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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

926 Unit 12 Rates

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 13, 64 – 68, 160, 168, 169

Key Concepts and Skills• Find multiples. 

[Number and Numeration Goal 3]

• Multiply and divide decimals by whole

numbers. 

[Operations and Computation Goal 4]

• Use repeated addition and scaling

to model multiplication problems. 

[Operations and Computation Goal 7]

• Analyze and interpret data. 

[Data and Chance Goal 2]

• Use patterns and rules to solve rate

problems. 

[Patterns, Functions, and Algebra Goal 1]

Key ActivitiesStudents calculate the unit prices of various

products. They calculate and compare the

unit prices of two products to decide which

is the better buy.

Ongoing Assessment: Informing Instruction See page 929.

Key Vocabularyconsumer � products � services � 

comparison shopping � unit price

MaterialsMath Journal 2, pp. 319 and 320

Study Link 12�3

Math Masters, p. 454 (optional)

calculator � slate

Playing Name That NumberStudent Reference Book, p. 254

Math Masters, p. 489

per partnership: complete deck of

number cards (the Everything Math

Deck, if available)

Students practice representing

numbers in different ways.

Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 489. [Patterns, Functions, and Algebra Goal 3]

Converting Units of MeasureMath Journal 2, pp. 319A and 319B

Students convert among units of

measure.

Math Boxes 12�4Math Journal 2, p. 321

Students practice and maintain skills

through Math Box problems.

Study Link 12�4Math Masters, p. 345

Students practice and maintain skills

through Study Link activities.

READINESS

Finding Unit PricesMath Masters, pp. 346 and 428

coins

Students use a concrete model to determine

unit prices.

ENRICHMENTTesting Productsproducts to test

Students test products and then analyze and

interpret the data.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

�

Comparison Shopping: Part 1

Objectives To introduce calculating the unit price for a product;

and to provide practice comparing unit prices and identifying

information needed for comparison shopping.

a

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1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 319)

Students share their definitions of the word consumer. Sample answer: A person who acquires products or uses services

Pose questions such as the following, and list students’ responses on the board.

● What are some products and services you have used recently? Sample answers: Products: food, clothing, school supplies; Services: public transportation, school, the postal service, utilities such as the telephone or electricity

● What are some of the qualities of a smart consumer? Sample answers: Makes thoughtful decisions based on the quality, price, and effect of the product or service on the environment, as well as on personal needs and taste

● What information might you want to know before choosing a baseball camp? Sample answers: The qualifications of the counselors, the types of activities offered, the location of the camp, the cost

● How would you go about getting the information you need to select the best product? Sample answers: Ask people who have used the products, read articles about the products in consumer magazines, compare prices. This kind of research is called comparison shopping.

Product TestingLESSON

12�4

Date Time

Some publications ask their readers to test many different kinds of products. The results of the

tests are then published to help readers make wise buying decisions. One example is the former

Consumer Reports for Kids Online. It featured articles previously published in Zillions, a child’s

version of Consumer Reports. In one test, 99 readers field tested several backpack models. The

readers considered fit, back friendliness, and comfort as they tried to decide which brand was

the best buy. In another test, a team of young people compared 40 brands of jeans in their search

for a brand that would not shrink in length.

When a reader wrote to complain about a board game she bought, the staff sent board

games to young people in every part of the country. Testers were asked to play each

game several times and then to report what they liked and disliked about the game.

1. If you were testing a board game, what are some of the features you would look for?

2. When readers of the magazine tested backpacks, they considered fit, back friendliness, and

comfort in determining the best one. Which of these factors is the most important to you? Why?

3. What is a consumer? Be prepared to share your definition with the class.

Answers vary.

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Math Journal 2, p. 319

Student Page

Lesson 12�4 927

Getting Started

Math MessageRead and complete journal page 319.

Study Link 12�3 Follow-UpHave small groups compare answers.

