Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Unit 06: Factors and Primes (7 days)
Possible Lesson 01 (7 days)
POSSIBLE LESSON 01 (7 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students draw on the operational skills of multiplication of prior units and the role of factors in multiplication, and connect it to finding factor pairs and prime numbers. The
concepts of factors and primes include using various representations such as arrays, area models, and patterns in factors.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
5.3
Number, operation, and quantitative reasoning.. The student adds, subtracts, multiplies, and divides to solve meaningful problems. The
student is expected to:
5.3D
Identify common factors of a set of whole numbers. Supporting Standard
5.5
Patterns, relationships, and algebraic thinking.. The student makes generalizations based on observed patterns and relationships. The
student is expected to:
5.5B
Identify prime and composite numbers using concrete objects, pictorial models, and patterns in factor pairs. Supporting Standard
Underlying Processes and Mathematical Tools TEKS:
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Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
5.14
Underlying processes and mathematical tools.. The student applies Grade 5 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
5.14C
Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
5.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
5.15
Underlying processes and mathematical tools.. The student communicates about Grade 5 mathematics using informal language. The
student is expected to:
5.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
5.15B
Relate informal language to mathematical language and symbols.
5.16
Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to:
5.16A
Make generalizations from patterns or sets of examples and nonexamples.
5.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
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Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Grade5 Mathematics Unit06 PI01
Select three numbers greater than 50, where two of the numbers are three-digits and only one of the numbers is prime (e.g., 61, 123, 276). Create a flip book that includes a
pictorial model (e.g., area model, factor rainbow, factor tree, etc.) identifying all the factors of each number. Write an explanation to show whether: (1) each number of the set as
prime or composite, (2) a common factor(s) exists among the set of numbers, and (3) the following statement is true or false: “All prime numbers are odd and all composite
numbers are even”.
Sample Performance Indicator:
Use the following three numbers to create a flip book that includes a pictorial model (e.g., area model, factor rainbow, factor tree, etc.) that
identifies all the factors of each of the following numbers in the set:
61 123 276
Write an explanation to show whether: (1) each number of the set is prime or composite, (2) a common factor(s) exist(s) among the set of numbers, and (3) the following
statement is true or false: “All prime numbers are odd and all composite numbers are even”.
Standard(s): 5.3D , 5.5B , 5.14C , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B
ELPS ELPS.c.1A , ELPS.c.5E , ELPS.c.5G
Key Understanding(s):
When a counting number can be described by several factor pairs, then it is composite; when a counting number can be described with only by one factor pair,
then it is prime.
The numbers 0 and 1 are considered neither prime nor composite since there are an infinite number of factor pairs that have the product of 0 and 1 has only one
factor pair – itself.
Prime and composite numbers can be even or odd.
Factors can be expressed as either prime or composite numbers.
Generalizations about whether a number is prime or composite can be made and justified by using concrete objects, pictorial models, patterns in factor pairs and
verbal descriptions.
A variety of problem solving strategies can be used to find the factors, both prime and/or composite, of a set of whole numbers.
A set of whole numbers can be described by its factors and common factors.
Misconception(s):
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Unit 06 :
Suggested Duration: 7 days
Some students may think that there is only one way to represent factor pairs. Factor pairs can be represented multiple ways: factors pairs of 12 are (1,12), (2,6),
(3,4), list of factors: (1,2, 3, 4, 6, 12), multiplication (1 x 12, 2 x 6, 3 x 4), factored tree pairs (
), and/or T-charts or tables
Some students may think that 0 and 1 are prime numbers.
Some students may think that all odd numbers are prime numbers.
Some students may think that if two numbers have a factor in common, then that is the only factor they have in common. That may be true for some numbers but
not all. When finding common factors of two numbers, students need to complete the list of factors for each number and then find all common factors.
