EM2_G4_M1_Learn_23B_970997_Updated 05.23

4 A Story of Units® Fractional Units

LEARN ▸ Module 1 ▸ Place Value Concepts for Addition and Subtraction

What does this painting have to do with math?

American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square?

On the cover

Tahkt-I-Sulayman Variation II, 1969

Frank Stella, American, born 1936 Acrylic on canvas Minneapolis Institute of Art, Minneapolis, MN, USA

Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York

Module 1 Place Value Concepts for Addition and Subtraction

2 Place Value Concepts for Multiplication and Division

3 Multiplication and Division of Multi-Digit Numbers

4 Foundations for Fraction Operations

5 Place Value Concepts for Decimal Fractions

6 Angle Measurements and Plane Figures

Contents

Place Value Concepts for Addition and Subtraction

Write numbers to 1,000,000 in standard form and word form.

Topic C

Rounding Multi-Digit Whole

Describe relationships between measurements by using multiplicative comparison.

Represent the composition of larger units of money by using multiplicative comparison.

Topic B

Place Value and Comparison Within 1,000,000

Organize, count, and represent a collection of objects.

Demonstrate that a digit represents 10 times the value of what it represents in the place to its right.

Write numbers to 1,000,000 in unit form and expanded form by using place value structure.

Write a rule for each pattern.

1.

Figure A

Figure B

Figure C

Figure

Rule:

Draw sticky notes to represent 4 times as many. Then fill in the blanks.

Partner B = ×

Partner B has times as many sticky notes as partner A. is times as many as .

2.

Figure M

Figure L

Figure N

Figure O

3. Partner A

7. Draw a tape diagram to represent 36 is 4 times as many as 9. Then complete the equation.

Use the tape diagram to fill in the blanks. Then complete the equation and statement. 8.

= × is times as many as .

= × is times as many as .

= × is times as many as .

1. Liz draws circles by using this rule: Multiply the number of circles by 2

a. How many circles should Liz draw for figure D? How do you know?

b. Complete the statements and equation to match the figures.

There are times as many circles in figure B than in figure A.

is times as many as 5

= × 5

There are times as many circles in figure C than in figure B.

is times as many as 10

= × 10

Figure A

Figure B

Figure C

Figure D

Draw tape diagrams to represent each statement. Then complete the equation.

5. 12 is 3 times as many as 4 12 = × 4

6. 28 is 4 times as many as 7

7. 5 times as many as 3 is 15. × =

8. 6 times as many as 8 is 48 × =

9. There are 9 tables in the cafeteria. There are 8 times as many chairs as tables. How many chairs are in the cafeteria?

Draw a model to represent the statement. Then complete the equation.

15 is 3 times as many as 5.

×

Draw a tape diagram to represent each statement.

Then write an equation to find the unknown and complete the statement.

4. is 2 times as many as 8.

5. 27 is 3 times as many as .

6. 35 is times as many as 7.

7. Ivan draws a tape diagram to represent a statement with an unknown.

a. Circle the statement that Ivan’s tape diagram represents.

48 is ? times as many as 8. ? is 6 times as many as 8.

48 is 6 times as many as ? .

b. Explain how Ivan’s tape diagram represents the statement you circled in part (a).

c. Write an equation to represent Ivan’s tape diagram.

Use the Read–Draw–Write process to solve each problem.

8. Mia scores 3 times as many points as Shen during a basketball game. Mia scores 21 points. How many points does Shen score?

9. Adam picks 9 apples. His mom picks 54 apples. Adam says, “My mom picked 7 times as many apples as I did.” Do you agree with Adam? Why?

Name            Date

Fill in the blanks to make true statements. Write an equation to show how you found each unknown.

1. is 4 times as many as 8.

2. 30 is times as many as 6.

3. 63 is 9 times as many as .

Name            Date

Record each measurement. Then complete the statement and the equation.

grams grams

The paint is 5 times as as the marker. g = 5 × g

The caterpillar is 3 times as as the ant. cm = × cm

Container B has times as water as container A.

× mL

heights of the library and the school.

How many times as tall as the library is the school? Complete the equation and the comparison statement.

15 ÷ 5 =

The school is times as as the library.

4. The tape diagram represents the

Use the Read–Draw–Write process to solve each problem.

5. Carla and Luke draw rectangles. The width of Luke’s rectangle is 3 centimeters. Carla’s rectangle is 4 times as wide as Luke’s rectangle. What is the width of Carla’s rectangle?

6. Fish tank A has 6 times as much water as fish tank B. There are 42 liters of water in fish tank A. How many liters of water are in fish tank B?

7. Eva weighs her dog and her cat. Her dog weighs 32 kilograms and her cat weighs 4 kilograms. How many times as heavy as Eva’s cat is her dog?

Name            Date

Use the Read–Draw–Write process to solve the problem.

Casey’s dog weighs 3 times as much as Luke’s dog. Luke’s dog weighs 8 kilograms. How much does Casey’s dog weigh?

Casey’s dog weighs kilograms.

Name            Date

1. Bundle pennies to show how to compose a larger unit.

dollars dimes pennies

2. Complete the chart to show how to use multiplication to compose a larger unit.

dollars dimes pennies

Complete the statement and multiplication equations to show how you composed a larger unit.

1 dime is worth times as much as 1 penny.

1 dime = × 1 penny 10¢ = × 1¢

3. Bundle dimes to show how to compose a larger unit.

dollars dimes pennies

4. Complete the chart to show how to use multiplication to compose a larger unit.

dollars dimes pennies ×

Complete the statement and multiplication equations to show how you composed a larger unit.

1 dollar is worth times as much as 1 dime.

1 dollar = × 1 dime

$1 = × 10¢

Use the Read–Draw–Write process to solve the problem.

5. Ivan and Zara play a game with money. Ivan hides 2 coins. He gives Zara the following clues. One of the coins is a penny. The other coin is worth 10 times as much as the penny. What is the other coin?

Use the Read–Draw–Write process to solve the problem.

6. Eva and Gabe both find money. Eva finds 1 dime. Gabe says, “The bill I found is worth 10 times as much as your dime.” What bill did Gabe find?

Name

Date

Bundle coins to make a new unit. Then complete the statement and equations.

1. dollars dimes pennies

2. dollars dimes pennies

1 dime is worth times as much as 1 penny.

1 dime = × 1 penny

10¢ = × 1¢

1 dollar is worth times as much as 1 dime.

1 dollar = × 1 dime

$1 = × 10¢

Complete the charts to show how to make a new unit. Then complete the statements and equations.

3. dollars dimes pennies

× 1 is worth times as much as 1 penny.

1 = × 1 penny

¢ = × 1¢

4. dollars dimes pennies

× 1 is worth times as much as 1 dime.

1 = × 1 dime

$ = × 10¢

Label the tape diagrams. Then complete the statements and equations.

5. ¢ or penny

¢ has the same value as dime

1 dime is worth times as much as 1 .

1 dime = × 1 10¢ = × 1¢

6. ¢ or dime

¢ has the same value as dollar

1 is worth 10 times as much as 1 .

1 = 10 × 1

$ = 10 × ¢

7. James says that since 1 dime is worth 10 times as much as 1 penny, 3 dimes must be worth 10 times as much as 3 pennies. Do you agree with James? Why?

Name            Date

Jayla and Miss Diaz draw on charts to show the relationship between the values of a dime and a penny.

Use the charts to help you answer parts (a) and (b).

Jayla’s Chart Miss Diaz’s Chart

a. What is similar about the charts?

b. What is different about the charts?

For this counting collection, I am partners with .

We are counting .

We think they have a value of . This is how we organized and counted the collection:

We counted altogether.

This is an equation that describes how we counted.

Self-Reflection

Write one thing that worked well for you and your partner. Explain why it worked well.

Write one challenge you had. How did you work through the challenge?

Use the place value disks to help you complete the equation.

ten = 10 ones

hundred = 10 tens

1 = 10 hundreds

ten thousand = 10 thousands

1 = 10 ten thousands

1 = 10 hundred thousands

1.

2.

3.

4.

5.

6.

Name

7. Write the correct unit names on the place value chart.

tens ones

Name            Date

1. What strategy did you use to count? How did it help you?

2. Explain another student’s strategy. What did you like about it?

Name millions hundred thousands ten thousands thousands hundreds tens ones

10 times as much as 1 one is 1 .

10 times as much as 1 ten is 1 .

10 times as much as 1 hundred is 1 .

10 times as much as 1 thousand is 1

10 times as much as 1 ten thousand is 1 .

10 times as much as 1 hundred thousand is 1 .

Draw and record 10 times as much 1. thousands ten thousands

2. thousands ten thousands hundreds tens ones

Bundle 10 disks to make a new unit. Then complete the statement and equations.

10 times as much as 1 one is ten.

10 × 1 one = ten

10 × 1 =

10 times as much as 1 ten is hundred.

10 × 1 ten = hundred

10 × 10 =

10 times as much as 1 hundred is thousand.

10 × 1 hundred = thousand

10 × 100 =

10 times as much as 1 thousand is ten thousand.

10 × 1 thousand = ten thousand

10 × 1,000 =

1.

2.

3.

4.

Name            Date

Use the place value chart to complete the statements and equations.

5. thousands hundreds tens ones × 10

10 times as much as 1 one is 1

10 × 1 =

1 ten is 10 times as much as 1

10 = 10 ×

7. thousands hundreds tens ones × 10

10 times as much as 3 tens is 3 . 10 × 30 =

6. thousands hundreds tens ones × 10

10 times as much as 1 ten is 1

10 × 10 =

1 hundred is 10 times as much as 1

100 = 10 ×

8. thousands hundreds tens ones × 10

10 times as much as 8 hundreds is 8 .

10 × 800 =

3 hundreds is 10 times as much as 3 .

300 = 10 ×

8 thousands is 10 times as much as 8 .

8,000 = 10 ×

Complete each statement by drawing a line to the correct value. 13. 2 thousands is 10 times as much as . 2 ones 14. 2 tens ÷ 10 =

Use the Read–Draw–Write process to solve the problem.

19. In the morning, there is $700 in the cash register. At the end of the day, 10 times as much money is in the cash register.

a. How much money is in the cash register at the end of the day?

b. Explain your thinking.

a. Fill in the blank to make a true statement.

1 ten thousand is times as much as 1 thousand.

b. Explain how you know your answer is correct.

Draw dots in the place value chart to represent the number. Then fill in the blanks to identify how many of each unit.

1. 270,364

millions hundred thousands ten thousands thousandshundredstensones

hundred thousands ten thousandshundreds tens ones thousands

2. 1,056,230 millions hundred thousands ten thousands thousandshundredstensones

millionhundred thousands ten thousandshundreds tens ones thousands

Express each number in expanded form in two ways.

3. 83,015

4. 620,409

1.

2.

hundred thousands ten thousands thousands hundreds tens ones

million hundred thousands ten thousands thousand hundreds tens ones

3.

4.

8. millions hundred thousands ten thousands thousands hundreds tens ones

Expanded form:

Fill in the blanks to write each number in expanded form in two ways.

13. Miss Diaz buys a fishing boat. The picture shows the amount of money she pays.

Pablo says the number of dollars is 30,000 + 5,000 + 40.

Amy says the number of dollars is 30 ten thousands 5 hundreds 4 tens.

Who is correct? Who made a mistake? Explain your thinking.

ones

tens

hundreds

thousands

ten thousands

hundred thousands

millions

Express the following numbers in standard form by using commas.

1. 4168

2. 72035

3. 183119

4. 6455007

5. 29301248

Use the place value disks on each chart to complete the table.

6.

7.

Fill in the blank to make a true number sentence.

8. 1,000 + 400 + 60 + 2 =

9. 400,000 + + 900 + 8 = 407, 908

10. = 35 thousands + 6 tens + 1 one

11. 920,902 = 900,000 + 900 + 2 +

Express each number in standard form.

12. 1 ten thousand 4 thousands 8 tens

13. 2 hundred thousands 6 thousands 9 hundreds 3 ones

14. Sixty-one thousand, forty-eight

15. Five hundred thousand, five hundred five

Express each number in word form.

16. 3,627

17. 84,100

18. 570,016

19. 900,509

20. Mrs. Smith sees a home for sale. Use pictures, numbers, or words to express the cost of the home in two other ways. FOR SA LE $396,000

ones

tens

hundreds

thousands

ten thousands

hundred thousands

millions

3. 12,984

5. Use problems 1–4 for parts (a) and (b).

a. In which number is the value of the 8 ten times as much as the value of the 8 in 368? Circle your answer.

b. Explain your thinking.

Write the value of each digit.

6. 5, 18 4

Fill in the blanks to make the statement true.

8. In 6,274, the value of the digit 6 is

9. In 91,307, the digit is in the ten thousands place.

10. In 520,841, the digit in the hundreds place is and the digit in the hundred thousands place is

Represent each number with digits on the place value chart. Then circle the number that is greater.

Use >, =, or < to compare the numbers. Explain your thinking.

Use

Arrange the numbers from least to greatest.

26. 16,832, 26,081, 26,108, 16,283 , , ,

27. 704,129, 710,009, 800,100, 704,219 , , ,

28. Robin has $8,615 in the bank. Deepa has $8,061 in the bank. Who has more money in the bank? Explain how you know.

29. Miss Wong asks her students to compare 37,605 and 37,065.

Jayla says 37,605 is less than 37,065.

Ray says 37,065 is less than 37,605

Who is correct? Explain how you know.

1. Rename 4,215 in different ways. thousands hundreds tens ones 4 2 1 5

a. thousands hundreds ten ones

b. hundreds ten ones

c. tens ones

d. ones

2. Rename 23,048 in different ways.

a. ten thousands thousands hundreds tens ones

b. thousands hundreds tens ones

c. hundreds tens ones

d. tens ones

e. ones

Name

3. Rename 847,520 in different ways.

a. ten thousands thousands hundreds tens ones

b. 83 ten thousands thousands hundreds tens ones

c. thousands 5 hundreds tens ones

d. thousands hundreds tens ones

4. Use unit form to rename 905,438 in different ways.

Name

1. Represent 1,315 on the place value chart to match the given unit form.

a. 1 thousand 3 hundreds 1 ten 5 ones

hundredstensones thousands

b. 13 hundreds 1 ten 5 ones

hundredstensones thousands

3. Rename 73,905 in different ways.

ten thousands thousands hundreds tens ones thousands hundreds tens ones hundreds tens ones tens ones ones

Write the answer for each question.

4. How many thousands are in the thousands place in 83,106? thousands

5. How many thousands are in 83,106? thousands

6. How many ten thousands are in the ten thousands place in 251,472? ten thousands

7. How many ten thousands are in 251,472?

ten thousands

8. Oka wants to represent 12,751 on a place value chart. Write two different ways Oka can show the number.

Find the mystery number and write it in standard form. Explain your thinking with pictures, numbers, or words.

9. I have 6 ones, 550 thousands, and 12 hundreds. What number am I?

10. I have 11 thousands, 8 ten thousands, 36 ones, and 9 hundreds. What number am I?

Name            Date

Think about the number 2,437

a. Which choice does not represent 2,437?

A. 2 thousands 4 hundreds 3 tens 7 ones

B. 24 hundreds 3 tens 7 ones

C. 24 tens 37 ones

D. 2,437 ones

b. Explain how you know.

ones

tens

hundreds

thousands

ten thousands

hundred thousands

millions

Draw or cross out disks on the chart to match the statement. Then complete the statement.

1 thousand more than 74,236 is .

1 ten thousand less than 850,314 is .

1.

2.

Complete each statement and equation.

3. 1,000 more than 82,764 is .

82,764 + 1,000 =

5. 10,000 less than 60,230 is

60,230 − 10,000 =

Use the rule to complete the number pattern.

7. Rule: Add 1,000 68,381

8. Rule: Subtract 10,000 821,049

4. is 10,000 more than 51,093. = 51,093 + 10,000

6. is 100,000 less than 579,018 = 579,018 − 100,000

13. What is the rule for problem 12? Explain how you found the rule.

Use the Read–Draw–Write process to solve each problem.

14. 359,286 people attended a music festival this year. That amount is 100,000 more people than last year. How many people attended the music festival last year?

15. Casey completes the pattern below by using this rule: Subtract 100,000. Explain Casey’s error.

Complete each statement.

1. 1,000 more than 341,268 is .

2. 100,000 less than 753,722 is . Use the rule to complete each number pattern.

3. Rule: Add 1,000 23,500

4. Rule: Subtract 10,000

649,015

Round to the nearest thousand. Draw a number line to show your thinking.

5. 189,735 ≈

6. 503,500 ≈

7. 99,631 ≈

8. 475,582 ≈

9. The Toy Company made 344,499 toys last year. To the nearest thousand, about how many toys did they make?

10. Mr. Davis buys 55,555 kilograms of gravel. He asks Shen and Zara to round the weight to the nearest thousand. Shen says 60,000 kilograms. Zara says 56,000 kilograms. Who is correct? Explain your thinking.

Round to the nearest thousand. Draw a vertical number line to show your thinking.

1. 6,215

Round to the nearest ten thousand. Show your thinking on the number line. The first one is started for you.

70,000 = 7 ten thousands

65,000 = 6 ten thousands 5 thousands

60,000 = 6 ten thousands

1. 62,012 ≈

2. 37,159 ≈

3. 155,401 ≈

4. 809,253 ≈

Name            Date

Round to the nearest hundred thousand. Use the number line to show your thinking. The first one is started for you.

400,000 = 4 hundred thousands

350,000 = 3 hundred thousands 5 ten thousands

300,000 = 3 hundred thousands

9. 899,604 people live in Sun City. About how many people live in Sun City? Round to the nearest ten thousand.

10. Mr. Lopez writes a number. He asks three students to round it to the nearest hundred thousand.

a. Which student correctly rounded the number to the nearest hundred thousand? Explain how you know.

b. Circle the mistakes and explain what the other students did that was incorrect.

Round to the nearest ten thousand. Draw a vertical number line to show your thinking.

a. 51,578 ≈

b. 35,124 ≈

Write the sum or difference.

Number Correct:

Write the sum or difference.

BImprovement:      1.

1. Round 870,215 to each given place value.

a. Nearest hundred thousand 870,215 ≈

b. Nearest ten thousand 870,215 ≈

c. Nearest thousand 870,215 ≈

2. Round 97,513 to each given place value.

a. Nearest ten thousand 97,513 ≈

b. Nearest thousand 97,513 ≈

c. Nearest hundred 97,513 ≈

3. A stadium has 97,513 seats.

a. About how many seats does the stadium have?

b. What place value unit did you choose for rounding? Explain.

Round each number to the given place. Show your thinking on a number line.

1. 123,400

a. Nearest hundred thousand 123,400 ≈

b. Nearest ten thousand 123,400

2. 262,048

3. 99,909

Nearest hundred thousand

Nearest hundred thousand

Nearest ten thousand

Nearest ten thousand

Nearest thousand

Nearest thousand

4. 53,604

5. 489,025

6. 4,509 rounded to the

7. 17,360 rounded to the nearest

8. 34,911 rounded to the nearest ten thousand is 30,000.

9. 628,903 rounded to the nearest ten thousand is 630,000

10. 554,207 rounded to the nearest hundred thousand is 500,000

11. Miss Diaz thinks of a number. She asks four students to determine the number. She tells them that the number is the lowest possible number that rounds to 40,000

Who is correct? Explain your answer.

764,903 to the given place.

Name

1. Company A needs to order computers for 7,165 people. It rounds 7,165 to the nearest hundred to estimate how many computers to order. Will there be enough computers for each person to get 1 computer? Explain.

2. Eva’s swimming pool has a capacity of 9,327 gallons. Eva’s parents each round the number of gallons needed to fill the pool.

Her dad rounds to the nearest thousand and her mom rounds to the nearest hundred.

Whose estimate is more accurate? Explain.

3. Gabe has $70. He wants to buy a book bag that costs $34, a book that costs $19, and a calculator that costs $24.

a. Gabe estimates the total cost of all three items by rounding each price to the nearest ten. What is his estimate?

b. Gabe thinks he has enough money. What is the actual total cost of the three items?

c. Does Gabe have enough money?

d. To make sure he has enough money, what strategy could Gabe use to estimate?

4. Amy will win a prize if she sells 300 boxes of cookies. She sells 51 boxes in January and 104 boxes in February. Should Amy round to the nearest hundred or nearest ten to estimate the number of boxes she still needs to sell? Explain.

Date

Mr. Lopez plans to buy snacks for his students. He has 24 students in his first class, 18 students in his second class, and 23 students in his third class.

Estimate how many snacks Mr. Lopez should buy. Explain how you estimated and why.

Name

ones

tens

hundreds

thousands

ten thousands

hundred thousands

millions

Use the Read–Draw–Write process to solve each problem.

13. At a fair, 5,862 tickets were sold on Saturday. 3,977 tickets were sold on Sunday.

How many total tickets were sold on the two days?

14. Deepa and Ivan are playing a video game. Deepa scores 108,572 points and Ivan scores 86,029 points.

How many points do they score altogether?

15. A national park had 496,625 visitors in June. There were 220,837 more visitors in July than in June.

How many visitors did the park have in July?

Add by using the standard algorithm.

1.

2.

3.

Name

Use the Read–Draw–Write process to solve the problem.

1. A flower shop sold 14,976 lilies in one year. They sold 7,488 more roses than lilies that year. How many flowers did the shop sell altogether?

Lilies Roses

Use the Read–Draw–Write process to solve the problem.

2. On Saturday, 125,649 more packages were delivered than were delivered on Sunday. On Sunday, 293,848 packages were delivered. How many packages were delivered on both days combined?

Use the Read–Draw–Write process to solve the problem.

3. A shoe factory made 218,050 pairs of men’s shoes. The factory made 83,960 more pairs of women’s shoes than men’s shoes. They also made 74,308 more pairs of children’s shoes than men’s shoes. How many pairs of shoes did the factory make altogether?

Use the Read–Draw–Write process to solve each problem.

1. A fish market sold 1,618 tunas. They sold 857 more salmon than tuna.

a. About how many fish did the fish market sell?

Estimate by rounding each number to the nearest hundred before adding.

b. Exactly how many fish did the fish market sell altogether?

c. Is your answer reasonable? Compare your estimate from part (a) to your answer from part (b). Explain your reasoning.

2. A museum has 273 Spanish stamps. It has 829 more French stamps than Spanish stamps. It has 605 Italian stamps.

a. About how many stamps does the museum have from all three countries? Round each number to the nearest hundred to find your estimate.

b. Exactly how many stamps does the museum have from all three countries?

c. Determine whether your answer in part (b) is reasonable. Use your estimate from part (a) to explain.

3. A national park had 17,842 visitors in December 2019. There were 9,002 more visitors in December 2018 than in December 2019.

How many visitors did the park have in December 2018 and 2019 combined? Is your answer reasonable? Explain.

4. Casey has 3,746 baseball cards. Jayla has 1,578 more baseball cards than Casey.

Zara has 1,096 more baseball cards than Casey. How many baseball cards do they have altogether?

Is your answer reasonable? Explain.

Use the Read–Draw–Write process to solve the problem.

An ice cream company sold their product and earned money.

• They earned $7,228 in January.

• They earned $2,999 more in February than in January.

• They earned the same amount in March as they did in February.

How much money did the ice cream company earn altogether? Is your answer reasonable? Explain.

ones

tens

hundreds

thousands

ten thousands

hundred thousands

Subtract by using the standard algorithm.

Use the Read–Draw–Write process to solve each problem.

10. The sum of two numbers is 25,286. One number is 4,983. What is the other number?

11. Mount Everest is the highest mountain on Earth. It has a height of 29,029 feet. Denali is the highest mountain in the United States. It has a height of 20,310 feet. How many feet higher than Denali is Mount Everest?

12. There are 105,894 people at a football game. 31,792 of them are children and the rest are adults. How many adults are at the football game?

Subtract by using the standard algorithm.

1. 2 54, 9 712,1

2. 3, 42 22 51, 11 0 –

3. 73,658 − 8,052

ones

tens

hundreds

thousands

ten thousands

hundred thousands

Subtract by using the standard algorithm.

Use the Read–Draw–Write process to solve each problem.

10. What number must be added to 7,918 to result in a sum of 14,739?

11. Building A is 1,776 feet tall. Building B is 2,717 feet tall. How many feet taller is building B than building A?

12. Mr. Endo’s company earned $79,075 in its first year. His company earned $305,608 in its second year.

How much more money did Mr. Endo’s company earn in the second year than in the first year?

Subtract by using the standard algorithm.

1.

50 9, 3 1

5, –7 61

2. 32,480 − 2,546

Use the Read–Draw–Write process to solve the problem.

3. A donut shop sold 1,232 donuts in one day. 876 of the donuts were sold in the morning. How many donuts were sold during the rest of the day?

ones

tens

hundreds

thousands

ten thousands

hundred thousands

millions

Subtract by using the standard algorithm.

Use the Read–Draw–Write process to solve each problem.

9. A school raised $17,852 during its fall fundraiser and $35,106 during its spring fundraiser. How much more money did the school raise in the spring than in the fall?

10. Robin’s website had 439,028 visitors. Luke’s website had 500,903 visitors. How many more visitors did Luke’s website have than Robin’s?

11. A book company sells 306,428 copies of a new book. The company’s goal is to sell 1 million copies.

How many more copies does the company need to sell to reach the goal?

Name

1. Subtract.

956,204 − 780,169

Use the Read–Draw–Write process to solve the problem.

2. A construction company is building a brick school. 100,000 bricks were delivered. The company uses 15,631 bricks during the first day. How many bricks are left?

Use the Read–Draw–Write process to solve each problem.

1. A farmer sold 16,308 pounds of corn on Monday. She sold 27,062 pounds of corn on Tuesday. She sold some more corn on Wednesday. In all, she sold 73,940 pounds of corn.

a. Estimate the number of pounds of corn the farmer sold on Wednesday. Round each value to the nearest thousand.

b. Find the number of pounds of corn the farmer sold on Wednesday.

c. Is your answer reasonable? Use your estimate from part (a) to explain.

2. In June, a farmer sold 342,651 liters of milk. In July, the farmer sold 113,110 fewer liters than in June.

a. Estimate the total number of liters of milk the farmer sold in June and July. Round each value to the nearest hundred thousand.

b. How many total liters of milk did the farmer sell in June and July?

c. Is your answer reasonable? Use your estimate from part (a) to explain.

3. A tuna fishing company’s boat costs $316,875. It costs $95,300 more than the catfish company’s boat.

What is the combined cost of the tuna company’s boat and the catfish company’s boat? Is your answer reasonable? Explain.

4. A shirt company made a total of 300,000 shirts on Monday and Tuesday. On Monday, the company made 141,284 shirts.

How many more shirts did the company make on Tuesday than on Monday? Is your answer reasonable? Explain.

Use the Read–Draw–Write process to solve the problem.

A company sold 74,002 pillows last week.

They sold 15,235 pillows on Monday. They sold 14,827 pillows on Tuesday. How many pillows did they sell during the rest of the week?

1. A factory has rolls of wire.

There is 10,650 feet of blue wire.

There is 3,780 fewer feet of red wire than blue wire.

There is 1,945 fewer feet of green wire than red wire.

How much wire does the factory have altogether?

Use the Read–Draw–Write process to solve the problem.

2. A water park had 240,140 visitors in the spring.

There were 81,394 more visitors in the summer than in the spring.

The water park is closed in the winter.

There were 708,488 total visitors for the year.

How many visitors were there in the fall?

Name

2. A company sells 13,463 friendship cards and 8,029 get well cards. It sells 1,774 more wedding cards than get well cards. It sells 868 more thank you cards than friendship cards.

What was the total number of cards sold?

3. A company has 3 locations.

Location A has 29,785 employees.

Location B has 2,089 fewer employees than location A.

The company has 81,802 total employees.

How many employees are at location C?

Use the Read–Draw–Write process to solve the problem.

Park A covers an area of 3,837 square kilometers.

Park A is 1,954 square kilometers larger than Park B.

Park C is 2,108 square kilometers larger than Park A.

What is the total area of all three parks? Is your answer reasonable? Explain.

Use the charts to complete the statements and equations.

1 meter is times as long as 1 centimeter.

1 m = × 1 cm 1 meter = centimeters

Complete the conversion tables.

1 kilometer is times as long as 1 meter.

1 km = × 1 m

1 kilometer = meters

Use the Read–Draw–Write process to solve each problem.

19. James is 138 centimeters tall. A giraffe is 4 meters 5 centimeters tall. How much taller is the giraffe than James?

20. Mrs. Smith has a red ribbon and a blue ribbon. The red ribbon is 9 meters 60 centimeters long. The blue ribbon is 264 centimeters long. What is the total length of both ribbons?

21. Ray, Zara, and Shen run a combined distance of 10 kilometers. Ray runs 4,970 meters.

Zara runs 3 kilometers 98 meters. How far does Shen run?

1. Complete the conversion table.

Use the Read–Draw–Write process to solve the problem.

2. Gabe hikes a trail that is 4 kilometers 578 meters long. The next day, he hikes a trail that is 3 kilometers 154 meters long. How far did Gabe hike altogether?

