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A Story of Units®

Ten Tens

Module 1 ▸ Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

Module 1 Place Value Concepts Through Metric Measurement and Data ∙ Place Value, Counting, and Comparing Within 1,000

2 Addition and Subtraction Within 200

3 Shapes and Time with Fraction Concepts

4 Addition and Subtraction Within 1,000

5 Money, Data, and Customary Measurement

6 Multiplication and Division Foundations

Topic C

Part 2: Place Value, Counting, and Comparing Within

Express Three-Digit Numbers In

Model Base-Ten Numbers Within

with Money

Use place value understanding to count and exchange $1, $10, and $100 bills.

FAMILY MATH Represent Data to Solve Problems

Dear Family,

Your student begins the year by collecting and representing data in tables and graphs. These activities show that math is part of the world around them. Your student explores how the same data can be represented in different graphs, such as a picture graph and a bar graph, and then uses the information in the graphs to solve problems.

Favorite Subject

This table shows the number of students who voted for each subject.

In this picture graph, the categories are Reading, Writing, Math, and Science. The key shows that each check mark stands for 1 vote.

At-Home Activities

Go on a Nature Walk

In a bar graph, the value of each category is represented by rectangular bars. The scale on this bar graph counts by 1. Each blue box represents 1 birthday.

Invite your student on a walk around your neighborhood or a park. Have them count or collect three or four types of objects they see, such as leaves, rocks, and sticks. Help your student make a table and use it to record the number of each object they saw. Consider asking questions about the data they’ve collected.

• “How many objects did you find in all?”

• “Which type of object did you find the most of?”

• “Which type of object did you find the least of?”

• “How many more leaves did you find than rocks?”

• “How many fewer sticks did you find than leaves?”

Make Real-World Graphs

Encourage your student to collect data about something around their home or in their daily life (such as the number of different-colored cars that go by in 10 minutes or the number of plates, bowls, and cups in the kitchen). Use stickers or sticky notes to make a picture graph that includes a key. Then use the data to make a bar graph with a title and a scale.

1. Make a picture graph. Vegetables We Like

A table is a chart that shows information. Pieces of information are called data.

Key: Each stands for vote.

First, I give the graph a title. I can use the title from the table, “Vegetables We Like.”

Next, I write the categories at the bottom of the graph. I use the same categories as the table: Broccoli, Carrots, Celery, and Lettuce.

I draw 1 check mark for each vote.

I need to make a key to show the value of the unit in my graph. My key is “Each ✓ stands for 1  vote.”

2. Which vegetable has the fewest votes?

3. Which vegetable has the most votes?

Broccoli

Carrots

I can use the data in the graph to answer the questions.

I know that 1 check mark stands for 1 vote.

I see that broccoli has the fewest check marks. So broccoli has the fewest votes.

Carrots has the most check marks. So carrots has the most votes.

Key: Each stands for vote.

REMEMBER

4. Read

The grasshopper is 3 centimeters long.

The bird is 13 centimeters long.

How much longer is the bird than the grasshopper?

I read the problem. I read again. I can use a 10 -stick and centimeter cubes to compare the lengths.

I see 3 centimeter cubes show the length of the grasshopper.

I see one 10 -stick and 3 centimeter cubes show the length of the bird.

I can draw a picture to match the cubes. I can draw 3 centimeter cubes to match the length of the grasshopper and a 10-stick and 3 centimeter cubes to match the length of the bird. I can see that the length of the bird is 10 centimeters longer than the grasshopper.

Sample:

Write 3 + 10 = 13

The bird is 10 centimeters longer than the grasshopper.

Grasshopper

Key: Each stands for vote.

2. Which fruit has the fewest votes?

3. Which fruit has the most votes?

4. Read

The bee is 4 centimeters long.

The frog is 14 centimeters long.

How much longer is the frog than the bee ?

The frog is centimeters longer than the bee .

I give the bar graph a title. I use the title in the table, “Favorite Season.”

There are four categories: Spring, Summer, Fall, and Winter. I write these on the bar graph.

The scale is a number line that shows the value of each unit. Each box stands for 1 vote, so I fill in the scale along the bottom of the graph from 0 to 11 .

Spring has 3 votes. I color in 3 boxes on the graph. I color in 1 box for each vote for the rest of the seasons.

1. Make a bar graph.

2. Which season got the most votes?

3. Which season got the fewest votes?

Summer

Winter

Summer has the longest bar.

Summer got the most votes.

Winter has the shortest bar.

Winter got the fewest votes.

2. Which snack has the most votes?

3. Which snack has the fewest votes?

1. Make a bar graph.

Name

Shoes We Like to Wear

Flip Flops

Dress Shoes

Boots

Tennis Shoes

1. How many votes are there in all? 18

Write a number sentence.

I count the votes for each category:

8 students voted for Flip Flops

1 student voted for Dress Shoes.

3 students voted for Boots.

6 students voted for Tennis Shoes.

2. Add 3 more votes for Flip Flops.

How many votes for Flip Flops are there now? 11

What is the new vote total? 21

The graph shows a total of 18 votes.

I add 3 more votes to the total.

18 + 3 = 21

3. Color the faces of the shape.

Rectangular Prism

The graph shows that 8 students like Flip Flops.

I add 3 more votes for Flip Flops.

8 + 3 = 11

A face is a flat surface.

A rectangular prism has six faces. The faces are squares and rectangles. I color the square and the rectangle. square rectangle

Toys We Like

1. How many votes are there in all?

Write a number sentence.

2. Add 2 more votes for the ball .

How many votes are for the ball now?

How many votes are there in all now?

REMEMBER

3. Color the faces of the shape.

Square Pyramid

Animals at the Zoo

1. How many more frogs than lizards are there at the zoo? 5

I can match up the colored boxes, 1 frog to 1 lizard.

Then I count the extra boxes. There are 5 more frogs than lizards at the zoo.

2. How many fewer alligators than snakes are there at the zoo? 6

I can match up the colored boxes, 1 alligator to 1 snake.

Then I count the empty boxes. There are 6 fewer alligators than snakes at the zoo.

Alligators Lizards Frogs Snakes

at the Zoo

Alligators Lizards Frogs Snakes

Name 4

Fruit in a Bowl

Strawberries

Pears

Cherries

Blueberries

1. How many more blueberries than cherries are there ?

2. How many more strawberries than pears are there ?

3. How many fewer pears than cherries are there ?

FAMILY MATH Metric Measurement and Concepts About the Ruler

Dear Family,

Key Terms

meter

tick mark

Your student is learning that metric measurement is related to place value, as both include units of ones, tens, hundreds, and thousands. Your student uses centimeter cubes to measure objects and they make their own 10-centimeter ruler. As they practice measuring objects, your student comes to understand that the tick marks on the ruler represent the distance, or length units, from zero. Your student begins to select appropriate measuring tools based on the size and shape of objects.

I can make my own 10-centimeter ruler by using a centimeter cube to draw tick marks on a paper strip.

I can use ten 10-centimeter rulers to make a meter stick. 100 centimeters is equal to 1 meter.

At-Home Activities

Measure with a Centimeter Ruler

Encourage your student to find familiar objects that can be measured with a centimeter ruler. For example, they may choose objects such as a toy car, a book, or a television remote. Help your student find the length of each object in centimeters.