Vocabulary of Instruction:
common factor(s)
composite number
divisibility
divisible
factor
factor pair
multiple
prime number
Materials List:
Bag of Color Tiles (previously created) (1 per 2 students)
color tiles (30 per 2 students)
map pencil (1 yellow, 1 pink) (1 set per student)
math journal (1 per student)
Multiplication Table (12 x 12) (optional) (1 per student as needed)
plastic zip bag (sandwich sized) (1 per 2 students)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Seating Problem
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Unit 06 :
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Factor Pair Area Model Practice KEY
Factor Pair Area Model Practice
Centimeter Grid Paper
Divisibility Rules – Notes
Am I a Factor? Table KEY
Am I a Factor? Table
Am I a Factor? Practice KEY
Am I a Factor? Practice
Find the Factor Practice KEY
Find the Factor Practice
Factor Rainbow Practice KEY
Factor Rainbow Practice
Common Factor Practice Part 1 KEY
Common Factor Practice Part 1
Common Factor Practice Part 2 KEY
Common Factor Practice Part 2
Prime and Composite KEY
Prime and Composite
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Unit 06 :
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Factor Trees to Find Prime and Composite Numbers KEY
Factor Trees to Find Prime and Composite Numbers
Sieve of Eratosthenes KEY
Sieve of Eratosthenes
Sign of the Primes KEY
Sign of the Primes
Prime Problem Solving KEY
Prime Problem Solving
Factors and Primes Practice KEY
Factors and Primes Practice
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Identifying factors
Engage 1
MATERIALS
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Suggested Instructional Procedures
Students use logic and reasoning skills to review andidentify factors.
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
math journal (1 per student)
Instructional Procedures:
TEACHER NOTE
1. Display the following numbers for the class to see: 1, 2, 3, 6, 9, 18. Instruct students to identify
what these numbers have in common and record their predictions in their math journal. Allow
time for students to complete the activity. Facilitate a class discussion about the displayed
numbers.
Ask:
Development of factor vocabulary has taken place in
the previous operations units. Remind students that
the word “factor” discussed in these lessons is the
same as what has been defined and discussed in
the multiplication and division operations units.
What do the numbers have in common? Answers may vary.
What is a factor? (A number multiplied by another number to find a particular product.)
How can you prove that each of the numbers is a factor of 18? Answers may vary. 18
is divisible evenly by each of the numbers; when I multiply certain pairs of the numbers, I
get 18; etc.
What does it mean to find the factors of a number? Answers may vary. A factor is a
number multiplied by another number to find a particular product. To find the factors of a
number means to find numbers that can be multiplied together to get that product; etc.
What numbers from the list can be multiplied together to make the product 18? (1 x
18, 2 x 9, 3 x 6. These are called factor pairs.)
What is the difference between listing the factors and factor pairs? Answers may
vary. When you list the factors, they are all the numbers in pairs but written together (1, 2,
3, 6, 9, 18). When you are listing the factor pairs, they are listed together with a
multiplication symbol between the pair (1 x 18, 2 x 9, 3 x 6); etc.
2. Display all the pairs of factors for 18 for the class to see.
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Unit 06 :
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Suggested Instructional Procedures
Notes for Teacher
Explain to students that 2 x 9 and 9 x 2 are not both listed in this situation because they
represent the same two factors and that each pair of numbers is called a factor pair. Allow
time for students to determine if any other whole numbers are missing. Monitor and assess
students to check for understanding. Facilitate a class discussion about the strategies used to
determine all the factors.
Ask:
How do you know that there are not more pairs of whole numbers whose product is
18? Answers may vary. Whole numbers between 1 and 18 were checked until factors
began to repeat: 1 x 18, 2 x 9, 3 x 6, 4 x __, 5 x ___, 6 x 3
factors are now repeating;
etc.
Topics:
Factor pairs
ATTACHMENTS
Teacher Resource: Seating Problem (1 per
teacher)
Explore/Explain 1
Teacher Resource: Factor Pair Area Model
Students investigate and discuss a real-life problem situation. Students identify factor pairs in order
Practice KEY (1 per teacher)
to solve the problem.
Handout: Factor Pair Area Model Practice
(1 per student)
Instructional Procedures:
1. Prior to instruction, create a Bag of Color Tiles for every 2 students by placing 30 color tiles in a
plastic zip bag.
Handout (optional): Centimeter Grid Paper
(1 per student as needed)
MATERIALS
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Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
2. Place students to pairs and distribute a Bag of Color Tiles to each pair.
3. Display teacher resource: Seating Problem.
Ask:
Notes for Teacher
color tiles (30 per 2 students)
plastic zip bag (sandwich sized) (1 per 2
students)
math journal (1 per student)
How can you use the color tiles to represent the solutions to this problem? Answers
may vary. I can create all the possible arrangements by building the rows that 24 students
TEACHER NOTE
can sit in; etc.
