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A Story of Units® Units of Ten

Module 1 ▸ Counting, Comparison, and Addition

Module 1 Counting, Comparison, and Addition

2 Addition and Subtraction Relationships

3 Properties of Operations to Make Easier Problems

4 Comparison and Composition of Length Measurements

5 Place Value Concepts to Compare, Add, and Subtract

6 Attributes of Shapes · Advancing Place Value, Addition, and Subtraction

FAMILY MATH Count and Compare with Data

Dear Family,

Your student is using graphs to organize, represent, and interpret data. They collect data by counting various things. Then they represent, or show, the data in different graphs and charts. Your student is also interpreting graphs and charts by comparing the categories. They use the greater than (>) and less than (<) symbols to write comparison number sentences.

Key Terms and Symbols graph greater than symbol > less than symbol < represent

fewer

than

Tally Chart

Animals We See

7

The number of squirrels is the same as the number of frogs.

There are more birds than squirrels. 7 is greater than 2.

7 > 2

There are

frogs

birds. 2 is less than 7.

2 < 7

2 is equal to 2.

2 = 2

At-Home Activities

Organize and Compare

Prepare a disorganized pile of two or three types of objects, like forks and spoons. Ask your student to predict whether there are more of one object or the other. Then, have your student line up the objects in separate rows and count the number in each row to check their prediction. Encourage your student to use comparison statements like the following examples to describe the relationship between the groups.

• “There are 4 spoons and 7 forks. 4 is less than 7. There are fewer spoons than forks.”

• “There are 4 spoons and 4 forks. 4 is equal to 4. There is an equal number of forks and spoons.”

Make a Graph

Collect data about objects around you, such as the number of buttons, pockets, and zippers on your clothing or your student’s clothing. Invite them to graph the data by creating a picture graph or tally chart. The graph can help your student to organize and compare the data. Help your student analyze the data by asking the following questions.

• “How many buttons are on your clothes? How many pockets are on your clothes?”

• “Do you have more buttons or more pockets? How do you know?”

1. Color to show how many hats.

I can mark the hats to help me count.

There are 5 hats so I color to the number 5 .

2. Color to show how many apples .

I can count the 4 apples.

I color to the number 4

3. Circle the number path that shows more.

There are more hats than apples.

5 is greater than 4 .

I circle the number path that shows 5 .

REMEMBER

4. There are 5 pencils in a cup.

Tam takes 1 out.

How many pencils are in the cup now?

I read the problem.

I see 5 pencils in the cup. Tam takes 1 pencil out, so I cross off 1 pencil.

I count 4 pencils in the cup now.

There are 4 pencils in the cup now.

1. Color to show how many bees.

Color to show how many ants.

REMEMBER

2. There are 9 bees.

4 fly away.

How many bees are left?

There are bees left.

Write the totals.

Pets We Like Totals

Write two totals.

14 > 10

greater than

A graph is a way of organizing and representing, or showing, information so that we can ask and answer questions.

This graph shows how many people like each pet.

14 is the total for cats.

10 is the total for dogs.

The graph shows more people like cats. I circle the cat.

I know 14 is greater than 10 . 14 > 10

1. Color to show how many. Write the totals.

I can count each animal.

There are 5 ducks.

There are 11 cats.

There are 4 dogs.

I color the graph and write the totals.

Circle the true sentences.

There are more than .

There are more than .

There are more than .

There are more cats than ducks.

The graph for cats has more shaded squares than the graph for ducks.

11 is greater than 5 11 > 5

There are more ducks than dogs.

5 is greater than 4 . 5 > 4

There are not more ducks than cats.

I did not circle this one because it is not true.

REMEMBER

2. Count up by ones. Write the numbers.

46

47

48

I start counting at 46 I count by ones.

I count 46 , 47 , 48 and write the missing numbers.

3

Name

1. Color to show how many.

Write the totals.

Animal Count

Totals

Circle the true sentences.

There are more than .

There are more than .

There are more than .

REMEMBER

2. Count up by ones. Write the numbers. 36

There are 17 flowers total.

Each check mark means 1 flower.

I count the check marks and write the totals.

I can count all the check marks to find the total number of flowers.

There are 17 flowers.

Write two totals. Sample:

8 > 3

greater than

There are more sunflowers than roses.

8 is greater than 3

Name 4

Write the totals.

Animals We See

Totals

There are animals total. Write two totals. =

equal to

Name

REMEMBER 1. Circle 10 birds.

Write the total.

