Focus Plan
Texarkana Independent School District
Grading
Period:
Plan Code:
Writer:
Refer to Scope and
Sequence
Barbara Fugitt
Course/subject:
Math
Grade(s):
Fifth Grade
Time allotted for
instruction:
2 or 3 - 45 minute class
periods
Title:
Prime or Composite, That is the Question?
Lesson Topic:
Understanding the difference between a prime and
composite number and their factorizations.
TAKS Objective:
Objective 2
The students will demonstrate an understanding of
patterns, relationships, and algebraic reasoning.
FoCUS TEKS and Student
Expectation:
5.5
Patterns, Relationships, and Algebraic Reasoning
The student makes generalizations based on observed
patterns and relationships.
(B) The student is expected to identify prime and composite
numbers using concrete models and patterns in factor
pairs.
Supporting TEKS and
Student Expectations:
5.3 Number, operation, and quantitative reasoning.
The student adds, subtracts, multiplies, and divides to solve
meaningful problems.
(D) The student is expected to identify prime factors of a
whole number and common factors of a set of whole
numbers.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
Concepts
Enduring Understandings/Generalizations/Principles
The student will understand that
Composite
Numbers that have more than two factors. Example: 6 is a
composite number since its factors are 1, 2, 3, and 6.
Prime
Numbers that have only two factors, 1 and the number itself.
Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31
Square Numbers
Generalize
A product that can be shown in a square array or model; a
product of two equal numbers. Examples: 2 x 2 = 4; 3 x 3 = 9;
4 x 4 = 16
To draw a general conclusion.
Possible
Having a potential.
Reasonable
The appropriateness or good approximation in a number
answer.
Data
Information that is displayed in a graph.
Array
A number of mathematical elements arranged in rows and
columns.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections/anticipatory set
1.
Start the lesson by discussing the vocabulary words. Talk about prime,
composite, and square numbers. You will need overhead square tiles. Start by
using 6 tiles and have students give ways that these 6 tiles could be arranged in
a rectangle. Have students brainstorm the ways and write them down on the
board. Once they have brainstormed, model their solutions to see if they work.
(You should come up with a 1 by 6, a 6 by 1, a 2 by 3, and a 3 by 2 rectangle.)
Explain to students that this is one way to find all the factors of a given number.
Next have students brainstorm how many rectangles could be done with only 5
tiles. (They should only come up with two, a 1 by 5 and a 5 by 1.) With this
activity, explain to students that the 5 is a prime number because it only has two
factors, 1 and 5 and that 6 is a composite number because it has more than two
factors.
B.
Instructional activities
1.
Objectives:
The student will determine if factors of numbers are prime or
composites.
2.
Procedures: The teacher will explain the difference in prime and composite and
students will complete activities in order to determine which numbers are prime
and composite.
3.
Modeling: The teacher will use square tiles, computers, and may use the
overhead or chart paper for recording answers to demonstrate prime and
composite numbers.
C.
Guided activity or strategy
Day 1
1. Divide students into small groups. Give each group a set of square tiles (give each
group 7 tiles) and have them practice arranging tiles. Students will also need a sheet
of paper to record their answers. Have students find solutions to the following
questions: In how many ways can you arrange 4 tiles to form a rectangle? 3
ways: 1x4; 4x1; and 2x2. How many ways can you arrange 7 tiles to form a
rectangle? 2 ways: 1x7 and 7x1. Ask students if there are any other ways to
arrange the 7 tiles? There aren’t any other ways. Ask students why they can not
arrange 7 tiles any other way? Because 7 is a prime number. Have students
arrange other sets of tiles to show different arrays of numbers. (This comes from
Math Advantage p. 286).
Day 3
1.
Review with students about Prime and Composite numbers. Put students into
small groups. Give each group a different amount of sugar free gummy bears or
gum drops and toothpicks. Put some different numbers in a container and have
each group draw two numbers. Demonstrate to students how to build a factor
tree. On the board put the number 21. Ask students what two factors equal 27.
They should say 9 and 3. See the diagram below to demonstrate how to create
a factor tree. Keep going until all the numbers at the bottom of the tree are prime
numbers. Tell students that this is the prime factorization of the number 27.