One possible example of the color tiles arrangement
Can the students in this problem be arranged in one row? (yes)
for 24 (showing 1 factor pair):
What would that look like? (1 row with 24 students (tiles) in a row)
Is it possible for the students to be arranged in five rows? Why or why not? (no)
Answers may vary. The rows have to all have the same number of students and 24 students
cannot be split evenly into 5 rows; etc.
4. Instruct student pairs to use their color tiles to demonstrate all the possible ways the students
TEACHER NOTE
could be arranged and record a model and description of each rectangular model built in their
When describing the area models that can be
math journals. Allow time for students to find and record all the possible arrangements.Monitor
created using 24 tiles, both representations are
and assess student pairs to check for understanding. Facilitate a class discussion about the
included for each factor pair (e.g., 1 x 24 and 24 x 1)
different arrangements for the problem situation.
because they represent different orientations of the
Ask:
model, which are distinctly different in space.
How many different area models did you form with the 24 tiles, representing the
rows for 24 students? (8 area models)
What are they? (1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3, and 6 x 4)
How many ways can the students be seated onstage? Explain. (8 ways, because
there are 8 different area models or arrangements.)
TEACHER NOTE
Handout (optional): Centimeter Grid Paper may be
used for students who may need to model the
arrangements.
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Unit 06 :
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Notes for Teacher
What are some things the students might consider when deciding which
arrangement to use? Answers may vary. How the students will look at the audience; how
big the stage is; etc.
What are the factors of 24? 1, 2, 3, 4, 6, 8, 12, 24
How can you be sure that you have listed all of the factors of 24? Answer may vary.
None of the other numbers less than 24 will work evenly; every number in our list has its
partner; etc.
How many factor pairs can be made from the factors of 24? Explain. (4 pairs (1 x 24,
2 x 12, 3 x 8, and 4 x 6), because those are the pairs of numbers that can be multiplied to
make 24. Even though the representation for this problem situation is different, 24 x 1, 12 x
2, 8 x 3, and 6 x 4 do not need to be listed because they have the same 2 factors as a pair
already listed.)
5. Distribute handout: Factor Pair Area Model Practice to each student. Instruct students to
complete the handout. Remind students that they may use their Bag of Color Tiles, if needed.
Allow time for students to complete the activity. Monitor and assess students to check for
understanding.
2
Topics:
Spiraling Review
Divisibility rules
Identifyingfactors
ATTACHMENTS
Explore/Explain 2
Handout: Divisibility Rules – Notes (1 per
Students investigate, analyze, and identify factors by using the divisibility rules.
student)
Teacher Resource: Am I a Factor? Table
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Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
Instructional Procedures:
1. Facilitate a class discussion to debrief previously assigned handout: Factor Pair Area Model
Practice.
Ask:
Notes for Teacher
KEY (1 per teacher)
Teacher Resource: Am I a Factor? Table (1
per teacher)
Teacher Resource: Am I a Factor? Practice
KEY (1 per teacher)
What are some of the ways you can find the factors of a number? Answers may vary.
Handout: Am I a Factor? Practice (1 per
You can use area models, grouping, skip counting;etc.
student)
How can an area model help find factors of a given number? Answers may vary. An
Teacher Resource: Find the Factor Practice
area model demonstrates the possible groupings of a number; etc.
KEY (1 per teacher)
When would an area model not be helpful? Answers may vary. When the numbers get
Handout: Find the Factor Practice (1 per
really large; if you did not have enough color tiles to build it; etc.
student)
2. Instruct students to brainstorm other possible methods, besides using area models, that can
MATERIALS
be used to find all the factors of a number. Allow time for students to brainstorm ideas.
Facilitate a class discussion about student methods including multiplication/division facts,
Multiplication Table (12 x 12) (optional) (1 per
basic number concepts, etc.
student as needed)
3. Explain to students that they are going to look at divisibility rules as another strategy to find the
factors of a number. Facilitate a class discussion about the word “divisibility” while referencing
the meaning “whole numbers.” Instruct students to record the formal definitions for “divisibility”
and “whole number” in their math journal.
4. Display teacher resource: Am I a Factor? Table and demonstrate the process of using
divisibility rules to find the factors of a number.
TEACHER NOTE
For students who are still struggling with basic facts,
have them use a Multiplication Table to help find all
the factors of a number. For example, to find the
factors of 12, have students circle all the 12s in the
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Unit 06 :
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Suggested Instructional Procedures
5. Place students in pairs and distribute handouts: Divisibility Rules – Notes and Am I a
Factor? Practice to each student.
