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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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158 Unit 3 Multiplication and Division; Number Sentences and Algebra

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 19, 278–284

“What’s My Rule?”Objective To review “What’s My Rule?” problems.

Key Concepts and Skills• Solve addition and subtraction problems. 

[Operations and Computation Goals 1 and 2]

• Solve multiplication and division problems. 

[Operations and Computation Goals 3 and 4]

• Use rules to complete “What’s My Rule?”

tables. 

[Patterns, Functions, and Algebra Goal 1]

• Use words and symbols to describe and

write rules for functions. 

[Patterns, Functions, and Algebra Goal 1]

Key ActivitiesStudents discuss problems in which one

quantity depends on another. They illustrate

this kind of relationship between pairs of

numbers with a function machine and a

“What’s My Rule?” table. They solve

“What’s My Rule?” problems.

Ongoing Assessment: Recognizing Student Achievement Use journal page 53. [Patterns, Functions, and Algebra Goal 1]

Key Vocabularyfunction machine � input � output � rule � 

“What’s My Rule?”

MaterialsMath Journal 1, p. 53

transparency of Math Masters, p. 407 � slate

� calculator (optional)

Identifying Polygon PropertiesMath Journal 1, p. 54

straightedge

Students design polygon letters.

Math Boxes 3�1Math Journal 1, p. 55

Students practice and maintain skills

through Math Box problems.

Study Link 3�1Math Masters, p. 72

Students practice and maintain skills

through Study Link activities.

READINESS

Modeling Functional Relationships with Pattern BlocksMath Masters, p. 73

pattern blocks (triangles, squares)

Students use pattern blocks to investigate

and describe functional relationships.

ENRICHMENTSolving a Perimeter ProblemMath Masters, p. 74

pattern blocks (squares, hexagons)

Students apply the “What’s My Rule?”

concept to solve a perimeter problem.

EXTRA PRACTICE

Completing “What’s My Rule?” TablesMath Masters, p. 407

calculator

Students practice using words and symbols

to describe and write rules for functions.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

�������

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1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Masters, p. 407)

Algebraic Thinking Have students compare their completed tables.

Display the function machine on the transparency of Math Masters, page 407. Remind students how a function machine works:

� A number (the input) is dropped into the machine.

� The machine changes the number according to a rule.

� A new number (the output) comes out the other end.

The rule for the Math Message problem is multiply by 50. Write “× 50” in the function machine. To support English language learners, discuss that the word rule has an everyday usage, such as a classroom rule, and a mathematical usage.

Point out the “What’s My Rule?” table in the Math Message problem. Ask:

● What do the numbers in the in column represent? Number of days

● What do the numbers in the out column represent? Average number of gallons of water used by one person in that many days

● How are the 2 in the in column and the 100 in the out column related? 2 × 50 = 100

Tell students that in this lesson they will review variations of function machines.

ELL

Lesson 3�1 159

Getting Started

Math Message Each person in the United States uses about 50 gallons of water per day. Use this information to complete the “What’s My Rule?” table.

Mental Math and ReflexesPose multidigit addition and subtraction problems. Suggestions:

30 + 50 = 80 60 + 40 = 100

90 - 20 = 70 80 - 40 = 40

42 + 20 = 62 53 + 30 = 83

56 - 10 = 46 75 - 20 = 55

32 + 62 = 94 98 + 22 = 120

66 - 41 = 25 76 - 25 = 51

in out (days) (gallons)

2 100

6 300

10 500

30 1,500

365 18,250

Adjusting the ActivityHave volunteers pose questions.

For example:

• If 8 is dropped into the function machine,

which number will come out? 400

• If 600 comes out of the function machine,

which number was dropped in? 12

AUDITORY � KINESTHETIC � TACTILE � VISUAL

Interactive whiteboard-ready

ePresentations are available at

www.everydaymathonline.com to

help you teach the lesson.

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in out

30 15

90 75

65 50

110 95

Rule

Subtract 15

Type 1

in out

7 49

2 14

9 63

600 4,200

Rule

Multiply by 7

Type 3

in out

250 350

20 120

565 665

321 421

Rule

Add 100

Type 2

in out

54 9

42 7

24 4

600 100

Rule

Divide by 6

Type 4

Try This

Date Time

“What’s My Rule?”LESSON

3 �1Complete the “What’s My Rule?” tables and state the rules.

1. 2.in out

30 6080 11020 50

150 180290 320

Rule

out

in

Add 30

in out

130 50

290 210

100 20

350 270

420 340

Rule

out

in

�80

3. 4. Rule: There are 12 inches in 1 foot.

Rule

out

in

�23

in out

49 72

151 174272 295

588 611

480 503

in out

17 �8

12 �1327 2

�5 �3025 0

in out

in out

3 36

5 60

10 12022 264

60 720

� �

5. Rule: 6. Create your own.

Rule:

�25

162–166

Answers vary.

Math Journal 1, p. 53

Student Page

� Reviewing Variations of the WHOLE-CLASS ACTIVITY

“What’s My Rule?” Routine(Math Masters, p. 407)

Algebraic Thinking Demonstrate each type of “What’s My Rule?” table (see margin) on the transparency of Math Masters, page 407.

