LESSO Lesson 7 OVERVIEW Add and Subtract Decimals · 2020. 3. 30. · Lesson 7 Add and Subtract Decimals ©Curriculum Associates, LLC Copying is not permitted. Lesson 7 Add and Subtract

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LESSON OVERVIEW

Lesson 7 Add and Subtract Decimals

Prerequisite SkillsLesson Objectives


Learning Progression

addition and subtraction to decimals. By using visual models such as place-value charts, number lines, and base-ten models, they conceptualize adding and subtracting decimals. Students also use their rounding and estimation skills to estimate a decimal sum or difference and to check whether a result is reasonable.

In Grade 6 students will be expected to fluently add and subtract multi-digit decimals.

In Grade 4 students achieved proficiency with adding and subtracting multi-digit whole numbers. Building on place-value strategies learned in earlier grades, students gained an understanding of the standard algorithm for addition and subtraction. They used place-value charts as a guide to lining up digits in the correct place before computing.

In this lesson students add and subtract decimals through hundredths. They apply the standard algorithm for

There is no new vocabulary. Review the following key terms.

• decimal a number containing a decimal point that separates a whole from fractional place values (tenths, hundredths, thousandths, and so on)

• to estimate to give an approximate number or answer based on mathematical thinking

• place value the value assigned to a digit based on its position in a number; for example, the 2 in 3.52 is in the hundredths place and has a value of 2 hundredths or 0.02.

• sum the result of addition

• difference the result of subtraction

Lesson Vocabulary

• Understand place value.

• Recall addition and subtraction basic facts.

• Recognize addition and subtraction as inverse operations.

Content Objectives• Add decimals to hundredths.

• Subtract decimals to hundredths.

• Explain how to add and subtract decimals to hundredths.

Language Objectives• Draw base-ten models to show decimal

addition and subtraction.

• Explain a model’s relationship to the decimal addition or subtraction problem and to the result.

• Orally discuss adding or subtracting like place values of decimal numbers using expanded word form of the numbers.

DomainNumber and Operations in Base Ten

ClusterB. Perform operations with multi-digit

whole numbers and with decimals to hundredths.

Standards5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Standards for Mathematical Practice (SMP)2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

5 Use appropriate tools strategically.

6 Attend to precision.

7 Look for and make use of structure.

CCSS Focus

Lesson Pacing Guide

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Teacher-Toolbox.com

Whole Class Instruction

Lesson 7


Small Group Differentiation

Personalized Learning

ReteachReady Prerequisite Lessons 45–90 min

Grade 4 • Lesson 3 Add and Subtract Whole Numbers

Student-led ActivitiesMath Center Activities 30–40 min

Grade 4 (Lesson 3)• 4.21 Add and Subtract Whole Numbers• 4.22 Sums and Differences

Grade 5 (Lesson 7)• 5.19 Decimal Sums and Differences

Independenti-Ready Lessons* 10–20 min

Grade 4 (Lesson 3)• Adding Multi-Digit Numbers• Subtracting Multi-Digit Numbers

i-Ready.com

Day 145–60 minutes

Toolbox: Interactive Tutorial*Add and Subtract Decimals

Practice and Problem SolvingAssign pages 55–56.

Introduction

• Use What You Know 15 min• Find Out More 15 min• Reflect 5 min


Modeled and Guided Instruction

Learn About Adding Decimals to Hundredths• Picture It/Model It 15 min• Connect It 20 min• Try It 10 min




Learn About Subtracting Decimals to Hundredths• Picture It/Model It 15 min • Connect It 20 min• Try It 10 min



Guided Practice

Practice Adding and Subtracting Decimals• Example 5 min• Problems 16–18 15 min• Pair/Share 15 min• Solutions 10 min



Independent Practice

Practice Adding and Subtracting Decimals• Problems 1–6 20 min• Quick Check and Remediation 10 min• Hands-On or Challenge Activity 15 min

Toolbox: Lesson QuizLesson 7 Quiz

* We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson.

Introduction

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Students use what they know about place value and addition to explore a decimal addition problem. First, students estimate the sum. Then they describe the place values of each number in words and add each place value to find the sum. Then students solve the decimal addition problem by using a place-value chart and rewriting a tenths decimal as a hundredths decimal. They solve a decimal subtraction problem in the same way.