Scavenger Hunt

Encourage your student to find objects around the house that can be measured with a centimeter ruler (a key, a toothbrush, a book) or a meter stick (a table, a desk, the countertop). Ask your student whether they would measure the length with a centimeter ruler or a meter stick and to explain why.

Name

1. Use the centimeter tile to find the length.

The pencil is 6 centimeter tiles long.

I cut out the centimeter tile and use it to measure. I line up my tile with the end of the pencil. I mark where the tile ends. The mark I make at the end of the tile is called a tick mark.

I move the tile forward and make another tick mark. I do not leave any gaps. I do this until I get to the end of the pencil.

There are 6 spaces. Each space is 1 centimeter. The pencil is 6 centimeter tiles long.

Instruments We Like

2. What is the title of the graph?

Instruments We Like

3. How many kinds of instruments are on the graph? 4

Guitar

4. What instrument got the most votes?

5. What instrument got the fewest votes?

Each blue square is equal to 1 vote.

Trumpet

I can count the squares to find the total number of votes for each instrument.

I count 8 votes for Drum.

I count 4 votes for Trumpet.

I count 10 votes for Guitar. I count 7 votes for Voice.

Guitar has 10 votes. It has the most votes.

Trumpet has 4 votes. It has the fewest votes.

Name

Cut out the centimeter tile.

Use the centimeter tile to find the length.

1. The dog bone is centimeter tiles long.

2.

The eye dropper is centimeter tiles long.

3. Pick an object. Use the line as an endpoint. Measure the object with the centimeter tile.

The is centimeter tiles long.

Name

Use your 10 cm ruler to measure.

1. The bow is 4 cm long.

I line up the edge of the ruler with the endpoint of the bow.

The numbers on a ruler tell me how many spaces or centimeters away from 0

The bow is 4 cm long.

2. The fork is 14 cm long.

I line up the edge of the ruler with the endpoint of the fork.

The fork is longer than the 10 cm ruler.

I make a mark for 10 cm. I move the ruler to measure to the end of the fork.

I add the lengths. 10 + 4 = 14

The fork is 14 cm long.

Name

Cut out the 10 cm ruler.

Use the 10 cm ruler to measure.

1. The ticket is cm long.

2. The spoon is cm long.

Name

1. Lan measures two ways.

Lan’s flashlight is 24 cm long.

He uses 24 1 cm cubes.

He uses 2 10 cm rulers and 4 1 cm cubes. I know that a 10 cm ruler is made up of ten 1 cm cubes.

I can measure 24 cm two ways. I can use twenty-four 1 cm cubes. Or I can use two 10 cm rulers and four 1 cm cubes.

2. Ling measures her skateboard. She uses five 10 cm rulers and eight 1 cm cubes.

Ling thinks her skateboard is 58 cm long. Is she correct?

Sample: Ling is correct.

Show how you know. Sample: 50 cm + 8 cm = 58 cm

A 10 cm ruler is made up of 10 centimeters.

Five 10 cm rulers is the same length as 50 centimeters.

Eight 1 cm cubes is the same as 8 centimeters.

I can add 50 and 8 .

The skateboard is 58 cm long.

REMEMBER

3. Use the 10-sticks and cubes.

Draw the tens and ones.

I count the 10 -sticks and cubes. I see 3 sticks of ten cubes and 12 extra cubes.

4 tens 2 ones

42 total

I can make another group of 10 . I compose ten ones into a group of 10 .

Now I can draw 4 tens 2 ones.

I count the tens and ones to find the total.

Name

Each friend measures two ways.

1. Hope’s stapler is 15 cm long.

She uses 1 cm cubes.

She uses 10 cm ruler and 1 cm cubes.

2. Matt’s gift is 26 cm long.

He uses 1 cm cubes.

He uses 10 cm rulers and 1 cm cubes.

3. Ann measures her desk . She uses six 10 cm rulers and five 1 cm cubes.

Ann thinks her desk is 56 cm long.

Is she correct?

Show how you know.

REMEMBER

4. Use the 10-sticks and cubes. Draw the tens and ones.

tens ones

total

Name

Circle the tool you would use to measure each object.

1. The length around a balloon

1 cm cube 10 cm ruler meter stick measuring tape

I can measure objects shorter than 10 cm with a 1 cm cube or a 10 cm ruler.

I can measure round objects with a measuring tape.

I can measure large objects with a meter stick. A meter is 100 cm.

The balloon is round. I will use a measuring tape to measure the length around the balloon.

1 cm cube 10 cm ruler meter stick measuring tape

A peanut is shorter than a 10 cm ruler.

I can measure it with centimeter cubes.

1 cm cube 10 cm ruler meter stick measuring tape

A sofa is much longer than a 10 cm ruler.

I can measure it with a meter stick.

2 meters

2. The length of a peanut

3. The length of a sofa

Name

Circle the tool you would use to measure each object.

1. The length of a cracker

1 cm cube 10 cm ruler meter stick measuring tape

2. The length around a ball

1 cm cube 10 cm ruler meter stick measuring tape

3. The length of a car

1 cm cube 10 cm ruler meter stick measuring tape

1. Circle the true statements.

5 m is the same length as 500 cm.

2 cm is the same length as 200 m.

1 m is the same length as 10 cm.

3 m 14 cm is the same length as 314 cm.

I know that 1 m is 100 cm.

So, 5 m is 500 cm. This is true!

2 cm is much shorter than 200 m.

1 m is 100 cm, not 10 cm.

3 m is 300 cm, so 3 m 14 cm is the same length as 314 cm. This is true!

2. A table is 127 cm long.

How can you make 127 cm with these units?

1 100 cm (1 m) 2 10 cm 7 1 cm

1 100 cm (1 m) 27 1 cm

12 10 cm 7 1 cm

I know that 1 m is 100 cm.

127 cm is 100 cm + 20 cm + 7 cm.

127 cm is 100 cm + 27 cm.

127 cm is twelve 10 cm and 7 cm.

Metric Units Chart

REMEMBER

3. Shade the triangle.

I color the triangle to make a new shape. Then I trace the outside of the shape and count the sides.

Trace the new shape. 4 sides

What is the composed shape? rhombus

4. Add. Show how you know.

51 + 39 =

50 1 9

90 30

1 + 9 = 10 50 + 30 = 80

80 + 10 = 90

The composed shape has 4 sides that are the same length and 2 pairs of parallel sides.

It is a rhombus.

I can make the problem easier. I break apart both numbers into tens and ones.

51 is 50 and 1 39 is 30 and 9

I add the tens. I add the ones.

The new equation is 80 + 10 = 90

So, 51 + 39 = 90 .

1. Circle the true statements.

3 cm is the same length as 300 m.

2 m is the same length as 200 cm.

1 m 25 cm is the same length as 125 cm.

10 cm is the same length as 1 m.

2. A sofa is 192 cm long.

How can you make 192 cm with these units?

REMEMBER

3. Shade the triangles.

Trace the new shape. sides

What is the composed shape?

4. Add. Show how you know.

38 + 22 =

1. Measure with cubits Cubit . Then measure with palms . Sample:

2. Circle the true statement.

A cubit is the length from my fingertips to my elbow. I can use cubits to measure the shirt.

