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Level 1, Unit 3 • Linear Patterns  A-1

Unit 3

Getting Ready

Practice AInput/Output Tables

A pattern is a list of numbers or figures that follows a rule. For numeric patterns, the rule can include any of the four operations. You may use an addition or subtraction pattern to find how old you will be when someone else is a certain age. You may use a multiplication or division pattern to find how many items are in a number of packages.

An input/output table can be used to organize patterns. To complete an input/output table with missing numbers, find the rule and use that rule to determine the missing numbers.

You can think of the input as the number that goes into a number machine and the output as the number that comes out when the rule is applied.

Sometimes an input/output table will be complete. In these cases, you only need to find the rule.

EXAMPLE 1What is the rule of the table?

Input 12 20 32 48

Output 3 5 8 12

Step 1: Determine whether the output is greater or less than the input.

Step 2: The differences between the numbers are not equal. Divide the input by the output to see if the quotients are equal.

Solution: The rule of the table is to divide the input by 4.

The input is always greater than the output. The rule could be subtraction or division12 ÷ 3 = 420 ÷ 5 = 432 ÷ 8 = 448 ÷ 12 = 4

A-2  Getting Ready Practice A Input/Output Tables

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Getting Ready

Unit 3 Practice AInput/Output Tables continued

You can create an input/output table if given a rule.

EXAMPLE 2Copy and complete each table using the rule you are given.

Rule: Multiply by 3

Input Output

6

9

13

18

Multiply each input number by 3.

6 × 3 = 18

9 × 3 = 27

13 × 3 = 39

18 × 3 = 54

Solution: Input Output

6 18

9 27

13 39

18 54

Level 1, Unit 3 • Linear Patterns  A-3

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Getting Ready

Unit 3 Practice AInput/Output Tables continued

EXAMPLE 3The input/output table below gives Sam’s and Cecilia’s ages at different points in their lives.

Sam’s Age (in years) 6 8 11 14

Cecilia’s Age (in years) 2 4 7

Find Cecilia’s age when Sam is 14 years old.

Step 1: Assign the input and output.

Step 2: Because the output (Cecilia’s age) is less than the input (Sam’s age), determine if the rule uses subtraction or division. Try subtracting Cecilia’s age from Sam’s age.

Step 3: Write the rule. Because the differences are equal, the rule uses subtraction.

Step 4: Use the rule, Subtract 4, to find Cecilia’s age when Sam is 14 years old.

Solution: When Sam is 14 years old, Cecilia will be 10 years old.

It may be necessary to use inverse operations when finding the rule. Inverse operations are operations that “undo” each other. The chart below shows examples of inverse operations.

Addition/Subtraction Multiplication/Division

3 + 6 = 95 × 4 = 20

9 − 6 = 320 ÷ 4 = 5

Sam’s age is the input, and Cecilia’s age is the output.6 − 2 = 48 − 4 = 411 − 7 = 4The rule is to Subtract 4 from Sam’s age.

14 − 4 = 10

A-4  Getting Ready Practice A Input/Output Tables

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Getting Ready

Unit 3 Practice AInput/Output Tables continued

EXAMPLE 4Complete the table.

Input 3 6 8 12

Output 8 13 17

Step 1: Because the output is always greater, determine if the rule uses addition or multiplication. Subtract the input from the output.

Step 2: Write the rule. Because the differences are equal, therule uses addition.

Step 3: Use the rule, Add 5, to find the missing number.

Solution: The missing output number is 11.

When the differences between the numbers are not equal, the rule may be multiplication or division. If the output is greater than the input, the rule is multiplication. If the input is greater than the output, the rule is division.

EXAMPLE 5Complete the table.

Input 2 4 7 11

Output 10 20 55

Step 1: Determine whether the output is greater or less than the input.

Step 2: See if the differences between the numbers are equal. If they are, the rule uses addition.

Step 3: The differences between the numbers are not equal. Divide the output by the input to see if the quotients are equal.

Step 4: Write the rule. Because the quotients are equal and the output is greater, the rule uses multiplication.

Step 5: Use the rule, Multiply by 5, to find the missing number.

Solution: The missing number is 35.

8 − 3 = 513 − 8 = 517 − 12 = 5The rule is to Add 5 to the input.

6 + 5 = 11

The output is always greater than the input. The rule could be addition or multiplication.10 − 2 = 820 − 4 = 1655 − 11 = 4410 ÷ 2 = 520 ÷ 4 = 555 ÷ 11 = 5The rule is to Multiply the input by 5.

7 × 5 = 35

Level 1, Unit 3 • Linear Patterns  A-5

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Getting Ready

Unit 3 Practice AInput/Output Tables continued

tRY tHESE

Write the rule of each table.

1. Input Output 8 112 521 14

25 18

2. Input Output 4 24 7 4211 6616 96

3. Input Output 2 12 5 1510 2020 30

Copy and complete each table using the rule you are given.

4. Rule: Add 15 5. Rule: Multiply by 9 6. Rule: Divide by 5

Input Output132436

48

Input Output 5 91318

Input Output 45 60 75100

Copy and complete each table. Write the rule you used.

7. Input Output 7 151116 242127

8. Input Output 3 21 7 9 631217 119

9. Input Output 7 1 9 3122032

10. Input Output 18 2 36 72 8 90144

11. Input Output 0 6 18 915 2724

12. Input Output 24 3  56 72 96 12160

13. Carl sold 16 school t-shirts in 2 days. He sold 40 t-shirts in 5 days, and 64 t-shirts in 8 days. Assume his pattern of sales continues. Write an input/output table to represent the data. Give the rule and use the rule to find how many t-shirts Carl will sell in 24 days. Explain how you found your answer.