• Work through Use What You Know as a class.

• Tell students that this page models addition of decimals, using place value.

• Have students read the problem at the top of the page.

English Language Learners

• Emphasize the importance of the estimate. The estimate helps students catch errors, including errors of magnitude.

Mathematical Discourse 1

• Ask students to explain their answers for the fourth problem. Have students demonstrate how they used place value to add the times.


• Ensure that students understand how to use the sums of tens, ones, tenths, and hundredths to write the decimal 25.45.

Hands-On Activity

At A Glance

Step By Step

Mathematical Discourse

1 Why is the estimate important? What does it tell you?

The estimate helps catch errors. Comparing an estimate with an actual answer allows students to see if the magnitude of the answer is correct and may alert them to double-check their calculations. Encourage students to use estimates prior to all calculations.

2 How does using expanded form in words help you add these decimals?

Using expanded form helps students understand the relationship of place value to the addition process and the importance of adding hundredths and hundredths, tenths and tenths, etc. Expanded form helps students avoid place-value errors, such as adding tenths and hundredths instead of tenths and tenths.

English Language LearnersExplain what a relay is. Runners work as a team and take turns running; each team member runs part of the race. The team’s time is the sum of all the runners’ times.

Hands-On ActivityUse base-ten blocks to add decimals.

Materials: base-ten blocks (cubes, flats, longs, and cubes) or cards that say “1 hundredth,” “1 tenth,” “1 one,” “1 ten”

• Students use the expanded form of 12.1 and 9.75 to model the numbers with blocks.

• Students combine the tens, ones, tenths, and hundredths, regrouping the ones as 1 ten and 1 one.

• Students write the sum in expanded form.

Introduction

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Use What You Know


Lesson 7Add and Subtract Decimals

a. About how many seconds did the girls run altogether? Explain your reasoning.

b. You can think of Sabrina’s time as 1 ten 1 3 ones 1 2 tenths 1 5 hundredths. Write

Christie’s time in the same way.

c. Combine Sabrina’s and Christie’s times. How many tens in all? How many ones

in all? How many tenths in all? How many hundredths in all?

d. Write the sum of the tens, ones, tenths, and hundredths as a decimal.

e. How does the sum compare to your estimate? Is your answer reasonable?

f. Use words to explain how you could find Sabrina and Christie’s total time.

Sabrina and Christie are running in a relay. Sabrina runs 100 meters in 13.25 seconds, and Christie then runs the same distance in 12.2 seconds. What is their total time?

In grade 4, you learned to add whole numbers by adding the values of digits with the same place value. Now you’ll add decimals the same way. Take a look at this problem.

5.NBT.B.7

1 ten 1 2 ones 1 2 tenths

25

2

5 4 5

Possible answer: I can round the decimals. Sabrina’s time was about 13 seconds

and Christie’s time was about 12 seconds. That’s about 25 seconds in all.

Possible answer: The sum is close to my estimate. The answer is reasonable.

Possible answer: You can add the values in each place, and then add the

partial sums to find the total time of 25.45 seconds.

25.45

50

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Lesson 7


©Curriculum Associates, LLC Copying is not permitted. 51Lesson 7 Add and Subtract Decimals

Find Out More

You can use what you know about adding whole numbers to add decimals. To add 13.25 and 12.2, you combine like place values.

One way to add decimals is to stack the numbers vertically. Lining up the decimal points is a way to keep track of place values. Using a place-value chart can help.

Tens Ones . Tenths Hundredths

1 3 . 2 5

1 1 2 . 2 0

2 5 . 4 5

The total time is 25.45 seconds.

To find the difference between Sabrina’s and Christie’s times, subtract 12.20 from 13.25. You can use what you know about subtracting whole numbers to subtract decimals.

Tens Ones . Tenths Hundredths

1 3 . 2 5

2 1 2 . 2 0

0 1 . 0 5

Christie was faster by 1.05 seconds.

Reflect1 If Sabrina’s time were 13.26 seconds instead of 13.25 seconds, would that change

your estimate for the total time? Explain.

2 ·· 10 is equivalent to 20 ··· 100 , so

you can write a 0 in the

hundredths column.

