Difficulty Level: 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 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:

\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.

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Date Created:
Jan 18, 2013