Name ___________________________________ Date ______________________________ Period ______

Module 1 Packet

DECIMAL OPERATIONS

Standard 6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. Standard 6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

In Module 1, you will learn how to…

● ___ 1-1 Represent decimals (5.NBT.3a)

● ___ 1-2 Find the sums and differences of decimals (6.NS.B.3)

● ___ 1-3 Find the products of decimals (6.NS.B.3)

● ___ 1-4 Divide multi-digit numbers using the standard algorithm (6.NS.B.2)

● ___ 1-5 Divide multi-digit decimals using the standard algorithm (6.NS.B.3)

● ___ 1-6 Apply decimal operations to problem solving (6.NS.B.3)

Your Grade for 6.NS.B

The skills and concepts that you learn in this packet will appear as your grade for 6.NS.B Number Fluency.

A = 4 EXCEEDS You exceed the learning targets in understanding or application.

B = 3 MEETS You have met all the learning targets for this standard.

C = 2 DEVELOPING You are approaching the standards or have only partial understanding.

D = 1 WELL BELOW You have not yet met many of the standards.

Name_________________________________________________________________________________ 5.NBT.3a Lesson 1-1

Decimal Place Value

Learning Target: I can read, write, and represent decimals through thousandths.

Do Now

Write the decimal and fraction and represented by the shaded grid.

________ ________

________ ________

________ ________

Example 1- Understanding Decimals

Decimals are numbers that are written according to their place value. Decimals name wholes and parts of a whole.

The decimal point is used to separate whole numbers from number values less than one.

Directions: Shade the following values in the decimal grids below.

= 111 1.0 one

110

0.1 one-tenth

1100

0.01 one-hundredth

11000

0.001 one-thousandth

Exercise 1- Understanding Decimals

Write the decimal and fraction or mixed number for each model.

1)

2)

Decimal: Fraction or Mixed Number:

Decimal: Fraction or Mixed Number:

1

Example 2- Decimal Place Value Chart

Wholes ←

Fractional Part →

Ones Tenths Hundredths Thousandths

1 0.1 0.01 0.001

As you move from left to right on the place value chart, the value of each place is one-tenth the value of the place to its left.

You can use a place value chart to find the value of each digit in a number. Whole numbers are to the left of the decimal point and decimals are to the right of it.

2.759

Ones Tenths Hundredths Thousandths

2 . 7 5 9

2 _____ = _____× 7 _____ = _____× 5 _____ = _____× 9 _____ = ______×

Standard Form: Expanded Form:

Word Form:

Exercise 2- Decimal Place Value Chart

1) Complete the place value chart to find the value of each digit. Then write the word form below.

Tens Ones Tenths Hundredths Thousandths

9 7 . 3 5 2

Word Form:

Write the value of the underlined digit. 2) 7.241 ___________ 3) 0.59 ___________ 4) 60.147 ___________

5) Standard Form: 4.083 Expanded Form: ____________________________________________________________________ Word Form: ________________________________________________________________________

2

Example 3- Equivalent Decimals

Equivalent decimals are different names for the same number or amount.

Ways to determine if two decimals are equivalent:

1) Draw models. 2) Line up the decimal points and compare the digits in the same place-value position. 3) Use a number line.

EQUIVALENT NOT EQUIVALENT

_______ _______

Ones Tenths Hundredths

_______ _______

Ones Tenths Hundredths

Exercise 3- Equivalent Decimals

Write equivalent or not equivalent to describe each pair of decimals.

1) 0.09 and 0.009 2) 3.8 and 3.80 3) 4 and 4.0 4) 7.2 and 7.02

Write an equivalent decimal for each number.

5) 5.3 6) 0.03 7) 2.120

8) How can you determine if three and twenty thousandths is equivalent to 3.02?

3

Problem Set

Write as a decimal and a fraction or mixed number.

1)

2) 3 + 0.5 + 0.07 3) eighty and two tenths 4) thirty-two thousandths

Shade in the following values on the decimal grids.

5) 0.6

6) 1.49

Write each decimal in expanded form and word form.

6) 8.067

7) 52.03

8) 0.948

9) 7.5

Write in standard form.

10) fifty-four hundredths 11) one and three tenths 12) twenty-nine and sixty-two thousandths

Find the value of the digit.

13) A penny is 0.061 inch thick. What is the value of the 6 in the thickness of a penny?

___________

14) The diameter of the head of a screw is 0.306 inch. What is the value of the 3 in the diameter?