Possible answer: My estimate would

not change because 13.26 is only one hundredth of a second more and it

would still round to 13.

51

• Read Find Out More as a class.

• Discuss the relationship between the place-value charts and the expanded forms in words used on the previous page.

SMP TIP Use Structure Using a place-value chart to solve decimal addition and subtraction problems highlights the structure of the quantities—whole number part and fractional part. (SMP 7)

• Point out the relationship between the decimal quantities and the fractional representations of the same quantities.

• Students complete Reflect on their own. Then, discuss as a class.

Visual Model

Real-World Connection

Assign Practice and Problem Solving pages 55–56 after students have completed this section.

Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING

Visual ModelUse grids to model adding decimals as mixed numbers.

• Draw a visual model of the fraction 12 1 ·· 10

by drawing and shading 12 full squares

and one tenth of another.

• Engage students in describing how to

subtract 9 75 ··· 100 from 12 1 ·· 10 .

• Draw gridlines to show hundredths in a

whole square and in the one tenth. The

model now shows 11 wholes and 110 ··· 100 .

• Cross out 9 wholes and 75 hundredths

to show that 12 1 ·· 10 2 9 75 ··· 100 5 2 35 ··· 100 .

Real-World Connection

Identify everyday examples of adding and subtracting decimals. Display everyday examples that involve decimal numbers, such as amounts on drink bottles and other food packages. A container of orange juice, for example, might show 1.89 liters. Ask students to find the amount in 2 different containers. Ask students to find the difference between the amounts in two different containers. Challenge students to find additional examples. Students may devise problems, swap with a partner, and solve each other’s problems.


52 ©Curriculum Associates, LLC Copying is not permittedLesson 7 Add and Subtract Decimals

Lesson 7 Add and Subtract Decimals Modeled and Guided Instruction

Learn About


Lesson 7


Adding Decimals to Hundredths

Read the problem below. Then explore different ways to understand how to add decimals to solve the problem.

From his home, Tim rides the bus 3.82 miles. Then he walks 0.4 mile from the bus stop to school. How many miles does Tim travel from home to school?

Picture It You can picture adding two decimals on a number line.

3.8 3.9 4.0 4.1 4.2 4.3 3.82

10.1 10.1 10.1 10.1

Starting at 3.82, you can make 4 jumps of 0.1 to the right to show the sum of 3.82 and 0.4.

Model It You can use a place-value chart to help you understand how to add decimals.

Ones . Tenths Hundredths

Bus ride 3 . 8 2

Bus stop to school 0 . 4 0

The sum is 3 ones 1 12 tenths 1 2 hundredths.

4 ·· 10 is equivalent to 40 ··· 100 , so you can

write a 0 in the hundredths column.

52


1 Why is a number line a good representation for this problem?

This problem is about distance. The number line gives a visual representation of distance, so it is a good model for distance problems.

2 When would you not want to use a number line to solve a decimal addition problem?

If the numbers are large or very far apart on the number line, such as 38.05 1 84.19. These would be difficult to represent accurately when drawing a number line.

3 What addition strategy does the number line in Model It represent?

Counting on. You start at one addend and count on four tenths.

Concept Extension 1Connect the number line to estimating sums.

• Draw a number line from 0 to 5, showing only whole numbers to represent the problem.

• Have a volunteer plot a point to represent 3.82 at the whole number that this addend is closest to. [4]

• Ask students what whole number 0.4 is closest to. [0]

• Demonstrate making a jump of 0 from the point that represents 3.82. Circle the number you land on [4] and say that this is the estimate of the sum of 3.82 and 0.4.

• Ask students to compare the estimate to the actual sum shown on the number line in the Student Book. [It is close, but the sum is a little greater.]

Students explore a number line model and a place-value chart for adding two decimal numbers. They use the number line to combine distances and to make incremental “jumps” to add. Then students revisit this problem and use the standard algorithm for addition to understand and solve the problem from another perspective.

• Read the problem at the top of the page as a class.

• Discuss what needs to be done to solve the problem. [add the distances]

Picture It• Have students look at the number line in

Picture It. Ensure that students can identify each addend and recognize each jump as one tenth, so four jumps is four tenths.

• Read the explanation as a class. Have a volunteer point out the sum on the number line.

