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eToolkitePresentations Interactive Teacher’s
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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