I count and circle 10 birds. There are 10 birds in a group. 10  birds are one part.

There are 6 birds in a group. 6 birds are the other part. 16

10 6

10 and 6 make ten 6 , or 16 .

2.

Count up by ones. Write the numbers.

I start counting by ones at 17 . I write the numbers that come next.

The numbers I write are 1 more than the number that came before.

1. Circle 10 balls. Write the total.

2. Count up by ones. Write the numbers.

Write the totals.

Classes We Like 5

7 Art

P.E.

I count all the tally marks starting at the group of 5. 5 6 7 I write the total.

Fewer students like art than like P.E. .

Write two totals.

5 < 7

less than

I look at the chart.

I see 7 students like P.E. and 5 students like art.

5 is less than 7 .

Name 6

Write the totals.

Pets We Have

Cats

Fish

There are fewer than . Write two totals.

<

less than

FAMILY MATH

Count On from a Visible Part

Dear Family,

Key Terms

doubles

unknown

Your student is practicing the addition strategy of counting on from a known part to find the total. For example, the dice in the images show two parts, 5 and 2. Rather than counting all the dots, they start with a part they know and count on from that number to find the total. As they count on, they may point to the dots or use their fingers to keep track of the counts. Starting with the larger part, such as 5, is more efficient, but your student discovers that counting on from either part results in the same total. Your student learns that the number we are trying to figure out is called the unknown, and that when both parts are the same number, they are called doubles.

Fiiiive, 6, 7

5 dots are on one die. Count on 2 more dots.

5 + 2 = 7

At-Home Activities

Let’s Count On

2 dots are on one die. Count on 5 more dots.

2 + 5 = 7

Gather a set of 10 objects such as coins, marbles, or cups. Arrange the objects into two groups with an easily countable pattern, like dots on dice or dominoes. Ask your student to find the total by counting on by asking these questions. After your student has counted, note that the total stays the same no matter which group they started with.

• “How many objects are in this group?”

• “Can you count on from that number to find the total of both groups?”

• “What would change if you started counting with the other group?”

Find Real-World Totals

Look for opportunities to practice the count on strategy with your student, such as those in the following examples. Encourage your student to count on by using their fingers to keep track of the amount they add on.

• “This new box of granola bars holds 10 bars. The open box in our cabinet still has some bars in it. Can you count on from 10 to find how many bars we have in all?”

• “There are 5 cars in this parking lot and 3 empty spaces. Can you count on from 5 to find the total number of parking spaces in the parking lot?”

1. How many pencils in all?

Show how you know.

3 5

I can count on from a part I know. 3

4 5

I draw to show a group of 3 . Then I draw 2 more.

I write numbers to show how I counted on.

REMEMBER

2. Draw lines to make parts in the shape.

Write how many parts.

Sample:

There are 4 parts.

I know I can draw lines on the square to make parts.

I can draw 1 or more lines.

I draw 2 lines and count 4 parts.

Name 7

1. How many forks in all?

Show how you know. 5

2. How many apples in all? Show how you know.

REMEMBER

3. Draw lines to make parts in the shape.

There are parts.

Name

Count on from a part.

I count on 2 from 6 : Siiiix, 7 , 8 .

Fill in the number bond.

6

6 7 8

6 and 2 are the parts.

6 2

6 and 2 make 8 .

8

PARTS

TOTAL

I can use number bonds to show parts that make a total.

Name 8

Count on from a part.

Fill in the number bond.

1. Count on two ways. Fill in the number bonds. Write the number sentences.

5 2 7

5 + 2 = 7

I can count on to find the total.

6

5 7

The dice show 5 and 2 . These are the parts.

5 2

7 is the total. I write a number sentence to show 5 and 2 make 7 .

2 and 5 are still the parts in a different order.

The total is still 7 .

I write a number sentence to show 2 and 5 make 7 .

When both parts are the same number, we call them doubles.

I count on from the other part.

If we roll any of these doubles, we can only count on one way.

REMEMBER

2. Sort in two different ways. Fill in the number bonds.

3 4 7

5 2 7

I can sort another way.

I see 7 birds.

I see 3 gray birds.

I see 4 blue birds.

3 and 4 are the parts.

7 is the total.

I see 2 birds on the ground.

I see 5 birds in the sky.

The parts are 2 and 5 .

The total is still 7 .

Name 9 1. Count on two ways. Fill in the number bonds. Write the number sentences.

REMEMBER

2. Sort in two ways. Fill in the number bonds.

Circle 5 and count on.