Mathematical Discourse 1–3

Model It• Read Model It as a class. Discuss the

importance of reading decimals by place value and not by digit (e.g., not “zero point four,” but “four tenths”).

• Ask students to think of 2 different ways to read 3.82 and describe how each is represented in the place-value chart. [3 and 82 hundredths; 3 and 8 tenths and 2 hundredths]

SMP TIP Use ToolsEncourage students to use tools strategically by discussing the similarities and differences between the two representations: number line and place-value chart. (SMP 5)

Concept Extension 1

At A Glance

Step By Step

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Lesson 7


Connect It Now you will use the picture and the model to help you understand how to add decimals.

2 How can you use the number line in Picture It to fi gure out how many miles Tim

travels from home to school?

3 Look at Model It on the previous page. What is another way to express 12 tenths?

What is another way to express the sum?

4 You can add the decimals without a place-value chart 3.821 0.40by stacking them vertically. Line up the decimal points

to keep track of place values.

Why do you align the 8 in 3.82 with the 4 in 0.40?

5 The addition problem to the right is partially completed. 3.821 0.40

.22

1

Explain why there is a 1 above the ones place.

6 Complete the problem. How many miles does Tim travel from home to school?

7 Explain how to add decimals.

Try It Use what you just learned about adding decimals to solve this problem. Show your work on a separate sheet of paper.

8 Yana made a trail mix with 128.25 grams of dried fruit and 41.8 grams of almonds.

How many grams of trail mix did Yana make?

Possible answer: The first jump takes you to 3.92,

the second jump lands at 4.02, the third jump to 4.12, and the fourth jump

takes you to 4.22. This is the distance Tim travels.

1 one and 2 tenths

4.22 miles

Possible answer: To add decimals, you add the digits that have the same

place value.

4 ones 1 2 tenths 1 2 hundredths

4

Because they are both tenths.

Possible answer: 8 tenths 1 4 tenths 5 12 tenths;

12 tenths equals 1 one and 2 tenths.

170.05 grams

53

Concept Extension 2Connect decimal addition to the associative and commutative properties.

• Break apart the addends in 0.4 1 3.82 by place value.

Write 0.4 as 0 1 0.4. Write 3.82 as 3 1 0.8 1 0.02.

• Rewrite the sum of the addends using the commutative property. 0 1 3 1 0.4 1 0.8 1 0.02.

• Group the addends using the associative property. (0 1 3) 1 (0.4 1 0.8) 1 0.02.

• Add. [3 1 1.2 1 0.02 5 4.22]

Connect It• Discuss students’ answers to

problems 2 and 3.

• Problem 4 is students’ first look at the standard algorithm for decimal addition. Discuss why 0.4 is written as 0.40 in the vertical expression. Tell students you write a zero in the hundredths place in order to add hundredths. Remind students that a tenths decimal can be written as an equivalent hundredths decimal.

• Ensure that students understand the regrouping in problem 5.

• Provide support for students who struggle with regrouping the tenths and then adding the ones.

Concept Extension 2

Try It• Students solve Try It on their own or in pairs

or small groups.

SMP TIP Critique ReasoningStudents may use a variety of approaches to solve the Try It problem. Ask volunteers to share their solutions. Have students practice critiquing the reasoning of others, perhaps by rephrasing, asking for clarification, or identifying a misconception. (SMP 3)

8 Solution170.05 grams; Students may solve this problem using fractions, number lines, place-value charts, or the standard algorithm.

Error Alert Students who answered 132.43 may have used the standard algorithm without the decimal point. Remind students that the addends are decimal numbers. Have students rewrite the decimals using place-value words and add.


Step By Step



54 Lesson 7 Add and Subtract Decimals


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Learn About


Lesson 7


Subtracting Decimals to Hundredths

Read the problem below. Then explore different ways to subtract decimals.

Marty cuts 2.05 ounces of cheese from a 4.6-ounce block of cheddar cheese. How many ounces of cheddar cheese are left in the block?

Picture It You can subtract decimals using base-ten models.

Model 4 wholes and 6 tenths.

6 tenths 5 60 hundredths

Model It You can subtract decimals using a place-value chart.

Using a place-value chart helps you make sure the place values are lined up correctly.

