multiply(whole( numbers expressions(andmultiplication...

Name: _______________________________________ Date: __________________

© Lincoln Public Schools, 2014 5th Grade Math

Chapter 3 Multiply Whole

Numbers HW 3.1A Expressions and Multiplication Properties

Practice to review…I can evaluate algebraic expressions and use the properties of multiplication!

_______________________ Property

The product of any number and one

is that number .

_______________________ Property

The product of any number and zero

is zero .

The _______________________ Property

I can change the way factors are grouped

without changing the product .

The _______________________ Property

I can change the order of factors

without changing the product

I can find the product of 5 × 2 × 3 in more than one way. Parentheses show what I evaluate first.

I can evaluate 5 × 2 first. I can evaluate 2 × 3 first. I can evaluate 5 × 3 first.

5 × 2 × 3 = × 3 = 5 × 2 × 3 = 5 × = 5 × 3 × 2 = × 2 =

Practice to remember… Write an algebraic expression for each statement.

1. a number divided by 6 2. a number multiplied by 9 3. a number increased by 7

____________________ ___________________ ____________________

4. twelve times a number 5. 55 more than a number 6. a number divided by 15

____________________ ___________________ ____________________

Use mental math and the properties of multiplication to evaluate each expression.

7. 1 × 15 × 2 8. 35 × 6 × 0 9. 25 × 7 × 4

________________________ _______________________ _______________________

Name: _______________________________________ Date: __________________



Numbers RE 3.1A Remembering

Practice for fluency… Solve each equation for the variable given.

10. 𝑓 − 26 = 44 11. 17+ 𝑏 = 30

a. 70 a. 3

b. 60 b. 13

c. 44 c. 27

d. 18 d. 47

Write each number in standard form.

12. 6 thousand, 430 13. 200,000 + 10,000 + 9,000 + 50 + 3

____________________ ___________________

Write the value of the underlined digit.

14. 482,509 _______________________ 15. 537,460 ______________________

Use the table to answer each question. Explain your thinking.

16. The distance listed for the Red Knot may actually be half of the distance the bird traveled during the year. If this is so, how far did the bird migrate in a year? Show how you know.

17. Using your answer from Problem #16, how many miles does the Red Knot travel in 3 years? Show how you know.

Name: _______________________________________ Date: __________________



Numbers HW 3.1B Expressions and Multiplication Properties

Practice to review…I can evaluate algebraic expressions and use properties of multiplication!

Identity Property

The product of any number and one

is __________________ .

Zero Property

The product of any number and zero

is __________________ .

The Associative Property

I can change the way factors are _____________

without changing the __________________ .

The Commutative Property

I can change the ________________ of factors

without changing the __________________ .

I can find the product of 3 × 2 × 4 in more than one way. Parentheses show what I evaluate first.

I can evaluate 3 × 2 first. I can evaluate 2 × 4 first. I can evaluate 4 × 3 first.

3 × 2 × 4 = × 4 = 3 × 2 × 4 = 3 × = 4 × 3 × 2 = × 2 =

Practice to remember… Write an algebraic expression for each statement.

1. a number multiplied by 6 2. a number added to 57 3. 64 divided by a number

________________________ _______________________ _______________________

Use mental math and the properties of multiplication to evaluate each expression.

4. 2 × 56 × 5 _________ 5. 5 × 34 × 20 _________ 6. 50 × (2 × 78) _________

Evaluate each expression, given 𝒏 = 𝟐, 𝒓 = 𝟓, and 𝒔 = 𝟔.

7. 4𝑠 ___________ 8. 3 • 𝑛 • 𝑟 ___________ 9. 4+ 𝑠 × 𝑟 ___________

Evaluate the expressions to answer the question.

10. Given that 𝒙 = 𝟒, 𝒚 = 𝟏𝟑, and 𝒛 = 𝟐𝟓, which expression equals 1,300?

a. 𝑥 + 6 × 𝑧 b. 𝑥 • 𝑧 + 13 c. 13− 𝑦 × 𝑥 + 𝑧 d. 𝑥 • 𝑦 • 𝑧

Name: _______________________________________ Date: __________________



Numbers RE 3.1B Remembering

Practice for fluency… Describe the relationship between the pair of lines.