Fill in the number bond.

Write the number sentence.

5 3 8

5 and 3 are the parts.

8 is the total. 5 3

5 + 3 = 8 shows 5 and 3 make 8

5 + 3 = 8

I circle 5 apples and count on 3 more.

5

6 7 8

Name

Circle 5 and count on.

Fill in the number bond .

Write the number sentence.

1. Circle a part. Fill in the number bond. Write a number sentence. 5

I count on from the part I circled. 5 6 7 8

5 and 3 are the parts. 8 is the total.

REMEMBER

2. There are 6 goats.

Some goats are on a rock .

Some goats are not on a rock .

I read the problem. 6 goats is the total. There could be 4 goats on a rock. I draw 4 dots. This is one part.

I need a total of 6 dots.

Draw how the goats could look.

I know that 4 and 2 are partners to 6 .

Fill in the number bond.

I draw 2 more dots to show the goats that are not on the rock. This is the other part.

4 6

Sample: 2

REMEMBER

2. There are 7 squirrels . Some are in the tree .

Some are on the grass.

Draw how the squirrels could look.

Fill in the number bond.

Count on from 10.

Fill in the number bond.

Write the number sentence.

The parts I know are 10 and 7

I do not know the total. It is unknown. The unknown is a number we need to figure out.

I can count on from 10 to find the total. 10 16

There are 17 dots total.

I write a number sentence to show 10 and 7 make 17 .

FAMILY MATH Count On to Add

Dear Family,

Your student is learning to find the total of an addition expression, such as 8 + 3. Your student counts on from a part to find the total just like they did when finding the total of a set of objects. They confirm that they can add in any order and come to recognize that counting on from the larger part is more efficient. When counting on, your student uses their fingers or a number path. They are also introduced to telling time on an analog clock. Your student will revisit telling time throughout the year.

Key Terms expression

hour hand

minute hand o’clock 3 + 8

An expression is like a number sentence but there is no equal sign.

“Eiiiight, 9, 10, 11”

“I can start at 8 and hop 3 to find the total.”

When the longer minute hand is pointing to 12 and the shorter hour hand is pointing to 3, we say 3 o’clock.

At-Home Activities

More and Some More

Look for opportunities to practice counting on during everyday situations such as when folding laundry, during a trip to the grocery store, or on a walk in the neighborhood. Consider the following examples.

• “I have 5 socks in this pile. Count on from 5 as you put some more socks in the pile.”

• “I have 3 apples in the cart. Count on from 3 as you put more apples in the cart until we have 7 apples.”

• “I see 4 mailboxes. Count on until you see 10 mailboxes.”

What Do You See?

Take turns practicing adding numbers within 10 with your student. Use variations of animals to add different amounts together that make totals that are 10 or fewer. Consider the following examples.

• “I see 3 camels and 2 tigers. What 5 animals do you see?” (I see 4 lions and 1 tiger.)

• “I see 2 seals and 5 monkeys. What 7 animals do you see?” (I see 4 bears and 3 penguins.)

• “I see 6 elephants and 4 otters. What 10 animals do you see?” (I see 7 kangaroos and 3 rhinos.)

Consider taking turns going first so your student can determine the first combination of animals.

1. Count on.

5 bees are in the hive.

3 more bees fly into the hive.

How many bees are in the hive now? 8 bees

5

I start with 5 , then count on to find the total.

Fiiiive,

.

There are 8 bees total.

REMEMBER

2. Count the parts and the total.

Fill in the parts and the total.

6 is 4 and 2 .

There are 4 blue flowers and 2 white flowers. The total is 6 . The parts are 4 and 2 I fill in the sentence and the number sentence to show how the parts are added to make the total.

6 = 4 + 2

Name

1. Count on.

4 squirrels are in the tree.

3 more squirrels run up the tree.

How many squirrels are in the tree now? squirrels

6 bees are in the hive.

4 more bees fly into the hive.

How many bees are in the hive now? bees

4 6

REMEMBER

2. Count the parts and the total.

Fill in the parts and the total.

1. Add. Count on with your fingers. 4 + 2 = 6

I hold up a fist to represent 4 .

I count on 2 more fingers.

4 5 6

2. Add. Count on with the number path.

The total is 6

1234578910 6

6 + 4 = 10

I circle 6 because it is the part I am starting with.

I make 4 hops and land on 10 10 is the total.

6 + 4 = 10 is a number sentence, but 6 + 4 is an expression.

An expression is like a number sentence, but there is no equal sign.