It will take more cubits Cubit than palms to measure the length of a bed.

It will take more palms than cubits Cubit to measure the length of a bed.

A palm is the width of my four fingers. I can use palms to measure the shirt again.

A palm is a smaller unit than a cubit.

It will take more palms than cubits to measure the length of a bed.

Name

1. Measure with cubits Cubit . Then measure with palms .

Object

Cubits Cubit Palms

2. Circle the true statement.

It will take more palms than cubits Cubit to measure the length of a bike .

It will take more cubits Cubit than palms to measure the length of a bike .

FAMILY MATH

Estimate, Measure, and Compare Lengths

Dear Family,

Your student is learning to make an estimate, or a thoughtful guess, for the length of familiar objects. They learn to draw tape diagrams to represent the difference between their estimate and the actual measurement. Then your student can use addition and subtraction number sentences to compare and solve.

My pinkie finger is about 1 cm. I can use that as a benchmark to estimate the length of a pencil.

At-Home Activities

Estimate in Meters

I can see the difference between 16 and 20 by comparing the tape diagrams.

Use the distance from the floor to a doorknob as a benchmark for 1 meter. With your student, find objects around the house that are about 1 meter, such as the length of a desk, the height

of a table, or the width of a window. Consider continuing the activity by looking for objects that are longer than 1 meter, such as the length of a sofa, length of a countertop, or the height of a door, and discuss the estimates.

Estimate and Measure in Centimeters

Knowing that the width of their pinkie finger is about 1 centimeter, have your student estimate the length of familiar objects, such as a fork or a marker. Then take turns estimating and then measuring the length of items, such as a shoe or a tissue box. Have your student find and explain the difference between the estimate and actual measurement.

Name

1. Estimate the length of the cracker . Then measure.

Sample:

Estimate: 4 cm

Measurement: 5 cm

I can use my pinkie finger as a benchmark. My pinkie . finger is about 1 cm wide.

I estimate the square cracker to be about 4 cm long.

I measure the length by using a 10 cm ruler.

The measurement of the cracker is 5 cm.

An estimate is a thoughtful guess. A benchmark is something I can use to estimate the length of an object.

2. Pick one of the objects you measured.

Show the difference in length between the estimate and the measurement.

Sample: 4 5

E M

The difference is 1 cm.

4 + 1 = 5

I pick the square cracker.

I draw a tape diagram to show my estimate and my measurement. 4 5

E M

4 is 1 less than 5 .

So, the difference is 1 .

REMEMBER 3. Draw and write a number sentence to compare. tens ones 2 0

tens ones 1 10 20 =

20

I look at the place value charts. I draw quick tens to show the numbers.

I see 2 tens 0 ones and 1 ten 10 ones.

I see a group of 10 ones. I can compose 10  ones into 1 ten.

I compare my drawings. =

I know 2 tens have a value of 20

The place value charts both represent 20

Name

Cut out the 10 cm ruler.

1. Estimate the length of each pencil . Then measure.

Estimate: cm

Measurement: cm

Estimate: cm

Measurement: cm

2. Pick one of the pencil s you measured. Show the difference in length between your estimate and the measurement.

The difference in length is cm.

3. Draw and write a number sentence to compare.

Name

1. Measure the object. Fill in the blank.

I estimate it is 10 cm long.

Measurement: 11 cm

To find the length of the envelope, I can use centimeter cubes or a 10 cm ruler.

The length of the envelope is 11 cm.

2. Show the difference in length two ways. Write an equation for each way. 10

10 + 1 = 11 11 -

The difference in length is 1 cm.

The difference is the distance between two lengths.

10 M 10 E 11

I can draw a tape diagram to compare the measurements.

The estimate is 10 cm. The measurement is 11 cm.

11 is 1 more than 10 .

The difference is 1 .

– 1 = 10 10 E 11 1 11

I can count on to show the difference.

I start with the part I know and count on to 11 .

10 + 1 = 11 11 20 E M

1 M 10 E 11 1 11 10 M

I can count back to show the difference.

I start at the total and count back to 10 .

10 is 1 less than 11

Name

1. Measure the object. Fill in the blank.

I estimate it is 5 cm long.

Measurement: cm

2. Show the difference in length two ways. Write an equation for each way.

The difference in length is cm

Name

1. How tall is each friend?

Friend Height Height (in centimeters)

1 meter stick

3 10 cm rulers

5 centimeter cubes

135 cm

Pam

1 meter stick

17 centimeter cubes

117 cm

Lan

I know that 1 m is 100 cm.

Three 10 cm rulers is 30 cm.

5 centimeter cubes is 5 cm.

100 + 30 + 5 = 135

Pam is 135 cm tall.

1 m is 100 cm and 17 centimeter cubes is 17 cm.

100 + 17 = 117

Lan is 117 cm tall.

2. Jade is 124 cm tall. How many of each do you need? 1 meter sticks 2 10 cm rulers 4 centimeter cubes

124 = 100 + 20 + 4

I know that 1 meter is 100 cm, so I can use 1 meter stick.

Two 10 cm rulers is 20 cm.

4 centimeter cubes is 4 cm.

3. Write another way to measure Jade’s height.

0 meter sticks 12 10 cm rulers 4 centimeter cubes

I know a meter stick is 100 cm.

I get 100 cm if I put ten 10 cm rulers together.

Two 10 cm rulers is 20 cm.

I add on 2 more 10 cm rulers.

Twelve 10 cm rulers is 120 cm.

4 centimeter cubes is 4 cm.

120 + 4 = 124

REMEMBER 4. Circle the word that matches the parts.

halves fourths

How many equal parts? 4

The cracker is partitioned into equal parts. I see 4 equal parts.

I know 4 equal parts is the same as fourths.

Name

1. How tall is each friend?

Friend

Height Height (in centimeters)

1 meter stick

2 10 cm rulers

8 centimeter cubes

Kevin

Kate

9 10 cm rulers

3 centimeter cubes

2. Nick is 112 cm tall. How many of each do you need?

meter sticks

10 cm rulers centimeter cubes

3. Write another way to measure Nick’s height.

meter sticks

10 cm rulers centimeter cubes

REMEMBER

4. Circle the word that matches the parts.

halves quarters

How many equal parts?

Name

Kevin and Jack are different heights.

K J

I can draw a tape diagram to represent the heights. 8

149 141 141 + 8 = 149

I show the difference by counting on. I start at 141 and count on to 149 149 is 8 more than 141

So, the difference is 8 cm.

Kevin 149 cm Jack 141 cm

1. Show the difference in height two ways. Write an equation for each way.

Name

Beth and Kate have different heights.

1. Show the difference in height two ways. Write an equation for each way.

The difference in height is cm.

FAMILY MATH

Solve Compare Problems by Using the Ruler as a Number Line

Dear Family,

Your student is learning to use a number line to add. They see a number line on a familiar tool—a measuring tape. The number line can help them count and make hops up and back as they solve problems. Your student looks for benchmark numbers (10, 20, 30, 40) on the number line. Benchmark numbers help your student add and subtract more efficiently.

Your student also uses tape diagrams to represent word problems. Flexibility is encouraged as they solve in a way that makes sense to them. Flexible thinking allows your student to notice the relationship between addition and subtraction and discover that different equations can be used to solve the same problem.

