# Working with Multiplication Input-Output Tables

Instructor: Dina Albert
In this lesson, we will find patterns in input-output tables, and use those patterns to find missing data in the tables. We will use the four operations: multiplication, division, addition and subtraction for these tables.

• Multiplication--the same as adding equal groups
• Multiples-- numbers that appear when adding equal groups.

For instance, 2, 4, 6, 8 are multiples of 2 because we are skip-counting, or adding by twos.

Likewise, 3, 6, 9, 12 are multiples of 3 because we are skip-counting, or adding by threes

## What Do Input-Output Tables Show?

Other data tables show relationships. These tables are called input-output tables:

## How Do Input-Output Tables Work?

Every input-output table works like a machine that follows a rule. You put a value into the machine, and the machine changes it using the rule. Notice in the table, the rule inside the grey box at the top that is +3. This specific machine will add 3 to any value you put into it. What the machine ''does,'' is called the rule.

#### What if you told your machine to multiply every input by 2?

In: 1 Rule: x 2 Out: 2 (1 x 2 = 2)

In: 2 Rule: x 2 Out: 4 (2 x 2 = 4)

In: 3 Rule: x 2 Out: 6 (3 x 2 = 6)

and so on until all the results are in the data table.

Since we know the machine will multiply every number by 2, we can write an expression to show that: In x 2 = Out

## What is the Rule?

Sometimes the machine breaks, and to fix it so that it keeps giving us results, we need to figure out what the rule is.

### Example 1

1 becomes 5

2 becomes 10

3 becomes 15

4 becomes 20

5 becomes 25

In this case, the rule is: multiply by 5. Input x 5 = Output

1 x 5 = 5

2 x 5 = 10 and so on.

The output is multiples of 5 after we multiply each input by 5: 5, 10,15, 20.25. 30.

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