Ones . Tenths Hundredths

Original amount 4 . 6 0

Amount cut 2 . 0 5

6 ·· 10 is equivalent to 60 ··· 100 , so you can

write a 0 in the hundredths column.

54

Students explore two models for subtracting decimals. They use base-ten grids and a place-value chart. Then students revisit this problem and connect the models to the standard algorithm for subtraction to understand the problem from another perspective.

• Read the problem at the top of the page as a class.

• Discuss as a class what operation is needed to answer the question. [subtraction]

• Have students estimate the difference. [4.6 is close to 4.5, and 2.05 is close to 2, so the difference is about 2.5.]

Picture It• Read Picture It as a class. Have a volunteer

explain why 6 tenths is equivalent to 60 hundredths. [They both represent the same part of the whole.]



Model It• Read Model It as a class. Have a volunteer

give the expanded form of each number in words. [four and six tenths and zero hundredths; two and zero tenths and five hundredths]

• Point out that the result is the same, no matter which method is used to subtract.


At A Glance

Step By Step


1 Why is it useful to think of 6 tenths as 60 hundredths?

So we can subtract like place values: 60 hundredths minus 5 hundredths is 55 hundredths.

2 How are the grid model and the place-value chart similar? How are they different?

You can see the whole parts and fractional parts in both models. You can use both models to illustrate the subtraction operation and show what’s left. The grids show wholes as 100 hundredths, and the place-value chart shows wholes as 10 tenths. The grids model the quantity while the chart shows the place value of each digit in the numbers.


Lesson 7


Connect It Now you will use the base-ten models and the place-value chart to understand how to subtract decimals.

9 Look at the base-ten models on the previous page. Explain why parts of the models are

crossed out.

10 According to Picture It, how many ounces of cheddar cheese are left in the block?

11 Look at the place-value chart in Model It on the previous page. Why can’t you just

subtract the 5 from the 6?

12 You can subtract the decimals without a place-value chart by stacking them 4.602 2.05vertically. Line up the decimal points to keep track of place values. You can

express 6 tenths as tenths 1 10 hundredths.

13 You can rewrite the problem as

Complete the subtraction problem. There are ounces of cheddar left.

14 Explain how to subtract two decimals and how to tell if your answer is reasonable.

Try It Use what you just learned about subtracting decimals to solve this problem. Show your work on a separate sheet of paper.

15 Gwen is sending a box to a friend. The box weighs 23.5 pounds. Gwen removes a 4.47-pound book to decrease the shipping cost. What is the new weight of the box?

4.602 2.05

5 10

Possible answer: To subtract decimals, line up the digits by place value, and

then subtract in each place. Regroup if necessary. You can round the numbers

and subtract to get an estimate to tell if your answer is reasonable.

Two wholes and five hundredths are crossed out to show

subtracting 2.05.

2.55 ounces

Possible answer: Their place values are not the

same. The 6 in 4.6 tells the number of tenths and the 5 in 2.05 tells the

number of hundredths.

19.03 pounds

2.55

5

2.55

55

Connect It• Be sure to point out that Connect It refers

to the problem on the previous page.

• Discuss students’ answers to problem 10. Ensure that students read 2.55 by place value and not as two point five five.

• Problems 12 and 13 are students’ first look at the standard algorithm for decimal subtraction. Point out how regrouping is represented in this example.

• Have students share and discuss their explanations for problem 14.

SMP TIP Attend to PrecisionMake sure that students attend to precision when they discuss the regrouping process. Monitor discussions and encourage them to state the meaning of each digit according to place value. (SMP 6)

Try It• Students solve Try It on their own. Provide

support for students who struggle with regrouping the tenths as hundredths and then subtracting.

15 Solution19.03 pounds; Students may estimate the new weight by rounding 23.5 to 24 and 4.47 to 4, for an estimate of 20. They may use a number line, place-value chart, fractions, or grid model to model 23 wholes and 5 tenths and then subtract 4 wholes and 47 hundredths.

Error Alert Students who answered 18.58 may have subtracted 23.05 2 4.47. Review decimal place value and how to write a zero in the hundredths place to write 23.5 as 23.50.


Step By Step



Remind students that the words tenths and hundredths refer to place values of digits to the right of the decimal point. Write the word, decimal, and fractional equivalents of each, as needed.

