages, ask students to visualize, act out, and solve these story problems,

as well as the others you create

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Solving a Story Problem

About Books

Corey was looking for books in the library.

She saw 5 books on the table

Corey took 2 of the books from the table to read.

How many books were left on the table?

These students acted

out the story.

1, 2, 3

Manuel

used cubes.

Cindy drew a picture.

Then I took off

2 cubes and counted the cubes left.

I put 5 cubes together

1 2 3 4 5

I drew 5 books Then

I crossed out 2 books and counted how many books were left.

1 2 3

Note to Teacher: How Many Do You Have? Session 4.4 Use this page to help students

make sense of a new type of problem, called How Many of Each?, that they will solve in this

Investigation and throughout first grade

Can you find other combinations of blue and red crayons?

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How Many of Each?

Here is a story problem.

I have 6 crayons.

Some are red Some are blue.

How many of each could I have?

How many red? How many blue?

There are many solutions.

Here are some solutions.

1 red and 5 blue

What else can you measure?

Note to Teacher: Measuring and Counting, Investigation 1 Use this page to facilitate a

discussion about the many purposes of measurement

What can you find that is shorter than 10 cubes?

What can you find that is longer than 10 cubes?

Note to Teacher: Counting and Comparing, Session 2.1 Students can consider these

visual representations of the concepts of shorter and longer either before or after they

have looked for objects that are shorter or longer than ten cubes

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Shorter or Longer

These students used a tower of 10 cubes to measure

some objects in their classroom.

Some objects were shorter than the 10 cubes.

Some objects were longer than the 10 cubes.

Measuring with Cubes

These students used cubes to measure the length of

some objects in their classroom

Note to Teacher: Measuring and Counting, Session 1.2 Students can consider these

examples of using cubes to measure objects Ask them to compare the lengths Which object

is the longest? Which is the shortest?

How long is the shoe?

What do you notice about these patterns? Do you see any patterns around you?

Note to Teacher: What Comes Next? Session 1.1 This page includes a variety of patterns

Ask students to describe the images and to explain why they think each is or is not a pattern

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Patterns All Around Us

Look at these patterns

Make your own cube train pattern

What color cube comes next?

Note to Teacher: What Comes Next? Sessions 2.1 and 2.2 After students have had

some opportunities to create their own patterns, you can use these examples of AB, ABC,

and AAB patterns to give students practice describing patterns and determining what

comes next in the sequence

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Cube Train Patterns

Look at these cube patterns.

What comes next?

What comes next?

What comes next?

What comes next?

Note to Teacher: What Comes Next? Sessions 2.1 and 2.2 Once students have had the

opportunity to construct their own patterns using a variety of materials, you can read them

the students’ descriptions of these patterns, ask them to determine what comes next, and

ask them to compare the patterns

How are these patterns alike?

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Making Patterns

These students used many different objects to make

patterns They describe their patterns in different

ways How do they describe their patterns?

Cube Train Patterns

Pattern Block Patterns

Two-Color Counter Patterns

I put down a triangle and a trapezoid and then did it again and again.

This is red, yellow, red, yellow, over and over and over.

Yellow comes after red and red comes after yellow.

Note to Teacher: What Comes Next? Session 2.9 Once students have had an opportunity to

make patterns using a variety of materials, they can describe patterns, determine what comes next, and compare patterns

What patterns can you make with other things?

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Making More Patterns

These students used different objects to make patterns.

Square Tile Patterns

What comes next?

Note to Teacher: What Comes Next? Sessions 3.1 and 3.2 Use this page to help students

understand how to identify the unit of a pattern.

What is the unit for this cube train pattern?

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Break the Train

The unit is the part of a pattern that repeats.

The unit is red, blue.

The unit is brown, orange, yellow.

Note to Teacher: After students have had a number of opportunities to do Today’s Question,

they can examine a set of data about another group of people Then, ask, “What do you think we’d find out if we answered this question?” Collect and discuss the data

What do the data tell you about this class?

Note to Teacher: Sorting and Surveys, Sessions 3.1, 3.2, and 3.3 Use this and the following

page to review the data collection process: choosing a topic, asking a survey question, collecting

and recording responses, and describing the resulting data Encourage students to compare the

different ways to record data

How many of Mary’s classmates like to play soccer?

How many do not like to play soccer?

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Mary’s Survey

Mary likes to play soccer.

She decided to survey her class to

find out who else likes soccer

Mary recorded their responses on