Notes for Teacher
table. For each circled number, they can find the
factors by determining which column and row the
number is in.
6. Instruct student pairs to complete the notes portion of handout: Am I a Factor? Practice.
Explain to students that they will systematically find all the factors of a number (e.g., 1 x ?, 2 x
?, 3 x ?, etc.) until the factors start repeating and when that happens, they have found all the
factors. Allow time for student pairs to complete the activity. Monitor and assess student pairs
to check for understanding. Facilitate a class discussion to discuss and debrief solutions.
7. Distributehandout: Find the Factor Practice to each student as independent practice or
homework.
3
Topics:
Spiraling Review
Factor rainbows
Explore/Explain 3
Students find all the possible factors of a number by using organized factor rainbows.
ATTACHMENTS
Teacher Resource: Factor Rainbow
Practice KEY (1 per teacher)
Instructional Procedures:
1. Remind students that they used divisibility rules and an organized list to find the factors of a
Handout: Factor Rainbow Practice (1 per
student)
number. Explain to students that you will demonstrate another organized method to list pairs of
factors to find all the possible factors of the number 42.
2. Instruct students to record the pair 1 and 42 in their math journal.
MATERIALS
math journal (1 per student)
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Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
TEACHER NOTE
Ask:
Why are these two factors connected? (they are a factor pair of 42)
This method of organizing factors is often called the
“rainbow” method because it looks as if you are
creating a rainbow when you connect factor pairs.
Why would there be a gap between the factors 1 and 42? (because there may be
other factors of 42 between 1 and 42)
TEACHER NOTE
Is 2 is a factor of 42?Why? (Yes, because 42 is even.)
Another methodto organize and display the factors of
What factor should be paired with 2? Why? (21, because 2 x 21 equals 42.)
a numbermay include using a factor tree.
Recordthe factor pairs 2 and 21 as shown below. Instruct students to replicate the model in
their math journal.
Note that these are not prime factorization trees.
This strategy exposes students to multiple methods
of organizing factors.
As one factor increases, what happens to the other factor in the factor pair? (The
other factor decreases)
TEACHER NOTE
Point out to students that there is a special name for
Continue filling in the factor pairs, listing the factors in increasing order from left to right.
numbers that have only 1 factor pair or 1 “rainbow.”
Instruct students to replicate the model in their math journal.
They are called prime numbers. Numbers that have
more than 1 factor pair or more than 1 “rainbow” are
called composite numbers.
How could you use this diagram to determine if you have found all the factors of a
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number? Answers may vary. I can look at the factors on the left: 1, 2, and 3. Since 4 and
Notes for Teacher
State Resources
5 are not factors, and there are no numbers between 6 and 7, the diagram must be
complete; etc.
TEXTEAMS: Rethinking Elementary
Mathematics Part I: MultipleTowersmay be used to
3. Explain to students that, together, you are going to find the factor pairs for 31.
Ask:
reinforce the concepts of prime and composite
numbers.
What factors of 31 could you name first? Explain. (1 and 31; when I name factor pairs,
it is easy to begin with 1 and the number itself because all numbers have 1 as a factor.)
Record the factor pairs, as shown below, for the class to see.
Are there other factors for the number 31? How do you know? (no) Answers may vary.
I used divisibility rules and an organized list, but could find no other factors; etc.
Explain to students that there is a special name for numbers that have only 1 factor pair or 1
“rainbow”; these numbers are called prime numbers. Numbers that have more than 1 factor
pair or more than 1 “rainbow” are called composite numbers.
4. Repeat this activity several more times as necessary, including numbers with only 2 factors
(prime numbers).
5. Distribute handout: Factor Rainbow Practice to each student as independent practice or
homework.
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4
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Common factors
Greatest common factor
ATTACHMENTS
Explore/Explain 4
Handout: Centimeter Grid Paper (1 per
Students explore and explain common factors with models and organized lists. Students identify
student)
greatest common factors.
Teacher Resource: Common Factor
Practice Part 1 KEY (1 per teacher)
Instructional Procedures:
1. Facilitate a class discussion about how to find the factors of a number.
Ask:
Handout: Common Factor Practice Part 1
(1 per student)
Teacher Resource: Common Factor
Practice Part 2 KEY (1 per teacher)
What are some strategies to finding factors of a number? Answers may vary. Using
Handout: Common Factor Practice Part 2
the rainbow method, factor tree model, factor pair area model; etc.
