Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55151
Find All the Factor Pairs
Students are asked to find all the factor pairs for each of four given numbers.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, factor pairs, factor, multiple
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FindAllTheFactorPairs_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Find All the Factor Pairs worksheet and reads aloud the directions to the student.
2. If the student struggles with the task, the teacher should determine if the student knows what a factor is. If not, the teacher should define the term factor for the
student and then allow the student to continue with the task.
TASK RUBRIC
Getting Started
Misconception/Error
The student identifies no more than one factor pair for each given number.
Examples of Student Work at this Level
The student only finds one factor pair for each number.
page 1 of 3 Questions Eliciting Thinking
Can you think of two other numbers that multiply to 18?
What number divides into every number?
What number divides into every even number?
Instructional Implications
Continue to work with the student on developing fluency with multiplication facts. Consider using the MFAS task Fluency With Multiplication (3.OA.3.7) to help build fluency
with both multiplication and division.
Review divisibility rules for two, three, and five. Model for the student how to use both knowledge of multiplication facts and divisibility to find factors of numbers. Explain
the meaning of factor pairs and model for the student a systematic method for finding all of the factor pairs of a given number. Encourage the student to write factor pairs
in an organized manner (e.g., writing the pairs so that the first factor in each pair is listed from least to greatest). Be sure the student understands that one is a factor of
every number and should be included when listing factors and factor pairs.
Allow the student to use manipulatives to build arrays for smaller numbers in order to find factors. After the student is able to find the factor pairs for a smaller number, allow
the student to practice on greater numbers.
Moving Forward
Misconception/Error
The student can only name a few of the factor pairs.
Examples of Student Work at this Level
For the number 24, the student only determines two factor pairs (3 x 8 and 1 x 24) and only includes one or two factor pairs with the other three given numbers. He or
she is unable to determine a factor pair for 31.
Questions Eliciting Thinking
What does 1 x 24 equal? So could we write that as a factor pair of 24?
What is 2 x 6? Can that help you find 4 x 6? So is there another factor pair for 24?
Instructional Implications
Provide tiles or graph paper for the student to use to make arrays to assist in finding all of the factor pairs.
Guide the student to systematically find all of the factors of a given number by checking each counting number in order up to half of the given number.* Start with smaller
numbers, such as six. Then have the student list the factors in order from least to greatest and use a “rainbow” to connect the factor pairs. The rainbow can also help the
student to determine if any factors were missed. Provide opportunities for the student to find factors independently; provide feedback as needed.
*It is only mathematically necessary to check up to the square root of the given number but it might be too soon to introduce the student to this concept.
Almost There
Misconception/Error
The student finds most, but not all of the factor pairs.
Examples of Student Work at this Level
The student finds most of the factor pairs for each number. For the number 24, the student writes 1 x 24, 3 x 8, and 6 x 4. He or she does not write 12 x 2.
Questions Eliciting Thinking
How did you organize your work to be sure you have all the factor pairs?
What is 2 x 6? Can that help you find 4 x 6? So is there another factor pair for 24?
Instructional Implications
Guide the student to systematically find all of the factors of a given number by checking each counting number in order up to half of the given number.* Start with smaller
numbers, such as six. Then have the student list the factors in order from least to greatest and use a “rainbow” to connect the factor pairs. The rainbow can also help the
student to determine if any factors were missed. Provide opportunities for the student to find factors independently; provide feedback as needed.
page 2 of 3 *It is only mathematically necessary to check up to the square root of the given number but it might be too soon to introduce the student to this concept.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student finds all of the factor pairs for each number.
Questions Eliciting Thinking
How do you know you found all of the factor pairs?
If eight is a factor of 24, will four also be a factor? Explain why or why not? What about two?
If six is a factor of a number, is three always a factor also? Explain why or why not? Give me an example.
Instructional Implications
Consider using the MFAS Task Factor Pairs (4.OA.2.4).
Encourage the student to discover that if b is a factor of n and a is a factor of b then a is a factor of n.
Encourage the student to look for patterns in factor pairs. Provide opportunities for the student to discover that 12 x 2 = 6 x 4 since 12 was halved and two was doubled.
Ask the student if another product equal to 12 x 2 can be generated by dividing 12 by three and multiplying two by three; or dividing 12 by four and multiplying two by
four. Encourage the student to consider why this approach will always generate a product equal to 12 x 2 (or any other given product).
Work with the student on identifying factors common to a set of two or more numbers. Then ask the student to find the greatest common factor of the set of numbers.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Find All the Factor Pairs worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.OA.2.4:
Description
Investigate factors and multiples.
a. Find all factor pairs for a whole number in the range 1–100.
b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the
range 1–100 is a multiple of a given one­digit number. c. Determine whether a given whole number in the range 1–100 is prime or composite.
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