Lesson 3A: Identifying Factors
Desired Outcomes
• Students will identify the factors of a variety of whole
numbers.
• Students will identify the greatest common factor of pairs of
numbers.
• Students will describe factors verbally and in writing.
Teacher Information
Materials
This lesson is designed to follow Lessons 1–3 in the fourth-grade
unit of Developing Number Concepts, Module B, Stories and
Statements. It allows further investigation into fractions,
particularly for the greatest common factor (GCF). Students
already have experience with factors from their work with
multiplication facts and divisibility rules.
For the class
1 sheet of newsprint
1 black marker w/eraser
For each student
Bright Idea Pen
This lesson allows students to develop their own strategies to
determine the greatest common factor for a pair of numbers.
After ideas about factors have been shared in whole group
discussions, students work in pairs to further investigate
common factors.
Teacher Preparation
• On a sheet of newsprint, prepare a chart with the title
“Common Factors.”
• Assemble for distribution: Bright Idea Pens.
m
Stories and Statements, Module B
Identifying Factors
1
Vocabulary
Composite number:
A positive integer that has
more than two factors.
Procedure for the Lesson
Engage
Discussing Factors
Factor: A number that is
multiplied by another
number.
Prime number: A positive
integer that has exactly two
factors, 1 and itself.
Product: The result of
multiplication.
1. Explain that the lesson is about factors. Give each pair of
students an opportunity to tell each other what they know
about factors.
2. After the students have shared their ideas, ask,
What do you know about factors?
What are the factors of 6?
What are the factors of 3?
3. Explain that whole numbers with factors of themselves and
1 are prime numbers, and numbers with factors of
themselves, 1, and other numbers are composite numbers.
Investigate
Listing Factors
1. Record the numbers 6 and 8 on the chart “Common
Factors.” Have each pair write the numbers and their
factors. Ask,
Which divisibility rules are helpful with determining
factors of 6 and 8?
Are there any other factors that can be multiplied
together to equal 6 or 8?
2. As the students explain their way of determining factors,
summarize the ideas on the chart. Explain that a list of
factors for a number should represent all of the factors,
including 1 and the number itself.
Common Factors
Factors of 6: 2, 3, 6, 1
Factors of 8: 2, 4, 8, 1
To determine factors of a number, think of
multiplication facts for that product.
Try dividing by 2, since 6 and 8 are even.
Don’t forget 1 and the number.
m
2
Identifying Factors
Stories and Statements, Module B
3. Call on the students to name the common factors of 6 and
8. Ask,
What is the greatest common factor of 6 and of 8?
4. Add information about the greatest common factor of 6 and
8 to the chart.
GCF = 2
5. Assign a set of numbers to each pair of students. Have them
list the factors of each number and identify the greatest
common factor. Numbers to assign:
4 and 8 (GCF = 4)
6 and 9 (GCF = 3)
7 and 14 (GCF = 7)
8 and 12 (GCF = 4)
10 and 15 (GCF = 5)
12 and 18 (GCF = 6)
12 and 15 (GCF = 3)
6 and 24 (GCF = 6)
24 and 36 (GCF = 4)
24 and 48 (GCF = 24)
64 and 72 (GCF = 8)
21 and 49 (GCF = 7)
Assign the same numbers to at least two pairs.
6. As students complete the assignment, have them explain
in writing their way of determining the greatest common
factor. Afterward, have pairs with the same assigned
numbers share their answers and their reasoning.
m
Stories and Statements, Module B
Identifying Factors
3
Reflect
Sharing Strategies
1. Have the students name the factors and the greatest
common factor for each pair of numbers. Lead a discussion
to address any differences in the solutions. Ask,
Does anyone have a question or comment about any of
the factors?
Were any of the numbers prime? Composite?
2. Select several pairs of students to share their strategies for
determining the greatest common factor of a pair of
numbers. Ask,
Is there another way to determine the greatest common
factor of a set of numbers?
Are there any questions or comments about determining
greatest common factors?
What is a description of a greatest common factor of two
or more numbers?
3. Give the students an opportunity to make changes to their
work with the Bright Idea Pens after hearing the ideas of
others.
Apply
Making Connections
The following activities can be used with whole groups, small
groups, or individuals, depending on the needs of your students.
The activities connect to past and future learning.
Identifying Common Factors
Have one pair of students identify two or three numbers less
than 100 for another pair of students to analyze for the greatest
common factor. Give the students an opportunity to share their
reasoning with others.
m
4
Identifying Factors
Stories and Statements, Module B
Venn Diagrams
Assign pairs of numbers to students, and have them determine
the greatest common factors by representing the factors in a
Venn diagram.
Assessment
Teacher Reflection
• Are students able to identify the factors of a variety of whole
numbers?
• Are students able to identify the greatest common factor of
pairs of numbers?
• Are students able to describe factors verbally and in writing?
What did my students learn
as they shared strategies for
determining greatest
common factors?
Information can be gathered from
What prior knowledge was
needed for students to
successfully determine
common factors?
Class Discussion
Teacher Observation
Individual and Group Questioning
Discussing Factors
Listing Factors
Sharing Strategies
Making Connections
m
Stories and Statements, Module B
Identifying Factors
5