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# 6.3: Follow the Rule 4

Difficulty Level: At Grade Created by: CK-12

Look at the table below. $a$ and $b$ 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.

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

$c$ $d=5c$
1. 4 20
2. 2 10
3. 9 45
4. 1 5
5. 3 15
6. 6 30
7. 5 25

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

#### Example B

Use the rule to complete the table.

Solution:

We can use the problem solving steps to help.

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

$e$ $f = e\div 3$
1. 6 2
2. 18 6
3. 15 5
4. 9 3
5. 24 8
6. 3 1
7. 27 9

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

#### Example C

Use the rule to complete the table.

Solution:

We can use the problem solving steps to help.

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

#### Concept Problem Revisited

We can use the problem solving steps to help.

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

### 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

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

1.

2.

3.

1. Here is the completed table:

$g$ $h$
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:

$j$ $k$
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:

$n$ $s$
3 5
1. 7 13
2. 5 9
3. 10 19
4. 2 3
5. 4 7
6. 9 17

### Explore More

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

Jan 18, 2013