5.4: What's My Rule
Look at the table below. and stand for numbers. Can you write a rule to represent the relationship between and ? 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.
7 | 9 | |
4 | 6 | |
1 | 3 | |
0 | 2 | |
1. | 2 | 4 |
2. | 9 | 11 |
3. | 3 | 5 |
4. | 8 | 10 |
5. | Rule: |
Example B
Write the rule represented by the table. Then, complete the table.
Solution:
We can use problem solving steps to help.
10 | 6 | |
15 | 11 | |
13 | 9 | |
5 | 1 | |
1. | 8 | 4 |
2. | 14 | 10 |
3. | 7 | 3 |
4. | 16 | 12 |
5. | Rule: |
Example C
Write the rule represented by the table. Then, complete the table.
Solution:
We can use problem solving steps to help.
7 | 37 | |
10 | 40 | |
18 | 48 | |
45 | 75 | |
1. | 31 | 61 |
2. | 14 | 44 |
3. | 8 | 38 |
4. | 29 | 59 |
5. | Rule: |
Concept Problem Revisited
We can use problem solving steps to help.
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:
48 | 28 | |
50 | 30 | |
28 | 8 | |
42 | 22 | |
1. | 67 | 47 |
2. | 59 | 39 |
3. | 75 | 55 |
4. | 34 | 14 |
5. | Rule: |
2. Here is the completed table and rule:
3 | 12 | |
8 | 32 | |
2 | 8 | |
5 | 20 | |
1. | 1 | 4 |
2. | 7 | 28 |
3. | 6 | 24 |
4. | 9 | 54 |
5. | Rule: |
3. Here is the completed table and rule:
10 | 2 | |
40 | 8 | |
25 | 5 | |
5 | 1 | |
1. | 15 | 3 |
2. | 35 | 7 |
3. | 20 | 4 |
4. | 45 | 9 |
5. | Rule: |
4. Here is the completed table and rule:
2 | 18 | |
5 | 45 | |
7 | 63 | |
1 | 9 | |
1. | 4 | 36 |
2. | 3 | 27 |
3. | 6 | 54 |
4. | 9 | 81 |
5. | Rule: |
Practice
Write the rule represented by each table. Then, complete each table.
Image Attributions
Description
Learning Objectives
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.