# 5.4: What's My Rule

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

Look at the table below. \begin{align*}p\end{align*} and \begin{align*}t\end{align*} stand for numbers. Can you write a rule to represent the relationship between \begin{align*}p\end{align*} and \begin{align*}t\end{align*}? Can you complete the table? In this concept we will learn how to write rules to represent what we see in tables.

### Guidance

In order to write rules for 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 write the rule for the table. - Third, make a
**plan**. In these problems, your plan should be to look for a pattern to help you figure out the rule. - Fourth,
**solve**. In these problems, you will state the rule in an equation or in words and then complete 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

Write the rule represented by the table. Then, complete the table.

**Solution:**

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& u \ \text{and} \ v \ \text{stand for numbers}.\\ & \mathbf{My \ Job} && \text{Figure out the rule}.\\ &&& \text{What do I have to do to} \ u \ \text{to get} \ v?\\ &&& \text{Then complete rows} \ 1, 2, 3 \ \text{and} \ 4.\\ & \mathbf{Plan} && \text{I can add, subtract, multiply or divide. I have to use the same operation on}\\ &&& \text{all} \ u \ \text{numbers to get the} \ v \ \text{numbers}.\\ & \mathbf{Solve} && \text{All} \ v \ \text{numbers are} \ 2 \ \text{more than } \ u \ \text{numbers}.\\ &&& \text{The rule is add 2 to } \ u \ \text{to get} \ v. \ \text{I can write} \ v=u+2 \end{align*}

\begin{align*}u\end{align*} | \begin{align*}v\end{align*} | |
---|---|---|

7 | 9 | |

4 | 6 | |

1 | 3 | |

0 | 2 | |

1. | 2 | 4 |

2. | 9 | 11 |

3. | 3 | 5 |

4. | 8 | 10 |

5. | Rule: \begin{align*}v=u+2\end{align*} |

\begin{align*}& \mathbf{Check:} && 2+2=4\\ &&& 9+2=11\\ &&&3+2=5\\ &&&8+2=10\end{align*}

#### Example B

Write the rule represented by the table. Then, complete the table.

**Solution:**

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& w \ \text{and} \ y \ \text{stand for numbers}.\\ & \mathbf{My \ Job} && \text{Figure out the rule}.\\ &&& \text{What do I have to do to} \ w \ \text{to get} \ y?\\ &&& \text{Then complete rows} \ 1, 2, 3 \ \text{and} \ 4.\\ & \mathbf{Plan} && \text{I can add, subtract, multiply or divide. I have to use the same operation on}\\ &&& \text{all} \ w \ \text{numbers to get the} \ y \ \text{numbers}.\\ & \mathbf{Solve} && \text{All} \ y \ \text{numbers are} \ 4 \ \text{less than } \ w \ \text{numbers}.\\ &&& \text{The rule is subtract 4 from } \ w \ \text{to get} \ y. \ \text{I can write} \ y=w-4. \end{align*}

\begin{align*}w\end{align*} | \begin{align*}y\end{align*} | |
---|---|---|

10 | 6 | |

15 | 11 | |

13 | 9 | |

5 | 1 | |

1. | 8 | 4 |

2. | 14 | 10 |

3. | 7 | 3 |

4. | 16 | 12 |

5. | Rule: \begin{align*}y=w-4\end{align*} |

\begin{align*}& \mathbf{Check:} && 8-4=4\\ &&& 14-4=10\\ &&&7-4=3\\ &&&16-4=12\end{align*}

#### Example C

Write the rule represented by the table. Then, complete the table.

**Solution:**

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& z \ \text{and} \ a \ \text{stand for numbers}.\\ & \mathbf{My \ Job} && \text{Figure out the rule}.\\ &&& \text{What do I have to do to} \ z \ \text{to get} \ a?\\ &&& \text{Then complete rows} \ 1, 2, 3 \ \text{and} \ 4.\\ & \mathbf{Plan} && \text{I can add, subtract, multiply or divide. I have to use the same operation on}\\ &&& \text{all} \ p \ \text{numbers to get the} \ t \ \text{numbers}.\\ & \mathbf{Solve} && \text{All} \ a \ \text{numbers are} \ 30 \ \text{more than } \ z \ \text{numbers}.\\ &&& \text{The rule is add 30 to } \ z \ \text{to get} \ a. \ \text{I can write} \ a=z+30 \end{align*}

\begin{align*}z\end{align*} | \begin{align*}a\end{align*} | |
---|---|---|

7 | 37 | |

10 | 40 | |

18 | 48 | |

45 | 75 | |

1. | 31 | 61 |

2. | 14 | 44 |

3. | 8 | 38 |

4. | 29 | 59 |

5. | Rule: \begin{align*}a=z+30\end{align*} |

\begin{align*}& \mathbf{Check:} && 31+30=61\\ &&& 14+30=44\\ &&&8+30=38\\ &&&29+30=59\end{align*}

#### Concept Problem Revisited

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& p \ \text{and} \ t \ \text{stand for numbers}.\\ & \mathbf{My \ Job} && \text{Figure out the rule}.\\ &&& \text{What do I have to do to} \ p \ \text{to get} \ t?\\ &&& \text{Then complete rows} \ 1, 2, 3 \ \text{and} \ 4.\\ & \mathbf{Plan} && \text{I can add, subtract, multiply or divide. I have to use the same operation on}\\ &&& \text{all} \ p \ \text{numbers to get the} \ t \ \text{numbers}.\\ & \mathbf{Solve} && \text{All} \ t \ \text{numbers are} \ 3 \ \text{times} \ p \ \text{numbers}.\\ &&& \text{The rule is multiply} \ p \ \text{by} \ 3 \ \text{to get} \ t. \ \text{I can write} \ t = 3 \times p\\ & \mathbf{Check}\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, we wrote**

*variable***that stated how the two**

*rules***in the table were related.**

*variables*### Guided Practice

Write the rule represented by each table. Then, complete each table.

1.

2.

3.

4.

**Answers:**

1. Here is the completed table and rule:

\begin{align*}b\end{align*} | \begin{align*}c\end{align*} | |
---|---|---|

48 | 28 | |

50 | 30 | |

28 | 8 | |

42 | 22 | |

1. | 67 | 47 |

2. | 59 | 39 |

3. | 75 | 55 |

4. | 34 | 14 |

5. | Rule: \begin{align*}c=b-20\end{align*} |

2. Here is the completed table and rule:

\begin{align*}d\end{align*} | \begin{align*}e\end{align*} | |
---|---|---|

3 | 12 | |

8 | 32 | |

2 | 8 | |

5 | 20 | |

1. | 1 | 4 |

2. | 7 | 28 |

3. | 6 | 24 |

4. | 9 | 54 |

5. | Rule: \begin{align*}e=4 \times d\end{align*} |

3. Here is the completed table and rule:

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

10 | 2 | |

40 | 8 | |

25 | 5 | |

5 | 1 | |

1. | 15 | 3 |

2. | 35 | 7 |

3. | 20 | 4 |

4. | 45 | 9 |

5. | Rule: \begin{align*}g=f \div 5\end{align*} |

4. Here is the completed table and rule:

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

2 | 18 | |

5 | 45 | |

7 | 63 | |

1 | 9 | |

1. | 4 | 36 |

2. | 3 | 27 |

3. | 6 | 54 |

4. | 9 | 81 |

5. | Rule: \begin{align*}j=9 \times h\end{align*} |

### Practice

Write the rule represented by each table. Then, complete each table.

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

Color | Highlighted Text | Notes | |
---|---|---|---|

Show More |

### Image Attributions

Students write rules that describe the relationship between the input and output columns of two-column tables. Students use the problem solving steps to help.