To add 76 and 7, begin at 76 on the number line.

Instead of counting by ones, hop 4 to get to the benchmark number 80.

Then hop 3 more to finish adding 7.

76 + 7 = 83

Choose to subtract or add to find the difference between 54 and 30.

To subtract, start at 54. Break apart 30 and count back.

To add, start at 30. Break apart 54 and count on.

At-Home Activity

Benchmark Math

Have your student practice using benchmark numbers to compare numbers. For example, “Use a benchmark number to find the difference between 26 and 33.” Your student can start at 26 and add 4 to get to 30 and then add 3 more to get to 33. Or they may show 4 fingers to add 4 all at once to get to 30 and then use their fingers to track counting on: 31, 32, 33. Your student may also draw a number line or tape diagram to show their thinking.

Name

1. Write the numbers on the number line.

A number line is a line with numbers and tick marks.

Each tick mark on this number line shows an equal length unit of 1

I know the numbers increase from left to right on the number line. So, I put the numbers in order from least to greatest.

43 48 50 55

I begin at 40 . I touch each tick mark as I count on to 43 . I label that tick mark 43

I touch each tick mark as I count on from 43 to 48 . I label that tick mark 48 .

I keep counting on to label the tick marks for 50 and 55 .

2. Use the number line to add.

I need to add 5 . I already added 2 . 2 and 3 is 5 . I hop 3 more from 40 to 43 .

The number line shows that 38 + 5 = 43 .

Name

Use the number line to subtract.

1. 56 – 8 = 48

I label 56 . I know 50 is a benchmark number close to 56 .

56 is 6 more than 50 . I hop back 6 to 50 .

I need to subtract 8 . I already subtracted 6

I know that 6 and 2 is 8

So, I hop back 2 more.

– 2 – 6

I land on 48 .

- 8 = 48

Name

1. How much farther does the big bee fly than the little bee?

Write an equation. 57 + 13 = 70

The big bee flies 13 cm farther than the little bee.

I can count on to find the difference between 57 and 70 .

I start at 57 . I can use 60 as a benchmark number. I hop 3 from 57 to 60 .

I hop 10 from 60 to 70 .

I know 10 and 3 is 13 .

2. How much farther does the blue butterfly fly than the green butterfly?

Write an equation.

181 – 14 = 167

The blue butterfly flies 14 cm farther than the green butterfly.

I can use subtraction to find the difference.

I draw a number line to find the difference between how far each butterfly flies.

I count back 1 from 181 to get to 180

I count back 10 from 180 to get to 170 .

I count back 3 more to 167 .

I subtracted 14 in all to get to 167 .

3. R ead

Hope has 13 tennis balls. Then she finds 5 more tennis balls.

How many tennis balls does Hope have now?

I read the problem. I read again. As I reread, I think about what I can draw.

I draw 13 solid dots to represent the tennis balls Hope has.

Then I can draw 5 open dots to represent the tennis balls she finds.

I’m trying to find how many tennis balls Hope has now.

I need to add 13 and 5 .

I see a group of ten. I can circle ten dots.

I know 3 + 5 = 8 and 10 + 8 = 18

I can write a number sentence to record my thinking. I add the ones first and then I add the ten.

Write 13 + 5 = 18

Hope has 18 tennis balls now.

Name

1. How much farther does the big bird go than the little bird ? Write

The big bird goes farther than the little bird .

2. How much farther does the squirrel jump than the grasshopper?

REMEMBER

Read

Tim sees 14 worms in the street.

He sees 5 worms in the grass.

How many worms does Tim see in all?

Draw

Write

Tim sees worms in all.

Name

Read

Matt rides 53 miles on a train.

Jill rides 26 miles on a bus.

How many more miles does Matt ride than Jill?

I read the problem.

I read again. As I reread, I think about what I can draw.

I draw a tape diagram.

I draw one tape to represent the miles Matt travels and one to represent the miles Jill travels

I know I need to find the difference between 53 and 26 . I can use benchmark numbers to count back.

I draw a number line.

I start at 53 and hop back 3 to get to 50 .

I hop back 20 more to get to 30 .

I hop back 4 more to get to 26 .

I hopped back 27 altogether.

Sample:

Matt rides 27 more miles than Jill.

Name

Read

Jack rides 41 miles in a car .

Beth rides 18 miles on a bike .

How many more miles does Jack ride than Beth?

Draw

Name

1. Read

Nick walks 64 steps.

Lee walks 40 steps.

How many more steps does Nick walk than Lee?

I read the problem.

I read again. As I reread, I think about what I can draw.

I draw a tape diagram to show Nick’s steps and Lee’s steps.

I can find the unknown number.

40

I start at 40 and count on to 64 .

40 + 20 = 60

60 + 4 = 64

REMEMBER

2. Read

Zan has 9 tokens. She gets some more tokens. Now she has 18 tokens.

How many more tokens did Zan get?

Draw

9

I read the whole problem. I read again. As I reread, I think about what I can draw.

Zan has 9 tokens. I draw 9 solid dots.

She gets some more tokens. Now she has 18 tokens.

I can draw open dots as I count from 9 to 18 to find the unknown part.

Sample:

Write 9 + 9 = 18

Zan got 9 tokens.

Name

1. Read

Tam has 55 blocks.

Kevin has 30 blocks.

How many more blocks does Tam have than Kevin?

Draw Write

Tam has more blocks than Kevin.

REMEMBER

2. Read

Dan has 7 stamps. He gets some more stamps.

Now he has 15 stamps.

How many more stamps did Dan get?

FAMILY MATH Understand Place Value Units

Dear Family,

Your student is exploring place value units (ones, tens, hundreds) as they bundle, or group together, craft sticks. They notice bundling makes it easier to count and keep track of numbers. For example, 10 of a smaller unit can be bundled to make 1 of the next larger unit. Your student also applies place value knowledge and drawings of bundles to solve addition problems. They use benchmark numbers, such as 10 or 100, to help count and record collections of objects efficiently.

Key Terms

The value of one craft stick is 1. The value of 10 ones is 1 ten, or 10. The value of 10 tens is 1 hundred, or 100. The value of 10 hundreds is 1 thousand, or 1,000.

At-Home Activities

Scavenger Hunt

Benchmark numbers make counting from 160 to 312 more efficient. Drawing sticks and bundles of 10 and 100 helps keep track of the count.

I can start at 64 and hop up to 100. I count the hops to find the unknown part.

Help your student make a list of numbers greater than 100 that they find around the house, such as the pages of a book, the oven temperature in a recipe, the quantity on a box of tissues or cotton swabs, or the number of grams on a package of food (such as a cereal box or can

of soup). After your student creates a list of numbers, have them represent each number by drawing sticks and bundles of tens and hundreds.

How Much Older Are You?

Have your student determine the difference between their age and your age. Consider asking them to draw individual sticks for ones and bundles for tens as they count on from their age. When they reach your age, ask your student to count the sticks and bundles they drew to determine the age difference. Repeat with another person’s age.

2 hundreds 4 tens 2 ones

The value of something is what it’s worth or what it represents.

I count 2 bundles of hundred.

I count 4 bundles of ten.

I count 2 ones.

