Name
Master 1.21
Date
Extra Practice 1
Lesson 1: Input/Output Machines
1. Complete this table.
The pattern rule that relates the input
to the output is:
Subtract 11 from the input.
Input
21
31
41
51
61
Output
Input
3
6
9
12
15
?
Output
3
?
?
6
?
8
a) Write the pattern rule for the input.
b) Write the pattern rule for the output.
2. The pattern rule that relates the input
to the output is:
Divide the input by 3, then add 2.
Find the missing numbers in the table.
How can you check your answers?
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Name
Master 1.22
Date
Extra Practice 2
Lesson 2: Patterns from Tables
1. The table shows the input and output from a
machine with one operation.
Input
81
72
63
54
Output
9
8
7
6
a) Identify the number and the operation in the machine.
b) Continue the pattern.
Write the next 4 input and output numbers.
c) Write the pattern rule that relates the input to the output.
2. The table shows the input and output from a
machine with two operations.
Input
5
10
15
20
25
Output
15
40
65
90
115
a) Identify the numbers and the operations in the machine.
b) Choose 4 different input numbers.
Find the output for each input.
c) Write the pattern rule that relates the input to the output.
d) Predict the output when the input is 60. Check your prediction.
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Name
Master 1.23
Date
Extra Practice 4
Lesson 4: Using Variables to Describe Patterns
1. Janine wants to have helium-filled balloons delivered to the home of a sick friend.
Each balloon costs $4. Delivery costs $5.
a) Make a table to show the cost of having 1, 2, 3, and 4 balloons delivered.
b) Write a pattern rule that relates the number of balloons to the total cost.
c) Write an expression with a variable to represent the pattern.
d) Find the cost of having 9 balloons delivered.
How can you check your answer?
2. For each table of values, write an expression that relates the input to the output.
a)
b)
Input
24
22
20
18
16
Output
10
9
8
7
6
Input
1
2
3
4
5
Output
6
9
12
15
18
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Name
Master 1.24
Date
Extra Practice 5
Lesson 5: Plotting Points on a Coordinate Grid
1. List the coordinates of each point on the grid.
A: _____________
B: _____________
D: _____________
E: _____________
C: _____________
2. Use grid paper.
Draw and label a coordinate grid.
Plot each ordered pair.
Explain how you moved to do this.
F(3, 5)
G(6, 7)
H(9, 2)
I(1, 10)
J(7, 0)
3. a) Point A has coordinates (0, 17).
What do you know about Point A?
b) Point B has coordinates (24, 0).
What do you know about Point B?
c) What is the location of a point with coordinates (0, 0)?
How do you know?
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Date
Extra Practice 6
Master 1.25
Lesson 6: Drawing the Graph of a Pattern
1. Use grid paper.
a) Graph the data in the table.
Input
1
2
3
4
5
Output
11
13
15
17
19
b) Describe the relationship shown on the graph.
c) Write an expression to represent the pattern.
d) Find the output when the input is 8.
What strategy did you use?
Could you use the same strategy to find the output when the input is 43?
Explain.
2. Make an Input/Output table for this graph.
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Name
Master 1.26
Date
Extra Practice 7
Lesson 7: Understanding Equality
1. Suppose you were using real balance scales.
You place counters in the left pan to represent the first expression.
You place counters in the right pan to represent the second expression.
Would the scales balance each time?
If not, tell what you could do to balance the scales.
a) 17 – 6; 10 + 3
b) 5  8; 18 + 22
c) 9  5; 55 – 10
d) 25  4; 10  20
2. Which expressions can be rewritten using a commutative property?
Justify your choices.
a) 8 + 34
b) 18 – 5
c) 6  19
d) 45  9
e) 93 + 78
f) 0  3
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Name
Master 1.27
Date
Extra Practice 8
Lesson 8: Keeping Equations Balanced
1. For each equation below:
•
•
•
•
Model the equation with counters.
Use counters to model the preservation of equality for the operation shown.
Draw a diagram to record your work.
