Apply | Level 1 Module 4 | Eureka Math² Florida B.E.S.T. Edition

Module

1 2 3 5 6

Counting, Comparison, and Addition

Addition and Subtraction Relationships

Properties of Operations to Make Easier Problems

Comparison and Composition of Length Measurements 4 Place Value Concepts to Compare, Add, and Subtract

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

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ISBN 979-8-88588-674-1

FAMILY MATH

Direct and Indirect Length Comparison

Dear Family,

Your student is comparing objects by length. They align the endpoints of the objects to determine if one object is shorter or longer than the other. Students are also ordering sets of objects and making comparison statements. Then they learn that they can compare the lengths of two objects even when the objects are not next to each other. They do this by seeing how each of the objects measures up to a third object. They use the comparisons they know to determine a comparison they do not know. This prepares students for measuring objects by using tools such as centimeter cubes in later work.

endpoints

Objects can be compared without measuring them by lining them up next to each other.

At-Home Activities Look Around

When ordering objects from shortest to tallest, each object is taller than those that come before it and shorter than those that come after it. The grasshopper is shorter than the squirrel. The dog is taller than the turkey.

With your student, compare the lengths of objects you see throughout the day. Ask questions like these that use comparative language.

• “Which is taller, the table or the chair?”

• “Which tree is the tallest?”

• “Which is longer, your shoe or my shoe?”

The frog is shorter than the zookeeper’s finger. The monkey is longer than the zookeeper’s finger. So, I know the frog is shorter than the monkey.

Kitchen Line Up

Help your student choose a variety of items in the kitchen to compare such as a cereal box, a can of soup, a bottle of water, and a package of crackers. Ask your student to place the items in order from tallest to shortest, or vice versa. Invite your student to analyze the order by using comparison statements like these.

• “The can of soup is shorter than the bottle of juice.”

• “The cereal box is taller than the package of crackers.”

Repeat this activity with other household items.

Name

C R F A P

1. Order from shortest to tallest . A R P C F

2. Write the letters to compare. Sample:

A is shorter than P .

C is taller than R .

I can compare the lengths of the items.

I see the acorn is shorter than the pine cone.

I see the cactus is taller than the rock.

The items are lined up by their endpoints. I can compare the lengths.

The acorn is the shortest. I write letter A first.

The rock is taller than the acorn but shorter than the other items. I write the letter R.

The pine cone comes next because it is taller than the rock but shorter than the other items. I write the letter P.

Then the cactus comes after the pine cone. I write the letter C.

The flower is last because it is the tallest. I write the letter F.

REMEMBER

3. How many dots?

8 dots

What if there is 1 more dot?

9 dots

I see 5 dots and 3 dots.

That is 8 dots.

I can draw 1 more dot.

I know 8 and 1 more is 9 .

1. Order from shortest to longest .

2. Write the letters to compare. is shorter than . is longer than .

REMEMBER

3. How many dots?

What if there is 1 more dot?

dots

dots

Name

1. Cut out the cards.

2. Read. Order from shortest to tallest . The hen is taller than the frog.

The dog is the tallest .

The clues tell me that the frog must be the shortest.

The cat is taller than the hen.

3. Write the animals in order from shortest to tallest .

The dog is the tallest. The cat is taller than the hen and shorter than the dog. D H C F

F H C D

Name

1. Cut out the birds.

2. Read. Order from shortest to tallest .

Bird H is taller than P.

Bird F is the tallest .

Bird E is taller than H.

Bird O is taller than P but shorter than H.

3. Write the letters of the birds in order from shortest to tallest .

Name

1. Circle. The blue flower is shorter

taller than the stick .

I can draw a line across the top endpoint of the flower. Now I see it is shorter.

The red flower is shorter

taller than the stick .

I can draw a line across the top endpoint of the flower. Now I see it is taller.

The red flower is shorter

taller than the blue flower.

The blue flower is shorter than the stick.

The red flower is taller than the stick.

So I know the red flower is taller than the blue flower.

REMEMBER

2. Count on from 10 to find the total. Fill in the number bond.

I circle 10 carrots.

I count on 6 more carrots from 10 : 11 , 12 , 13 , 14 , 15 , 16

There are 16 carrots total. The parts are 10 and 6

3. Cross out to make them equal.

Write the number sentence.

6 – 3 = 3

Equal means both groups are the same.

I cross off smiley faces in the top group until each group has the same number.

I take away 3 smiley faces from the top group.

Now, each group has 3 smiley faces. They are equal.

4. Circle the number sentences that are true .

13 = 13 + 1

10 = 10

I look at both sides of the equal sign and ask myself, “Does each side have the same amount?”