___________

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15) Write the correct letter on the blank line next to each decimal.

0.38 ______ 1.16 ______ 1.75 ______ 0.54 ______

0.70 ______ 1.47 ______ 0.02 ______ 1.50 ______

1.29 ______ 0.25 ______ 1.83 ______ 0.91 ______

Circle the two decimals that are equivalent.

16) 0.55

0.505

0.550

17) 3.300

3.3

3.030

18) 0.180

0.0180

0.018

Write an equivalent decimal for each number.

19) 6.2 20) 0.09 21) 0.400 22) 31.55

Problem Solving

23) Damian wrote the number four and twenty-three thousandths as 4.23. Describe and correct his error. 24) Explain how you know that the digit 6 in the numbers 0.675 and 0.756 does not have the same value. 25) Billy has $3.05 and Sean has $3.50. Write equivalent or not equivalent to describe these amounts. Explain your answer choice.

5

Name: __________________________________________________________________________________

6.NS.B.3 Lesson 1-2

Adding and Subtracting Decimals Learning Target: I can fluently add and subtract multi-digit decimals using the standard algorithm. Do Now

1) What is value of the digit 7 in New Mexico’s average annual rainfall? 2) The average annual rainfall in Maine is one and seventy four thousandths of a meter per year. Write that amount in the table. 3) Which of the states has an average annual rainfall with the least number in the thousandths place? 4) Write New York’s average annual rainfall in expanded form.

Average Annual Rainfall

(in meters)

California 0.564

New Mexico 0.372

New York 1.041

Wisconsin 0.820

Maine

Opening- Modeling Addition of Decimals

A chemist combines 0.17 mL of water and 0.49 mL of hydrogen peroxide in a beaker. How much total liquid is in the beaker?

A) How many grid squares should you shade to represent 0.17 mL of water? Why?

________________________________________________________________

B) How many grid squares should you shade to represent 0.49 mL of hydrogen peroxide? Why? ________________________________________________________________

C) Use the grid at the right to model the addition. Use one color for 0.17 mL

of water and another color for 0.49 mL of hydrogen peroxide.

D) How much total liquid is in the beaker? 0.17 + 0.49 = ________ mL

6

Example 1- Adding Decimals

Adding decimals is similar to adding whole numbers:

1) First align the numbers by place value. 2) Add zeros as placeholders when necessary. 3) Start adding at the right and regroup when necessary. 4) Bring down the decimal point into your sum.

Susan rode her bicycle 3.12 miles on Monday and 4.7 miles on Tuesday. How many miles did she ride in all?

Expression: ___________________________

Solve:

Estimate:

1) Why can you rewrite 4.7 as 4.70? 2) Why is it important to align the decimal points when adding?

Exercise 1- Adding Decimals

Calculate each sum. Then estimate to check if your answer is reasonable.

1) 0.42 + 0.27 = _______

2) 5.61 + 0.829 = _______

3) Perry connects a blue garden hose and a green garden hose to make one long hose. The blue hose is 16.5 feet. The green hose is 14.75 feet. How long is the combined hose?

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Example 2- Subtracting Decimals

The procedure for subtracting decimals is similar to the procedure for adding decimals:

1) First align the numbers by place value. 2) Add zeros as placeholders when necessary. 3) Start subtracting at the right and regroup when necessary. 4) Bring down the decimal point into your difference.

Matthew throws a discus 58.7 meters. Zachary throws the discus 56.12 meters. How much farther did Matthew throw the discus?

Expression: ___________________________

Solve:

Estimate:

Exercise 2- Subtracting Decimals

Calculate each difference. Then estimate to check if your answer is reasonable.

1) 18.419 - 6.47 = _______

2) 7.2 - 5.69 = _______

3) Ms. Tulips bought $56.12 worth of groceries. However, she had coupons worth $9.85. How much did Ms. Tulips spend for groceries?

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Problem Set

Calculate each sum or difference. Then estimate to check.

1) 5.4 + 8.7 = _______

2) 74.906 + 0.03 + 42 = _______

3) 462 - 31.2 = _______

4) 28.341 + 37.5 = _______

5) 25.36 - 2.004 = _______

6) 150.25 - 78 = _______

Solve. Show your work in the space provided.

7) A band can play as much as 8 minutes of music in a competition. If a band plays a 2.33 minute song and a 4.25 minute song, how many minutes does it have left?