The value of this bundle is 1 hundred.

This value of this bundle is 1 ten.

The value of this single stick is 1 .

A single stick is 1 one.

10 ones can be bundled to make 1 ten. A ten is the next larger unit after ones.

10 tens can be bundled to make 1 hundred. A hundred is the next larger unit after tens.

10 hundreds make 1 thousand. A thousand is the next larger unit after hundreds.

Name

1. Fill in the blanks to match the picture.

2. Draw hundreds, tens, and ones. 952

I draw bundles and sticks to show the value of each place value unit.

I draw 9 hundreds.

I draw 5 tens.

I draw 2 ones.

Name 20

Fill in the blanks to match the picture.

1. hundred tens ones

2.

hundreds tens ones hundreds tens ones hundreds tens ones hundreds tens hundreds tens ones

Draw hundreds, tens, and ones.

hundred tens

hundred tens ones

hundred tens

3. 262

4. 509

5. 394

6. 815

2. Draw units to count from 222 to 600. Sample:

Next, I draw ones to 230 .

Then, I draw tens to 300

Last, I draw hundreds to 600

REMEMBER Circle the tool you would use to measure each object.

3. The length of a dollar bill

1 cm cube 10 cm ruler meter stick measuring tape

4. The length of a grasshopper

1 cm cube 10 cm ruler meter stick measuring tape

5. The length around a basketball

1 cm cube 10 cm ruler meter stick measuring tape

6. The length of a horse

1 cm cube 10 cm ruler meter stick measuring tape

I use a centimeter cube to measure things that are very small.

I know that ten 1 cm cubes are the same length as one 10 cm ruler.

I know that using a ruler is faster than using ten cubes.

I know that a meter stick is 1 meter.

1 meter is 100 centimeters.

I use a measuring tape to measure things that are round.

Name

1. Draw units to count from 112 to 200.

2. Draw units to count from 476 to 800.

REMEMBER Circle the tool you would use to measure each object.

3. The length of a turtle

1 cm cube 10 cm ruler meter stick measuring tape

4. The length around a soccer ball

1 cm cube 10 cm ruler meter stick measuring tape

5. The length of a fly 1 cm cube 10 cm ruler meter stick measuring tape

6. The length of a skateboard

1 cm cube 10 cm ruler meter stick measuring tape

Name

1. R ead

Nick has 34 stamps. He wants 110 stamps.

How many more stamps does Nick need? Draw Write 34 + 76 = 110

Nick needs 76 more stamps.

I read the problem. I read again. As I reread, I think about what I can draw.

I know the total is 110 and one part is 34 . I need to find the other part.

I draw a number line. I start at 34 and count on to 110 to find the unknown part.

I count by ones until I reach 40 . Then I count by tens until I reach 110 .

I counted on 76 .

76 is the unknown part.

First, I draw 326 .

Next, I draw 4 ones to get to 330 .

Then, I draw 7 tens to get to 400 .

Then, I draw 3 hundreds to get to 700 .

Last, I draw 5 tens to get to 750 .

2. Draw units to count from 326 to 750.

Name

1. Read

Kate baked 52 muffins.

She needs 110 muffins.

How many more muffins does Kate need?

Draw

Write

Kate needs more muffins.

2. Draw units to count from 578 to 920.

1. Find the unknown part. Show how you know.

I add 6 to 74 because I know 4 + 6 = 10 . So, 74 and 6 make the next ten, 80

I add 20 to 80 because I know

8 + 2 = 10 . So, 80 + 20 = 100

I add 6 and 20 to 74

The unknown part is 26

6 + 20 = 26

2. Ren and Nate have different heights. Show the difference in height two ways. Write an equation for each way. Ren 148 cm Nate 141 cm

I represent Ren and Nate’s height with a tape diagram.

I represent Ren and Nate’s height with a tape diagram.

I count on from 141 until I get to 148 . I count on 7 .

I subtract to make the tapes the same.

I count back from 148 until I reach 141 . I counted back 7 .

I write an equation.

The difference in height is 7 cm.

I write an equation. 148 – 7 = 141

Name

REMEMBER

1. Find the unknown part. Show how you know. 58 + = 100

2. Beth and Jill have different heights. Show the difference in height two ways. Write an equation for each way.

The difference in height is cm.

Express Three-Digit Numbers in Different Forms

Dear Family,

Your student is reading, writing, and counting numbers up to 1,000. They learn that 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits. The placement of a digit in a number tells us how much the digit is worth. To help them understand the meaning of the digits, your student learns to write numbers in different forms, including word form, expanded form, and unit form. This understanding helps them to see that place value gives meaning to numbers and builds a strong foundation that will extend to work with decimal numbers.

Key Terms

The digits 1, 2, and 5 make up the number 125. The digit 1 has a value of 100. The digit 2 has a value of 20. The digit 5 has a value of 5.

The order of the addends does not change the total value.

At-Home Activity Numbers in Your World

Have your student think about a familiar three-digit number or look for a three-digit number around their home. For example, your student may think about their home address or area

code, or they may find a three-digit number on a food label. Ask your student to tell you how many hundreds, tens, and ones are in each number. Then ask questions to help them compare the value of each digit.

• “What is the value of the 2 in the number?”

• “Do any digits repeat? What is the value of each digit?”

• “Which digit has the greatest value? What is the value of that digit?”

I use ones, tens, and hundreds to count from 76 to 400

76 is close to the benchmark number 80 . I count by ones to 80 .

80 is close to the benchmark number 100 . I count by tens to 100 .

Digits are the numerals we use to write numbers. 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 are digits.

For the number 76 , the digit 7 is in the tens place, so its value is 70 . The digit 6 is in the ones place, so its value is 6 .

Then I count by hundreds to 400 .

Name

1. Count from 84 to 300.

hundreds tens ones

2. Count from 685 to 920.

hundreds tens ones

Name

Show the hundreds, tens, and ones. Then write the unit form.

1.

216

200

216

6

10

Unit form: 2 hundreds 1 ten 6 ones

A number in standard form is written only with digits, or numerals. The number 216 is in standard form.

Unit form tells how many of each place value unit. The unit form for 216 is 2 hundreds 1 ten 6 ones.

2. Ann has $350 in $100 and $10 bills.

How many $100 and $10 bills could Ann have?

Show one way.

Sample:

100 100 100 10 10 10 10 10

3 $100 bills

5 $10 bills

Ann has $350 .

3 hundreds

5 tens

I use what I know about place value to find the value of each digit.

The 3 is in the hundreds place, so the value of the 3 is 300 . I draw three $100 bills.

The 5 is in the tens place, so the value of the 5 is 50 . I draw five $10 bills.

REMEMBER

3. Make 10 to add. Show how you know.

9 + 5 = 14

Write a new number sentence.

9 + 1 + 4 = 14

I can draw dots to represent 9 + 5

I draw 9 solid dots and 5 open dots.

I can move 1 open dot to make 10

This helps me write a new number sentence.

9 and 1 make 10 . Then I add 4 more.

9 + 1 + 4 = 14

Name

Show the hundreds, tens, and ones.

Then write the unit form.

1.

385

385

Unit form: hundreds tens ones

2. Matt has $320 in $100 and $10 bills. How many $100 and $10 bills could Matt have?

Show one way.