(1 per student)
2. Instruct students to find the factors for 16 and 18 using whichever method they choose and
MATERIALS
record the factors in their math journal. Allow time for students to find all the factors. Monitor
and assess students to check for student understanding. Facilitate a class discussion about
math journal (1 per student)
the factors for 16 and 18.
3. Place students in pairs. Instruct student pairs to compare their strategy for finding all the factor
pairs to their partner's strategy. Invite several students to share their method for finding the
factors of 16 and 18. Facilitate a class discussion about the methods that were the most
efficient.
TEACHER NOTE
The concept of GCF (Greatest Common Factor): The
greatest number that is a factor of 2 or more
numbers) is taught in Grade 6 (6.1E). Grade 5
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Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
4. Display the list of factors of 16 and 18 for the class to see.
Notes for Teacher
students should not be held accountable for finding
the GCF. The focus for Grade 5 is finding all the
factors and then finding the common factors of a
5. Instruct students use their list to identify (circle) the common factors for 16 and 18 in their math
journal. Explain to students that the greatest common factor is often called the GCF and it is
given set of numbers. The error most students make
is not finding all the factors of a given number.
the greatest factor that the numbers have in common. Facilitate a class discussion about the
common factors and GCF of 16 and 18.
Ask:
How can you determine whether a number is a common factor of 16 and 18? (It
appears in both lists.)
What are the common factors of 16 and 18? (1 and 2)
What is the Greatest Common Factor of 16 and 18? (2)
TEACHER NOTE
When finding common factors of 2 numbers,
students may not complete the list of factors for
each number. Students must find all the factors of
each number before finding the common factors.
Remind students that they can do this by testing 1,
2, 3, etc. and listing factor pairs until they repeat.
6. Display the numbers 14 and 25 for the class to see. Invite student volunteers to identify the
factors of these numbers and the common factor for these numbers. Remind students that
TEACHER NOTE
some numbers may have only 1 factor in common, the factor 1.
If students have trouble remembering how to find
common factors, have the students use the letters
CF (Common Factors) backwards to remind them of
the steps:
7. Remind students of the definition for common factors. Explain to students that common factors
F→Find the Factors
can be found for more than just 2 numbers. Display the numbers 10, 15, and 20 for the class to
C→Find the Common factors
see. Invite student volunteers to identify the factors of these numbers and the common factors
Note: Later in Grade 6, when students are asked to
for these numbers.
find GCF, they can apply this same mnemonic
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Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
device for remembering how to find GCF by simply
adding the G at the end. Example:
F→Find the Factors
Ask:
C→Find the Common factors
G→Find the Greatest common factor
Can you find common factors of more than three numbers? Explain. (yes) Answers
may vary.As long as you can find the factors of a set of numbers you can find the common
factors for that same set; etc.
State Resources
What is the GCF for 10, 15, and 20? (5)
TEXTEAMS: Rethinking Elementary
8. Display the number 30 with the previous list of 10, 15, and 20. Instruct student pairs to
generate the factors for the new number and identifythe common factors for this new set.Allow
Mathematics Part I: What’s in Each Box? may be
used to reinforce the concepts of common factors.
time for students to complete the activity. Monitor and assess student pairs for to check for
understanding. Facilitate a class discussion to debrief student solutions.
Ask:
Did the common factors change when you added the new number? Why or why
not? (no) Answers may vary. Although the factors of 30 had many of the same factors as
the other numbers, the only factors all 4 numbers had in common were 1 and 5; etc.
Will this be true for all numbers? Explain. (no) Answers may vary. All numbers are
different and have their own unique set of factors. Sometimes the common factors will stay
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Notes for Teacher
the same when you add a new number to the set of given numbers, and sometimes the
common factors will not stay the same; etc.
What is the GCF for these numbers? (5)
9. Distribute handout: Common Factor Practice Part 1 to each student. Instruct student pairs to
identify the common factors. Allow time for students to complete the activity. Monitor and
assess students to check for understanding. Facilitate a class discussion to debrief student
solutions.
10. Distribute handout: Common Factor Practice Part 2 to each student as independent practice
or homework.