� In Type 1, as in the Math Message problem, the rule and sample inputs are known, and the outputs must be determined.

� In Type 2, the rule and sample outputs are known, and the inputs must be determined.

� In Type 3, the inputs and outputs are known, and the rule must be determined.

� In Type 4, some inputs and outputs are known, and the missing numbers and the rule must be determined.

To find the rule, students should use the pairs in which both the in and out numbers are given. Then students can use the rule to fill in the missing in and out numbers. Also discuss any other patterns not stated in the rule. For example, the Type 3 table in the margin shows that when an even number is multiplied by an odd number, the result is an even number, and when an odd number is multiplied by an odd number, the result is an odd number.

Pose problems like Type 4 to the class. Rules may be stated as simple statements, such as “Subtract 15,” or rules may be stated in a context like the problem in the margin (A pound of nuts costs $3.75) or as in the Math Message (50 gallons per day). Encourage students to supply both types of rules. Supplying a context for a rule will be more difficult.

� Completing “What’s My PARTNER ACTIVITY

Rule?” Tables(Math Journal 1, p. 53)

Students complete Problems 1 and 2 on their own. They work in partnerships to complete the remainder of the page. Have calculators on hand for students to use as necessary while solving the “What’s My Rule?” problems.

Ongoing Assessment: Journal

page 53 �Problems 1 and 2 Recognizing Student Achievement

Use journal page 53, Problems 1 and 2 to assess students’ ability to use rules

to complete “What’s My Rule?” tables. Students are making adequate progress if

they are able to correctly identify the in and out numbers when given the rule.

Some students may be able to identify the rules in Problems 3 and 5 and use

these rules to complete the tables.

[Patterns, Functions, and Algebra Goal 1]

160 Unit 3 Multiplication and Division; Number Sentences and Algebra

pounds cost

1 $3.75

2 $7.50

5 $18.75

11 $41.25

RuleA pound of

nuts costs $3.75

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2 Ongoing Learning & Practice

� Identifying Polygon Properties INDEPENDENTACTIVITY

(Math Journal 1, p. 54)

Students design polygon letters.

� Math Boxes 3�1 INDEPENDENTACTIVITY

(Math Journal 1, p. 55)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 3-3 and 3-5. The skill in Problem 6 previews Unit 4 content.

Writing/Reasoning Have students write a response to the following: Explain how you found the range of the data set in Problem 2. Sample answer: I subtracted the smallest number (16) from the largest number (25) to find the range (9).

� Study Link 3�1 INDEPENDENTACTIVITY

(Math Masters, p. 72)

Home Connection Students complete several types of “What’s My Rule?” problems.

A Polygon AlphabetLESSON

3�1

Date Time

Try reading this message:

1. Use a straightedge to design a polygon letter for each of the letters shown below. You’ll haveto simplify, because a polygon can’t have any curves, and it can’t have any “holes.”

For example, if you look at the letter “P,” you see that there is no opening in the upper part.Making it look like this, , would make it easier to read, but it would not be a polygon.

2. Which of the letters you drew are nonconvex (concave) polygons? B, C, F, M, and XHow do you know?

3. Do any of the letters you drew have special names as polygons? Explain.

4. On a separate sheet of paper, design polygon letters for the rest of the uppercase (capital)letters in the alphabet, the 26 lowercase (small) letters, or the 10 digits (0–9).

D is a hexagon. Sample answers: B is a pentagon. C is an octagon.

Sample answer: At least one vertex is pushed inward.

B C D

F M X

96 97

Sample answers:

Try This

Math Journal 1, p. 54

Student Page

Date Time

Math Boxes LESSON

3 �1

5. Complete.

a. 7, 15, 23, , ,

Rule:

b. 49, 42, , 28, ,

Rule:

c. , , 53, 59, , 71

Rule: �6654741

�7142135

�8473931

1. Write �, �, or � to make each numbersentence true.

a. 1 million 100,000

b. 73,099 71,999

c. 304,608 304,809

d. 5,682 7 hundred

e. 5,000,236 5,000,099�

�

�

�

�

3. Make a ballpark estimate. Write a numbermodel to show your strategy.

a. 3,389 � 2,712

� �

b. 3,452 � 1,147

� �2,4001,1003,500

6,0003,0003,000

4. Complete.

a. 21 ft � yd

b. 4 ft � in.

c. 16 ft � yd ft

d. 2 yd 2 ft � in.

e. ft in. � 568 in.44796

1548

7

6. Solve mentally or with a paper-and-pencilalgorithm.

a. $3.56 b. $6.25� $2.49 � $5.01

181 129

160 161 34–37

2. Number of spelling words correct for 10 students on the spelling test:

25, 19, 16, 25, 18, 19, 25, 24, 25, 23

a. What is the range for this set of

numbers?

b. What is the median? 23.59

6 149

Sample answers:

$6.05 $1.24

73

Math Journal 1, p. 55

Student Page

Lesson 3�1 161

STUDY LINK

3�1 “What’s My Rule?” 162–166

Name Date Time

Complete the “What’s My Rule?” tables and state the rules.

