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Fourth Grade Mathematics
STAAR
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Evaluate and Pass
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Texas STAAR Exam—Lesson 16, 4.5(B)
Reporting Category 2:
Computations and Algebraic Relationships
(4.5) Algebraic reasoning. The student applies mathematical process standards to develop
concepts of expressions and equations. The student is expected to
(B)
represent problems using an input-output table and numerical expressions to
generate a number pattern that follows a given rule representing the relationship of the
values in the resulting sequence and their position in the sequence. Readiness
Standard
Say:
Today we are going to learn what an input/output table is and how to follow the rules of
the table.
Put lesson slide 1 on white board / overhead.
Read lesson slide 1
Say:
Now that we have an understanding of how patterns of paired numbers work, let's try to
fill in an input-output table.
Put lesson slide 2 on white board / overhead.
Read lesson slide 2
Answers for example 1:
(x)
(y)
3
7
5
9
7
11
9
13
11
15
Say:
Answers for example 2:
(x)
(y)
1
11
5
55
6
66
9
99
12
132
Do STAAR practice 4.5(B) and logic/manipulative 4.5(B)
© 2014 TripleNterprises Educational Publishing
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Lesson 16 LESSON SLIDE 1
Input-Output Tables
An input-output table contains pairs of numbers that are related to one
another based on a rule.
Look at the description of the table below:
The input is the position in
the sequence
Input
value
(x)
1
2
3
4
5
Output
value
(y)
5
10
15
20
25
The output is the value of
the position
The output value is
based on the rule
associated with the
table. In this case, the
output value is 5 times
the input value.
In the table above, the rule for the table is
𝒊𝒏𝒑𝒖𝒕 𝒗𝒂𝒍𝒖𝒆 × 𝟓
As we can see, the output value in each position is five times the value in
the input column.
For example, input position 3 has an output value of 15, because:
𝟑 × 𝟓 = 𝟏𝟓.
What would the value be for the 10th position in the input value?
𝟏𝟎 × 𝟓 = 𝟓𝟎
What about an x value of 15?
𝟏𝟓 × 𝟓 = 𝟕𝟓
Sometimes we are given the output value and have to determine the input
value. For example, what would the input value be for the output value of
60?
In this case we do the opposite operation, division, to find the answer:
𝟔𝟎 ÷ 𝟓 = 𝟏𝟐
So for the output value of “60”, the input value is 12
© 2014 TripleNterprises Educational Publishing
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Lesson 16 LESSON SLIDE 2
Input-Output Tables
Example 1
Using the pattern 𝑦 = 𝑥 + 4, fill in the blanks in the table below:
(x)
3
5
7
9
11
(y)
7
Solution Strategy:
Our last table was a multiplicative table, meaning each input value was
multiplied by some factor to get the output value.
This table is an additive table, which means each input value is added to a
given number to get the output value.
In this case, each input value needs to be added to “4” in order to get the
output value.
As a class, work together to fill in the missing table values.
Example 2
Using the pattern 𝑦 = 𝑥 × 11, fill in the blanks in the table below:
(x)
1
5
(y)
11
66
99
12
Solution Strategy:
 When determining the “y” value in the chart, we multiply the “x” value
by 11.
 When determining the “x” value in the chart, we divide the “y” value
by 11.
As a class, fill in the chart.
© 2014 TripleNterprises Educational Publishing
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STAAR Practice 4.5(B)
1 Each bag of marbles at the toy store comes with a certain number of marbles and a
certain number of stickers. This relationship is represented by the equation:
Total items (T) = marbles (m) + 3
Based on this rule, fill in the missing number in the table below:
Marbles (m)
Total Items
4
7
6
9
10
13
15
___?___
2 The grocery store sells juice boxes in cartons of 12. This is represented by the
equation:
Number of cartons (C) = Juice Boxes (j) x 12
Based on this rule, fill in the missing numbers in the table below:
Cartons (C)
Juice boxes (j)
2
_____
5
60
8
_____
11
_____
3 Which expression below correctly states the relationship of the ordered pairs of
numbers in this table:
A
B
C
D
X
y
51
60
55
64
61
70
65
74
𝑥+9 = 𝑦
𝑥−9 = 𝑦
𝑥−2+5 = 𝑦
𝑥 + 10 − 2 = 𝑦
© 2014 TripleNterprises Educational Publishing
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