What’s the Rule?
TEACHERS:
Jenene Woodruff
SUBJECT:
Input/Output Tables—Discovering
Adapted from Hands-On Standards (Common Core) Operation Rules
STANDARD:
 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent
features of the pattern that were not explicit in the rule itself.
OBJECTIVE (EXPLICIT):
 I can complete an input/output function table and identify the rule.
EVIDENCE OF MASTERY (MEASURABLE):
Completed Input/Output tables with function/rule stated.
KEY VOCABULARY:
Input, output, function rule
MATERIALS:
 Centimeter Cubes ( at least 120 per
pair/group)
 Input/Output Table (1 per pair/group)
 “Secret Numbers” clue cards
 Paper
 Pencils
BEFORE
ENGAGE (MAKE CONTENT AND LEARNING RELEVANT TO REAL LIFE AND CONNECT TO
STUDENT INTEREST)
“Every day, Mrs. Renfroe has “secet numbers of the day.” She gives her class clues. Today’s clue
is an input/output table, and the “secret numbers of the day” are the two missing numbers in the
table. How can the students find the missing numbers?
TEACHER WILL:
STUDENT WILL:
 Use the following clues to create an
 Discuss the model and clues with a
Input/Output Table model for the
partner or group to discover the rule
process. (Use the actual Table and
and the secret numbers.
Centimeter Cubes for your
 Gather supplies for partner/group
example.):
work.
Input
2
?
4
5

Output
4
5
6
?
Ask students to discuss with a
partner the possible answers for the
“secret numbers” and what the
function rule would be to accomplish
the correct answers.
 Provide “Secret Numbers” clue cards
to each pair/group
CO-TEACHING STRATEGY IF APPLICABLE
DURING
TEACHER WILL:
STUDENT WILL:
 Monitor groups for misconceptions
 Use “Secret Numbers” clue cards to
or mathematical errors.
complete a model using the
centimeter cubes.
 Check for function rules as well as
completed charts.
 Solve for the missing numbers and
the function rule for each
 Guide groups that are struggling by
input/output.
reminding them of the four
mathematical operations and the use
of inverse operations.
AFTER
CO-TEACHING STRATEGY IF APPLICABLE
TEACHER WILL:
 Have students share their resulting
input/output charts, function rules,
and any patterns or commonalities
they found in the numbers.
 Have students complete the
following problem:
Which number completes the table?
A. 25 B. 29 C. 30 D. 42
Input
Output
4
24
5
?
6
36
CO-TEACHING STRATEGY IF APPLICABLE
STUDENT WILL:
 Communicate results of the activity,
as well as reasoning/explanation for
the function rule the group agreed
upon for each input/output table.
 Complete the formative assessment
problem.
Input
Output
Input
Output
35
33
24
Input
5
22
15
22
11
2
Output
17
27
20
Function Rule:
Function Rule:
______________________________
______________________________
Input
10
Output
6
Input
3
Output
7
7
4
9
11
14
16
9
6
Function Rule:
Function Rule:
______________________________
______________________________
Input
9
Output
1
Input
2
21
18
27
Output
14
3
6
4
8
Function Rule:
______________________________
56
Function Rule:
______________________________
Answer Key
Input
44
Output
35
Input
5
Output
17
33
24
10
22
22
13
15
27
11
2
20
32
Function Rule:
Function Rule:
____Subtract the input by 9____
____Add 12 to the input____
Input
10
Output
6
Input
3
Output
7
12
7
4
9
14
8
5
11
16
9
6
13
Function Rule:
Function Rule:
__Divide the input by 2, then add 1_
_Multiply the input by 2, then add 1_
Input
9
Output
1
Input
1
Output
7
18
2
3
21
27
3
5
35
36
4
7
49
Function Rule:
______Divide the input by 9______
Function Rule:
______Multiply the input by 7_____