“What’s My Rule?”
Objective To review “What’s My Rule?” problems.
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eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Identifying Polygon Properties
• Solve addition and subtraction problems. Math Journal 1, p. 54
straightedge
Students design polygon letters.
[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 Activities
Math Boxes 3 1
Math Journal 1, p. 55
Students practice and maintain skills
through Math Box problems.
Study Link 3 1
Math Masters, p. 72
Students practice and maintain skills
through Study Link activities.
Students 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 Vocabulary
function machine input output rule “What’s My Rule?”
Materials
Math Journal 1, p. 53
transparency of Math Masters, p. 407 slate
calculator (optional)
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 19, 278–284
158
Unit 3
Multiplication and Division; Number Sentences and Algebra
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Modeling Functional Relationships
with Pattern Blocks
Math Masters, p. 73
pattern blocks (triangles, squares)
Students use pattern blocks to investigate
and describe functional relationships.
ENRICHMENT
Solving a Perimeter Problem
Math 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?” Tables
Math Masters, p. 407
calculator
Students practice using words and symbols
to describe and write rules for functions.
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8
Getting Started
Content Standards
4.OA.5
Mental Math and Reflexes
Math Message
Pose multidigit addition and subtraction
problems. Suggestions:
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.
30 + 50 = 80
90 - 20 = 70
42 + 20 = 62
56 - 10 = 46
32 + 62 = 94
66 - 41 = 25
60 + 40 = 100
80 - 40 = 40
53 + 30 = 83
75 - 20 = 55
98 + 22 = 120
76 - 25 = 51
in
(days)
2
100
6
300
10
500
30
1,500
365
18,250
1 Teaching the Lesson
Math Message Follow-Up
(Math Masters, p. 407)
out
(gallons)
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
ACTIVITY
ELL
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
Adjusting the Activity
Have 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
Tell students that in this lesson they will review variations of
function machines.
Lesson 3 1
159
Type 1
Type 2
Rule
Rule
Subtract 15
Add 100
Reviewing Variations of the
WHOLE-CLASS
ACTIVITY
“What’s My Rule?” Routine
in
out
in
out
(Math Masters, p. 407)
30
15
250
350
90
75
20
120
Algebraic Thinking Demonstrate each type of “What’s My Rule?”
table (see margin) on the transparency of Math Masters, page 407.
65
50
565
665
110
95
321
421
Type 3
In Type 2, the rule and sample outputs are known, and the
inputs must be determined.
Type 4
Rule
Rule
Multiply by 7
Divide by 6
in
In Type 1, as in the Math Message problem, the rule and
sample inputs are known, and the outputs must be determined.
out
In Type 3, the inputs and outputs are known, and the rule
must be determined.
in
out
7
49
54
9
2
14
42
7
9
63
24
4
600 4,200
600
100
pounds
cost
1
$3.75
2
$7.50
5
$18.75
11
$41.25
Rule
A pound of
nuts costs $3.75
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
Student Page
Date
Time
LESSON
“What’s My Rule?”
3 1
䉬
162–166
Complete the “What’s My Rule?” tables and state the rules.
夹
in
1.
Rule
in
out
30
60
110
50
180
320
80
Add 30
20
150
out
in
3.
Rule
23
out
290
夹
2.
in
in
Rule
80
out
4.
Rule: There are
12 inches in 1 foot.
130
290
100
350
420
in
out
20
270
340
out
out
49
72
3
36
151
174
5
60
272
295
10
611
22
60
503
120
264
720
Try This
5.
Rule:
25
in
in
out
17
8
12
13
27
5
25
2
30
6.
Create your own.
Rule:
Answers
vary.
Rule?” Tables
(Math Journal 1, p. 53)
50
210
in
588
480
out
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:
Recognizing Student Achievement
Journal
page 53
Problems 1 and 2
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.
0
Math Journal 1, p. 53
160
PARTNER
ACTIVITY
Unit 3 Multiplication and Division; Number Sentences and Algebra
[Patterns, Functions, and Algebra Goal 1]
Student Page
2 Ongoing Learning & Practice
Identifying Polygon Properties
Date
Time
LESSON
A Polygon Alphabet
3 1
䉬
96 97
Try reading this message:
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 54)
Use a straightedge to design a polygon letter for each of the letters shown below. You’ll have
to simplify, because a polygon can’t have any curves, and it can’t have any “holes.”
1.
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.
Students design polygon letters.
Sample answers:
Math Boxes 3 1
INDEPENDENT
ACTIVITY
(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
INDEPENDENT
ACTIVITY
(Math Masters, p. 72)
B
C
D
F
M
X
B, C, F, M, and X
2.
Which of the letters you drew are nonconvex (concave) polygons?
How do you know?
3.
Do any of the letters you drew have special names as polygons? Explain.
Sample answer: At least one vertex is pushed inward.
Sample answers: B is a pentagon. C is an octagon.
D is a hexagon.
Try This
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).
Math Journal 1, p. 54
NOTE To further explore
function rules, see
www.everydaymathonline.com.
Home Connection Students complete several types of
“What’s My Rule?” problems.
Study Link Master
Name
Date
STUDY LINK
Date
3 1
䉬
162–166
Complete the “What’s My Rule?” tables and state the rules.
1.
in
in
53
Rule
54
Add 13
55
out
56
57
3.
Rule:
+46
in
out
out
1.
in
2. in
66
67
68
69
70
Rule
-60
out
4.
Time
LESSON
“What’s My Rule?”
31
Student Page
Time
×7
Rule:
out
110
80
310
240
390
250
in
out
50
Write , , or to make each number
sentence true.
d.
100,000
73,099 71,999
304,608 304,809
5,682 7 hundred
e.
5,000,236
a.
20
b.
c.
180
330
131
177
70
34
80
104
150
9
50
629
675
20
140
54
100
60
420
3.
490
Math Boxes
2.
25, 19, 16, 25, 18, 19, 25, 24, 25, 23
1 million
5,000,099
a.
a.
dollars nickels
3
6.
60
2
40
5
100
20
400
2,000
100
Create your own.
in
out
d.
181
Answers
vary.
5.
Complete.
Rule:
a.
b.
= 47 + 68
8.
359 + 253 =
612
9.
787 + 653 =
1,440
c.
Math Masters, p. 72
EM3MM_G4_U03_072-105.indd 72
4 ft c.
Practice
115
21 ft b.
e.
Rule: There
are 20 nickels
in $1.00.
7 yd
48 in.
5 yd 1 ft
16 ft 2 yd 2 ft 96 in.
47 ft 4 in. 568 in.
a.
3,452 1,147
Try This
7.
Complete.
3,389 2,712
3,500 1,100 2,400
5.
23.5
73
4.
3,000 3,000 6,000
b.
9
What is the median?
6 149
Sample answers:
63
What is the range for this set of
numbers?
b.
Make a ballpark estimate. Write a number
model to show your strategy.
350
Number of spelling words correct for
10 students on the spelling test:
31 , 39 , 47
8
Rule:
49, 42, 35 , 28, 21 , 14
Rule: 7
41 , 47 , 53, 59, 65 , 71
6
Rule:
129
6.
Solve mentally or with a paper-and-pencil
algorithm.
7, 15, 23,
a.
$3.56
$2.49
$6.05
b.
$6.25
$5.01
$1.24
34–37
160 161
Math Journal 1, p. 55
11/10/10 1:57 PM
Lesson 3 1
161
Teaching Master
Name
Date
LESSON
3 Differentiation Options
“What’s My Rule?” Polygon Sides
31
䉬
1.
Time
Use square pattern blocks to help you complete the table.
162–166
Number of
Squares
Number of
Sides
1
4
2
8
3
12
20
28
32
5
7
8
2.
READINESS
▶ Modeling Functional
Suppose there are 12 squares. Explain how to find the number of sides without counting.
Sample answer: Multiply 12 squares by
4 sides. This equals 48 sides. (12 4 48)
3.
4.
Number of
Sides
1
2
3
5
4
3
6
15
5–15 Min
Relationships with Pattern
Blocks
(Math Masters, p. 73)
Use triangle pattern blocks to help you complete the table.
Number of
Triangles
PARTNER
ACTIVITY
6
12
9
18
Suppose there are 30 sides. Explain how to find the number of triangles without counting.
Sample answer: Divide 30 sides by 3. This
equals 10 triangles. (30 3 10)
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
Solving a Perimeter Problem
Math Masters, p. 73
PARTNER
ACTIVITY
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.
Teaching Master
Name
Date
LESSON
NOTE Perimeter is defined as the distance around a closed 2-dimensional
Time
“What’s My Rule?” Perimeter
䉬
11114
1 in.
162–166
131
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.
1 in.
The distance around a shape is called its
perimeter. The perimeter of a square
pattern block is 4 inches.
1 in.
31
1 in.
EXTRA PRACTICE
1.
6
2.
3.
Completing “What’s My
Place 2 square pattern blocks side by side.
What is the perimeter of the shape?
inches
Complete the “What’s My Rule?” table.
Use square pattern blocks to create
the shapes.
Number of Square
Pattern Blocks
Perimeter of
Shape (inches)
1
4
Explain the rule for finding the perimeter
of the shapes.
2
6
8
10
12
14
16
18
Sample answer:
Multiply the number of
squares by 2, then add 2.
3
4
5
6
7
8
4.
Use your rule to complete the following: 214 square pattern blocks
are placed side by side. What is the perimeter of the shape?
430
Rule?” Tables
inches
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.
Use words or symbols to explain the rule for finding the perimeter of shapes
made by placing hexagon pattern blocks side by side.
Sample answer: Multiply the number of hexagons by 4, then
add 2. (h 4) 2
Math Masters, p. 74
162
5–15 Min
(Math Masters, p. 407)
Try This
5.
INDEPENDENT
ACTIVITY
Unit 3 Multiplication and Division; Number Sentences and Algebra
Name
STUDY LINK
31
Date
Time
“What’s My Rule?”
162–166
Complete the “What’s My Rule?” tables and state the rules.
in
in
1.
out
53
Rule
20
55
out
250
out
56
180
57
3.
Rule:
330
in
out
131
177
104
out
50
Rule
-60
54
Add 13
in
2. in
4.
Rule:
in
out
70
490
80
63
150
350
629
20
100
140
60
Try This
5.
dollars nickels
3
Create your own.
in
out
60
40
5
6.
Copyright © Wright Group/McGraw-Hill
Rule: There
are 20 nickels
in $1.00.
Rule:
100
20
100
Practice
7.
72
= 47 + 68
8.
359 + 253 =
9.
787 + 653 =