Curriculum Tie:


Summary: This activity provides an introduction to composite numbers and prime numbers through factorization.
Main Curriculum Tie: Mathematics  6th Grade Standard 1 Objective 3 Use number theory concepts to find prime factorizations, least common multiples, and greatest common factors. Materials: Invitation to Learn
 Ink pads (1 per group)
 1 1/2 x 2 Postitฎ
Notes
 Wet wipes
 Poster of main
fingerprint patterns
Instructional Procedures
Additional Resources
Books
Discovering Mathematics with the TI73: Activities for Grades 5 and 6, by Melissa Nast;
ISBN 18886309221
Attachments
Web Sites
Background For Teachers: The number one is a unique number because it only has itself as
a factor. A prime number is a counting number larger than one that
has exactly two factors. The two factors are one and the number itself.
A composite number is a counting number that has more than two
factors. Each composite number is divisible by three or more whole
numbers.
Each composite number can be renamed as a product of prime
numbers. This is known as prime factorization. Understanding
prime factorization helps students understand the composition and
decomposition of numbers.
Prime factorization is a strategy students may employ to find the
Greatest Common Factor (GCF) of two or more numbers. Students
may also use prime factorization to find the Least Common Multiple
(LCM) of two or more numbers. It may be interesting to note that
the product of the LCM and the GCF of two numbers is equal to the
product of the two numbers themselves.
Instructional Procedures: Invitation to Learn
Pretend you are a detective. What is one piece of evidence
that would help you to identify suspects from a crime scene?
Fingerprints would be one type of evidence. Every person has a
oneofakind fingerprint. Have students make a fingerprint of their
right index finger on a Postitฎ note. Have students place their
Postitฎ note on the line plot, matching their fingerprint with one of
the nine main patterns pictured on a teachermade categorical line
plot poster. Even though there are nine fingerprint patterns, allow
students time to notice that each individual fingerprint is still oneofakind.
Write the following analogy on the board: human is to fingerprint
as number is to factorprint. Tell students that just as each human
has a oneofakind fingerprint, we will learn that each number has a
oneofakind factorprint.
Instructional Procedures
(The activities listed below are intended to be taught sequentially.
They will take several lessons/days to complete with students.)
 Explain to students that you will be creating a pattern with
color tiles. They will copy the pattern by coloring the same
pattern on their graph paper. Students are to observe,
reflect, and predict the pattern after they see the first few
representations
 Have students copy the following pattern demonstrated on the
overhead with color tiles:
 To begin the first row, color one square black near the top
lefthand corner. Label underneath 1.
 Skip two squares horizontally and color one square red. Label
underneath 2.
 Skip two squares horizontally and color one square green.
Label underneath 3.
 Skip two squares horizontally and color two vertical squares
red. Label underneath 4.
 Skip two squares horizontally and color one square yellow.
Label underneath 5.
 Skip two squares horizontally and color one square red and
one square green, placed vertically. Label underneath 6.
 Skip two squares horizontally and color one square blue.
Label underneath 7.
 Have students predict what will be next in the pattern. Have
students justify their prediction.
 Continue the pattern, stopping to predict and justify answers at
each number, as follows:
 Skip two squares horizontally and color three vertical squares
red. Label underneath 8.
 Skip two squares horizontally and color two vertical squares
green. Label underneath 9.
 Skip two squares horizontally and color one square red and
one square yellow, placed vertically. Label underneath 10.
 By this time, students may have discovered that 4 was created
by multiplying the value of the red square by itself or 2 x 2.
They may have found that 6 was created by multiplying the
value of the red square by the value of the green square or 2 x
3. Go back over the first 10 numbers and label the expressions
for the composite numbers. Label 4 as 2 x 2, 6 as 2 x
3, 8 as 2 x 2 x 2, 9 as 3 x 3, and 10 as 2 x 5. Write
PRIME under each prime number.
 If a horizontal row is full, start a new row about halfway down
the page. Continue the pattern, stopping to predict and justify
answers at each number, as follows:
 Skip two squares horizontally and color one square orange.
Label underneath ll and write PRIME.
 Skip two squares horizontally and color two squares red and
one square green, placed vertically. Label underneath 12,
and label with the expression 2 x 2 x 3.
 Skip two squares horizontally and color one square purple.
Label underneath 13 and write PRIME.
 Skip two squares horizontally and color one square red and
one square blue, placed vertically. Label underneath 14, and
label with the expression 2 x 7.
 Skip two squares horizontally and color one square green and
one square yellow, placed vertically. Label underneath 15,
and label with the expression 3 x 5.
 Skip two squares horizontally and color four squares red,
placed vertically. Label underneath 16, and label with the
expression 2 x 2 x 2 x 2.
 Remind students that each composite number is being formed
by the multiplication of prime numbers. As you are labeling the
expression for 16, teach students that there is another way to
write this expression that would use fewer symbols and would
be more efficient. We could use base numbers and exponents.
Have students write the expression underneath 16 and 2 x
2 x 2 x 2 as 2^4. Look back over earlier numbers and write
the expressions using base numbers and exponents on each
composite number.
 Continue the pattern, stopping to predict and justify answers at
each number as follows:
 Skip two squares horizontally and color one square pink.
Label underneath 17 and write PRIME.