Use symbols to record your work.
a) 7 + 8 = 15 (addition)
b) 3  6 = 18 (subtraction)
c) 25 – 18 = 21  3 (multiplication) d) 3  4 = 7 + 5 (division)
2. For each equation below:
•
•
•
a)
Apply the preservation of equality.
Write an equivalent form of the equation.
Use paper strips to check that equality has been preserved.
2n = 16
b) 5b = 25
c) 42 = 6s
d) 49 = 7t
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Name
Master 1.28
Date
Extra Practice Answers
Extra Practice 1 – Master 1.21
Lesson 1
1.
Input Output
21
10
31
20
41
30
51
40
61
50
a) Start at 21. Add 10 each time.
b) Start at 10. Add 10 each time.
d) $41; I can check by substituting b = 9
into the expression.
2. a) n  2 – 2
b) 3n + 3
Extra Practice 5 – Master 1.24
Lesson 5
1. A(0, 9), B(5, 8), C(8, 5), D(6, 2), E(1, 12)
2.
2.
Input Output
3
3
6
4
9
5
12
6
15
7
18
8
When the input was given, I used
the pattern rule to find the output.
When the output was given, I worked
backward and used the inverse
operations:
I subtracted 2, then multiplied by 3.
Extra Practice 2 – Master 1.22
Lesson 2
1. a)
b)
c)
2. a)
b)
c)
d)
9
45, 5; 36, 4; 27, 3; 18, 2
Divide the input by 9 to get the output.
 5, – 10
30, 140; 35, 165; 40, 190; 45, 215
Multiply the input by 5, then subtract 10.
290; 60  5 = 300 and 300 – 10 = 290
To plot point F, I moved 3 squares right
and 5 squares up.
To plot point G, I moved 6 squares right
and 7 squares up.
To plot point H, I moved 9 squares right
and 2 squares up.
To plot point I, I moved 1 square right
and 10 squares up.
To plot point J, I moved 7 squares right
and 0 squares up.
3. a) The point is on the vertical axis.
b) The point is on the horizontal axis.
c) The point is at the origin. To plot a point,
I always start at the origin. Since I move
0 squares right and 0 squares up,
I am still at the origin.
Extra Practice 4 – Master 1.23
Extra Practice 6 – Master 1.25
Lesson 4
Lesson 6
1. a)
1. a)
Number of
Cost ($)
Balloons
1
9
2
13
3
17
4
21
b) Multiply the number of balloons by 4,
then add 5.
c) Let b represent the number of balloons.
Then an expression that represents the
pattern is: 4b + 5
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Date
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b) The graph shows that as the input
increases by 1, the output increases by 2.
c) Let n represent the input. An expression
that represents the pattern is: 2n + 9
d) 25; I extended the table to the 8th term.
No, it would take a long time to extend the
table to the 43rd term. It would be more
efficient to substitute n = 43 into the
expression: 2  43 + 9 = 95;
the output is 95.
2.
Date
c)
For clarity, only one group of 7 is
shown on the right side.
72=72
d)
Input
1
2
3
4
5
Output
9
16
23
30
37
For clarity, only one group of 6 is
shown on each side.
12  2 = 12  2
Extra Practice 7 – Master 1.26
Lesson 7
1. a) No, I could take away 2 counters from the
right pan.
b) Yes
c) Yes
d) No, I could multiply the number of counters
in the left pan by 2.
2. a) Yes, 34 + 8, addition is commutative.
b) No, subtraction is not commutative.
c) Yes, 19  6; multiplication is commutative.
d) No, division is not commutative.
e) Yes, 78 + 93; addition is commutative.
f) Yes, 0  3; multiplication is commutative.
2. a) 2n  2 = 16  2
b) 5b  5 = 25  5
c) 42  2 = 6s  2
d) 49 + 5 = 7t + 5
Students’ answers should include
drawings of paper strips.
Extra Practice 8 – Master 1.27
Lesson 8
1. a)
15 + 2 = 15 + 2
b)
18 – 6 = 18 – 6
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