Math 7 Standard 1 08-06
8/21/02
4:18 PM
Page 33
7.1.4, 7.1.5
Prime Factorization
Purpose
Students will find the prime factorization of a composite number
and write the results using exponents.
Materials
For the teacher: chalkboard, chalk
For each student: copy of Black Line Master (BLM) Factor Trees
Activity
A. Class Activity
1. Write the words “composite,” “prime,” and “neither” each
on different sections of the chalkboard.
2. Ask students to give you examples of whole numbers less
than 100.
3. Write each given number under the proper category on the
chalkboard until several numbers appear under both the
“composite” and “prime” categories.
4. Write the number “1” under the category of “neither,” if not
already there.
5. Ask a student to give a verbal description of a prime number
by looking at the numbers written under “prime” on the
chalkboard. Discuss the response with the class.
6. Ask another student to give a verbal description of a composite
number by looking at the numbers written under “composite”
on the chalkboard. Discuss the response with the class.
7. Tell students that a prime number is a whole number greater
than one that has exactly two factors, one and itself. Explain
that a factor is a number that is multiplied by another number
to obtain a product.
8. Choose a number listed under the “prime” category on the
chalkboard. Explain to students that the only two numbers that
can be multiplied to obtain the prime number is one and itself.
Since the number has only two factors, the number is prime.
9. Tell students that a composite number is a whole number greater
than one that has more than two factors. Choose a number listed
under the “composite” category on the chalkboard. Write at least
three factors of the number, and tell students that since the
number has more than two factors, the number is composite.
(continued)
Standard 1 / Activity 3
Indiana Mathematics Grade 7 Curriculum Framework, October 2002
incorporating
TECHNOLOGY
Have students play
an interactive game
at www.saab.org/
mathdrills/primef.cgi.
Ask students to choose
from one of the five
levels of difficulty
and try several of the
online prime
factorization drills.
extending
THE
ACTIVITY
Have students create
a prime factorization
mobile. Give students
a hanger, construction
paper, and yarn. Assign
a composite number to
each group of students.
Have the group create
a prime factorization
mobile by stringing
each branch of the
tree onto the hanger.
Standards Link
7.2.5
page 33
Standard 1
Standard Indicators
Math 7 Standard 1 08-06
8/21/02
4:18 PM
Page 34
Standard 1
Activity (continued)
10. Tell students that prime factorization is a process in which
a composite number is expressed as a product of prime numbers.
11. Write the number “48” on a separate area of the chalkboard.
Show students how to construct a factor tree. Explain to students
that the tree branches continue until all factors are prime.
[48 = 2 × 3 × 2 × 2 × 2]
12. Explain that prime factorization must be written in exponential
form. Tell students that any factor appearing more than once in
the product needs to be rewritten as an exponent. Have students
count the number of 2s appearing in the product. Explain that
2 × 2 × 2 × 2 is rewritten as 24.
13. Write “48 = 24 × 3” on the chalkboard. Say: “The prime
factorization of 48 is two to the fourth power times three.”
B. Individual Activity
1. Give one copy of the BLM Factor Trees to each student.
2. Read through the directions with the class and instruct students
to complete the BLM on their own.
C. Discussion
1. Ask volunteers to draw factor trees and write the prime
factorization for each problem on the chalkboard.
2. Discuss results with the class.
Classroom Assessment
Basic Concepts and Processes
During the activity and when reviewing the BLM, discuss the
following questions with your students to gauge their understanding
of the Standard Indicators:
Why is the number one neither prime nor composite?
What is the exponential form of the expression 3 × 3 × 3?
Give me an example of a prime number greater than 100.
page 34
Standard 1 / Activity 3
Indiana Mathematics Grade 7 Curriculum Framework, October 2002
Math 7 Standard 1 08-06
8/21/02
4:18 PM
Page 35
Name:
Factor Trees
Circle whether each number is prime or composite.
If composite, draw a factor tree and write the number’s
prime factorization using exponents.
1.
139
prime or composite?
2. 162
3. 87
prime or composite?
prime or composite?
prime factorization
prime factorization
prime factorization
_______________
_______________
_______________
4. 268
5. 479
6. 111
prime or composite?
prime or composite?
prime or composite?
prime factorization
prime factorization
prime factorization
_______________
_______________
_______________
Standard 1 / Activity 3
Indiana Mathematics Grade 7 Curriculum Framework, October 2002
Black Line Master 1
page 35
Math 7 Standard 1 08-06
8/21/02
4:18 PM
Page 36
Factor Trees
Teacher Directions
Distribute one copy of the BLM Factor Trees to each student. Ask students to determine whether
the number is prime or composite and circle their choice. Tell students to draw factor trees for all
composite numbers in the space provided and write the prime factorization using exponents
in the blank.
Answer Key
1.) prime
2.) 162
3.) 87
2 × 81
3 × 29
2 × 9×9
3 × 29 or 29 × 3
2 × 3×3 ×3×3
2 × 34 or 34 × 2
4.) 268
4 × 67
2 × 2 × 67
5.) prime
6.) 111
3 × 37
3 × 37
22 × 67 or 67 × 22
Black Line Master 1
page 36
Standard 1 / Activity 3
Indiana Mathematics Grade 7 Curriculum Framework, October 2002