Name
14.3
Graph Number Patterns
ALGEBRA
?
Essential Question
Geometry and
Measurement—5.8.C
Also 5.4.C
MATHEMATICAL PROCESSES
5.1.A, 5.1.C, 5.1.D
How can you display number patterns in the coordinate grid?
Unlock
Unlock the
the Problem
Problem
When Alice completes each level in her favorite video game, she wins
2 extra lives. Use a graph. How many extra lives will Alice have after
4 levels?
STEP 1 Make an input/output table.
Input
Completed Level
1
Output
Extra Lives
2
2
3
4
STEP 2 Write the related pairs of data as ordered pairs.
The input is the x-coordinate and the output is the y-coordinate.
(1, 2)
Level 1: __
Level 3: __
Level 2: __
Level 4: __
STEP 3 Plot the ordered pairs in the coordinate grid.
© Houghton Mifflin Harcourt Publishing Company
Extra Lives
y
Math Talk
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Mathematical Processes
Describe the number pattern
for extra lives.
x
1 2 3 4 5 6 7 8 9 10
Level Completed
So, Alice will have _ extra lives after completing 4 levels.
Module 14
523
Example
The pattern below follows the rule y = x + 3, where y is the number of squares
and x is the figure number. Use the pattern to find how many squares will be in
Figure 5. Display the pattern in the coordinate grid.
Figure 1
Figure 2
Figure 3
STEP 1 The pattern in the number of squares is 4, 5, 6, _, _.
STEP 2 Write ordered pairs using the figure number and the number of squares.
(1, 4) (2, 5) (_, _) (_, _) (_, _)
y
STEP 3 Plot the ordered pairs in the graph.
10
8
6
4
2
0
x
1 2 3 4 5 6 7 8 9 10
Share
Share and
and Show
Show
Use the given rules to complete the pattern. Display the pattern in the coordinate grid.
1. Multiply the number of nickels by 5 to find the
2. Add 5 to the input.
number of pennies that equal the value.
Nickels
1
2
Output
Pennies
5
10
4
Input
1
y
2
25
20
15
10
5
3
0
524
3
4
x
1 2 3 4 5
Output
y
10
9
8
7
6
5
4
3
2
1
0
x
1 2 3 4 5 6 7 8 9 10
© Houghton Mifflin Harcourt Publishing Company
Input
Name
Problem
Problem Solving
Solving
3.
Write Math
The rule for a pattern is add 4
to the input. Explain how you can use the rule to write ordered
pairs that represent the pattern.
y
4. Write five ordered pairs that represent the pattern rule
x
multiply input by 3. Display the pattern in the coordinate grid
to the right.
0
Problem
Problem Solving
Solving
y
Use the coordinate plane for 5–7.
5. Multi-Step Emily has a road map with a key that shows an inch
on the map equals 5 miles of actual distance. Use the table and
the coordinate grid to show the pattern.
Input
Output
Distance on
the Map (in.)
Actual
Distance (mi)
1
2
3
4
6. Use Graphs What is the actual distance if the distance on
the map is 6 inches? Write the ordered pair. Plot a point in the
coordinate grid to show the appropriate ordered pair.
5
70
65
60
55
50
45
40
35
30
25
20
15
10
5
© Houghton Mifflin Harcourt Publishing Company
0
7.
x
1 2 3 4 5 6 7 8 9 10
What is the distance on the map
if the actual distance is 45 miles? Plot a point in
the coordinate grid to show the appropriate
ordered pair.
Module 14 • Lesson 3
525
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
8. Ted gets a $10 allowance every week and saves $6 of it. He makes a graph
to show his savings, where the x-coordinate represents the number of
weeks and the y-coordinate represents the number of dollars saved.
Which of the following ordered pairs could be on the graph?
(6, 60)
C
(1, 60)
B
(36, 6)
D
(6, 36)
9. Tina owns a flower shop. The table shows
the prices for different numbers of flowers.
She makes a graph that compares number
of flowers to total price. Which ordered pair
should NOT be on the graph?
A
(8, 12)
C
(6, 9)
B
(6, 4)
D
(10, 15)
Input
Number of Flowers
2
4
6
Output
Price (in dollars)
3
6
9
10. Multi-Step Steve mixes 4 cups grape juice with
3 cups ginger ale to make a punch. Steve makes
a graph to compare the amounts of juice needed
for several batches. Which ordered pairs could be
on the graph?