5
Topics:
Spiraling Review
Prime and composite models
Explore/Explain 5
Students apply prior knowledge and resources to investigate prime and composite numbers.
ATTACHMENTS
Teacher Resource: Prime and Composite
KEY (1 per teacher)
Instructional Procedures:
1. Facilitate a class discussion to debrief previously assigned handout: Common Factor
Practice Part 2 as a class.
2. Place students in pairs and distribute handout: Prime and Composite,1 yellow colored pencil,
and 1 pink colored pencil to each student.
Handout: Prime and Composite (1 per
student)
Teacher Resource: Factor Trees to Find
Prime and Composite Numbers KEY (1 per
teacher)
Handout (optional): Factor Trees to Find
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Suggested Instructional Procedures
3. Invite a student to read the directions from handout: Prime and Composite activity aloud.
Instruct student pairs to complete the table on page 1, using whichever method they choose.
Notes for Teacher
Prime and Composite Numbers (1 per
student)
Allow time for students to complete the activity. Monitor and assess student pairs to check for
understanding. Facilitate a discussion with each pair of students about the list of factor pairs
MATERIALS
created.
Ask:
map pencil (1 yellow, 1 pink) (1 set per
student)
What method did you and your partner choose to find the factor pairs for each
number? Why? Answers may vary. My partner and I decided to make area models for
some of the numbers because we weren't sure if we were skip counting correctly to find the
Bag of Color Tiles (previously created) (1 per
2 students)
math journal (1 per student)
other factor; my partner and I used a factor rainbow because it is fast and organized; etc.
How does an area model represent the factors and the product of a number? (The
dimensions of the area model are the factors and the total number of square units is the
TEACHER NOTE
product.)
Another method to determine if a number is prime or
According to this table, what do prime and composite numbers have in common?
composite is to use a factor tree.
Answers may vary. They both have factors of 1 and the number itself; etc.
Do you need to find all the factors of a number to know if it is prime or composite?
Explain. (No, when you find factors other than 1 and itself, then you know the number is
composite.)
4. Distribute a Bag of Color Tiles to each student pair. Instruct student pairs to determine whether
The number 12 has factors other than 1 and itself.
each number from 21 – 30 is prime or composite, and record the numbers they believe to be
So it is not a prime number. It is a composite
prime in their math journal. Remind students that they may use the color tiles to create area
number. The number 19 has no other factors other
page 19 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
models, as needed. Monitor and assess student to check for understanding. Facilitate a class
discussion about prime numbers.
Ask:
Which numbers did you determine were prime? (23 and 29)
Notes for Teacher
than 1 and itself, so it is a prime number.
Since 12 is a composite number, a factor tree could
be used to show all of the prime factors of 12 and
not just the factor pairs of 12.
How can you be sure that they are prime? (Ilisted the factor pairs, and the only factors
were 1 and itself.)
What are the factor pairs for 23 and for 29? (1, 23 and 1, 29)
What factor(s) do these factor pairs have in common? (1)
Looking back in your math journal and observing all of the model representations
for numbers 1 – 30, which of these numbers are prime? (2, 3, 5, 7, 11, 13, 17, 19, 23,
Note that prime factorization is a Grade 6 TEKS.
29)
Grade 5 students should not be held responsible for
Are all prime numbers odd? Explain. (No, because 2 is an even number.)
finding the prime factorization of a number. Factor
Are all odd numbers prime? Explain. (No, many odd numbers like 9, 15, and 21 are not
trees should be used only to determine whether a
prime.)
number is prime or composite. Handout (optional):
Are there any other prime numbers that are even? Explain. (No, because the number
would be divisible by 2 and another factor.)
What are the other numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27,
28, 30 called? (composite numbers)
Is it possible to determine that a number is composite without listing every one of
Factor Trees to Find Prime and Composite
Numbers may be used to assist students to further
their understanding of prime and composite
numbers.
its factor pairs? (Yes, once I determine that it has more than 1 factor pair, I know it is
composite.)
Is 1 prime or composite? Explain. (1 is neither prime nor composite because it does not
have 2 distinct factors – the factors of 1 are 1 and 1 and the definition of prime is 2 different
factors one of which includes 1. It is not composite because it does not have 2 distinct
factors and other factors that when multiplied have a product of 1.)