Mental Math and ReflexesPose measurement conversion problems. Suggestions:

1 hour is 60 minutes. How many minutes are in

2 hours? 120

4 hours? 240

7 hours? 420

1 pound is 16 ounces. How many ounces are in

2 pounds? 32

30 pounds? 480

100 pounds? 1,600

1 kilogram is 1,000 grams. How many grams are in

3 1

__ 2 kilograms? 3,500

7 1

__ 4 kilograms? 7,250

15 1

__ 2 kilograms 15,500

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928 Unit 12 Rates

� Introducing Unit Prices WHOLE-CLASS ACTIVITY

(Math Masters, p. 454)

NOTE Although the sequence of lessons on unit pricing focuses on the

arithmetic of buying products and services, it is also important to discuss the

more general aspects of what it means to be a consumer.

Throughout the sequence of lessons on unit pricing, remind students that

comparison shopping is not simply a matter of determining which of several

comparable products or services is the cheapest. There are other important

factors that enter into making wise decisions.

Consumer Link The unit price is the cost of an item per unit of measure. Give several examples and write them in

rate tables so that students will understand that unit prices are rates. To support English language learners, help students make connections between the terms unit fraction and unit rate from prior lessons and the term unit price. Suggestions:

● A 10-pound bag of potatoes costs $5.00. The unit price is the cost of 1 pound. $0.50

● A package of 6 pens costs $4.20. The unit price is the cost of 1 pen. $0.70

● A dozen bagels cost $3.60. The unit price is the cost of 1 bagel. $0.30

Ask how the unit price is calculated from the cost information that is given. Divide the cost by the number of units or items. For example, $5.00 ÷ 10 = $0.50, $4.20 ÷ 6 = $0.70, and $3.60 ÷ 12 = $0.30. Explain that finding the unit price is like solving an equal-sharing problem: Division is used to find the cost of each unit, item, or share.

Now pose several practice problems on comparison shopping. Work through these as a class, and encourage students to use calculators. Calculate unit prices for similar items, and then compare these unit prices to determine which item is the better buy. Point out that unit prices are not easily compared unless they are for the same unit. (For example, $3.20/1 lb and $0.10/1 oz are not easily compared, but $0.20/1 oz and $0.10/1 oz are.)

ELL

Dollars 0.50 5.00

Pounds 1 10

Dollars 0.70 4.20

Pens 1 6

Dollars 0.30 3.60

Bagels 1 12

Converting Units of MeasureLESSON

12� 4

Date Time

315

1 pound (lb) = 16 ounces (oz)

1 ton (T) = 2,000 pounds (lb)

Complete the conversions between ounces, pounds, and tons.

Write the information you needed to make the conversion.

1. 5 lb = 80 oz 1 lb = 16 oz

2.1__2 lb = 8 oz 1 lb = 16 oz

3. 129 lb = 2,064 oz 1 lb = 16 oz

4. 2 T = 4,000 lb 1 T = 2,000 lb

5. 6 1__4 T = 12,500 lb 1 T = 2,000 lb

6. 112 oz = 7 lb 1 lb = 16 oz

7. 20,000 lb = 10 T 1 T = 2,000 lb

8. 4,240 oz = 265 lb 1 lb = 16 oz

9. 3,000 lb =1 1 _

2 T 1 T = 2,000 lb

10. 1 1__4 lb = 20 oz 1 lb = 16 oz

Complete the table.

11. Ounces Pounds Tons

160,000 10,000 5

304,000 19,000 9.5

16,000 1,000 1 _ 2

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Math Journal 2, p. 319A

Student Page

Unit PricesLESSON

12�4

Date Time

Solve the unit price problems below. Complete the tables if it is helpful to do so.

1. A 12-ounce can of fruit juice costs 60 cents. The unit price is per ounce.

47

$0.05

Dollars

Ounces 1 3 6 12

0.05 0.15 0.30 0.60

Dollars

Pounds 1 2 3 4

0.29 0.58 0.87 1.16

Dollars

Pounds 1 2 3 4 5

0.38 0.76 1.14 1.52 1.90

Dollars

Pounds 1 2 3 4 7

7.00 14.00 49.00 66.5028.0021.00

2. A 4-pound bunch of bananas costs $1.16. The unit price is per pound.$0.29

$0.383. A 5-pound bag of apples costs $1.90. The unit price is per pound.

4. Three pounds of salmon cost $21.00.

a. The unit price is per pound.

b. What is the cost of 7 pounds of salmon?

c. What is the cost of 9 1

_

2 pounds of salmon?

