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# 3.4: Function Machines 1

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Can you use the rule described in the picture below to finish the table? In this concept, we will use rules, addition, and subtraction to complete function tables.

### Guidance

In order to complete function tables like the one above, we can use the problem solving steps to help.

• First, describe what you see in the table.
• Second, identify what your job is. In these problems, your job will be to complete the table.
• Third, make a plan . In these problems, your plan should be to use the rule to help you to complete the table.
• Fourth, solve . In these problems you will solve by completing the table.
• Fifth, check . In these problems you will check by counting up or down to make sure that you completed the table correctly.

#### Example A

Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

$& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\&&& \text{numbers. Some OUT numbers are missing. The rule says add 1.}\\& \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\& \mathbf{Plan:} && \text{Add} \ 1 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\& \mathbf{Solve:}$

In Out
2 3
6 7
0 1
8 9
4 5

$& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 6, 7\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 0, 1\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 8, 9\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 4, 5$

#### Example B

Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

$& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\&&& \text{numbers. Some OUT numbers are missing. The rule says add 3.}\\& \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\& \mathbf{Plan:} && \text{Add} \ 3 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\& \mathbf{Solve:}$

In Out
4 7
5 8
1 4
2 5
7 10

$& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 5, 6, 7, 8\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 1, 2, 3, 4\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 2, 3, 4, 5\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 7, 8, 9, 10$

#### Example C

Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

$& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\&&& \text{numbers. Some OUT numbers are missing. The rule says add 5.}\\& \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\& \mathbf{Plan:} && \text{Add} \ 5 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\& \mathbf{Solve:}$

In Out
1 6
4 9
5 10
3 8
2 7

$& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 1, 2, 3, 4, 5, 6\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 4, 5, 6, 7, 8, 9\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 5, 6, 7, 8, 9, 10\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 3, 4, 5, 6, 7, 8\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 2, 3, 4, 5, 6, 7$

#### Concept Problem Revisited

We can use the problem solving steps to help us solve this problem.

$& \mathbf{Describe:} && \text{The box is an} \ \mathbf{Add \ 2} \ \text{machine. The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\&&& \text{numbers. Some OUT numbers are missing.}\\& \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\& \mathbf{Plan:} && \text{Add} \ 2 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\& \mathbf{Solve:}$

In Out
1 3
4 6
3 5
0 2
5 7

$& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 4, 5, 6\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 3, 4, 5\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 0, 1, 2\\&&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 5, 6, 7$

### Vocabulary

A function is an example of a rule that states a relationship between two quantities. In this concept, our rule told us how to go from the in number to the out number in each table. To add means to combine or to put together. To subtract means to take away. In this concept, our rules told us to add or subtract.

### Guided Practice

Follow the rules. Complete the tables.

1.

2.

3.

4.

1. Here is the completed table:

In Out
6 10
0 4
3 7
4 8
5 9

2. Here is the completed table:

In Out
7 9
5 7
8 10
3 5
6 8

3. Here is the completed table:

In Out
5 9
2 1
6 10
8 12
3 7

4. Here is the completed table:

In Out
0 6
6 12
2 8
3 9
4 10

### Practice

Follow the rules. Complete the tables.

Jan 18, 2013

May 27, 2014