Guided Practice

Teacher Notes


Lesson 7 Add and Subtract Decimals Guided Practice

Practice


Lesson 7


Adding and Subtracting Decimals

Pair/ShareDoes it matter in what order you add the decimals?

Pair/ShareHow do you know what operation to use to solve this problem?

How many hundredths are equivalent to 7 tenths?

The student needed two steps to solve the problem.

Example

16 On average, outdoor cats live 3.18 years and indoor cats live 16.7 years. How much longer does an average indoor cat live than an average outdoor cat?

Show your work.

Solution

Diana has 3 different beads on her necklace. The red bead is 0.68 centimeter long, the multi-colored bead is 1.22 centimeters long, and the blue bead is 0.8 centimeter long. What is the total length of the beads on Diana’s necklace?

Look at how you could show your work using equations.

1.221 0.68

1.90

1

1.901 0.80

2.70

1

0.68 1 1.22 1 0.8 5 2.7

Solution

Study the example below. Then solve problems 16–18.

2.7 centimeters

Possible student work using a model:

16 2 3 5 13

0.7 2 0.18 5 0.52

13.52 years

56

Students study a model for solving a decimal addition word problem. Then they solve word problems involving adding and subtracting decimals.

• Ask students to solve the problems individually. Circulate to monitor and provide support.

• Encourage students to determine which operation to use and then estimate the solution.

• Provide support for those students who struggle with regrouping. Have them use models to understand the process.

• Encourage students to compare solutions to their estimates.

• Pair/Share When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

Example 2.7 centimeters; The standard algorithm is shown as one way to solve this problem. Students should realize that this is a two-step problem.

16 Solution13.52 years; See possible work on the Student Book page. Students could solve the problem by subtracting the whole number parts and then drawing a model to subtract the decimal parts.

DOK 2

At A Glance

Step By Step

Solutions

Teacher Notes


Lesson 7


Pair/ShareHow could Cambria have checked her answer?

Pair/ShareExplain how to check if your answer is reasonable.

This problem takes more than one step to solve.

What operation will solve this problem?

17 Kenton is shopping for clothes at a twelfth anniversary sale. He buys a pair of jeans priced at $24.99 and a clearance-priced shirt for $5.25. The store reduces the amount of his entire purchase by $12.12. How much does Kenton pay for his clothes?

Show your work.

Solution

18 Three boxes of cereal have masses of 379.4 grams, 424.25 grams, and 379.37 grams. What is the diff erence between the box of cereal with the greatest mass and the box of cereal with the least mass?

A 44.15 grams

B 44.85 grams

C 44.88 grams

D 45.12 grams

Cambria chose D as the correct answer. How did she get that answer?

Possible student work using equations:

24.991 5.25

30.24

1 1 1

30.242 12.12

18.12

210

$18.12

Possible answer: When Cambria subtracted 379.37 from

424.25, she incorrectly subtracted 25 from 37 to get the

decimal part of the answer, and then she subtracted 379 from

424 to get the whole number part.

57

17 Solution$18.12; See possible work on the Student Book page. Students could solve the problem by using the standard algorithm to first add the prices of the jeans and shirt, and then subtract the reduced amount from that total.

DOK 2

18 SolutionC; Students could solve the problem by using the standard algorithm to subtract 379.37 from 424.25.

Explain to students why the other two answer choices are not correct:

A is not correct because 379.4 has a greater mass than 379.37 and it was incorrectly subtracted from 424.25.

B is not correct because 379.4 has a greater mass than 379.37.

DOK 3


Solutions





Quick Check and Remediation

• Ask students to add 3.6 1 12.74. [16.34]

• For students who are struggling, use the chart to guide remediation.

• After providing remediation, check students’ understanding. Ask students to add 28.17 1 0.88. [29.05]

• If a student is still having difficulty, use Ready Instruction, Grade 4, Lesson 3.


Practice


Lesson 7


Adding and Subtracting Decimals

Solve the problems.

1 Randy rode his bike 1.23 miles to school from his house. After school, he rode 0.9 mile farther to the library. Randy biked home along the same route, stopping at a park 1.05 miles from the library. How many miles is the park from Randy’s house?