11.

a. parallel 12.

a. parallel

b. perpendicular b. perpendicular

c. intersecting c. intersecting

Write in standard form. Write the value of the underlined digit in words.

13. five hundred three thousandths 14. 5.782

__________________________________ _________________________________

Write in word form.

15. 2.014 16. 0.023

__________________________________ _________________________________

Answer each question. Explain your thinking.

17. Draw a 4-‐sided polygon with opposite sides parallel and 4 right angles. What is the best name for your shape? Why?

18. Becca is running a 26.2-‐mile marathon. She has just reached the 14 mile mark. Write an equation to show how many miles she still needs to run. Solve the equation and explain what the variable represents.

Name: _______________________________________ Date: __________________



Numbers HW 3.2 Model the Distributive Property

Practice to review…I can use the Distributive Property to multiply!

The ____________________ ____________________ of Multiplication over Addition says that multiplying a sum by a number is the same as

multiplying each addend by that number and then adding the partial products.

Here are some examples of using The Distributive Property of Multiplication to find the product of 4 × 23.

I can multiply 4 × 20 and then add 4 × 3. I can double 23 twice.

4 × 23 = 4 × +

4 × 23 = 4 × + 4 ×

4 × 23 = +

4 × 23 =

4 × 23 = + × 23

4 × 23 = × 23 + × 23

4 × 23 = +

4 × 23 =

Practice to remember… Use the grid to find the product.

1.

2.

4 × 13 = 5 × 22 =

3.

4.

8 × 16 = 7 × 19 =

Name: _______________________________________ Date: __________________



Numbers RE 3.2

Practice to remember, continued… Find each product.

5. 3 × 17 = 6. 6 × 24 =

Remembering Practice for fluency… Which property of multiplication is illustrated?

7. 3 × 4 = 4 × 3 8. 12 × 2 × 5 = 12 × 2 × 5 a. Associative Property a. Associative Property b. Commutative Property b. Commutative Property c. Identity Property c. Identity Property d. Zero Property d. Zero Property Label each angle as acute, obtuse, right, or straight. 9.

______________

10.

______________

11.

______________

12.

______________


13. Tell if the statement below is true or false. Explain.

Some polygons are open figures.

14. A drama club sold 768 tickets to Friday’s show and 922 tickets to Saturday’s show. About how many tickets did the club sell altogether? Show how you know.

Name: _______________________________________ Date: __________________



Numbers HW 3.4A Multiply by One-‐Digit Numbers

Practice to review…I can multiply by one-‐digit numbers! I can use different strategies to find the product of 7 × 364. Distributive Property Show All Products

!

7×364 = 7×( ) + 7×( ) + 7×( )7×364 = + +

7×364 =

!

364× 7

7×4← ###7×60← ###

+ 7×300← ###

Regrouping

!

364× 7

Practice to remember… Find each product. Show your thinking.

1. 3 × 56 = 2. 8 × 615 = 3. 9 × 31 =

4. 2,778

× 6 5. 782

× 7 6. 8,113

× 2

Name: _______________________________________ Date: __________________




Practice for fluency… Multiply or divide.

7. 9 × 6 8. 7 ÷ 0 a. 3 b. 15 a. 0 b. 7 c. 54 d. 56 c. 70 d. no solution Add or subtract.

9. 7,778,673− 4,211,002 = 10. 785,928 + 216,904

11. 862,094 − 74,198

12. 2,880,199+ 3,857,735 =


13. Complete the pattern. Show how you know.

1 , 2 , 4 , 7 , 11 , , , 29

14. The circle graph shows how Jocelyn spent her day. Which activity did Jocelyn spend the most time doing? Explain.

Name: _______________________________________ Date: __________________



Numbers HW 3.4B Multiply by One-‐Digit Numbers

Practice to review…I can multiply by one-‐digit numbers! I can use different strategies to find the product of 4 × 384. Distributive Property Show All Products

!

4 ×384 = 4 ×( ) + 4 ×( ) + 4 ×( )4 ×384 = + +

4 ×384 =

!

384× 4

4×4← ###4×80← ###

+ 4×300← ###

Regrouping

!

384× 4

Practice to remember… Find each product. Show your thinking.

1. 7 × 95 = 2. 6 × 58 = 3. 9 × 561 =

4. 3,815

× 4 5. 737

× 5 6. 16,529

× 3

Name: _______________________________________ Date: __________________



Numbers RE 3.4B

Practice to remember, continued… Answer the question. Explain your thinking.

7. There are 144 notebooks in one carton. How many notebooks are in 8 cartons? Show how you know.

Remembering Practice for fluency… 8. Solve for 𝑚.

21−𝑚 = 16 9. Estimate 5,722− 1,490 by rounding to the

greatest place.

a. 4 b. 15 a. 7,000 b. 5,000 c. 5 d. 37 c. 6,000 d. 4,000

Compare. Write > , < , or = for each . Round to the place of the underlined digit.

10. 0.7 0.008 11. 0. 343 ________________________

12. 1.475 1.494 13. 0.635 ________________________

Write and solve a multiplication equation for each model. Show how you find the product.

14.

15.

Name: _______________________________________ Date: __________________



Numbers HW 3.5A Mental Math: Patterns in Multiples of 10

Practice to review…I can use basic facts and mental math to multiply!

I can find the product of 7 × 500

I know that 500 is equivalent to 5 hundreds, 7 × 5 hundreds = _______ hundreds

so 7 × 500 = 7 × 5 hundreds 7 × 500 = ____________

I can also find the product of 40 × 60 I know that 40 × 6 = _______ because 4 × 6 = _____

I know that 60 is equivalent to 6 tens 40 × 6 tens = _______ tens

so 40 × 60 = 40 × 6 tens 40 × 60 = ____________ Practice to remember… Use basic facts and patterns to find each product.

1. 4 × 40 2. 7 × 50 3. 8 × 90 4. 3 × 800

_________ _________ _________ _________

5. 20 × 10 6. 40 × 30 7. 50 × 40 8. 300 × 80

_________ _________ _________ _________

Compare. Choose >, <, or = for each .

9. 20×90 1,800 10. 20×500 1,000

Solve. Use pictures, numbers, or words to show how you know.

11. The school sold 200 books each day for 10 days. How many books did the school sell?

THINK

THINK

Name: _______________________________________ Date: __________________




Practice for fluency… Complete each equation.

12. 36÷ 4 = 13. ÷ 4 = 6 a. 7 b. 8 a. 20 b. 24 c. 9 d. 10 c. 28 d. 32 Multiply.

14. 9 × 8,720 = 15. 564 × 6

16. 972 × 4

17. 721,053 × 4 =

18. Write and solve a multiplication equation for the model. Show how you find the product.

19. According to the graph, which grade read more books in all? How many more? Explain.

Name: _______________________________________ Date: __________________



Numbers HW 3.5B Mental Math: Patterns in Multiples of 10

Practice to review…I can use basic facts and mental math to multiply!

I can find the product of 20 × 500 I know that 20 × 5 = _______ because 2 × 5 = _____

I know that 500 is equivalent to 5 hundreds 20 × 5 hundreds = _______ hundreds

so 20 × 500 = 20 × 5 hundreds So 20 × 500 = ____________ Practice to remember… Solve. Use pictures, numbers, or words to show how you know.

1. The post office sells books of 20 stamps and rolls of 100 stamps. If a customer buys 5 books of stamps and 4 rolls of stamps, how many stamps does the customer buy? Show how you know.

2. Paper hinges attach stamps to albums. A stamp dealer has 20 packages of hinges with 1,000 hinges per package. If she sells all but 9 packages, how many hinges does she sell? Show how you know.

3. A stamp dealer sells packages of assorted stamps. There are 200, 300, 400, 600, or 800 stamps in a package. A customer buys 3 of the same package and gets a total of 2,400 stamps. Which set of stamps did the customer buy? Explain.

THINK

Name: _______________________________________ Date: __________________



Numbers RE 3.5B

Practice to remember, continued… Solve. Use pictures, numbers, or words to show how you know.

4. A sheet of one-‐cent stamps is set in an array of 5 stamps × 10 stamps. How many stamps are on 300 sheets? Show how you know.

Remembering Practice for fluency… Use a pattern or mental math to find each product.

5. 80 × 80 6. 3,000 × 70 a. 64 b. 640 a. 210 b. 2,100 c. 6,400 d. 64,000 c. 21,000 d. 210,000 Do the figures in each pair appear to be congruent? Write yes or no.

7.

___________

8.

___________

9.

___________

10.

___________

Use the graph on the right. Write the letter for each ordered pair.

11. (1, 4) ________ 12. (2, 0) ________

Use the graph on the right. Write the ordered pair for each point.

13. 𝐼 __________ 14. 𝐻 __________

Name: _______________________________________ Date: __________________



Numbers HW 3.6A Estimate Products

Practice to review…I can round numbers to estimate products! I can estimate the product of 47 × 238

Step 1 Round each factor: 47 × 238 is about is about

�

↓

�

↓

Step 2 Use mental math to estimate: _________ × _________

47 × 238 is about ______________

Practice to remember… Estimate the product by rounding each factor to its greatest place.

1. 33 × 45 2. 803 × 72 3. 81 × 31 4. 75 × 46

______________ ______________ ______________ ______________

5. !

83× 55 6.

!

185× 43 7.

!

68× 24

8. !

387× 29

9. It takes Earth 365 days to make 1 complete trip around the sun. About how many days will it take the Earth to travel around the sun 12 times? Show how you know.

THINK What basic

fact wil l help?

Name: _______________________________________ Date: __________________




Practice for fluency… Evaluate each expression

10. 6 • 𝑠 • 𝑡 when 𝑠 = 14 and 𝑡 = 29 11. 76𝑦 when 𝑦 = 42 a. 84 b. 406 a. 3,192 b. 2,982 c. 2,436 d. 2,706 c. 2,812 d. 118 Write a fact family for each set of numbers.

12. 2 , 4 , 8 13. 3 , 8 , 24

14. 2 , 7 , 14 15. 9 , 9 , 81

16. Jacob walks !!" of a mile to school. Luis walks 0.77 miles to school. Who walks farther? Explain how you

know.

17. A student wrote 0.328 in word form as three hundred and twenty-‐eight hundredths. Is the student correct? Explain.

Name: _______________________________________ Date: __________________



Numbers HW 3.6B Estimate Products

Practice to review…I can find a range to estimate products! I can use what I know about Rounding to find a low estimate and a high estimate (a range). The actual product will be between my two estimates!

!

200 ←"" 238 "→"

× ←"" × 47 "→" × 50< <

Practice to remember… Round to find a range.

1. 67 × 41 Range: _______________________ 2. 798 × 43 Range: _______________________

3. 74 × 88 Range: _______________________ 4. 909 × 52 Range: _______________________

5. 888 × 29 Range: _______________________ 6. 43 × 67 Range: _______________________

The product is between the low estimate and the high estimate!

47 is between

_____ and 50

238 is between 200

and _____

Name: _______________________________________ Date: __________________




Practice for fluency… Order from greatest to least. Round to the nearest billion.

7. 623,406 632,460 623,640 632,046 8. 43,567,819,210 a. 623,406 623,640 632,046 632,460 a. 44,000,000,000 b. 623,406 623,640 632,460 632,046 b. 43,000,000,000 c. 623,640 632,460 623,406 632,046 c. 43,600,000,000 d. 632,460 632,046 623,640 623,406 d. 40,000,000,000 Add or subtract.

9. 694,056+ 702,895 = 10. 359,561− 140,000 =

11. 3,254,082+ 2,100,000 = 12. 5,700,060− 2,532,049 =

Answer each question. Show your thinking.

13. Bob gave the cashier two $10 bills for groceries that were $16.57. How much change should he get back? Show how you know.

14. It is 294 miles from Indianapolis to Cleveland. A bicyclist plans to make this trip by traveling about 75 miles per day. Can he complete the trip in 4 days? Explain.

Name: _______________________________________ Date: __________________



Numbers HW 3.7A Multiply by Two-‐Digit Numbers

Practice to review…I can use the Distributive Property to multiply! I can use different strategies to find the product of 238 × 47. The Distributive Property

47 × 238 = 40 + 7 × 200 + 30 + 8

Regrouping (Standard U.S. Algorithm)

Show All Products

!238

× 47

!

238× 47

7×8← ###7×30← ###7×200← ###40×8← ###40×30← ###

+ 40×200← ###

Practice to remember… Multiply. Show your work. Estimate to check that your answer is reasonable.

1. 33 × 45

___________

2. 68 × 24

___________

3.

!

81× 31

4.

!

75× 46

THINK

Name: _______________________________________ Date: __________________




Practice for fluency… 5. What is the best estimate of 824 × 78 ? 6. Which product is between 2,100 and 3,200 ? a. 52,000 b. 56,000 a. 62 × 28 b. 72 × 38 c. 64,000 d. 72,000 c. 82 × 48 d. 92 × 58 Find each sum.

7. 0.45+ 2.39+ 7.7 ___________ 8. 72.34+ 48.31+ 8.49 ___________

9. $103.75+ $99.08 ___________ 10. 55+ 1.03+ 0.67 ___________

Answer each question. Show your thinking.

11. If you use this spinner, on which two letters is the arrow equally likely to land? Explain.

12. Mr. Rosa’s new carpet business, made $234 on Monday, $452 on Tuesday, $1,609 on Wednesday, $567 on Thursday, and $973 on Friday. Over the same five days, his competitor made $4,206. How much more did his competitor make than Mr. Rosa? Show how you know.

Name: _______________________________________ Date: __________________



Numbers HW 3.7B Multiply by Two-‐Digit Numbers


59 × 23 = 50 + 9 × +


Show All Products

!59

× 23

!

59× 23

3×9← ###3×50← ###20×9← ###

+ 20×50← ###


1. 74 × 88

___________

2. 387 × 29

___________

3.

!

798× 43

4.

!

99× 32

THINK

Name: _______________________________________ Date: __________________




Practice for fluency… 5. Which is the best estimate of

34.76+ 82.9+ 15.03 ? 6. Round to the greatest place to estimate the

difference 0.943− 0.472 a. 130 b. 100 a. 0.3 b. 0.4 c. 90 d. 13 c. 0.5 d. 0.6 Add or subtract.

7. 18+

58

___________ 8. 29+

19

___________

9. 710−

610

___________ 10. 58−

18

___________

Answer the questions. Show your thinking.

11. Marcy has 1 five-‐dollar bill, 4 quarters, and 7 dimes. Mathias has 4 one-‐dollar bills and 7 quarters. Who has more money? Show how you know.

12. Six bands each have 18 baton twirlers. How many baton twirlers are there in all? Show how you know.

Name: _______________________________________ Date: __________________



Numbers HW 3.7C Multiply by Two-‐Digit Numbers


72 × 803 = 70 + × 800 +


Show All Products

!803

× 72

!

803× 72

2×3← ###2×800← ###70×3← ###

+ 70×800← ###


1. 88 × 55

___________

2. 67 × 41

___________

3.

!

185× 43

4.

!

909× 52

THINK

Name: _______________________________________ Date: __________________



Numbers RE 3.7C

Practice to remember, continued… Answer the question. Show your work. 5. A plane carries 425 passengers. How many passengers can the plane carry in 24 trips? Show how you

know.

Remembering Practice for fluency… Order the numbers from greatest to least. 6. 0.38; 0.28; 0.47 7. 5.01; 0.52; 0.58 a. 0.47; 0.38; 0.28 b. 0.38; 0.47; 0.28 a. 5.01; 0.58; 0.52 b. 0.52; 5.01; 0.58 c. 028; 0.38; 0.47 d. 0.47; 0.28; 0.38 c. 5.01; 0.52; 0.58 d. 0.58; 0.52; 5.01 Match the model to the description. Write A or B.

8. !! is

9. !! is either or

___________ ___________

10. !! is

11. !! is not

___________ ___________

Use the table to answer the questions.

12. The tallest active volcano in the world is Llullaillaco in Chile. It is 4,127 feet taller than Popocatépetl, a volcano in Mexico. About how tall is Llullaillaco? Explain.

13. List the mountains in order of height from least to greatest.

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