State Resources
TEXTEAMS: Rethinking Elementary
Mathematics Part I: Marissa’s Garden
page 20 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Suggested Instructional Procedures
Notes for Teacher
5. Facilitate a class discussion with various examples of prime and composite numbers, as
needed.
Ask:
Is 63 a prime or composite number? How do you know? (Composite, because it has
factors other than 1 and itself.)
What are the factors of 63? (1, 3, 7, 9, 21, 63)
What are the factors of 63 that are prime? (3, 7)
6. Instructstudents to complete page 2 of handout: Prime and Composite as independent
practice or homework.
6
Topics:
Spiraling Review
Sieve of Eratosthenes
Explore/Explain 6
ATTACHMENTS
Students use the Sieve of Eratosthenes to find prime numbers. Students apply knowledge of
Teacher Resource: Sieve of Eratosthenes
number concepts to determine what characteristics a set of numbers have in common.
KEY (1 per teacher)
Teacher Resource: Sieve of Eratosthenes (1
Instructional Procedures:
1. Distribute handout: Sieve of Eratosthenes to each student.
2. Display teacher resource: Sieve of Eratosthenes. Explain to students that over 2,000 years
ago there was a mathematician named Eratosthenes who studied prime numbers. He
per teacher)
Handout: Sieve of Eratosthenes (1 per
student)
Teacher Resource: Sign of the Primes KEY
(1 per teacher)
page 21 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
developed a process that "strains" out composite numbers and leaves prime numbers behind.
Handout: Sign of the Primes (1 per student)
His process has become known as the "Sieve of Eratosthenes" – with "sieve" being another
Teacher Resource (optional): Prime
name for a "strainer."
Problem Solving KEY (1 per teacher)
3. Instruct students to complete their handout: Sieve of Eratosthenes as you demonstrate the
process of "straining" out composite numbers to find primes.
Handout (optional): Prime Problem Solving
(1 per student)
4. Instruct students to cross out the 1 on their handout: Sieve of Eratosthenes.
Ask:
What are the factors of 1? (1)
ADDITIONAL PRACTICE
Is 1 prime or composite? Explain. (Neither, because it has only 1 factor – itself.
Use handout (optional): Prime Problem Solving to
Therefore, it follows neither rule for being prime nor composite.)
further facilitate understanding of prime and
composite numbers.
5. Instruct students to circle the 2, the least prime number, and then shade all the numbers
divisible by 2 or all the multiples of 2 on their handout: Sieve of Eratosthenes.
6. Instruct students to circle the 3, the next prime number, and then shade all the numbers
divisible by 3 or all the multiples of 3 on their handout: Sieve of Eratosthenes.
Ask:
When you shaded all the multiples of 2 (except 2), why are all the multiples of 4
also shaded? Explain. (because all the multiples of 4 are also multiples of 2)
Are there any other multiples that are shaded because they are also all multiples of
2? Explain. (Yes, all the multiples of 10 are shaded because they are also multiples of 2.
The multiples of 6 and 8 are also multiples of 2.)
page 22 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
7. Instruct students to circle the 5, the next prime number, and then cross out all the numbers
divisible by 5 or all the multiples of 5 on their handout: Sieve of Eratosthenes.
Ask:
Do you think you will need to shade all the multiples of 5 or have some of them
already been shaded? Explain. (No, I won’t have to shade in all the multiples of 5
because some of them were shaded as multiples of 2, and some of the odd multiples of 5
like 15, were already shaded as multiples of 3.)
Will you need to shade the multiples of 6? Why or why not? (No, these were all
shaded as multiples of 2.)
8. Instruct students to circle the 7, and then shade in all the multiples of 7 on their handout:
Sieve of Eratosthenes.
Ask:
What do you notice about the shaded numbers on your grid? Answers may vary. They
are all multiples of some number other than 1; they are composite numbers; etc.
What can you tell me about the numbers that are not shaded on your grid? Answers
may vary. They are not multiples of any other numbers except for 1; they are prime
numbers; etc.
Instruct the students to list the prime numbers for each row out to the right-hand side of the
grid. Allow time for students to complete the activity. Monitor and assess for student
understanding.
9. Distribute handout: Sign of the Primes to each students. Instruct students to use their "Sieve
page 23 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
of Eratosthenes" to complete the handout. Allow time for students to complete the activity.
Monitor and assess students to check for understanding. Facilitate a class discussion to
debrief student solutions, as needed.