1. Add. Count on with your fingers. 5 + 3 = 4

2. Add. Count on with the number path.

Name

1. Circle the larger part.

on. Fill in the number bond.

2 + 4

6

6

It is easier to count from the larger part. 4 is larger than 2 . I circle it.

I can use the number path with my finger. I start at 4 and count on 2 more. I land on 6 . So 4 + 2 and 2 + 4 equal 6 .

I fill in the number bond. 4 and 2 are the parts.

The total is 6 .

REMEMBER 2. Circle 10.

I count 10 acorns and circle them.

I see a group of 10 acorns. I know 10 acorns is 10 ones.

I count 5 acorns. I know that 5 acorns is 5 ones. I count 15 acorns in all.

Fill in the parts. 10 ones and 5 ones

Name

1. Circle the larger part. Count on. Fill in the number bond. 5 + 3 =

ones

Circle the larger part.

Count on with your fingers or the number path.

It is easier to count on from the larger part. 8 is the larger part. I circle it. With my fingers or the number path, I start at 8 and count on 5 .

I end on 13 , so the total is 13 .

Name

Circle the larger part.

Count on with your fingers or the number path.

When I add 1 to a number, I get the next number.

When I add 0  to a number, I get the same number.

REMEMBER 2. 10 muffins are in the box.

3 muffins are out of the box.

How many muffins are there in all?

Fill in the number bond.

I count the muffins to find the total.

I write 13 at the top of the number bond.

The 10 muffins in the box are one part.

I write 10 in the number bond.

The 3 muffins out of the box are the other part. I write 3 in the number bond.

10 and 3 make 13 .

REMEMBER

2. 10 apples are in a tree.

4 apples are in a basket.

How many apples are there in all?

Fill in the number bond.

FAMILY MATH

Make the Same Total in Varied Ways

Dear Family,

Your student is learning about the meaning of the equal sign. They learn that an equal sign means that the expression or number on either side of the sign have the same total. This is important so your student doesn’t only think of the equal sign as a signal for an answer. Your student continues exploring different expressions with the same total by finding all of the ways to add two numbers to make any value from 0 to 10. They also build on their work with doubles facts to find the total of doubles +1 facts.

If the totals on each side of the equal sign are the same, the number sentence is true. If the totals on each side of the equal sign are not the same, the number sentence is false.

The cubes show that the totals on each side of the equal sign are the same.

Color counters show all of the expressions that add to 6.

Thinking of a doubles fact and adding 1 is referred to as doubles +1 facts.

At-Home Activities

Number Names

Look for or think of places or things common to you that have numbers in their names. Examples include the names of stores or roads. Then rename the place or thing you chose by breaking apart the number. For example, Route 9 can be renamed as Route 7 + 2, or the game four square can be renamed as 3 + 1 Square. See if you and your student can think of all the different combinations for the number.

Seeing Doubles +1

You and your student can look at magazines, picture books, or anywhere in daily life for images with things in sets of 2s, 3s, 4s, or 5s. Then take turns doubling the amounts you see and adding 1.

• “I see 4 bananas in that bunch. Double that is 8 and 1 more is 9 bananas.”

• “I see a bouquet of 5 flowers. Double that is 10 and 1 more is 11 flowers.”

Name Circle the number sentence if it is true.

Draw an X on the number sentence if it is false .

1 + 2 = 2 + 1

The expressions on each side of the equal sign have the same totals.

1 + 2 = 2 + 1

3 3

3 equals 3 , so the number sentence is true. I circle it.

5 + 1 = 2 + 3

The expressions on each side of the equal sign do not have the same total.

5 + 1 = 2 + 3

6 5

6 does not equal 5 , so the number sentence is false.

I draw an X on it.

Name

Circle the number sentence if it is true .

Draw an X on the number sentence if it is false.

1. Circle the number sentence if it is true.

Draw an X on the number sentence if it is false .

2 + 2 = 0 + 4 4 4

The totals of the expressions on each side of the equal sign are the same, or equal, so the number sentence is true. I circle it.

6 + 3 = 1 + 4

9

5

The totals of the expressions on each side of the equal sign are not the same, or equal.

6 + 3 = 9

1 + 4 = 5

The number sentence is false.

I draw an X on it.

REMEMBER

2. Circle a part.

Fill in the number bond.

Write a number sentence.

Sample:

5 8 5 + 3 = 8

I see 5 fish. That is one part.

I see 3 more fish, That is the other part.

I can count on 3 more from 5 .

