# 3.4: Function Machines 1

**At Grade**Created by: CK-12

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.

\begin{align*}& \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:}\end{align*}

In |
Out |
---|---|

2 | 3 |

6 | 7 |

0 | 1 |

8 | 9 |

4 | 5 |

\begin{align*}& \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\end{align*}

#### Example B

Follow the rule. Complete the table.

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

\begin{align*}& \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:}\end{align*}

In |
Out |
---|---|

4 | 7 |

5 | 8 |

1 | 4 |

2 | 5 |

7 | 10 |

\begin{align*}& \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\end{align*}

#### Example C

Follow the rule. Complete the table.

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

\begin{align*}& \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:}\end{align*}

In |
Out |
---|---|

1 | 6 |

4 | 9 |

5 | 10 |

3 | 8 |

2 | 7 |

\begin{align*}& \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\end{align*}

#### Concept Problem Revisited

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

\begin{align*}& \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:}\end{align*}

In |
Out |
---|---|

1 | 3 |

4 | 6 |

3 | 5 |

0 | 2 |

5 | 7 |

\begin{align*}& \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\end{align*}

### Vocabulary

A ** function** is an example of a

**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**

*rule***means to combine or to put together. To**

*add***means to take away. In this concept, our rules told us to add or subtract.**

*subtract*### Guided Practice

Follow the rules. Complete the tables.

1.

2.

3.

4.

**Answers:**

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.

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### Image Attributions

Students follow rules presented in words and with symbols to complete two-column function tables. Students use problem solving steps to help solve the problems.