# 6.3: Follow the Rule 4

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

Look at the table below. \begin{align*}a\end{align*} and \begin{align*}b\end{align*} stand for numbers. Can you follow the rule to complete the table? In this concept, we will practice using one or two step rules 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 rules 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 making sure that the numbers in the table work with the rule.

#### Example A

Use the rule to complete the table.

**Solution:**

We can use the problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{The table has two columns.}\!\\ &&& \text{The letters} \ c \ \text{and} \ d \ \text{stand for numbers.}\!\\ &&& \text{The rule is: Multiply} \ c \ \text{by} \ 5 \ \text{to get} \ d.\!\\ & \mathbf{Job} && \text{Figure out the numbers for} \ c \ \text{and} \ d \ \text{to complete the table.}\!\\ & \mathbf{Plan} && \text{I'll start by \ figuring out} \ d \ \text{for Rows} \ 1, 3, 5 \ \text{and} \ 6.\!\\ &&& \text{For Rows} \ 2, 4, \ \text{and} \ 7, \ \text{I will divide} \ d \ \text{by} \ 5 \ \text{to get} \ c.\!\\ & \mathbf{Solve}\end{align*}

\begin{align*}c\end{align*} | \begin{align*}d=5c\end{align*} | |
---|---|---|

1. | 4 | 20 |

2. | 2 | 10 |

3. | 9 | 45 |

4. | 1 | 5 |

5. | 3 | 15 |

6. | 6 | 30 |

7. | 5 | 25 |

\begin{align*}& \mathbf{Check} \\ &1. \ 4 \times 5 = 20\\ &2. \ 2 \times 5 = 10\\ &3. \ 9 \times 5 = 45\\ &4. \ 1 \times 5 = 5\\ &5. \ 3 \times 5 =15\\ &6. \ 6 \times 5 = 30\\ &7. \ 5 \times 5 =25\end{align*}

#### Example B

Use the rule to complete the table.

**Solution:**

We can use the problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{The table has two columns.}\!\\ &&& \text{The letters} \ e \ \text{and} \ f \ \text{stand for numbers.}\!\\ &&& \text{The rule is: Divide} \ e \ \text{by} \ 3 \ \text{to get} \ f.\!\\ & \mathbf{Job} && \text{Figure out the numbers for} \ e \ \text{and} \ f \ \text{to complete the table.}\!\\ & \mathbf{Plan} && \text{I'll start by \ figuring out} \ f \ \text{for Rows} \ 1, 2, 5 \ \text{and} \ 7.\!\\ &&& \text{For Rows} \ 3, 4, \ \text{and} \ 6, \ \text{I will multiply} \ f \ \text{by} \ 3 \ \text{to get} \ e.\!\\ & \mathbf{Solve}\end{align*}

\begin{align*}e\end{align*} | \begin{align*}f = e\div 3\end{align*} | |
---|---|---|

1. | 6 | 2 |

2. | 18 | 6 |

3. | 15 | 5 |

4. | 9 | 3 |

5. | 24 | 8 |

6. | 3 | 1 |

7. | 27 | 9 |

\begin{align*}& \mathbf{Check} \\ &1. \ 6 \div 3 = 2\\ &2. \ 18 \div 3 = 6\\ &3. \ 15 \div 3 = 5\\ &4. \ 9 \div 3 = 3\\ &5. \ 24 \div 3 =8\\ &6. \ 3 \div 3 = 1\\ &7. \ 27 \div 3 =9\end{align*}

#### Example C

Use the rule to complete the table.

**Solution:**

We can use the problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{The table has two columns. }\!\\ &&& \text{The rule is: Multiply} \ p \ \text{by} \ 2 \ \text{and add} \ 1 \ \text{to get} \ q.\!\\ & \mathbf{My \ Job} && \text{Figure out} \ q \ \text{numbers and complete the table.}\!\\ & \mathbf{Plan} && \text{Start with a number in the} \ p \ \text{column. First, multiply it by} \ 2.\!\\ &&& \text{Then add} \ 1 \ \text{to that product.}\end{align*}

#### Concept Problem Revisited

We can use the problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{The table has two columns.}\!\\ &&& \text{The letters} \ a \ \text{and} \ b \ \text{stand for numbers.}\!\\ &&& \text{The rule is: Multiply} \ a \ \text{by} \ 3 \ \text{to get} \ b.\!\\ & \mathbf{Job} && \text{Figure out the numbers for} \ a \ \text{and} \ b \ \text{to complete the table.}\!\\ & \mathbf{Plan} && \text{I'll start by \ figuring out} \ b \ \text{for Rows} \ 3 \ \text{and} \ 5.\!\\ &&& \text{For Rows} \ 2, 4, \ \text{and} \ 6, \ \text{I will divide} \ b \ \text{by} \ 3 \ \text{to get} \ a.\end{align*}

### Vocabulary

A ** function** is an example of a

**that states a relationship between two quantities. A**

*rule***is a letter that represents a number that can change value. In this concept, our**

*variable***told us how the two**

*rule***in the table were related.**

*variables*### Guided Practice

For each problem, use the rule to complete the table.

1.

2.

3.

**Answers:**

1. Here is the completed table:

\begin{align*}g\end{align*} | \begin{align*}h\end{align*} | |
---|---|---|

24 | 33 | |

1. | 30 | 49 |

2. | 41 | 60 |

3. | 20 | 39 |

4. | 23 | 42 |

5. | 48 | 67 |

6. | 42 | 61 |

7. | 65 | 84 |

2. Here is the completed table:

\begin{align*}j\end{align*} | \begin{align*}k\end{align*} | |
---|---|---|

6 | 54 | |

1. | 3 | 27 |

2. | 1 | 9 |

3. | 9 | 81 |

4. | 5 | 45 |

5. | 7 | 63 |

6. | 2 | 18 |

7. | 4 | 36 |

3. Here is the completed table:

\begin{align*}n\end{align*} | \begin{align*}s\end{align*} | |
---|---|---|

3 | 5 | |

1. | 7 | 13 |

2. | 5 | 9 |

3. | 10 | 19 |

4. | 2 | 3 |

5. | 4 | 7 |

6. | 9 | 17 |

### Practice

For each problem, use the rule to complete the table.

### Notes/Highlights Having trouble? Report an issue.

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### Image Attributions

Students follow rules presented in symbols or words to complete two-column function tables. Rules are one or two steps and use addition, subtraction, multiplication, and/or division. Students use problem solving steps to help.