1. 2.

3. Rule: +46 4. Rule: ×7

5. Rule: There

are 20 nickels

in $1.00.

6. Create your own.

Rule:

Answersvary.

Try This

7. 115 = 47 + 68 8. 359 + 253 = 612 9. 787 + 653 = 1,440Practice

in out

53 66

54 67

55 68

56 69

57 70

in out

110 50

80 20

310 250

240 180

390 330

in out

131 177

34 80

104 150

629 675

54 100

in out

70 490

9 63

50 350

20 140

60 420

dollars nickels

3 60

2 40

5 100

20 400

100 2,000

in out

Rule

out

in

Add 13

Rule

out

in

-60

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Math Masters, p. 72

Study Link Master

NOTE To further explore

function rules, see

www.everydaymathonline.com.

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162 Unit 3 Multiplication and Division; Number Sentences and Algebra

3 Differentiation Options

READINESS PARTNER ACTIVITY

▶ Modeling Functional 5–15 Min

Relationships with Pattern Blocks(Math Masters, p. 73)

To explore the relationships between pairs of numbers in “What’s My Rule?” tables using a concrete model, have students determine the relationship between the number

of squares and triangles and the number of sides they have. Ask students to share strategies for Problem 4.

ENRICHMENT PARTNER ACTIVITY

� Solving a Perimeter Problem 5–15 Min

(Math Masters, p. 74)

To apply students’ understanding of functional relationships, have them explore the perimeter of shapes created by placing square pattern blocks side by side.

Students record their data in a table and use the relationships between pairs of numbers to generate a rule for finding the perimeter of any shape made by n number of squares placed side by side.

Problem 5 challenges students to explain the rule for finding the perimeter of shapes created by placing hexagon pattern blocks side by side.

NOTE Perimeter is defined as the distance around a closed 2-dimensional

shape. Square and hexagon pattern blocks are prisms, not 2-dimensional

polygons, as the names imply. For this activity, have students consider only

the square or hexagonal bases of the pattern blocks.

EXTRA PRACTICE INDEPENDENTACTIVITY

� Completing “What’s My 5–15 Min

Rule?” Tables(Math Masters, p. 407)

Algebraic Thinking To practice using words and symbols to describe and write rules for functions, have students solve “What’s My Rule?” problems. Use Math Masters, page 407 to create problems to meet the needs of individual students, or have students create and solve their own problems. Afterward, discuss any patterns that were not part of the rule.

LESSON

3�1

Name Date Time

“What’s My Rule?” Polygon Sides

162–166

1. Use square pattern blocks to help you complete the table.

2. Suppose there are 12 squares. Explain how to find the number of sides without counting.

3. Use triangle pattern blocks to help you complete the table.

4 sides. This equals 48 sides. (12 � 4 � 48)

Sample answer: Multiply 12 squares by

4. Suppose there are 30 sides. Explain how to find the number of triangles without counting.

equals 10 triangles. (30 � 3 � 10)

Sample answer: Divide 30 sides by 3. This

Number of Number ofSquares Sides

1 42 83 12

5 20

7 28

8 32

Number of Number ofTriangles Sides

1 3

2 6

5 15

4 12

3 9

6 18

Math Masters, p. 73

Teaching Master

LESSON

3�1

Name Date Time

“What’s My Rule?” Perimeter

2. Complete the “What’s My Rule?” table.

Use square pattern blocks to create

the shapes.

3. Explain the rule for finding the perimeter

of the shapes.

squares by 2, then add 2.

Multiply the number of

Sample answer:

The distance around a shape is called its

perimeter. The perimeter of a square

pattern block is 4 inches.

1 in.

1 in

.1 in

.

1 in.

1. Place 2 square pattern blocks side by side.

What is the perimeter of the shape?

inches6

1 � 1 � 1 � 1 � 4

Number of Square Perimeter ofPattern Blocks Shape (inches)

1 4

2 63 84 105 126 147 168 18

4. Use your rule to complete the following: 214 square pattern blocks

are placed side by side. What is the perimeter of the shape? inches430

Try This

5. Use words or symbols to explain the rule for finding the perimeter of shapes

made by placing hexagon pattern blocks side by side.

add 2. (h � 4) � 2

Sample answer: Multiply the number of hexagons by 4, then

162–166 131

Math Masters, p. 74

Teaching Master

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STUDY LINK

3�1 “What’s My Rule?”C

opyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

72

162–166

Name Date Time

Complete the “What’s My Rule?” tables and state the rules.

1. 2.

3. Rule: 4. Rule:

5. Rule: There

are 20 nickels

in $1.00.

6. Create your own.

Rule:

Try This

7. = 47 + 68 8. 359 + 253 = 9. 787 + 653 =

Practice

in out

53

54

55

56

57

in out

50

20

250

180

330

in out

131 177

80

104 150

629

100

in out

70 490

63

350

20 140

60

dollars nickels

3 60

40

5 100

20

100

in out

Rule

out

in

Add 13

Rule

out

in

-60

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