I add or subtract to find the amount on each side of the equal sign.

If the amounts are equal, the number sentence is true.

12 - 6 = 6

6

If the amounts are not equal, the number sentence is false.

9 = 9 - 1

8

12 - 6 = 6

9 = 9 - 1

Name

1. Circle. shorter

taller shorter

than the paper clip.

taller

The yellow butterfly is The white butterfly is The white butterfly is than the yellow butterfly.

taller shorter

than the paper clip.

REMEMBER

2. Count on from 10 to find the total. Fill in the number bond.

3. Cross out to make them equal. Write the number sentence.

4. Circle the number sentences that are true.

FAMILY MATH Length Measurement and Comparison

Dear Family,

Key Terms

Your student is learning to measure and compare lengths. They use tools to find how long or tall something is from one end of it to the other end. Students begin by lining up centimeter cubes and transition to using 10-centimeter sticks and cubes. They see that when they measure longer objects, the sticks are more efficient because they can count by tens and then by ones to find the total length. Students compare lengths of objects to determine which one is longer or shorter and they write number sentences with the symbols < (less than), > (greater than), and = (equal to). They draw and label the 10-centimeter sticks and centimeter cubes to show how they measured.

To measure accurately, students line up cubes at their endpoints with no gaps or overlaps.

10 centimeters

12 centimeters

10 < 12

The leopard paw on the left is shorter than the lion paw on the right because 10 is less than 12.

Your student uses drawings to represent total lengths in terms of tens and ones.

At-Home Activity

Measuring Like A Pro

Help your student develop good measuring behaviors by asking questions about objects around the house like the following examples.

• “If we were going to measure this table, where would we start measuring?”

• “Where would we stop measuring?”

• “What do we call the space between the endpoints of the table?”

Encourage your student to use comparison language, such as taller than and shorter than, when discussing lengths. Gather items such as a sheet of paper, crayon, coffee mug, pen, etc., and line up the items at their endpoints asking questions such as the following.

• “Which is taller, the coffee mug or the crayon?”

• “Which is shorter, the pen or the crayon?”

15 centimeter cubes

We can use a tool like cubes to measure how long or how tall something is.

The centimeter cubes are lined up endpoint to endpoint without any gaps.

I find the length by counting all the centimeter cubes.

The magnifying glass is 15 centimeter cubes long.

Name 4 Write the lengths .

centimeter cubes

centimeter cubes

centimeter cubes

Name

1. Write the lengths.

7 centimeters

The centimeter cubes are used to measure the length of the flowers.

I count the cubes from endpoint to endpoint.

I know a cube is 1 centimeter.

The length of the white flower is 7 centimeters.

The length of the red flower is 14 centimeters.

14 centimeters

2. The is the . Circle . taller than shorter than 14 centimeters is longer than 7 centimeters.

So, the red flower is taller than the white flower.

3. Write < or > to compare the and . > Sample: 14 7

< means less than > means greater than The wide part goes next to the greater number.

I write 14 > 7 to show 14 is greater than 7 .

I can also write 7 < 14 .

REMEMBER 4. Subtract.

I see 9 ones.

I take 6 ones.

There are 3 ones left.

I see 1 ten and 9 ones.

I take 6 ones from the 9 ones.

There are 1 ten and 3 ones left.

Name

1. Write the lengths. centimeters centimeters

2. The is than the . Circle. longer than shorter than

3. Write < or > to compare and .

4. Subtract.

Name

1. Write the lengths of the toys.

I find each length by counting the centimeter cubes from endpoint to endpoint.

R 8 centimeters

B 6 centimeters

J 11 centimeters

2. Write the lengths from shortest to longest .

B R J

6 centimeters 8 centimeters

11 centimeters

6 is less than 8 and 11 . The bike is the shortest.

11 is the greatest number. The jet is the longest.

8 is greater than 6 and less than 11 .

The length of the rocket is between the lengths of the bike and the jet.

Name 6

1. Write the lengths of the toys.

B centimeters

S centimeters

D centimeters

2. Write the lengths from shortest to longest . centimeters centimeters centimeters

Name

1. Write the lengths.

10 centimeter cubes are the same length as a 10 -stick.

I find the length of the pencil by counting the 13 centimeter cubes. Then I find the length of the pencil by counting on 3 from the 10 -stick. It is still 13 centimeters long!

REMEMBER

I see 7 dots.

I draw 3 more dots to make 10

7 and 3 are the parts. 10 is the total.

7 + 3 = 10

2. Draw dots to make 10. Fill in the number bond.

1 more than 18 is 19 .

I can count on to find the missing numbers.

1 less than 18 is 17 .

Thiiiirteen, 14 , 15 , 16 , 17 , 18 , 19 , 20

Sample:

4. 10 is less than 15. 16 is greater than 15.

I know less than means smaller. I write a number that is smaller than 15 .

I know greater than means more. I write a number that is more than 15 .

3. Write.

Name 7 1. Write the lengths.

centimeters centimeters

REMEMBER

2. Draw dots to make 10. Fill in the number bond.

1 more than 17 is .

1 less than 17 is .

is less than 15. is greater than 15.

4.

Write the length. 11 centimeters

10

. 11 1

Baz used a 10 -stick and 1 centimeter cube to measure the butterfly.

10 + 1 = 11

I can draw 1 ten and 1 one and show the total length is 11 centimeters.

Name

1. Baz

2. Draw how Baz measured the butterfly

2. Draw how Val measured the butterfly.

Ben used a 10 -stick and 1 centimeter cube to measure the shark.

I draw 1 ten and 1 one. I show the total length is 11 centimeters.

I can draw a number bond to show that 11 can be made up of 10 and 1

11

Name

1. Ben measured the shark.

2. Draw to show how he measured .

3. Show the total using tens and ones.

REMEMBER

4. Circle the number sentence if it is true.

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

I can find the total of the expressions on each side of the equal sign.

5 is the same as or equal to

So, 4 +

=

+ 2 is true.

.

9 is not the same as or equal to 8 .

So, 4 + 5 = 6 + 2 is false.

5. Read

Mr. West has 18 pencils.

He loses 7 pencils.

How many pencils does Mr. West have left?

Draw Write

Sample: 18 – 7 = 11

Mr. West has 11 pencils left.

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

I draw 18 dots to show Mr. West’s pencils.

I cross off 7 circles from the 8 ones to show the pencils Mr. West loses.

I see 10 and 1. There are 11 pencils left.

Name 9

1. Baz measured the skateboard .

Draw to show how he measured .

Show the total using tens and ones.

REMEMBER

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

3. Read Liv has 14 books.

She gives away 5 books.

How many books does Liv have left?

Draw

Write Liv has books left.

Comparison Word Problems with Measurement

Dear Family,

Your student is solving comparison word problems with real-world situations. They use cubes and tape diagrams to measure and compare the lengths of objects to see how much longer or shorter one is than the other. They find unknown lengths by adding to or taking away from the known length. One way to find the difference is to think about the number of cubes in the shorter length that are needed to make it equal to the longer known length, and then add them. Another way is to identify extra cubes in the longer length that do not match up with cubes in the shorter length, and then take them away.

The pencil measures 4 more cubes than the frog measures. The frog needs 4 more cubes to be the same length as the pencil.

At-Home Activity

Draw to Compare

Your student needs to add 4 cubes to find the length of the pencil.

Your student needs to take away 4 cubes to find the length of the frog.

Ask your student to compare the measurements of these objects by using drawings to represent their thinking.

• “A cucumber is 17 centimeters long. A carrot is 11 centimeters long. How much shorter is the carrot than the cucumber? What could you draw to show the measurements? How can you find the difference?”

• Draw a 10-stick and 7 more cubes (17), then a 10-stick and 1 more cube. (11)

• Take 6 cubes from the length of the cucumber or add 6 cubes to the carrot’s length.

• “A book is 5 centimeters longer than a marker. The marker is 14 centimeters long. How long is the book?” What could you draw to show the measurements? How can you find the length of the book?”

• Draw a 10-stick and 4 more cubes (14), then draw 5 more cubes (19).

• Add 5 cubes to the length of the marker to find the length of the book.

If you have a ruler at home, you can also use it to measure and compare objects in the home. Invite your student to make drawings to show their thinking.

Name Write the lengths.

12 centimeters

15 centimeters

I know the blue stick is 10 centimeters. Each yellow cube is 1 centimeter.

I see the pen has one 10 -stick and 2 cubes.

= 12

I see the pencil has one 10 -stick and 5 cubes.

The pencil is 3 centimeters longer than the pen .

Sample: 12 + 3 = 15

I can compare the lengths. I know the pen is 12 centimeters long. I know the pencil is 15 centimeters long. The pencil has 3 more centimeter cubes than the pen has.

Name

Write the lengths.

The spoon is centimeters longer than the candy.

centimeters

centimeters

Name 1. Read

The fork is 15 centimeters long.

The lollipop is 10 centimeters long.

How much shorter is the lollipop than the fork?

Draw

Sample:

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

I draw and label a 10-stick and 5 cubes to show the fork is 15 centimeters long.

To compare the lengths, below the fork length, I draw and label a 10 -stick to show the lollipop is 10 centimeters long.

I know 10 needs 5 more to make the lengths equal.

10 + 5 = 15

The lollipop is 5 centimeters shorter than the fork.

REMEMBER

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

6 + 8 = 14

8 and 2 make 10 , so I break apart 6 into 4 and 2 .

2 and 8 make 10 , and 4 and 10 is 14 .

6 + 8

4 + 2 + 8 = 14

3. Order from shortest to tallest .

The items are lined up by their endpoints so I can compare their heights.

The pinwheel is the shortest because the other items are taller.

The water bottle is taller than the pinwheel.

The trophy is last because it is the tallest. T P W

Name

1. Read

The pencil is 13 centimeters long.

The glue stick is 10 centimeters long.

How much shorter is the glue stick than the pencil?

The glue stick is centimeters shorter than the pencil.

REMEMBER

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

8

B C R

3. Order from shortest to tallest.

Name Read

The muffin is 6 centimeters long.

The hot dog is 10 centimeters longer than the muffin.

How long is the hot dog?

Draw

Sample:

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

I draw and label to show the muffin is 6  centimeters long.

I draw and label to show the hot dog is 10 centimeters longer than 6 centimeters.

10 and 6 is 16 so the hot dog is 16  centimeters long.

Write

The hot dog is 16 centimeters long. 6 + 10 = 16

Name

Read

The rock is 6 centimeters long.

The stick is 10 centimeters longer than the rock .

How long is the stick ?

Compare the lengths with sticks and cubes. Draw

Write

The stick is centimeters long.

Name 1. Read

The boot is 17 centimeters tall.

The shoe is 7 centimeters shorter than the boot.

How tall is the shoe ?

Sample:

The shoe is 10 centimeters tall.

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

I draw and label to show the boot is 17 centimeters tall.

I draw and label to show the shoe is 7 centimeters shorter than the boot.

17 minus 7 is 10 , so the shoe is 10  centimeters tall.

REMEMBER

2. Circle to make 10. Write a number sentence with three parts. Write the total.

I started with 5 as one part and broke 7 into two parts, 5 and 2 .

5 and 5 make 10 , so I circle 5 cubes in each part.

10 and 2 make 12 .

= 12

Name

1. Read

The red bird is 15 centimeters tall.

The blue bird is 5 centimeters shorter than the red bird.

How tall is the blue bird ?

Compare the lengths with sticks and cubes.

The blue bird is centimeters tall.

2. Circle to make 10. Write a number sentence with three parts. Write the total. 5

Name

1. Fill in the lengths.

I can use the cubes to measure each item.

I see a pattern. The items are 2 centimeters shorter each time.

4 – 2 = 2

6 8

4

2

The height of the acorn will be 2 centimeters. centimeters centimeters centimeters centimeters

2. How much shorter is each? 2 centimeters

Name

1. Fill in the lengths .

centimeters centimeters centimeters centimeters

2. How much taller is each snack? centimeters

Credits

Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. For a complete list of credits, visit http://eurmath.link/media-credits.

All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History.

Page 3, blickwinkel / Alamy Stock Photo; pages 3, 49, 51, blickwinkel / Alamy Stock; page 21, Metelitsa Viktoriya/Shutterstock, aodaodaodaod/Shutterstock; page 25, Anatolii Riabokon/Alamy Stock Vector; All other images are the property of Great Minds

Acknowledgments

Kelly Alsup, Leslie S. Arceneaux, Melissa Brown, Dawn Burns, Jasmine Calin, Mary Christensen-Cooper, Hazel Coltharp, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Melissa Elias, Lacy Endo-Peery, Scott Farrar, Ryan Galloway, Krysta Gibbs, Danielle Goedel, Melanie Gutierrez, Jodi Hale, Karen Hall, Eddie Hampton, Tiffany Hill, Robert Hollister, Christine Hopkinson, Rachel Hylton, Travis Jones, Kelly Kagamas Tomkies, Jennifer Koepp Neeley, Liz Krisher, Marie Libassi-Behr, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Ashley Meyer, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Andrea Neophytou Hart, Kelley Padilla, Shelley Petre, Kim L. Pettig, Marlene Pineda, Jay Powers, Elizabeth Re, John Reynolds, Meri Robie-Craven, Jessica Sims, Robyn Sorenson, Lori Sponenburgh, Marianne Strayton, James Tanton, Julia Tessler, Philippa Walker, Lisa Watts Lawton, MaryJo Wieland, Jackie Wolford, Leslie Zuckerman

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

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

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, and Measurement

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