Fiiiive, 6 , 7 , 8 . 5 and 3 make 8 .

3

Name 1. Circle the number sentence if it is true. Draw an X on the number sentence if it is false . 7 = 5 + 2

Name

Show two ways to make 5. Sample:

5 3 2 5

I color some circles to show a part of 5

3

2

I see 3 and 2 make 5 .

I fill in the parts of the number bond.

I write a number sentence.

3 + 2 = 5

1 + 4 = 5

I show 5 a different way. I can color more or fewer circles this time.

1 4

I see 1 and 4 also make 5 .

I fill in the parts of the number bond.

I write a number sentence.

Name

1. Show two ways to make 6. Sample:

3 = 6 6

5 + 1 = 6 3 +

I color some circles to show a part of 6 5 1

I see 5 and 1 make 6 .

I fill in the parts of the number bond.

I can show a different way by coloring more or fewer circles. 3 3

I see 3 and 3 also make 6

I fill in the parts of the number bond.

I write a number sentence to match.

REMEMBER 2. Circle.

The chicken is

I can draw a line to help me see that the endpoints start at the same place.

I see the cow sticks up more than the chicken. The chicken is short, not tall.

The chicken is not heavy. I can pick up a chicken.

Name

7

7

1. Show three ways to make 7. 7

Name

Show two ways to make 8. Sample:

8 5 3 8 0 8

I can color some circles to show a part of 8 .

5 + 3 = 8

I see 5 and 3 make 8 .

0 + 8 = 8

To show a different way, I can color more or fewer circles.

I leave all the circles white.

I see 0 and 8 also make 8 .

1. Show two ways to make 10. 10 10

2. Show two ways to make 9.

Name

1. Add. Circle doubles that help you.

4 + 4 = 8

2. Add. Show how you know.

4 + 5 = 9

4 + 4 + 1 = 9

Doubles happen when both parts are the same number.

4 + 4 = 8 is a doubles fact I know!

4 + 5 = 9

5 is 1 more than 4 .

I can use the doubles fact, then add 1 more.

4 + 4 = 8

8 + 1 = 9

I can make a doubles + 1  problem by drawing a number bond to break 5 into 4 and 1 .

4 + 4 + 1 has the same total as 4 + 5 .

4 + 5 = 9

4 1

REMEMBER

3. Draw more dots to make the number.

26

I see 2 groups of 10 . That is 20 .

I can start at 20 and count on to 26 .

I draw a dot for each number.

1. Add. Circle doubles that help you. 3 + 3

2. Add. Show how you know.

+ 3

3. Draw more dots to make the number.

Name

1. Color the circles . Circle doubles that help you. Write the total. 6 + 8 = 14

I color 6 circles then 8 circles.

I circle the doubles fact, 6 + 6 = 12 .

I add 2 more.

12 and 2 make 14 , so 6 + 8 = 14 .

2. Add. Show how you know.

7 + 6 = 13

I can use a doubles fact to make this problem easier. I break 7 into 6 and 1 7 + 6

Name

1. Color the circles . Circle doubles that help you. Write the total.

2. Add. Show how you know.

Acknowledgments

Kelly Alsup, Lauren Brown, Dawn Burns, Jasmine Calin, Mary Christensen-Cooper, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Melissa Elias, Lacy Endo-Peery, Scott Farrar, Krysta Gibbs, Melanie Gutierrez, Eddie Hampton, Tiffany Hill, Robert Hollister, Christine Hopkinson, Rachel Hylton, Travis Jones, Kelly Kagamas Tomkies, Liz Krisher, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Ashley Meyer, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Andrea Neophytou Hart, Kelley Padilla, Kim L. Pettig, Marlene Pineda, Elizabeth Re, John Reynolds, Marianne Strayton, Meri Robie-Craven, Robyn Sorenson, Marianne Strayton, James Tanton, Julia Tessler, Philippa Walker, 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 978-1-64497-636-4

Module 1

Counting, Comparison, and Addition

Module 2

Addition and Subtraction Relationships

Module 3

Properties of Operations to Make Easier Problems

Module 4

Comparison and Composition of Length Measurements

Module 5

Place Value Concepts to Compare, Add, and Subtract

Module 6

Attributes of Shapes • Advancing Place Value, Addition, and Subtraction

What does this painting have to do with math?

American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten.

On the cover

Tables for Ladies, 1930

Edward Hopper, American, 1882–1967 Oil on canvas

The Metropolitan Museum of Art, New York, NY, USA

Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine

N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY