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Practice Lesson 8 Number and Shape Patterns
Practice and Problem Solving
CC04MM RPPS TG TEXT.indb 30
Lesson 8
Number and Shape Patterns
Solve.
Name:
M
Prerequisite: Identify Number Patterns
3 Fill in the missing numbers to show patterns with
addends and sums.
Study the example showing a number pattern.
Then solve problems 1–5.
Example
Leo noticed a pattern in the addition table.
What pattern did Leo notice?
What is the rule for the pattern?
What is the next number in the pattern?
Pattern: 0, 2, 4, 6, 8
Rule: add 2
Use the rule to find the next number in the pattern:
8 1 2 5 10
0
1
2
3
4
0
0
1
2
3
4
5
1
1
2
3
4
5
6
2
2
3
4
5
6
7
3
3
4
5
6
7
8
Addend
100
90
80
70
60
5
4
4
5
6
7
8
9
5
5
6
7
8
9
?
M
a. What pattern do you see in the first Addend
column?
Possible answer: As you go down the column,
each number is 10 less than the number above it.
b. What pattern do you see in the second Addend
column?
1 Use the number line below to answer the questions.
110
110
110
Sum
110
110
110
110
110
4 Look at problem 3.
10 is the next number in the pattern.
B
Addend
10
20
30
40
50
Possible answer: As you go down the column,
110
each number is 10 more than the number above it.
0
10
20
30
40
c. When the sum remains the same, what do you
notice about the two addends?
a. What pattern of numbers do you see on the number line?
Possible answer: When the first addend goes up by 10,
0, 10 , 20, 30 , 40
B
the second addend goes down by 10.
2 Use the number line below to answer the questions.
15
0
15
5
15
10
15
a. What pattern of numbers do you see on the number line?
b. Label the number line to show the rule for the pattern.
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5 What is the same and what is different about the
number pattern a
series of numbers that
follow a rule to repeat or
change.
20
0 , 5 , 10 , 15 , 20
C
Vocabulary
15
Pattern A: 5, 10, 15, 20, 25, 30
Pattern B: 30, 25, 20, 15, 10, 5 Possible answers are shown.
Same: The numbers are the same in both patterns, but in a different order.
rule a procedure to
follow to go from one
number or shape to the
next in a pattern.
Lesson 8 Number and Shape Patterns
two patterns below?
Different: The rule for pattern A is add 5. The rule for pattern B is subtract 5.
78
78
77
77
Lesson 8 Number and Shape Patterns
Key
B Basic
M Medium
C Challenge
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Unit 2
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Unit 2 Operations and Algebraic Thinking
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b. What is the rule for the pattern? add 10
Name:
Solve.
Use Number Patterns
Copying is not permitted.
M
Study the example showing how to use a pattern on a number line
to solve a word problem. Then solve problems 1–8.
3 Use the table below to answer the questions.
Jeff
Eric
Example
110
110
Tuesday
2
4
Wednesday
3
6
Thursday
4
8
Friday
5
10
a. What is the rule for the pattern in Jeff’s row? add 1
Riley wants to save $10 from her weekly babysitting job for the next
4 weeks. She has $50 in savings now. How much will Riley have in
savings at the end of 4 weeks?
110
Monday
1
2
b. What is the rule for the pattern in Eric’s row? add 2
c. Look at both Jeff’s and Eric’s numbers from day
to day. What pattern do you see?
110
Possible answer: Jeff’s number is half of Eric’s number. Eric’s number
50
Now
60
Week
1
70
Week
2
80
Week
3
90
Week
4
is two times Jeff’s number.
d. If Saturday were shown in the table, what would
be the numbers in Jeff’s row and in Eric’s row?
Rule: add 10
Pattern: 50, 60, 70, 80, 90
Jeff’s row: 6, Eric’s row: 12
Riley will have $90 in savings at the end of 4 weeks.
Eve’s soccer team has 48 water bottles in the locker
room. Each of the 12 players takes a water bottle
before a game.
Eduardo practices the flute each weekday. His
music teacher wants him to practice 5 minutes
longer each day this week. Eduardo practices for
20 minutes on Monday. How many minutes will
Eduardo practice on Friday?
B
M
B
Tuesday
Wednesday
Thursday
Friday
20
25
30
35
40
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40 minutes
Copying is not permitted.
2
24
3
12
5 Use words and numbers to explain how you found the
+5
Possible answer: There were 48 bottles before Game 1. 12 players each took
a bottle, so I subtracted 12 from 48. 48 2 12 5 36
+5
2 Complete the sentence.
Eduardo will practice for
1
36
number of bottles left after Game 1.
Monday
+5
48
on Friday.
M
6 What is the rule for the pattern? subtract 12
M
7 What number would come after 12 in the pattern?
C
Lesson 8 Number and Shape Patterns
79
79
0
8 What does this number mean? No more water bottles left.
80
80
Lesson 8 Number and Shape Patterns
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4/7/16 2:37 PM
Unit 2
Unit 2 Operations and Algebraic Thinking
C
Eduardo will practice each day this week.
+5
in the locker room at the end of each of the first three games.
Game
Number of Bottles
1 Complete the table to show how many minutes
Day
Number
of Minutes
4 Complete the table to show how many water bottles are left
Practice Lesson 8 Number and Shape Patterns
Practice and Problem Solving
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CC04MM RPPS TG TEXT.indb 31
Lesson 8
32
Name:
Solve.
Identify Shape Patterns
M
Study the example showing ways to describe a
shape pattern. Then solve problems 1–7.
4 Sasha draws a shape pattern that goes back and
forth between a 5-pointed star and 4-pointed star.
Example
A banner along a classroom wall has the shape pattern below.
What is another way to describe the pattern?
Possible answer: The odd-numbered spots have stars, with an odd number of points.
The even-numbered spots have stars, with an even number of points.
You can describe the pattern in words:
circle, triangle, square, pentagon, circle, triangle, square, pentagon
M
5 Look at the shape pattern in problem 4. Choose Yes
or No for each statement below.
You can describe the pattern by the number of sides in each shape:
0, 3, 4, 5, 0, 3, 4, 5
a. The 7th spot has a 4-pointed star.
What will the next shape in the pattern be?
A circle follows a pentagon in the shape pattern.
B
b. The 8th spot has a 5-pointed star.
c. The 99th spot has a 5-pointed star.
d. The 100th spot has a 4-pointed star.
1 Draw the next two shapes in the shape pattern
shown below.
M
M
3 No
u
u
3 No
u No
u No
6 Jamel used pattern blocks to make the shape pattern
shown below.
2 What two ways could you describe the shape
pattern below?
C
2) 3 sides, 0 sides, 4 sides, 3 sides, 0 sides, 4 sides
7 Look at the shape pattern in problem 6. Choose Yes
3 Look at problem 2. The 3rd shape and the 6th shape
are the same. Explain how to figure out what the
30th shape will be without drawing all 30 shapes.
Possible explanation: The 3rd and the 6th shape are rectangles. 3 and 6 are
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Lesson 8 Number and Shape Patterns
a.
will always be in an even spot.
b.
will always be on a multiple of 3.
c. The 12th spot is
multiples of 3. 30 is a multiple of 3 so a rectangle will be the 30th shape.
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or No for each statement below.
d.
81
81
82
82
.
is in every 5th spot.
Lesson 8 Number and Shape Patterns
3 Yes
u
u Yes
u
3 Yes
u Yes
u No
3 No
u
u No
u
3 No
Vocabulary
shape pattern a series
of shapes that follow a
rule to repeat or change.
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Unit 2
Copying is not permitted.
4/7/16 2:37 PM
Unit 2 Operations and Algebraic Thinking
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Draw the next 2 shapes in the pattern.
Possible answer: 1) Triangle, circle, rectangle, triangle, circle, rectangle;
M
u Yes
u Yes
u
3 Yes
u
3 Yes
Practice Lesson 8 Number and Shape Patterns
Practice and Problem Solving
CC04MM RPPS TG TEXT.indb 32
Lesson 8
Name:
Solve.
Number and Shape Patterns
Copying is not permitted.
M
Solve the problems.
4 Vivian wrote the number pattern below.
There may be
several ways to
describe a pattern.
8, 16, 32, 64, 128
M
1 How are the two number patterns below different?
Pattern A: 11, 22, 44, 88
Pattern B: 11, 22, 33, 44
Which of the following could be a rule for this
pattern?
What is the rule for
each pattern?
A Multiply by 2.
Possible answer: The rule for pattern A is
multiply by 2. You multiply to get the next
number in the pattern. The rule for pattern B
B
Add 16.
C
Double the number.
D Multiply by 4.
is add 11. You add to get the next number in
Tori chose D as the correct answer. How did she get
that answer?
the pattern.
Answers will vary. Possible answer: Tori looked at 8 and 32: 8 3 4 5 32;
she also looked at 16 and 64: 16 3 4 5 64. She saw that the rule worked for
M
2 Describe a rule you see in the shape pattern below.
Possible answer: The pattern goes back and
forth between a letter with curves and a letter
with only straight lines.
some numbers; she didn’t try the rule for all the numbers in the pattern.
Look at how the
letters are formed.
What do some
letters have in
common? What do
other letters have in
common?
C
5 Complete the pattern below. The pattern follows
the rule “add 2, subtract 1.”
+2 –1 +2 –1
1,
3,
2,
4,
3,
5,
4,
6,
, 6___
, 8 ___
, 7 ___
5, 7___
M
3 Use the letters T, P, J, and I to continue the pattern
in problem 2.
Possible answer: P, T, J, I or J, T, P, I or P, I, J, T
a. The number in the 15th spot is 7 8 9.
How can you use the
rule to find the next
letter in the pattern?
b. The difference between the numbers in every
other spot is 1 2.
or J, I, P, T
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Lesson 8 Number and Shape Patterns
83
83
84
84
Lesson 8 Number and Shape Patterns
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Unit 2
Unit 2 Operations and Algebraic Thinking
Circle one number in each sentence below that
makes the sentence true about the pattern.
It can be helpful to
write the number of
the spot (1st, 2nd,
3rd, 4th, and so on)
beneath each
number in the
pattern.
Practice Lesson 8 Number and Shape Patterns
Practice and Problem Solving
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CC04MM RPPS TG TEXT.indb 33
Lesson 8