$100 bills

$10 bills

3. Make 10 to add. Show how you know. 7 + 6 =

Write a new number sentence.

Name

1. Write in expanded form.

234 =

Expanded form shows a number written as an addition expression. Each addend represents the value of a digit.

200 + 30 + 4

To write a number in expanded form, I can say it in unit form to help me.

234 is 2 hundreds 3 tens 4 ones. I add the value of each unit.

200 + 30 + 4

Expanded form: 200 + 30 + 4

2. Write in standard form.

60 + 500 + 4 = 564

When I write a number in standard form, I write the units in order from greatest to least: hundreds, tens, and ones.

I write a 5 in the hundreds place to represent 500 .

I write a 6 in the tens place to represent 60 .

Then I write a 4 in the ones place to represent 4

Name

1. Write in expanded form.

452 = 245 = 205 = 250 =

2. Write in standard form.

400 + 30 + 1 =

40 + 1 + 300 = 600 + 7 = 60 + 700 =

Name

1. Write the number in word form. Use the word bank.

nine hundred six eight hundred thirty one hundred sixty-five

165 830 906

one hundred sixty-five eight hundred thirty nine hundred six A number in word form is written with words only. I can use the word bank to help me. 906 is nine hundred six.

2. Write 417 in each form.

Word form:

Unit form:

Expanded form:

four hundred seventeen 4 hundreds 1 ten 7 ones

400 + 10 + 7

417 is in standard form.

When I write word form, I write the words.

When I write in unit form, I write how many of each unit.

When I write in expanded form, I write an addition expression.

3. Make 10 to add. Show how you know.

There are 2 muffins in the first case. There are 4 muffins in the second case.

I count 6 muffins in the third case.

I know that 4 and 6 make 10 , so I add them first.

Then I add 2 and 10 .

4. Add. Show how you know.

46 + 7 = 53

I can make a 10 to add.

50 is the next 10 after 46 . 46 needs 4 more ones to make 50 I can break apart

7 into 4 and 3

46 + 7 3

4

Then I can make 50 .

Now I add 50 and 3 to find the total.

46 + 4 + 3 50 + 3 = 53

2. Write 784 in these forms. Word form: Unit form: Expanded form:

3. Make 10 to add. Show how you know.

4. Add. Show how you know. 27

FAMILY MATH Model Base-Ten Numbers Within 1,000 with Money

Dear Family,

Key Term exchange

Your student continues to explore place value by using paper $1, $10, and $100 bills to represent ones, tens, and hundreds. They exchange 10 of a smaller value bill for 1 of the next larger value bill and they see how the same amount of money can be represented in different ways. Your student counts by $1, $10, and $100 bills and shows their counts on an open number line. They also solve word problems involving money and choose a strategy that makes sense to them.

This open number line shows skip-counting from 776 to 900 with one hop of 4, two hops of 10, and one hop of 100.

At-Home Activities

Shopping Trip

Pretend you and your student are going to buy something to donate to the local animal shelter. Use play money, or make $1, $10, and $100 bills with scraps of paper. Gather some of each type of bill (such as 15 one-dollar bills, 6 ten-dollar bills, and 2 hundred-dollar bills), and have your student figure out the total amount. Have them exchange some bills if they need to. You can both take some bills and exchange as needed to make one amount. Together, think about what you might buy with that amount.

Step, Hop, Skip to 1,000

With your student, practice skip-counting by ones, tens, and hundreds. Pick any three-digit number, such as your area code or street address. Act out the skip-counting by taking small steps to represent counting by ones, larger steps to represent counting by tens, and jumps to represent counting by hundreds.

• Let’s start at 776. Take 4 small steps (777, 778, 779, 780). Then take 2 large steps (790, 800). Then jump 2 times (900, 1,000).

I can show $100 with 1  hundred-dollar bill or 10 ten-dollar bills.

I can show $10 with 1 ten-dollar bill or 10  one-dollar bills.

1. Draw bills for $121. Draw two ways.

Exchange

means trade one thing for another that has equal value.

Name

1. Draw bills for $210.

2. Draw bills for $212. Draw two ways.

I label 378 on the open number line. I count by ones to the nearest ten: 379 , 380 . I draw and label the hops.

I count by tens to the nearest hundred: 390 , 400 . I draw and label the hops.

I count by hundreds: 500 , 600 , 700 . I draw and label the hops.

2. Use the number line to subtract.

54 – 6 = 48

3. Read Beth has 8 pretzels Peg has 6 pretzels.

How many pretzels do Beth and Peg have in all?

I start at 54 on the number line.

I hop back 4 to 50

Then I hop back 2 more to 48

I read the problem. I read again.

As I reread, I think about what I can draw.

I draw 8 dots for the pretzels Beth has.

I draw 6 dots for the pretzels Peg has.

The total is unknown. I make 10 to add.

Write Beth and Peg have 14 pretzels in all.

Name

Count by ones, tens, and hundreds.

1. 200 to 830

2. 447 to 600

3. 500 to 744

REMEMBER

4. Use the number line to subtract.

63 – 9 =

5. Read Ling has 9 T-shirts. Sal has 6 T-shirts.

How many T-shirts do Ling and Sal have in all?

Write Ling and Sal have T-shirts in all.

Name

1. How many more $100 bills make $1,000?

Show how you know. $100 $100 $100 $100 $100 $100 $100 $100 100 100

I know there are 10 hundreds in 1 , 000

I count 8 groups of $100 I know that is $800

I need 2 more groups of $100 to make $1 , 000

2 more $100 bills make $1,000.

2. How many more $10 bills make $1,000? Show how you know. Sample: $100 $100 $100 $100 $100 $100 $100 $100

100 100

= 10 tens = 10 tens 10 + 10 = 20

20 more $10 bills make $1,000.

I know I need 2 more groups of $100 . There are 10 tens in 100 . 100 100

I have 2 groups of 10 bundles of ten.

I know 2 groups of 10 is 20

I need 20 more $10 bills to make $1 , 000

Name

1. How many more $100 bills make $1,000? Show how you know.

$100 $100 $100 $100 $100 $100

$100 more $100 bills make $1,000.

2. How many more $10 bills make $1,000? Show how you know. $100 $100 $100 $100 $100 $100 $100 more $10 bills make $1,000.

FAMILY MATH

Compose and Decompose with Place Value Disks

Dear Family,

Key Term

Your student is using place value disks to represent numbers up to 1,000. They exchange disks and rename numbers by using unit form. Flexibly naming numbers sets the foundation for adding larger numbers when there are more than 9 of a unit and for subtracting larger numbers when there are not enough of one unit to subtract. They can also draw place value disks as dots on a place value chart. The value of each dot is based on which column it is in. Representing numbers with place value disks helps your student now, as they learn to add and subtract, and later when they learn to multiply and divide.

Bundles, bills, and place value disks represent numbers. All three representations develop an understanding of the units in the place value system.

At-Home Activities

Drawing Dots

Place value disks are similar to bills. The value of the disk is written on the disk. 512 is shown as 5 hundreds 1 ten 2 ones.

10 ones is exchanged for 1 ten. 2 hundreds 4 tens 17 ones is renamed as 2 hundreds 5 tens 7 ones.

