Patterns - Table of Values worksheet - Free Printable

Let’s solve each part step by step.

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Question 1:

Table:
x | 1 | 2 | 3 | 4 | 5 | 6
y | 3 | 6 | 9 | ? | ? | ?

We see that when x = 1, y = 3 → 1 × 3 = 3
x = 2, y = 6 → 2 × 3 = 6
x = 3, y = 9 → 3 × 3 = 9

So the pattern is: y = x × 3

Now fill in the rest:

x = 4 → y = 4 × 3 = 12
x = 5 → y = 5 × 3 = 15
x = 6 → y = 6 × 3 = 18

a) Describe the pattern:
Each y value is 3 times the x value. Or, you add 3 each time as x increases by 1.

b) What would the 9th term be?
That means x = 9 → y = 9 × 3 = 27

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Question 2:

Table:
x | 1 | 2 | 3 | 4 | 5 | 6
y | 5 | 10| 15| ? | ? | ?

x = 1 → y = 5 → 1 × 5 = 5
x = 2 → y = 10 → 2 × 5 = 10
x = 3 → y = 15 → 3 × 5 = 15

Pattern: y = x × 5

Fill in:

x = 4 → 4 × 5 = 20
x = 5 → 5 × 5 = 25
x = 6 → 6 × 5 = 30

a) Describe the pattern:
Each y value is 5 times the x value. Or, you add 5 each time as x increases by 1.

b) What would the 8th term be?
x = 8 → y = 8 × 5 = 40

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Question 3:

a) Rule: ★ × 2 = □
Input (★): 1, 2, 3, 4, 5, 6, 7, 8
Output (□): multiply each by 2

So:
1×2=2
2×2=4
3×2=6
4×2=8
5×2=10
6×2=12
7×2=14
8×2=16

b) Rule: ★ + 5 × 2 = □
Wait — order of operations! Multiplication comes before addition.

So it’s: ★ + (5 × 2) = ★ + 10

Inputs are odd numbers: 1, 3, 5, 7, 9, 11, 13, 15

Add 10 to each:

1 + 10 = 11
3 + 10 = 13
5 + 10 = 15
7 + 10 = 17
9 + 10 = 19
11 + 10 = 21
13 + 10 = 23
15 + 10 = 25

c) Rule: ★ × 10 - 6 = □
Again, multiplication first, then subtract 6.

Inputs: 1, 3, 5, 7, 9, 11, 13, 15

Calculate:

1 × 10 = 10 → 10 - 6 = 4
3 × 10 = 30 → 30 - 6 = 24
5 × 10 = 50 → 50 - 6 = 44
7 × 10 = 70 → 70 - 6 = 64
9 × 10 = 90 → 90 - 6 = 84
11 × 10 = 110 → 110 - 6 = 104
13 × 10 = 130 → 130 - 6 = 124
15 × 10 = 150 → 150 - 6 = 144

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Final Answer:

Question 1:
Completed table: y values for x=4,5,6 → 12, 15, 18
a) Pattern: Multiply x by 3 (or add 3 each time)
b) 9th term: 27

Question 2:
Completed table: y values for x=4,5,6 → 20, 25, 30
a) Pattern: Multiply x by 5 (or add 5 each time)
b) 8th term: 40

Question 3:
a) Outputs: 2, 4, 6, 8, 10, 12, 14, 16
b) Outputs: 11, 13, 15, 17, 19, 21, 23, 25
c) Outputs: 4, 24, 44, 64, 84, 104, 124, 144