Diagram:
27
9
3 3
3
This is a prime number so
underline it.
The prime factorization of 27 is 3x3x3.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
II.
D.
Accommodations/modifications
See student IEP for modifications.
E.
Enrichment
Students can create a number pyramid by finding the missing numbers in that pyramid.
Enrichment from Math Advantage p. E93 (Activity sheet 4).
STUDENT PERFORMANCE
A.
Description
The students should be able to recognize a prime or composite number and be able to
decipher a prime factorization of a number.
Day 1
1.
Students will continue to work in small groups. Give each group more tiles,
about 20 for each group and have students find the arrays for the following
numbers: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. Have students draw
the arrays on graph paper (Activity Sheet 1), write their factors for those
numbers, and determine whether they are prime or composite.
Day 2
1.
Students will use the following website from the school adoption to find prime and
composite numbers. http://www.harcourtschool.com. Go to The Learning Site,
Math, Math Advantage (at the very bottom), E-Lab, 5th grade, and scroll down to
Prime and Composite numbers. (Students will use Activity Sheet 2 with this
activity or you can print it from the website.)
2.
Guide students through just questions 1-4 and 9-10 of the computer experiment.
Have students complete the rest of the questions on their own.
Day 3
1.
After showing students the prime factorization tree, instruct them to create prime
factorization trees with their gummy bears and tooth picks. Have them write the
prime factorization for their number and their factor tree on a sheet of paper.
Monitor to make sure students are doing this right. (You may be wondering how
they are to do this factor tree. Students need to brainstorm how to get the 3
gummy bears needed for that factor on the toothpick. Not every factor tree will
look the same because of the fact that students will come up with different ways
to show their factor tree. Just make sure they are on the right track.) After
students have completed their factor bears and turned in their papers to you,
have students complete Activity sheet 3, On My Own p. P93 from Math
Advantage.
B.
Accommodations/modifications
See student’s IEP for specific modifications.
C.
Enrichment
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
III.
IV.
Assessment of Activities
A.
Description
The teacher will know the students have mastered prime and composite numbers when
they:
 Complete the Day 2 activity with a 70% or higher.
 Complete the Prime and Composite Assessment with 70% or higher.
 One other Assessment that can be done is having students write the first 20
prime numbers from memory with a 70% success or higher. (2, 3, 5, 7, 11, 13,
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71)
B.
Rubrics/grading criteria
 Complete all Activities with a 70% or higher.
C.
Accommodations/modifications
All accommodations/modifications need to align with the student’s IEP.
D.
Enrichment
E.
Sample discussion questions
1.
Name the first 10 prime numbers? 2,3,5,7,11,13,17,19,23,29
2.
What is the difference between a prime number and a composite number? A
prime number only has two factors, 1 and itself, where a composite number has
more than two factors.
3.
What is a prime factorization? It is the all the prime factors that make up the
whole number.
4.
How do you find the prime factorization of a composite number? Create a factor
tree.
TAKS Preparation
A.
Transition to TAKS context
1. Students will complete a TAKS formatted Assessment.
B.
Sample TAKS questions
The teacher needs to take sample questions from the 2003 and 2004 TAKS released
tests to emphasis how probability is tested on the TAKS test.
(Use TAKS Transparency)
V.
Key Vocabulary
Prime numbers, composite numbers, square numbers, prime factorization, factors,
reasonableness, data, array, possible, generalize
VI.
Resources
A.
B.
Textbook
Math Advantage
Step Up to TAKS
Harcourt Brace
Supplementary materials/equipment
 Transparency: Sample TAKS questions from 2003 and 2004 Released TAKS test.
 Students will complete activity sheets from Step Up to TAKS Step 1A-1B and Step 2.
 Toothpicks
 Sugar free Gummy Bears or Gumdrops.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
C.
Technology
1.
Overhead projector: Modeling prime and composite arrays and prime
factorization trees.
VII.
Follow up activities
The next lesson in this sequence would move into finding common factors and greatest common
factors.
VIII.
Teacher Notes
The teacher should make sure that students have a complete understanding of prime and
composite numbers. The teacher can make other accommodations as they see fit for their
students.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District