A 3.18

B 2.37

C 1.08

D 0.27

2 Tim tracked the change in outside temperature one afternoon. He recorded a temperature of 85.4°F at noon. The temperature then rose 3.85°F over the next 4 hours. At 5:00 PM, Tim recorded a temperature of 89.25°F. How did the temperature change between 4:00 PM and 5:00 PM?

A The temperature increased 0.8°F.

B The temperature decreased 0.2°F.

C The temperature increased 1°F.

D There was no change in temperature.

3 Tell whether each equation is True or False.

a. 198.5 2 42.81 5 155.69

True False

b. 73.27 1 251.6 5 98.43

True False

c. 37.04 1 56.20 5 93.6

True False

d. 70.64 2 (9.3 1 29.36) 5 90.7

True False

e. 38.2 2 (11.11 1 23.76) 5 3.33

True False

4 The sum of three decimal numbers is 6. Exactly one of the numbers is less than 1. What could the numbers be?

Show your work.

Solution

Answers will vary. Students may use trial and error. They may start with two decimal numbers, one less than 1, find their sum, and then subtract that sum from 6 to find the third number. Possible solution: 0.99, 1.01, and 4.00.

3

3

3

3

3

58

If the error is . . . Students may . . . To remediate . . .

15.34 or 15.134 not have regrouped

Have students use base-ten blocks to solve the problem, regrouping 13 tenths as 1 one and 3 tenths. Guide the students through each step. When explaining, be sure to say each place value, not just the digit. Then model the problem using a grid model or a place-value chart.

9.14have found a difference rather than a sum

Write the words sum and difference on the board. Draw a plus sign (1) under sum and a minus sign (2) under difference. Brainstorm other words that are clues for adding and subtracting, such as total or take away.

15.8 or 15.80have interpreted 6 tenths as 6 hundredths

Have students write each addend as a fraction. Point out the difference between tenths and hundredths (1 tenth is 10 times 1 hundredth). Have students use fractions or a place-value chart to solve the problem.

Students add and subtract decimals to solve word problems that might appear on a mathematics test.

1 SolutionC; First add 1.23 and 0.9. Then subtract 1.05 from this value. DOK 2

2 SolutionD; First add 85.4 and 3.85. Then compare this value to 89.25. DOK 2

3 Solutiona. True; b. False; c. False; d. False; e. True

DOK 1

4 SolutionAnswers will vary. Students may add 2 decimals (one less than 1) and subtract that sum from 6 to find the third number. Students may also use a grid model or number line showing 6 wholes. DOK 2

At A Glance

Solutions


Lesson 7

Self Check


Go back and see what you can check off on the Self Check on page 1.

5 Choose all the models or expressions that represent the diff erence 3.7 2 1.02.

A

B 3.73.63.53.43.33.23.13.02.92.82.72.62.5

C 2 ones 1 6 tenths 1 8 hundredths

D 3.73.63.53.43.33.23.13.02.92.82.72.62.5

E

6 Ryan and Sarah are looking at cell phone plans. A group plan will cost $120.95 per month. An individual plan will cost $62.77 per month. Should Ryan and Sarah purchase a group plan or two individual plans? Justify your answer. How much money could they save?

Show your work.

Possible answer: They should choose a group plan. It costs $4.59 less than

2 individual plans.

Possible student work using equations:

62.771 62.77

125.54

1 1

125.542 120.95

4.59

4 14 14

59

Hands-On Activity Use counters to add decimals.

Materials: counters, poster board, markers

• Organize students into small groups and distribute counters, poster board, and markers.

• Have students create a large place-value chart showing ones, tenths, and hundredths on the poster board.

• Write two decimal numbers on the board. Have students use counters to model both numbers. For example, for the number 4.18, students would put 4 counters in the ones place, 1 counter in the tenths place, and 8 counters in the hundredths place.

• Tell students to add the numbers together and use counters to show the sum. Direct students to regroup the counters so they never have more than 9 counters in any square of the place-value chart. Be sure that students regroup a group of 10 counters in one column as one counter (not 10) in the column to its left.

Challenge Activity Given an answer, write a problem.

• Organize students into pairs. Tell each student to write an addition problem that involves one regrouping and has a sum of 8.16. [Possible addends: 3.53 1 4.63; 4.07 1 4.09; 4.45 1 3.71; etc.]

