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Look at the table below. s 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.

& \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}

r v = r - 2
7 5
3 1
9 7
10 8
15 13
36 34
20 18
29 27
54 52

& \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

Example B

Use the rule to complete the table.

Solution:

We can use problem solving steps to help.

& \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}

q w=q+20
5 25
8 28
6 26
4 24
19 39
53 73
20 40
48 68
69 89

& \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

Example C

Use the rule to complete the table.

Solution:

We can use problem solving steps to help.

& \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}

b a=b-100
538 438
810 710
662 562
626 526
149 49
479 379
905 805
700 600
568 468

& \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

Concept Problem Revisited

We can use problem solving steps to help.

& \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}

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.

Answers:

1. Here is the completed table:

m p=m-200
741 541
800 600
306 106
449 249
530 330
361 161
427 227
936 736
958 758

2. Here is the completed table:

a q = 3 \times a
2 6
5 15
9 27
4 12
3 9
10 30
1 3
8 24
7 21

3. Here is the completed table:

d r=d \div 2
8 4
12 6
10 5
4 2
18 9
2 1
20 10
16 8
14 7

4. Here is the completed table:

z m=5 \times z
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.

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Difficulty Level:

At Grade

Grades:

Date Created:

Jan 18, 2013

Last Modified:

May 27, 2014
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