Write a three-digit number such as your area code or a street address. Help your student create a place value chart on paper with three columns labeled “100s”, “10s”, and “1s” from left to right. Help them represent the number on the chart by drawing dots in the correct columns.

Bundle and Exchange Names

Use the table that shows a number for each letter. Have your student find the numbers that go with the initials of their first, middle, and last names. For example, the initials J, R, and M go with the numbers 10, 18, and 13. Create a place value chart and place dots in the correct columns for those amounts. Exchange disks as needed to say the total as a number. Repeat the activity with other names or initials.

Name

Write the number in expanded form. Then write it in standard form.

Expanded form: 90 + 2

Standard form: 92

I count 9 tens disks. That’s 90

I count 2 ones disks. That’s 2 .

I write 90 + 2 to show expanded form.

I know 90 + 2 is equal to 92 .

The standard form is 92 .

REMEMBER

2. Make a picture graph.

Insects We Like

Ants

4 2 7 9

I read the title of the table.

I write “Insects We Like” as the title of my picture graph.

I write the categories at the bottom of the graph.

I use the same categories as the table.

Insects We Like

Key: Each stands for vote. ✓ 1

I know each ✓ stands for 1 vote.

I read the key and add my data. Ants has 4 votes. I put 4 ✓ above Ants.

Bees has 2 votes. I put 2 ✓ above Bees.

Ladybugs has 7 votes. I put 7 ✓ above Ladybugs.

Butterflies has 9 votes. I put 9 ✓ above Butterflies.

Ladybugs Butterflies

Bees

3. Make a picture graph.

Fruit We Like

Apples Bananas

Blueberries

9 4 5 8

Grapes

Key: Each stands for vote.

How many more ones make a new ten? 4 ones

What is the new number? 550

I need 4 more ones disks to make a ten.

I exchange 10 ones for 1 ten.

Now there are 5 hundreds disks and 5 tens disks. The new number is 550

How many more tens make a new hundred? 5 tens

What is the new number? 800

I need 5 more tens disks to make a hundred.

I exchange 10 tens for 1 hundred.

Now there are 8 hundreds disks. The new number is 800

How many more ones make a new ten? ones

What is the new number?

How many more tens make a new hundred? tens

What is the new number?

Name

1. Draw 521 with hundreds, tens, and ones.

10s 1s 100s

I draw dots on the place value chart to represent the units.

10s 1s 100s

I know 521 is 5 hundreds 2  tens 1 one.

Draw 521 with only hundreds and ones.

10s 1s 100s

To use only hundreds and ones to show 521 , I can rename 2 tens as 20 ones.

10s 1s 100s

When we make an exchange or unbundle a unit, we rename it with a different unit. The total stays the same.

Now I have 5 hundreds 21 ones.

Shortest

I see the items are lined up by their endpoints. I can compare the heights.

Tallest

I know the pinwheel is the shortest because all the other things are taller. I write the letter P first.

The water bottle is next. It is taller than the pinwheel but shorter than the trophy. I write the letter W.

The trophy is last because it is the tallest item. I write the letter T.

2. Put in order from shortest to tallest

3. Circle the shapes with square corners .

A square fits perfectly in a square corner.

Squares fit perfectly in the corners of the rectangle and the square.

Squares do not fit perfectly in the corners of the other shapes.

So, only the rectangle and the square have square corners.

Name

1. Draw 27 with tens and ones. 10s 1s 100s

Draw 27 with only ones. 10s 1s 100s

2. Draw 419 with hundreds, tens, and ones. 10s 1s 100s

Draw 419 with only hundreds and ones. 10s 1s 100s

3. Put in order from shortest to tallest . Shortest Tallest

4. Circle the shapes with square corners .

Name

1. Draw on the place value chart.

Rename 10 ones as 1 ten.

5 hundreds 7 tens 17 ones

10s1s 100s

hundreds 5 tens 8 ones 7 Then write in unit form.

5 hundreds 8 tens 7 ones

I draw 5 dots in the hundreds place and 7 dots in the tens place. Then I draw 17 dots in the ones place.

I circle 10 ones to show that I can rename 10 ones as 1 ten. I draw an arrow to the tens place. I add another dot there.

Now there are 5 hundreds, 8 tens, and 7 ones.

2. Draw on the place value chart.

Rename.

2 hundreds 1 ten 15 ones

10s1s 100s

Standard form: 225

Then write in standard form.

Standard form: 225

I draw 2 dots in the hundreds place. I draw 1 dot in the tens place. I draw 15 dots in the ones place.

I can rename 10 ones as 1 ten. I circle 10 ones. I draw an arrow to the 10 s place. I add another dot there.

Now there are 2 hundreds, 2 tens, and 5 ones.

Name

1. Draw on the place value chart.

Rename 10 ones as 1 ten.

2 hundreds 3 tens 13 ones 10s 1s 100s

hundreds tens ones Then write in unit form.

hundreds tens ones

2. Draw on the place value chart.

Rename.

4 hundreds 16 tens 5 ones 10s 1s 100s

Standard form: Then write in standard form.

Standard form:

FAMILY MATH

Compare Two Three-Digit Numbers in Different Forms

Dear Family,

Your student is learning to use place value to compare three-digit numbers. Students draw on a place value chart and use their place value understanding to help them explain why one number is greater than or less than another number. Your student uses the greater than (>), equal to (=), and less than (<) symbols to write comparison statements.

427 and 472 have the same digits but different values.

Both have a 4 in the hundreds place.

427 has a 2 in the tens place and 472 has a 7 in the tens place.

20 is less than 70, so 427 is less than 472.

427 < 472

At-Home Activities Around the House

3 hundreds 1 ten 14 ones and 3 hundreds 24 ones each have more than 9 ones.

When the ones are renamed with the next largest unit (tens), the numbers have the same digits in the same places.

324 = 324

Build three-digit numbers with your student by using household items to represent the different values. For example, a plate represents a hundred, a bowl represents a ten, and a spoon represents one. Take turns selecting objects to build a number. Then ask your student to rename and compare the numbers represented.

• “Here are 2 plates, 2 bowls, and 3 spoons. What number is represented by these objects?”

• “Here are 5 more spoons. What number is represented now?”

• “How can you rename that amount a different way?”

• “Which number is greater than (or less than) the other number? How do you know?”

Phone Number

Write each digit from a seven-digit phone number on separate slips of paper. Invite your student to pick three paper slips. Have them rearrange the three slips to make the smallest three-digit number they can make. Choose three slips from the remaining paper slips and arrange yours to make the smallest possible three-digit number. Discuss which of you has the smaller number and how they can tell. Then you both rearrange your paper slips to make the greatest possible three-digit number. Ask your student which number is greater than (or less than) the other number and how they know.

Draw the number on the place value chart.

Then circle >, =, or < to compare.

I draw 3 hundreds, 8 tens, and 2 ones for 382 .

I draw 3 hundreds, 4 tens, and 9 ones for 349 .

I compare the hundreds. Both numbers have 3 hundreds.

I compare the tens.

382 has 8 tens, and 349 has 4 tens.

100s10s1s

100s10s1s

I know 8 tens is greater than, or more than, 4 tens.

382 is greater than 349 .