A
(4, 3), (5, 4), (6, 5)
B
(3, 4), (5, 6), (6, 7)
C
(4, 3), (8, 6), (12, 9)
D
(3, 4), (8, 6), (12, 9)
8
10
y
Cups of Ginger Ale
A
12
11
10
9
8
7
6
5
4
3
2
1
0
x
1 2 3 4 5 6 7 8 9 10 11 12
Cups of Grape Juice
TEXAS Test Prep
of pineapple juice for every cup of orange juice. Which
ordered pair shows how many cups of pineapple juice
he needs for 3 cups of orange juice?
526
A
(4, 8)
C
(3, 12)
B
(1, 2)
D
(3, 4)
Orange Juice (c)
x
1
2
Pineapple Juice (c)
y
4
8
3
© Houghton Mifflin Harcourt Publishing Company
11. Rob is making a fruit punch for a party. He adds 4 cups
Geometry and Measurement—5.8.C
Also 5.4.C
MATHEMATICAL PROCESSES 5.1.A, 5.1.C, 5.1.D
H o mewo rk
and Practice
14.3
Name
Graph Number Patterns
ALGEBRA
Use the given rules to complete the pattern. Display the pattern
in the coordinate grid.
1. Multiply the number of cans by 3 to find the
2. Add 2 to the input.
number of tennis balls.
Input
Cans
1
2
Output
Balls
3
6
3
4
Input
1
2
3
4
5
Output
y
y
30
27
24
21
18
15
12
9
6
3
0
10
9
8
7
6
5
4
3
2
1
0
x
1 2 3 4 5 6 7 8 9 10
3. Write four ordered pairs that represent the pattern rule
x
1 2 3 4 5 6 7 8 9 10
y
multiply input by 4. Display the pattern in the coordinate grid
to the right.
Problem
Problem Solving
Solving
x
Use the coordinate grid for 4–5.
0
4. An architect makes a drawing of a building. One inch in
© Houghton Mifflin Harcourt Publishing Company
the drawing equals 10 feet in actual measurement. Use the
table and the coordinate grid to show the pattern.
Input
Drawing (in.)
Output
Actual
Measurement (ft)
1
2
3
4
5
5. What is the actual measurement if the length in the graph
drawing is 7 units? Plot a point in the coordinate grid to
show the ordered pair. _____
y
100
90
80
70
60
50
40
30
20
10
0
x
1 2 3 4 5 6 7 8 9 10
Module 14 • Lesson 3 527
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
6. Carson purchases tulip bulbs for his garden.
7. For every $1 the students raise for the new
Each package contains 6 bulbs. Which
ordered pair shows the number of bulbs in
4 packages?
Input
Packages
1
2
Output
Bulbs
6
12
3
A
(4, 24)
C
(3, 16)
B
(4, 18)
D
(18, 24)
8. Multi-Step Shakira saves $2 for every $3
she spends. She makes a graph that compares
the amount she spends to the amount she
saves. Which ordered pairs could be on
Shakira’s graph?
10
9
8
7
6
5
4
3
2
1
A
(20, 30)
C
(20, 200)
B
(20, 10)
D
(20, 2,000)
9. Multi-Step When the cook at Barney’s
Restaurant makes chili, he adds 3 cups
of water for every 2 cups of tomato sauce.
If you make a graph to compare the
amounts of tomato sauce needed for
several batches of chili, which ordered
pairs could be on the graph?
y
0
1 2 3 4 5 6 7 8 9 10
Amount Spent ($)
528
10
9
8
7
6
5
4
3
2
1
0
x
1 2 3 4 5 6 7 8 9 10
A
(6, 9), (8, 12)
B
(2, 3), (4, 6)
A
(3, 2), (6, 4), (9, 6)
C
(3, 6), (6, 12)
B
(2, 3), (3, 4), (5, 6)
D
(9, 6), (12, 8)
C
(3, 2), (5, 5), (7, 10)
D
(2, 3), (4, 6), (6, 9)
Cups of Tomato Sauce
© Houghton Mifflin Harcourt Publishing Company
x
Cups of Water
Amount Saved ($)
y
4
playground equipment fund, the parents
association donates $10 to the fund. If the
x-coordinate is the amount the students
raise and the y-coordinate is the amount the
parents donate, which ordered pair could be
on the graph?