 Skip two squares horizontally and color one square red and
two squares green, placed vertically. Label underneath 18,
label with the expression 2 x 3 x 3, and label with the
expression 2^1 x 3^2.
 Skip two squares horizontally and color one square brown.
Label underneath 19 and write PRIME.
 Skip two squares horizontally and color two squares red
and one square yellow, placed vertically. Label underneath
20, label with the expression 2 x 2 x 5, and label with the
expression 2^2 x 5^1.
 Have students complete the patterns to the number 50. This
could be done as cooperative teams or as a homework project.
Since there is a new color for each prime number, the teacher
will need to provide these patterns to create uniformity in
correcting:
 23 is a blackoutlined box with a red dot in the center
29 is a blackoutlined box with a green dot in the center
 31 is a blackoutlined box with a yellow dot in the center
 37 is a blackoutlined box with a blue dot in the center
 41 is a blackoutlined box with an orange dot in the center
 43 is a blackoutlined box with a purple dot in the center
 47 is a blackoutlined box with a pink dot in the center
 Have students complete the handout Prime Factorization. Label
the number one with the word UNIQUE. Label each prime
number with the word PRIME. For each composite number,
write the prime factorization expressions found in the color tile
activity.
 Have students place centimeter cubes on the handout Prime
Factorization Centimeter Cubes in the same number and color
as the color tile pattern. For example, 1 would have one
black cube, 2 would have one red cube, 3 would have one
green cube, 4 would have two red cubes, and so on.
 To find the greatest common factor of two numbers, students
must first find what prime factors they have in common.
Have students write the numbers 8 and 12 as the two selected
numbers on the GCF Mat with dryerase marker. Have students
take the cubes from Prime Factorization Centimeter Cubes, for
8 and 12 and place them on the GCF Mat in the proper squares.
Help students to see what factors (represented by the colored
centimeter cubes) these two numbers share. The number 8 has
three red cubes, while the number 12 has two red cubes and
one green cube. These two numbers each have two red cubes,
so students would place two red cubes in the GCF column.
Thus, the GCF of 8 and 12 is 2x2 or 4.
 Repeat Step 12 with other pairs of numbers such as 9 and 18,
15 and 20, 8 and 24, 10 and 22, and so on.
 To find the least common multiple of two numbers, students
must first find the prime factors of each number. Have
students write the numbers 8 and 12 as the two selected
numbers on the LCM Mat with dryerase marker. Have students
take the cubes from for 8
and 12 and place them on the LCM Mat in the proper squares.
Help students to see what factors (represented by the colored
centimeter cubes) these two numbers each has. The number
8 has three red cubes, while the number 12 has two red cubes
and one green cube. Place three red cubes in the LCM column
to represent 8. Add one green cube (using two of the red cubes already there) to complete the factors of 12. Thus, there will be
three red cubes and one green cube or 2x2x2x3 and the LCM of
8 and 12 is 24.
 Repeat Step 14 with other pairs of numbers such as 3 and 9, 4
and 5, 4 and 7, and so on.
Extensions:
 Find the prime factorization of a number using the tree method.
 Find the prime factorization of a number using the cake
method.
 Find the Greatest Common Factor of two numbers using the
prime factorization of the numbers from the color tile activity.
 Find the Least Common Multiple of two numbers using the
prime factorization of the numbers from the color tile activity.
Family Connections
 Have students share their graph paper patterns of prime
factorization with parents.
 Ask students to explain to parents the difference between
unique, prime, and composite numbers.
 Have students explain how a composite number may be
renamed as a product of prime numbers to their parents.
 Have parents select a composite number under fifty and have
students share a strategy for determining the prime factorization
of that number.
 Have students teach parents how to find the GCF and LCM of
two numbers using prime factorization.
Assessment Plan:
 Informal assessment includes observation of students as they
complete the color tile activity to the number 50.
 Have a class discussion of answers for the numbers 21 through
50. Model the answers on the overhead projector using color
tiles or pictorial representations.
 Correct the handout Prime Factorization with the expressions
from the color tile activity. Have students save this in a math
journal or portfolio for future reference.
 Make a concentration game with 20 index cards. Put composite
numbers on ten different cards, and put the prime factorization
of the selected composite numbers on the other ten cards.
Bibliography:
Gerlic, I., & Jausovec, N. Multimedia: Differences in cognitive processes observed with EEG.
Educational technology research and development, September 1999, Vol. 47, Number 3,
p514.
This study investigated the cognitive processes involved in learning
information presented in three different methods: with text; with
text, sound, and picture; and with text, sound, and video. Students
brain activity was measured using an EEG in each format. Less
mental activity was found using the text only presentation. The results showed higher mental activity with the video and picture
presentations, confirming the assumption that these methods induced
visualization strategies on the part of the learners.
Zazkis, R., & Liljedahl, P. Understanding primes: The role of representation. Journal for
research in mathematics education, May 2004, Vol. 35 Issue 3, p164186.
The authors of this article investigated how preservice elementary
teachers understood the concept of prime numbers. They attempted
to describe the factors that influenced their understanding. The
authors suggested that an obstacle to a full conceptual understanding
is a lack of a representation for a prime number. The importance of
representations in understanding math concepts is examined. Author: Utah LessonPlans
Created Date : Jul 09 2007 10:32 AM