$7.00$49.00$66.50

9 1

_

2

5. Energy granola bars come in packages of 25 and cost $3.50 per package. Super granola bars

come in packages of 30 and cost $3.60 per package. Which is the better buy? Explain.

It depends. Super bars are $0.12 each, and Energy bars are

$0.14 each. So Super bars are cheaper per bar. However, an

Energy bar may be much larger than a Super bar.

Try This

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Math Journal 2, p. 320

Student Page

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Date Time

12. Record measurement equivalents in the two-column tables below.

a. Feet Inches

1 12

2 24

3 36

4 48

5 60

b. Liters Milliliters

1 1,000

2 2,000

3 3,000

4 4,000

5 5,000

c. Minutes Seconds

1 60

2 120

3 180

4 240

5 300

Find the equivalent measures.

13. a. 6 km = 6,000 m b. 2 L = 2,000 mL

c. 6 yd = 18 ft d. 3.25 L = 3,250 mL

e. 5 1 _ 2 kg = 5,500 g f. 8 1

_ 2 hr = 510 min

g. What do you notice when you convert from a larger unit to a

smaller unit (such as from L to mL)?

Sample answer: You need to multiply to

find the equivalent measure.

14. a. 4,000 g = 4 kg b. 200 cm = 2 m

c. 875 mL = 0.875 L d. 660 sec = 11 min

e. 1,500 mL = 1.5 L f. 156 in. = 13 ft

g. What do you notice when you convert from a smaller unit to a

larger unit (such as from mL to L)?

Sample answer: You need to divide to

find the equivalent measure.

Sample answers: Sample answers:

Converting Units of Measure continuedLESSON

12�4 315

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Math Journal 2, p. 319B

Student Page

Lesson 12�4 929

321

Math Boxes LESSON

12�4

Date Time

5. Add blocks to the bag so it is likely that

Arjan will pick a C block without looking.

CC C CA B C

A B C

Sample answer:

1. a. Complete the table.

3. Find the solution of each open sentence.

a. t + 30 = -120 t =

b. 75 + n = 20 n =

c. 16 + b = 0 b =

d. c + (-61) = -97 c =

148

47

80

2. Complete.

a. 7 gal = 28 qt

b. 8 L = 8,000 mL

c. 0.25 L = 250 mL

d. 6 gal 1 qt = 25 qt

e. 3 qt 1 pt = 14 c

b. How many inches are in 329 yards?

inches11,844

-55

-16

-36

-150

137

149

38 39

6. Calculate.

a. 10% of 520 = 52

b. 5% of 180 = 9

c. 40% of 10 = 4

d. 50 % of 30 = 15

e. 40 % of 35 = 14

f. 40 % of 95 = 38

15

Number of Inches

72

540

Number of Yards 1 2 9 12

36 324432

4. Which one of the names below is not a

name for 3.16? Fill in the circle next to

the best answer.

A 4.8 - 1.64

B 15.8 / 5

C 2.47 ∗ 6

D 2.5 + 0.66

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Math Journal 2, p. 321

Student Page

Suggestions:

� Lightbulbs

Brand A: package of 4 bulbs for $2.08

Brand B: package of 6 bulbs for $3.00

Brand A: $0.52/1 bulb; Brand B: $0.50/1 bulb; Brand B is the better buy.

� Crackers

Brand A: 1-pound box for $2.40

Brand B: 24-ounce box for $3.84

Brand A: $0.15/1 oz; Brand B: $0.16/1 oz; Brand A is the better buy.

� Calculating and Comparing PARTNER ACTIVITY

Unit Prices(Math Journal 2, p. 320)

Have partners complete Problems 1–5 on journal page 320.

Ongoing Assessment: Informing Instruction

Watch for students who assume that the lower-cost package of Energy granola

bars in Problem 5 is the better buy. Have students compare quantities and

explain that even though the price of the package may be lower, the price per

granola bar may be higher because there are not as many bars in the package

or the size of the bars is smaller.

