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# 5.3: Follow the Rule 3

Difficulty Level: At Grade Created by: CK-12

Look at the table below. s\begin{align*}s\end{align*} stands for a number. Can you follow the rule and complete the table? In this concept, we will practice using rules to complete 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 problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& \text{The letter} \ r \ \text{stands for a number}.\\ &&& \text{The rule tells me to subtract} \ 2 \ \text{from} \ r \ \text{to get} \ v.\\ & \mathbf{My \ Job} && \text{Figure out the missing numbers to fill in the table}.\\ & \mathbf{Plan} && \text{I will start by figuring out} \ v. \ \text{That's rows} \ 2., 3., 6., 7. \ \text{and} \ 9. \ \text{in the table}.\\ &&& \text{For rows} \ 4., 5. \ \text{and} \ 8., \text{I will add} \ 2 \ \text{to} \ v \ \text{to get} \ r.\\ & \mathbf{Solve}\end{align*}

\begin{align*}r\end{align*} \begin{align*}v = r - 2\end{align*}
7 5
3 1
9 7
10 8
15 13
36 34
20 18
29 27
54 52

\begin{align*}& \mathbf{Check:} && 3-2=1\\ &&& 9-2=7\\ &&&10-2=8\\ &&&15-2=13\\ &&&36-2=34\\ &&&20-2=18\\ &&&29-2=27\\ &&&54-2=52\end{align*}

#### Example B

Use the rule to complete the table.

Solution:

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& \text{The letter} \ r \ \text{stands for a number}.\\ &&& \text{The rule tells me to add} \ 20 \ \text{to} \ q \ \text{to get} \ w.\\ & \mathbf{My \ Job} && \text{Figure out the missing numbers to fill in the table}.\\ & \mathbf{Plan} && \text{I will start by figuring out} \ w. \ \text{That's rows} \ 2., 3., 5., 7. \ \text{and} \ 8. \ \text{in the table}.\\ &&& \text{For rows} \ 4., 6. \ \text{and} \ 9., \text{I will subtract} \ 20 \ \text{from} \ w \ \text{to get} \ q.\\ & \mathbf{Solve}\end{align*}

\begin{align*}q\end{align*} \begin{align*}w=q+20\end{align*}
5 25
8 28
6 26
4 24
19 39
53 73
20 40
48 68
69 89

\begin{align*}& \mathbf{Check:} && 8+20=28\\ &&& 6+20=26\\ &&&4+20=24\\ &&&19+20=39\\ &&&53+20=73\\ &&&20+20=40\\ &&&48+20=68\\ &&&69+20=89\end{align*}

#### Example C

Use the rule to complete the table.

Solution:

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe} && \text{I see a table with two columns}.\\ &&& \text{The letter} \ r \ \text{stands for a number}.\\ &&& \text{The rule tells me to subtract} \ 10 \ \text{from} \ b \ \text{to get} \ a.\\ & \mathbf{My \ Job} && \text{Figure out the missing numbers to fill in the table}.\\ & \mathbf{Plan} && \text{I will start by figuring out} \ a. \ \text{That's rows} \ 2., 3., 6., 7. \ \text{and} \ 8. \ \text{in the table}.\\ &&& \text{For rows} \ 4., 5. \ \text{and} \ 9., \text{I will add} \ 100 \ \text{to} \ a \ \text{to get} \ b.\\ & \mathbf{Solve}\end{align*}

\begin{align*}b\end{align*} \begin{align*}a=b-100\end{align*}
538 438
810 710
662 562
626 526
149 49
479 379
905 805
700 600
568 468

\begin{align*}& \mathbf{Check:} && 810-100=710\\ &&& 662-100=562\\ &&&626-100=526\\ &&&149-100=49\\ &&&479-100=379\\ &&&905-100=805\\ &&&700-100=600\\ &&&568-100=468\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}.\\ &&& \text{The letter} \ s \ \text{stands for a number}.\\ &&& \text{The rule tells me to add} \ 6 \ \text{to} \ s \ \text{to get} \ t.\\ & \mathbf{My \ Job} && \text{Figure out the missing numbers to fill in the table}.\\ & \mathbf{Plan} && \text{I will start by figuring out} \ t. \ \text{That's rows} \ 1., 2., \ \text{and} \ 5. \ \text{in the table}.\\ &&& \text{For rows} \ 3. \ \text{and} \ 4., \text{I will subtract} \ 6 \ \text{from} \ t \ \text{to get} \ s.\\ & \mathbf{Check}\end{align*}

### Vocabulary

A function is an example of a rule that states a relationship between two quantities. A variable is a letter that represents a number that can change value. In this concept, our rule told us how the two variables in the table were related.

### Guided Practice

Use the rules to complete the tables.

1.

2.

3.

4.

1. Here is the completed table:

\begin{align*}m\end{align*} \begin{align*}p=m-200\end{align*}
741 541
800 600
306 106
449 249
530 330
361 161
427 227
936 736
958 758

2. Here is the completed table:

\begin{align*}a\end{align*} \begin{align*}q = 3 \times a\end{align*}
2 6
5 15
9 27
4 12
3 9
10 30
1 3
8 24
7 21

3. Here is the completed table:

\begin{align*}d\end{align*} \begin{align*}r=d \div 2\end{align*}
8 4
12 6
10 5
4 2
18 9
2 1
20 10
16 8
14 7

4. Here is the completed table:

\begin{align*}z\end{align*} \begin{align*}m=5 \times z\end{align*}
3 15
7 35
8 40
2 10
9 45
4 20
1 5
5 25
6 30

### Practice

Use the rules to complete the tables.

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

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Date Created:
Jan 18, 2013