• When students are finished, they should trade with their partners to make sure that the sum is correct, and that the problem requires one regrouping.

• Repeat the activity as many times as desired, giving specific sums or differences.

5 SolutionB; The number line shows 1.02 subtracted from 3.7 in two parts: the arrow from 3.7 to 2.7 represents subtracting 1, and the arrow from 2.7 to 2.68 represents subtracting 0.02. The second arrow ends on the difference, 2.68.

C; 3.7 2 1.02 5 2.68. The number 2.68 has 2 ones, 6 tenths, and 8 hundredths.

E; The model shows 3.7 shaded and 1.02 crossed off, leaving 2.68 shaded. DOK 1

6 SolutionThey should choose a group plan. It costs $4.59 less than 2 individual plans; See possible student work on the Student Book page. Students may use equations, place-value charts, models, or combinations of methods. DOK 3

Solutions

Lesson 7 Add and Subtract Decimals59b ©Curriculum Associates, LLC Copying is not permitted

Teacher-Toolbox.com


LESSON QUIZ

2©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 7 Add and Subtract Decimals

Name ___________________________________________________________ Date ____________________

Lesson 7 Quiz continued

3 Which models or expressions represent the sum 2.84 1 1.2?

Circle all the correct answers.

A

2.8 3.63.53.43.33.23.1 4.14.03.93.0 3.82.9 3.7

B 4 ones 1 4 tenths

C

D 4 tenths 1 8 hundredths

E

2.8 3.63.53.43.33.23.1 4.14.03.93.0 3.82.9 3.7

F

4 Sam is looking at cell phone plans. A local company off ers a monthly plan for $58.95. The company is having a sale and off ering a discount of $4.75 off the monthly plan. Sam says that the new cost is $11.45.

Explain Sam’s error and fi nd the correct new cost.

1©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 5 Lesson 7 Add and Subtract Decimals

Name ___________________________________________________________ Date ____________________

Lesson 7 QuizReady® Mathematics

Solve the problems.

1 It snows 0.7 inch on Wednesday and 0.31 inch on Thursday. Brandon draws this model to fi nd how much more snow fell on Wednesday than on Thursday.

Which equation does the model represent?

A 0.7 1 0.31 5 1.01

B 0.7 1 0.31 5 0.38

C 0.7 2 0.31 5 0.39

D 0.7 2 0.31 5 0.31

2 Three limes weigh 4.28 ounces, 4.82 ounces, and 2.85 ounces. What is the diff erence between the weights of the heaviest lime and the lightest lime?

Show your work.

Answer: ounces

Overview

Assign the Lesson 7 Quiz and have students work independently to complete it.

Use the results of the quiz to assess students’ understanding of the content of the lesson and to identify areas for reteaching. See the Lesson Pacing Guide at the beginning of the lesson for suggested instructional resources.

Tested Skills

Assesses 5.NBT.B.7

Problems on this assessment form require students to be able to use base-ten models and number lines to add and subtract decimals to hundredths. Students will also need to be familiar with writing decimal numbers in expanded form and word form, writing addition and subtraction equations to model real-world situations, and comparing decimals to hundredths.

Lesson 7 Add and Subtract Decimals 59c©Curriculum Associates, LLC Copying is not permitted

Lesson 7

Grade 5 Lesson 7 Add and Subtract Decimals ©Curriculum Associates, LLC

Lesson 7 Quiz Answer Key

Ready® Mathematics

1. CDOK 1

2. 1.97DOK 2

3. A, FDOK 1

4. Possible explanation: Sam forgot to line up the decimal points when he subtracted $4.75 from $58.95. The new cost is $54.20.DOK 3

Common Misconceptions and Errors

Errors may result if students:

• align the left- or right-most digits instead of the decimal point.

• disregard the size of each jump or tick mark on a number line.

• do not regroup when subtracting.

• add instead of subtracting or vice versa.

Documents

LESSO Lesson 7 OVERVIEW Add and Subtract Decimals · 2020. 3. 30. · Lesson 7 Add and Subtract Decimals ©Curriculum Associates, LLC Copying is not permitted. Lesson 7 Add and Subtract