Use the Read–Draw–Write process to solve the problem.

6. Mrs. Smith mixes iced tea and lemonade for a party. She combines 2,250 mL of iced tea with 1 L 750 mL of lemonade. How much iced tea and lemonade does she have altogether?

Use the Read–Draw–Write process to solve the problem.

7. A bag of dog food weighs 13 kg. Eva’s dog has already eaten 11 kg 75 g of the food. How many grams of dog food are left?

Use the charts to complete the statements and equations.

Use the Read–Draw–Write process to solve each problem.

13. The table shows the weights of 3 dogs. What is the difference in weight between the heaviest dog and lightest dog?

Dog Weight

Spot 24 kg 9 g Duke 2,458 g

Teddy 24 kg 50 g

14. Amy drinks 2 L 80 mL of water. She drinks 265 mL more than Oka. How much water does Oka drink?

15. A baker has 50 kilograms of flour. He uses 19 kilograms 50 grams for cupcakes and 7,860 grams for pretzels. He uses the rest for bread. How much flour does the baker use for bread?

Use the Read–Draw–Write process to solve the problem.

3. A watermelon weighs 8 kilograms 749 grams. Another watermelon weighs 10 kilograms 239 grams. What is the difference in weight between the two watermelons?

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.

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

Cover, Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Arts, MN. Gift of Bruce B. Dayton/Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York; All other images are the property of Great Minds.

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

Acknowledgments

Kelly Alsup, Lisa Babcock, Adam Baker, Reshma P. Bell, Joseph T. Brennan, Leah Childers, Mary Christensen-Cooper, Jill Diniz, Janice Fan, Scott Farrar, Krysta Gibbs, Torrie K. Guzzetta, Kimberly Hager, Eddie Hampton, Andrea Hart, Rachel Hylton, Travis Jones, Liz Krisher, Courtney Lowe, Bobbe Maier, Ben McCarty, Ashley Meyer, Bruce Myers, Marya Myers, Victoria Peacock, Maximilian Peiler-Burrows, Marlene Pineda, Elizabeth Re, Jade Sanders, Deborah Schluben, Colleen Sheeron-Laurie, Jessica Sims, Tara Stewart, Mary Swanson, James Tanton, Julia Tessler, Jillian Utley, Saffron VanGalder, Rafael Velez, Jackie Wolford, Jim Wright, Jill Zintsmaster

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

Share Your Thinking

Talking Tool

I know . . . .

I did it this way because . . . .

The answer is because . . . .

My drawing shows . . . .

Agree or Disagree

I agree because . . . . That is true because . . . .

I disagree because . . . .

That is not true because . . . .

Do you agree or disagree with ? Why?

Ask for Reasoning

Why did you . . . ?

Can you explain . . . ?

What can we do first?

How is related to ?

Say It Again

I heard you say . . . . said . . . .

Another way to say that is . . . .

What does that mean?

Thinking Tool

When I solve a problem or work on a task, I ask myself

Before Have I done something like this before?

What strategy will I use?

Do I need any tools?

During Is my strategy working?

Should I try something else?

Does this make sense?

After

What worked well?

What will I do differently next time?

At the end of each class, I ask myself

What did I learn?

What do I have a question about?

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

Place Value Concepts for Addition and Subtraction

Module 2

Place Value Concepts for Multiplication and Division

Module 3

Multiplication and Division of Multi-Digit Numbers

Module 4

Foundations for Fraction Operations

Module 5

Place Value Concepts for Decimal Fractions

Module 6

Angle Measurements and Plane Figures

What does this painting have to do with math?

American abstract painter Frank Stella used a compass to make brightly colored curved shapes in this painting. Each square in this grid includes an arc that is part of a design of semicircles that look like rainbows. When Stella placed these rainbow patterns together, they formed circles. What fraction of a circle is shown in each square?

On the cover

Tahkt-I-Sulayman Variation II, 1969

Frank Stella, American, born 1936 Acrylic on canvas

Minneapolis Institute of Art, Minneapolis, MN, USA

Frank Stella (b. 1936), Tahkt-I-Sulayman Variation II, 1969, acrylic on canvas. Minneapolis Institute of Art, MN. Gift of Bruce B. Dayton/ Bridgeman Images. © 2020 Frank Stella/Artists Rights Society (ARS), New York