1. 382 349

100s1s10s 100s1s10s

Write >, =, or < to compare.

2. 129 < 133

3. 308 = three hundred eight

I can use place value charts to compare.

100s 10s 1s 129

I know that 308 has 3 hundreds, 0 tens, and 8 ones.

When I read 308 , I say “three hundred eight.”

I know they are equal.

100s 10s 1s 133

I look at the hundreds place first, then tens, then ones. Both numbers have 1 hundred.

129 has 2 tens and 133 has 3  tens.

I know 2 tens is less than 3 tens, so 129 is less than 133 .

REMEMBER

The first hexagon is made of 2 trapezoids.

The second hexagon is made of 2 triangles and 2 rhombuses.

The hexagon made with 2 trapezoids is made with fewer blocks.

I see one 10 -centimeter stick.

I see 2 extra centimeter cubes.

I know 10 + 2 = 12 .

The pencil is 12 cm long.

4. Circle the hexagon made with fewer blocks.

5. Kevin measures a pencil.

Draw the number on the place value chart.

Then circle >, =, or < to compare. 1.

3. 223 two hundred twenty-three

REMEMBER

4. Circle the trapezoid made with fewer blocks.

Write the length.

5. Ling measures a frog.

Name

1. Draw each number on the place value chart. Then write >, =, or < to compare.

I draw 3 hundreds 17 ones in the first chart. I rename 17 ones as 1 ten 7 ones.

I draw 3 hundreds 7 tens 1 one for 371 in the next chart.

I compare the hundreds. Both numbers have 3 hundreds.

I compare the tens. 3 hundred 17 ones has 1 ten, and 371 has 7 tens.

So, 3 hundred 17 ones is less than 371

Write >, =, or < to compare.

2. 752 > five hundred seventy-two

I can use place value charts to compare.

I show 7 hundreds 5 tens 2 ones for 752 .

Five hundred seventy-two has 5 hundreds 7 tens 2 ones. 100s 10s 1s 100s 10s 1s

I compare the hundreds.

752 has 7 hundreds, and five hundred seventy-two has 5 hundreds.

7 hundreds is greater than 5 hundreds.

So, 752 > five hundred seventy-two.

3. 834 = 30 + 800 + 4

I know 834 is the same as 8 hundreds 3 tens 4 ones.

I know 30 + 800 + 4 is the same as 3 tens 8 hundreds 4 ones.

I can use place value charts to compare.

100s 10s 1s 100s 10s 1s

The hundreds, tens, and ones are the same for both numbers.

So, 834 = 30 + 800 + 4 .

Name

1. Draw each number on the place value chart. Then write >, =, or < to compare.

591

100s10s1s

591 5 hundreds 19 ones

100s10s1s 5 hundreds 19 ones Write >,

2. 467 60 + 400 + 7

3. 705 seven hundred fifty

Name

Read

Pam’s pet rat is 5 cm long.

Lan’s pet rat is 10 cm longer than Pam’s rat

How long is Lan’s pet rat?

Sample:

Lan’s pet rat is 15 cm long.

I read the problem.

I read again. As I reread, I think about what I can draw.

I notice the cubes look like a tape diagram. I draw a tape diagram to match the cubes.

Pat’s tape has 5 cubes. Lan’s tape has 5 cubes and a 10 -centimeter stick.

I count the centimeter stick and cubes to find how long Lan’s pet rat is.

Read

Ann’s lizard is 9 cm long.

Nick’s lizard is 10 cm longer than Ann’s lizard.

How long is Nick’s lizard?

Nick’s lizard is cm long.

Write the numbers from least to greatest. Use standard form.

three hundred twenty

First, I write each number in standard form. 338 three hundred twenty 1 + 90 + 400 320 491

I can use place value charts to compare 338 , 320 , and 491 .

491 is the greatest number because it has 4 hundreds.

338 and 320 both have 3 hundreds.

338 has 3 tens, and 320 only has 2 tens.

So, 320 < 338 .

From least to greatest, the numbers are 320 , 338 , 491 .

Write the numbers from greatest to least. Use standard form.

I write each number in standard form. 2 hundreds 14 ones

I can use place value charts to compare 214 , 263 , and 255 .

All the numbers have 2 hundreds.

214 has 1 ten, 263 has 6 tens, and 255 has 5 tens.

So, I know 263 is the greatest number.

I also know that 255 > 214

From greatest to least, the numbers are 263 , 255 , 214

Write the numbers from least to greatest. Use standard form.

1. 432 871 650 , ,

2. 529 four hundred fifty-one

5 + 400 + 30 , ,

Write the numbers from greatest to least. Use standard form.

3. 47 tens 4 ones

3 + 80 + 400

three hundred eight , ,

4. 711

7 hundreds 15 ones

9 + 10 + 700 , ,

Acknowledgments

Beth Barnes, Dawn Burns, Karla Childs, Mary Christensen-Cooper, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Lacy Endo-Peery, Krysta Gibbs, Melanie Gutierrez, Torrie K. Guzzetta, Eddie Hampton, Andrea Hart, Sara Hunt, Rachel Hylton, Travis Jones, Jennifer Koepp Neeley, Liz Krisher, Leticia Lemus, Marie Libassi-Behr, Ben McCarty, Cristina Metcalf, Ashley Meyer, Bruce Myers, Marya Myers, Maximilian Peiler-Burrows, Marlene Pineda, Carolyn Potts, Meri Robie-Craven, Colleen Sheeron-Laurie, Robyn Sorenson, Tara Stewart, Theresa Streeter, James Tanton, Julia Tessler, Philippa Walker, Rachael Waltke, Lisa Watts Lawton, MaryJo Wieland

Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

Credits

For a complete list of credits, visit http://eurmath.link/media-credits

MATH IS EVERYWHERE

Do you want to compare how fast you and your friends can run?

Or estimate how many bees are in a hive?

Or calculate your batting average?

Math lies behind so many of life’s wonders, puzzles, and plans. From ancient times to today, we have used math to construct pyramids, sail the seas, build skyscrapers—and even send spacecraft to Mars.

Fueled by your curiosity to understand the world, math will propel you down any path you choose.

Ready to get started?

ISBN 978-1-64497-642-5

Module 1

Place Value Concepts Through Metric Measurement and Data • Place Value, Counting, and Comparing Within 1,000

Module 2

Addition and Subtraction

Within 200

Module 3

Shapes and Time with Fraction

Concepts

Module 4

Addition and Subtraction

Within 1,000

Module 5

Money, Data, and Customary Measurement

Module 6

Multiplication and Division Foundations

What does this painting have to do with math?

The bold brushstrokes and vivid colors in Maurice Prendergast’s painting invite us to step inside this lively street scene in Venice, Italy. A group of ladies with parasols is crossing a bridge. Getting lost in a crowd can be intimidating, but as we learn about base ten, counting large numbers—of people, parasols, or anything—will be a breeze.

On the cover

Ponte della Paglia, 1898–1899; completed 1922 Maurice Prendergast, American, 1858–1924 Oil on canvas

The Phillips Collection, Washington, DC, USA

Maurice Prendergast (1858–1924), Ponte della Paglia, ca. 1898/reworked 1922. Oil on canvas. The Phillips Collection, Washington, DC, USA. Acquired 1922.