2 Ongoing Learning & Practice

� Playing Name That Number PARTNER ACTIVITY

(Student Reference Book, p. 254; Math Masters, p. 489)

Students play Name That Number to practice representing numbers in different ways. See Lesson 2-2 for additional information.

Ongoing Assessment: Math Masters

Page 489Recognizing Student Achievement

Use Math Masters, page 489 to assess students’ ability to insert grouping

symbols to make true number sentences. Students are making adequate

progress if they are able to use parentheses in number sentences to show

combinations of numbers and operations that name the target numbers. Some

students may be able to use nested parentheses in their number sentences.

[Patterns, Functions, and Algebra Goal 3]

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930 Unit 12 Rates

STUDY LINK

12�4 Unit Prices

Name Date Time

Solve the unit price problems below. Complete the tables if it is helpful to do so.

1. A 12-oz bag of pretzels costs 96 cents. The unit price is 8 cents

per ounce.

Dollars 0.08 0.24 0.72 0.96

Ounces 1 3 9 12

Dollars 0.35 0.70 1.05 1.40

Liters 1 2 3 4

Dollars 0.69 1.38 2.07

Rolls 1 2 3

2. A package of 3 rolls of paper towels costs $2.07. The unit price is $0.69

per roll.

3. A 4-liter bottle of water costs $1.40. The unit price is $0.35 per liter.

4. Choose 4 items from newspaper ads. In the table below, record the name,

price, and quantity of each item. Leave the Unit Price column blank.

Item Quantity Price Unit Price

Golden Sun 24 ounces $2.99 12.4 cents per ounce Raisins

Answers vary.

Practice

Name the factor pairs for each number.

5. 12 1, 12; 2, 6; 3, 4 6. 50 1, 50; 2, 25; 5, 10

47

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Math Masters, p. 345

Study Link Master

� Converting Units of Measure INDEPENDENTACTIVITY

(Math Journal 2, pp. 319A and 319B)

Students convert among units of weight, capacity, length, and time. They look for patterns in how they make the conversions.

� Math Boxes 12�4 INDEPENDENTACTIVITY

(Math Journal 2, p. 321)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 12-2 and 12-6.

� Study Link 12�4 INDEPENDENTACTIVITY

(Math Masters, p. 345)

Home Connection Students calculate unit prices. They also look for supermarket ads in newspapers and record the information contained in four of them. In Lesson 12-5, students will calculate the unit prices of these items.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Finding Unit Prices 5–15 Min

(Math Masters, pp. 346 and 428)

To explore unit prices using a concrete model, have students determine the unit prices for items sold during a summer stock-up sale. Encourage students to use bills (Math Masters, page 428) and coins to act out dividing the stock-up price by the number of items to find the unit price.

ENRICHMENT PARTNER ACTIVITY

� Testing Products 30+ Min

To apply students’ ability to analyze and interpret data, have students create guidelines for testing a product such as colored markers. They may want to consider factors such as brightness, cost, and drying time. Encourage students to use a scale to rate each criterion for each brand. For example: 4 = excellent, 3 = good, 2 = not so good, 1 = poor. Have students test three brands of the chosen product using their guidelines. Students should tally and report their findings with a chart or graph.

LESSON

12�4

Name Date Time

Stock-Up Sale

Party Town is having a summer stock-up sale. The ad below shows the original price of each

item and the sale price if you buy a certain number of items. Use bills and coins to help you

find the stock-up price per item.

Party Music CDs

$8.00 each

1.

You pay $5.00

per CD.Stock-Up Price: Buy 5 for $25.00.

String in a Can

$3.00 each

2.

You pay $2.00

per can.Stock-Up Price: Buy 8 for $16.00.

3.

Stock-Up Price: Buy 12 for $14.40.

4.

Stock-Up Price: Buy 3 for $29.97.

Glow bracelets

$2.50 each

5.

Stock-Up Price:

Buy 6 for $10.50.

Party Hats

$9.99 for a package of 45

6.

Stock-Up Price: Buy

4 packages for $19.96.

Mylar Balloon

$1.99 each

Piñata

$14.99 each

You pay $1.20

per balloon.

You pay $1.75

per bracelet.

You pay $9.99

per piñata.

You pay $4.99

per package.

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Math Masters, p. 346

Teaching Master

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