8) You receive $50 for your birthday. You buy a book for $14.95 and a baseball cap for $24.95. How much money do you have left?

9) Steve spent $9.45 on a ticket to the game and $3.75 for snacks. He had $7.35 left at the end of the day. How much did he have at the beginning of the day?

9

Use the cafe menu to answer 10-12. Show your work in the space provided.

10) Stephen and Jahmya are having lunch. Stephen buys a garden salad, a veggie burger, and a lemonade. Jahmya buys a fruit salad, a toasted cheese sandwich, and a bottle of water. Whose lunch cost more? How much more?

11) Jahmya wants to leave $1.75 as a tip for her sever. She has a $20 bill. How much change should she receive after paying for her food and leaving a tip?

12) In addition to his meal, Stephen orders a fruit salad for take-out, and wants to leave $2.25 as a tip for his server. He has a $10 bill and a $5 bill. How much change should he receive after paying for his lunch, the fruit salad, and the tip?

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Name: __________________________________________________________________________________

6.NS.B.3 Lesson 1-3

Multiplying Decimals

Learning Target: I can fluently multiply multi-digit decimals using the standard algorithm.

Do Now

The Great Western Circus buys 100 pound quantities of cotton candy. On day one of the circus, they sold 21.66 pounds of cotton candy, and on day two, they sold 34.57 pounds of cotton candy. How much cotton candy in pounds was left over to sell on day three?

Example 1- Multiply Decimals and Whole Numbers

To multiply a whole number and a decimal, modeling with money can be helpful.

2 $0.21 = ________×

Model Algorithm

1) In the decimal grid, shade 0.21, two times. Use a different color each time.

1) Multiply the two factors the same way you multiply whole numbers.

0 . 2 1 ( ___ decimal places) 2 ( ___ decimal places)×

__________ ( ___ total decimal places)

2) Find the total number of decimal places in both factors. ___ + ___ = ___ total decimal places

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2) Count the number of shaded hundredths.

2 0.21 = ________×

3) Place the decimal point in the product by moving right the same number of places as the total number of decimal places in the factors.

2 0.21 = ________×

Exercise 1- Multiply Decimals and Whole Numbers

1) Giant tortoises move very slowly. They can travel a distance of about 0.17 mile in one hour. If it travels at the same speed, how far could the tortoise move in 4 hours?

A) Expression:

B) Model:

C) Algorithm:

D) Explain how the product of 4 groups of 0.17 is similar to the product of 4 groups 17. How is it different?

2) Jared has a parakeet that weighs 1.45 ounces. Susie has a parrot that weighs 3 times as much as Jared’s parakeet. How many ounces does Susie’s parrot weigh?

A) Expression:

B) Algorithm:

C) Explain how you know the product of the expression above is greater than 3.

3) One day on the planet Mercury lasts about 58.6 Earth days. How many Earth days are there in 24 days on Mercury?

A) Expression: B) Algorithm:

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Example 2- Multiply Decimals

The distance from Charlene’s house to her school is 0.8 mile. Charlene rides her bike 0.6 of the distance and walks the rest of the way. How far does Charlene ride her bike to school?

Expression: ____________________________

Model Algorithm

1) Shade columns on the grid to represent the distance to Charlene’s school.

How many columns did you shade? _____ columns 2) Using a different color, shade rows that overlap the shaded columns to represent the distance to school that Charlene rides her bike.

How many rows did you shade? _____ rows

3) Count the number of squares that you shaded twice.

_____ squares are double-shaded.

Each square represents _____.

Record the value of the squares as the product:

_____ _____ = _____×

So, Charlene rides her bike for _______ mile.

1) Multiply the two factors the same way you multiply whole numbers.

2) Find the total number of decimal places in both factors.

___ + ___ = ___ total decimal places

3) Place the decimal point in the product by moving right the same number of places as the total number of decimal places in the factors.

_______ _______ = _______×

So, Charlene rides her bike for _______ mile.

Exercise 2- Multiply Decimals

1) Multiply: 0.3 1.4×

A) Model:

B) Algorithm:

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Example 2 Continued- Multiply Decimals

Tiffany catches a fish that weighs 3.2 pounds. Frank catches a fish that weighs 2.1 times as much as Tiffany’s fish. How many pounds does Frank’s fish weigh?

Expression: ____________________________

Model Algorithm

Use an area model:

● The large squares represent wholes.

● The small rectangles along the right and lower edges represent tenths.

● The small squares at the lower right represent hundredths.

The model is ____ units long, and ____ unit wide.

The area of the model is:

_____ whole(s) + _____ tenth(s) + _____ hundredth(s)

square units

_____ _____ = _____×

So, Frank’s fish weighs _____ pounds.

1) Multiply the two factors the same way you multiply whole numbers. 2) Place the decimal point in the product.

* Remember! The number of decimals places in the

product equals the total number of decimal places in the factors.

_______ _______ = _______×

So, Frank’s fish weighs

_____ pounds.

Estimation

Estimate to check whether your answer is reasonable:

Round 3.2 to the nearest whole number. ________

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Round 2.1 to the nearest whole number. ________

Multiply the whole numbers.

________ ________ = ________×

The answer is reasonable because _______ is close to ________.

(actual) (estimate) Exercise 2- Multiply Decimals

1) On Monday, Jenny took 1.1 hours to complete her homework. On Tuesday, she took 2.4 times as many hours as she did on Monday to do her homework. How many hours did Jenny do homework on Tuesday?

A) Expression: _______________________

B) Draw an Area Model:

_____ whole(s) + _____ tenth(s) + _____ hundredth(s) = ______

C) Algorithm:

2) Blades of grass grow 3.75 inches per month. If the grass continues to grow at this rate, how much will the grass grow in 6.25 months?

A) Expression: _______________________

B) Algorithm: C) Estimate:

3) Multiply: 7.14 6.8 =× 4) Multiply: 11.49 8.27 =×

A) Algorithm:

B) Estimate: A) Algorithm: B) Estimate:

15

Example 3- Zeros in the Product

Sometimes when you multiply with decimals, there are zeros in the product.

A worker ant weighs 0.004 gram. It can walk while holding in its mouth an object weighing 5 times as much as its own body. How many grams can a worker ant carry?

Expression: _______________________

Algorithm

Since ____ decimal places are needed in the product, write zeros in these places.

Exercise 3- Zeros in the Product

1) Multiply: 0.003 24× 2) Multiply: 0.53 0.12×

Example 4- Multiplying Money

At the grocery store, Delia bought 3.5 pounds of green peppers. The peppers cost $1.99 per pound. What was the total cost of Delia’s peppers?

Expression: _______________________

Algorithm Estimate

16

Round your answer to the hundredths place to show a dollar amount.

Exercise 4- Multiplying Money

1) Adita earns $9.40 per hour working at an animal shelter. How much money will she earn for 18.5 hours of work?

A) Expression: _______________________

B) Algorithm: C) Estimate:

Problem Set

Find the product. Then estimate to check.

1) 0.79 6× 2) 5 6.32×

3) 28 9.6× 4) 0.81 43×

17

5) 207 1.5×

6) $53.75 60×

Multiply. Use the decimal model. Then calculate the product using the algorithm.

7) 0.9 0.7 =×

8) 0.3 1.5 =×

Find the product. Then estimate to check.

9) 35.15 2.7×

10) 0.18 0.02×

11) 9.2 7.4×

12) 6.19 30.5×

13) 0.03 0.27×

14) 5.6 21.48×

18

15) Use the fact that 13 27 = 351. Without doing any calculations, explain how to find the product of× 1.3 2.7.×

Solve. Show your work in the space provided.

16) Carissa bought 3.7 pounds of coffee that cost $6.95 per pound. How much did she spend on coffee?

17) Marta walked around her neighborhood at 3.9 miles per hour for 0.72 hours. How far did Marta walk?

18) A gallon of water weighs 8.35 pounds. Simon uses 11.6 gallons of water while taking a shower. How many pounds of water did Simon use?

19) John runs for 2.25 hours, burning 375.5 calories per hour. How many total calories does John burn?

20) Cindy made a banner for the football game that was 12 feet long. Betsy made a banner that was 0.625 times as long as Cindy’s banner. Will Betsy’s banner be larger or smaller than 8 feet?

21) Gus has a pumpkin with a mass of 4.8 kilograms. If 0.9 of the pumpkin’s mass is water, how much of its mass is water? How much is not water?

19

22) Describe the error in the problem below and explain how to correct it.

Name ___________________________________________________________________________________ 6.NS.B.2 Lesson 1-4

Dividing Multi-Digit Numbers Using the Algorithm

Learning Target: I can fluently divide multi-digit numbers using the standard algorithm.

Do Now

Kaylynn and Amanda both work at the same store. The table shows how much each person earns, and the number of hours each person works in a week. Calculate the exact difference between Kaylynn and Amanda’s weekly salaries.

Wage Hours worked

per week

Kaylynn $8.75 per hour 37

Amanda $10.25 per hour 30.5

Key Vocabulary

dividend divisor = quotient÷ 472 8 = 59÷

= 598472

Example 1- Estimate Quotients

20

Compatible numbers can help you estimate a quotient. These numbers are close to the actual numbers and are easy to compute mentally.

Estimate: 1,574 42 ÷

Step 1: Round the divisor. The number 42 can be rounded to 40. It can also be rounded to 50.

Step 2: Round the dividend. The number 1,574 can be rounded up to 1,600 or rounded down to 1,500.

Step 3: Rewrite the division problem with the compatible numbers, and solve.

1,600 40 = _______÷ 1,500 50 = _______÷

So, one estimate of the quotient is _______, and a second estimate is _______. Exercise 1- Estimate Quotients

Write two pairs of compatible numbers for each. Give two possible estimates.

1) 4,831 68÷ 2) 263,970 73÷ 3) 41,797 561÷

Estimate the quotient.

4) 33,842 36÷ 5) 5,583 92÷ 6) 631,245 879÷

Example 2- Dividing Whole Numbers Using the Standard Algorithm

There were 70,072 people who visited the shopping mall during a 19-day period. On average, how many people visited the mall each day?

Expression: 70,072 19÷

Estimate: Remember to use compatible numbers to estimate quotients.

70,072 19÷

↓ ↓ ______ ___ = ______÷

Create a table to show the multiples of 19:

Multiples of 19

Algorithm:

Check:

quotient divisor = dividend×

21

Exercise 2- Dividing Whole Numbers Using the Standard Algorithm

1) Divide: 484,692 78÷

A) Estimate:

B) Algorithm:

2) Divide: 14,175 315÷

A) Estimate:

B) Algorithm:

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3) Divide: 87,628 931÷

A) Estimate:

B) Algorithm:

Example 3- Dividing with a Remainder

INTERPRETING THE REMAINDER

Drop It Use it

Ignore the remainder and only use the quotient

as your answer.

Use this when the question asks for full or whole items or when the item cannot easily

be split in real life.

Use the remainder (and not the quotient) as your answer.

Use this when the question asks how much is

left over, left out, or partially filled.

Add it Share It

Take the quotient and add one more.

Use this when everything or everyone has to fit and you can’t leave anything out.

Include the remainder in your answer

as a fraction or decimal.

Use this with food, money, or measurements that are easy to split in real life.

Callie has 1,850 books. She must pack them into boxes to ship to a bookstore. Each box holds 12 books. How many boxes will she need to pack all of the books?

Expression: _______________________

Algorithm What does the remainder mean in this situation?

23

How many boxes does Callie need to pack the books? Explain.

Exercise 3- Dividing with a Remainder

1) Lee’s bakery sells muffins by the dozen. The bakery has 2,395 muffins prepared. Does the bakery have enough muffins to complete 200 orders?

2) There are 473 students signed up to take a swimming course. Each class can have 18 students. What is the least number of classes needed?

3) A museum gift shop manager wants to put 1,578 polished rocks into small bags to sell as souvenirs. If the shop manager wants to put 15 rocks in each bag, how many complete bags can be filled? How many rocks will be left over?

4) Mrs. Clarke brought a 145-inch rope to demonstrate tying knots. She divided the rope into 4 pieces of equal length. How long was each piece of rope?

24

Problem Set

Write two pairs of compatible numbers for each. Give two possible estimates.

1) 6,080 88÷ 2) 751,483 12÷ 3) 13,506 424÷

Estimate the quotient.

4) 23,659 57÷ 5) 4,491 72÷ 6) 341,175 632÷

For problems 7-12, estimate the quotient, then divide using the algorithm.

7) 34,874 53÷

8) 182,727 257÷

9) 50,779 590÷ 10) 2,357,558 38÷

25

11) 970,839 424÷ 12) 70,434 78÷

Solve. Show your work in the space provided.

13) A theater has 3,570 seats in 85 equal rows. How many seats are in each row?

14) Landon is building new bookshelves for his bookstore’s new mystery section. Each shelf can hold 34 books. There are 2,278 mystery books. How many shelves will he need to build?

15) Tickets to a country music concert cost $48. If the sale of tickets brought in $270,672, how many tickets were sold?

16) Camilla makes and sells jewelry. She has 8,160 silver beads and 2.880 black beads to make necklaces. Each necklace will contain 85 silver beads and 30 black beads. How many necklaces can Camilla make?

26

17) Mason has 1,350 pennies that he wants to display in his coin collection. If he can fit 24 pennies on a display sheet, how many complete display sheets will he have? How many pennies will be left over?

18) Describe the error in the problem below and explain how to correct it.

Name ___________________________________________________________________________________ 6.NS.B Lesson 1-5

Dividing Decimals Learning Target: I can fluently divide multi-digit decimals using the standard algorithm. Do Now

Each year each person in the U.S. eats about...

68 quarts of popcorn

53 pounds of bread

19 pounds of apples

14 pounds of turkey

A) How many years would it take for a person in the United States to eat 855 pounds of apples?

B) How many years would it take for a person to eat 1,120 pounds of turkey?

Example 1- Dividing a Decimal by a Whole Number

Model

Divide: 6.39 3÷

27

Shade the grids to model 6.39. Then separate the model into 3 equal groups.

How many are in each group? __________

6.39 3 = __________÷

Dividing a Decimal by a Whole Number:

1) Divide using long division as with whole numbers. 2) Place a decimal point in the quotient directly above the decimal point in the dividend.

A high school track is 9.76 meters wide. It is divided into 8 lanes of equal width for track and field events. How wide is each lane?

Expression: ____________________________

Algorithm Check

Aerobics classes cost $153.86 for 14 sessions. What is the fee for one session?

Expression: ____________________________

Algorithm Check

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Exercise 1- Dividing a Decimal by a Whole Number

1) Divide: 29.5 4÷

A) Algorithm:

B) Check:

2) Divide: 207.4 61÷

A) Algorithm:

B) Check:

Example 2- Dividing a Decimal by a Decimal

Model

Divide: 6.39 2.13÷

Shade the grids to model 6.39. Then separate the model into groups of 2.13.

29

How many groups do you have? __________

6.39 2.13 = __________÷

Multiplying Decimals by Powers of 10

* Look for patterns-- Patterns can help you place the decimal point in the product. *

3.85 1 = ________ ×

3.85 10 = ________ ×

3.85 100 = ________ ×

0.264 1 = ________ ×

0.264 10 = ________ ×

0.264 100 = ________ ×

0.264 1000 = ________ ×

As you multiply by increasing powers of 10, how does the position of the decimal point change in the product?

Dividing a Decimal by a Decimal:

1) Change the divisor to a whole number by multiplying the divisor by a power of 10. 2) Multiply the dividend by the same power of ten. 3) Divide using long division as with whole numbers. 4) Place a decimal point in the quotient directly above the decimal point in the dividend.

Ella uses 0.5 pounds of raspberries in each raspberry cake that she makes. How many cakes can Ella make with 3.25 pounds of raspberries?

Expression: ____________________________

Step 1 Step 2

The divisor has _____ decimal place, so multiply both the dividend and the divisor by _____ so that the divisor is a whole number.

= 0.53.25 ×

Divide:

30

Anthony spent $11.52 for some pens that were on sale for $0.72 each. How many pens did Anthony buy?

Expression: ____________________________

Step 1 Step 2

The divisor has _____ decimal places, so multiply both the dividend and the divisor by _____ so that the divisor is a whole number.

= 0.7211.52 ×

Divide:

Exercise 2- Dividing a Decimal by a Decimal

1) Divide: 1.38 0.6÷

A) Step 1:

B) Step 2:

2) Divide: 15.12 0.84÷ 3) Divide: 1.23 0.06÷

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Problem Set

For problems 1-6, divide to find the quotient.

1) $4.24 8÷

2) 90 0.36÷

3) 0.144 0.96÷ 4) 23.85 9÷

5) 78.74 12.7÷

6) 5.6372 0.17÷

For problems 7-10, solve. Show your work in the space provided.

7) Corinne has 9.6 pounds of trail mix to divide into 12 bags. How many pounds of trail mix will go in each bag?

8) Michael paid $11.48 for sliced cheese at the deli counter. The cheese cost $3.28 per pound. How much cheese did Michael buy?

32

9) A four-person relay team completed a race in 72.4 seconds. On average, what was each runner’s time?

10) Elizabeth has a piece of ribbon that is 4.5 meters long. She wants to cut the ribbon into pieces that are 0.25 meter long. How many pieces of ribbon will she have?

11) Brenda is inviting 25 guests to her birthday party. She will have 10.92 gallons of ice cream. Brenda and each guest will eat the same amount of ice cream. How much ice cream will each person eat?

12) Describe the error in the problem below and explain how to correct it.

13) Victoria went shopping for ingredients to make a stew. The table shows the weight and the cost of each of the ingredients that she bought.

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A) What is the price for one pound of potatoes?

B) What is the price for one pound of carrots?

C) Which ingredient costs the most per pound?

D) If carrots were $0.50 less per pound, how much would Victoria have paid for 8.5 pounds of carrots?

Name ___________________________________________________________________________________ 6.NS.B Lesson 1-6

Applying Decimal Operations to Problem Solving

Learning Target: I can fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Do Now

Isabella is buying art supplies. The table below shows the prices of the items she wants to buy.

A) Isabella spends $3.75 on poster boards. How many poster boards does she buy?

B) Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? Explain how you found your answer.

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PROBLEM SOLVING KEY WORDS

Addition Subtraction Multiplication Division

Example 1- Identifying Key Words

Word problems contain information that helps you choose which operation to use. Read the problem carefully and circle key words to decide whether to add, subtract, multiply, or divide.

Corin bought 8.4 pounds of almonds. She split them equally into 30 snack size bags. How many pounds of almonds are in each bag?

What do I need to find? What information do I need to use? How will I use the information?

Solve

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Exercise 1- Identifying Key Words

1) On Friday, Gail talks for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 as many minutes as she did on Friday. How long does Gail talk on her cell phone on Saturday?

What do I need to find? What information do I need to use? How will I use the information?

Solve

Example 2- Solving Multi-Step Problems

Not all problems can be solved by using just one operation. Sometimes, word problems require you to do more than one step to arrive at the solution. These problems are called multi-step problems.

Meghan earns $20.00 by walking dogs. She uses all of her earnings to buy a shirt for $12.85 and some stickers for $0.65 each. How many stickers does she buy?

What do I need to find? What information do I need to use? How will I use the information?

Solve

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Exercise 2- Solving Multi-Step Problems

1) A family of two adults and four children is going to an amusement park. Admission is $21.75 for adults and $15.25 for children. What is the total cost of the family’s admission?

What do I need to find? What information do I need to use? How will I use the information?

Solve

Problem Set

Solve. Show your work in the space provided.

1) A bunch of 4 bananas contains a total of 5.92 grams of protein. Suppose each banana contains the same amount of protein. How much protein is in each banana?

2) Pete wants to make ham sandwiches for five friends and himself. He wants each sandwich to contain 3.82 ounces of ham. How many ounces of ham does he need?

3) Naomi earned $54 mowing lawns in two days. She worked 2.5 hours yesterday and 4.25 hours

4) Helen earn $12.50 each weekend babysitting her brother. After the fourth weekend, Helen buys a new

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today. If Naomi was paid the same amount for every hour she works, how much did she earn per hour?

CD for $12.48. How much money does Helen have left after buying the CD?

5) A coconut tree is 7.6 meters tall and a mango tree is 3.49 meters shorter than the coconut tree. What is the total height of the two trees?

6) Mitchell has $18.78 in his savings account. Jeremy has 0.5 as much money as Mitchell. Sean has $4.57 more than Jeremy. How much money does Sean have in his savings account?

7) Keri walks her dog every morning. The length of her walk is 0.55 kilometers on each weekday. On each weekend day, the walk is 1.4 times as long as her walk on the weekday. How many many kilometers does Keri walk in one week?

8) To prepare for a wedding, Aiden bought 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at a sale where she paid $0.05 less for each candle than Aiden did.

A) How much did Aiden spend on candles?

B) How much did Aiden’s sister spend on candles?

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C) Who spent more on candles? How much more?

Use the table for Problems 9-11.

Custom Printing Costs

Quantity 25 50 75 100

Mugs $107.25 $195.51 $261.75 $329.00

T-shirts $237.50 $441.00 $637.50 $829.00

9) What is the price per mug for 25 coffee mugs?

10) What is the price per T-shirt for 75 shirts?

11) What is the price per T-shirt for 100 shirts?

Name ___________________________________________________________________________________ Module 1 Review

Module 1 Study Guide Review

Lesson 1-1: Decimal Place Value

1) Write the decimal and fraction for the model.

2) Write the decimal and fraction for the model.

Decimal: Fraction: Decimal: Fraction:

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3) Standard Form: 72.048 Expanded Form: __________________________ Word Form: _____________________________

4) Write equivalent or not equivalent.

16.03 and 16.300

______________________

Lesson 1-2: Adding and Subtracting Decimals

1) 2.19 + 34.925 + 0.8

2) 9.28 - 0.596

3) Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 bill. How much change should Kelly get back?

4) The Smiths are on a summer road trip. They travel 10.9 hours the first day, 8.75 hours the second day, and 12 hours the final day. How many hours does the Smith family travel over the 3-day trip?

Lesson 1-3: Multiplying Decimals

1) 94.05 82×

2) 34.6 1.53×

3) At the deli, one pound of turkey costs $7.98. Mr. Epstein buys 3 pounds of turkey. How much will the turkey cost?

4) Sue buys material to make a costume. She buys 2.75 yards of red material. Sue buys 3.5 times as many yards of blue material. How many yards of blue material does Sue buy?

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Lesson 1-4: Dividing Multi-Digit Numbers Using the Algorithm

1) 76,255 309÷

2) 171,475 25÷

3) Volunteers at an animal shelter divided 13,248 pounds of dry dog food equally into 48 containers. How many pounds of dog food did they put in each container?

4) A pond at a hotel holds 23,520 gallons of water. The groundskeeper drains the pond at a rate of 96 gallons of water per hour. How long will it take to drain the pond?

Lesson 1-5: Dividing Decimals

1) 138.4 16÷

2) 10.81 2.3÷

3) On Saturday, 12 friends go ice skating at the local rink. Altogether, they pay $83.40 for admission.

4) Lee walked a total of 4.48 miles. If he walks 1.4 miles each hour, how long did he walk?

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They share the cost equally. How much does each person pay?

Lesson 1-6: Applying Decimal Operations to Problem Solving

1) Ricki has 76.8 feet of cable. She cuts off 6 pieces that measure 4.6 feet each. How much cable is left over?

2) Jan has $37.50. She spent $12.95 on a t-shirt. Tickets to a concert cost $5.25 each. How many tickets can Jan buy?

Extension #1

Pizza Party Mrs. Jackson wants to buy pizza for her students to celebrate the end of the school year. There are 32 students in her class and she will serve 2 slices of pizza to each student. Mrs. Jackson will order the pizza from The Pizza Shoppe where each large pizza is cut into 10 slices and costs $18.75 each.

Part A: Mrs. Jackson wants to buy enough pizza for her students and wants to have the least amount of pizza left over. How many large pizzas should Mrs. Jackson buy? Show your thinking.

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Part B: If Mrs. Jackson buys the number of large pizzas that you determined in Part A, how much money will she spend on pizza? Show your thinking.

Part C: Mrs. Jackson will have the pizzas delivered to her classroom. Along with the total cost for the pizzas, she will tip the delivery driver $25.00. If Mrs. Jackson pays with two 100 dollar bills, how much change will she receive? Show your thinking.

Extension #2

Jewelry Store

Suni uses glass beads to make jewelry. The beads come in six colors. Each color is a different size.

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Part A: Design a bracelet using no fewer than 10 and no more than 20 beads. Include beads of at least two colors. Find the length of the bracelet. Show your thinking.

Part B: Suni sells her bracelets and necklaces for $0.98 per centimeter. How much would the bracelet you designed cost? Show your thinking.

Part C: Suni designs a necklace of 40 beads with red, orange, and yellow colors. What could be the length and cost of your necklace? Show your thinking.

Extension #3

Distance Between Hurdles

There are 10 equally spaced hurdles on a race track. The first hurdle is 13.72 meters from the start line. The final hurdle is 14.02 meters from the finish line. The race track is 110 meters long.

Part A: Draw a diagram that shows the hurdles on the race track. Label all known measurements.

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Part B: How far are the hurdles from one another? Explain or show your reasoning.

Part C: A professional runner takes 3 strides between each pair of hurdles. The runner leaves the ground 2.2 meters before the hurdles and returns to the ground 1 meter after the hurdle.

About how long are each of the runner’s strides between the hurdles? Show your reasoning.

Extension #4

Buying Newspaper A daily newspaper costs $0.50. A Sunday newspaper costs $1.25. Keisha’s bill for the month of May is $7.75.

How many daily and Sunday newspapers could she have bought for exactly $7.75? Write all the possible answers in the table. Show your thinking in the space below.

Number of Sunday Papers Number of Daily Papers

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