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Look at the table below. p and t stand for numbers. Can you write a rule to represent the relationship between p and t ? 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.

& \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

u v
7 9
4 6
1 3
0 2
1. 2 4
2. 9 11
3. 3 5
4. 8 10
5. Rule: v=u+2

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

Example B

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

Solution:

We can use problem solving steps to help.

& \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.

w y
10 6
15 11
13 9
5 1
1. 8 4
2. 14 10
3. 7 3
4. 16 12
5. Rule: y=w-4

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

Example C

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

Solution:

We can use problem solving steps to help.

& \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

z a
7 37
10 40
18 48
45 75
1. 31 61
2. 14 44
3. 8 38
4. 29 59
5. Rule: a=z+30

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

Concept Problem Revisited

We can use problem solving steps to help.

& \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}

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, we wrote rules that stated how the two variables in the table were related.

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:

b c
48 28
50 30
28 8
42 22
1. 67 47
2. 59 39
3. 75 55
4. 34 14
5. Rule: c=b-20

2. Here is the completed table and rule:

d e
3 12
8 32
2 8
5 20
1. 1 4
2. 7 28
3. 6 24
4. 9 54
5. Rule: e=4 \times d

3. Here is the completed table and rule:

f g
10 2
40 8
25 5
5 1
1. 15 3
2. 35 7
3. 20 4
4. 45 9
5. Rule: g=f \div 5

4. Here is the completed table and rule:

h j
2 18
5 45
7 63
1 9
1. 4 36
2. 3 27
3. 6 54
4. 9 81
5. Rule: j=9 \times h

Practice

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

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Difficulty Level:

At Grade

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Date Created:

Jan 18, 2013

Last Modified:

May 27, 2014
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