7
Topics:
Spiraling Review
Common factors
Prime and composite numbers
ATTACHMENTS
Elaborate 1
Teacher Resource: Factors and Primes
Students generate a list of factors to identify the common factors in a set of numbers. Students
Practice KEY (1 per teacher)
identify a number as prime or composite.
Handout: Factors and Primes Practice (1
per student)
Instructional Procedures:
1. Distribute handout: Factors and Primes Practice to each student. Instruct students to
complete the handout. Allow time for students to complete the activity. Monitor and assess
students to check for understanding. Facilitate a class discussion to debrief student solutions,
as needed.
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
page 24 of 58 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit 06 :
Suggested Duration: 7 days
Notes for Teacher
Performance Indicator(s):
Grade5 Mathematics Unit06 PI01
Select three numbers greater than 50, where two of the numbers are three-digits and only one of the
numbers is prime (e.g., 61, 123, 276). Create a flip book that includes a pictorial model (e.g., area
model, factor rainbow, factor tree, etc.) identifying all the factors of each number. Write an explanation
to show whether: (1) each number of the set as prime or composite, (2) a common factor(s) exists
among the set of numbers, and (3) the following statement is true or false: “All prime numbers are
odd and all composite numbers are even”.
Sample Performance Indicator:
Use the following three numbers to create a flip book that includes a pictorial
model (e.g., area model, factor rainbow, factor tree, etc.) that identifies all the
factors of each of the following numbers in the set:
61 123 276
Write an explanation to show whether: (1) each number of the set is prime or composite, (2) a
common factor(s) exist(s) among the set of numbers, and (3) the following statement is true or false:
“All prime numbers are odd and all composite numbers are even”.
Standard(s): 5.3D , 5.5B , 5.14C , 5.14D , 5.15A , 5.15B , 5.16A , 5.16B
ELPS ELPS.c.1A , ELPS.c.5E , ELPS.c.5G
04/02/13
page 25 of 58 Grade 5
Mathematics
Unit: 06 Lesson: 01
Seating Problem
A fifth grade class is preparing for an
awards ceremony. There are 24 students in
the class. The students are to be seated in a
single row or equal rows on the stage. How
many different possible arrangements can the
24 students be seated?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Pair Area Model Practice KEY
Use color tiles to create an area model for each problem. Students may record each area model on centimeter grid paper
and label each model if needed. List all factors and describe the factors with a written description.
(1)
Rory has a collection of 21 guitars. He has placed his guitars in equal groups. In what ways can Rory arrange
his guitars?
1 x 21
21 x 1
3x7
7x3
1 group of 21 guitars, 21 groups of 1 guitar, 3 groups of 7 guitars, 7 groups of 3 guitars.
Area Models on grid paper to match (4 different area models)
(2)
Enrique is arranging 9 posters to create a rectangle on the wall? If it does not matter where each poster is placed
within the rectangle, how can he put his posters on the wall?
1x9
9x1
3x3
1 row of 9 posters, 9 rows of 1 poster each, 3 rows of 3 posters
Area models on grid paper to match (3 different area models)
(3)
Clementina has 6 dimes. How many different ways can she arrange her dimes if she places them in equal
groups?
1x6
6x1
2x3
1 group of 6 dimes 6 groups of 1 dime
2 groups of 3 dimes
Area models on grid paper to match (4 different area models)
(4)
3x2
3 groups of 2 dimes
Sherry has 16 CDs that she wants to put into equal stacks. What are the different stacks she can make?
1 x 16
16 x 1
2x8
8x2
4x4
1 stack of 16 cds,
16 stacks of 1 cd 2 stacks of 8 cds 8 stacks of 2 cds 4 stacks of 4 cds
Area models on grid paper to match (5 different area models)
(5)
A marching drill team has 36 members. Identify all the different ways the members line up in equal rows on the
football field.
1 row of 36 members
1 x 36
3 rows of 12 members
3 x 12
36 rows of 1 member 2 rows of 18 members 18 rows of 2 members
36 x 1
2 x 18
12 rows of 3 members
12 x 3
18 x 2
4 rows of 9 members
4x9
9 rows of 4 members
9x4
6 rows of 6 members
6x6
Area models on grid paper to match (9 different area models)
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Pair Area Model Practice
Use color tiles to create an area model for each problem. Students may record each area model on
centimeter grid paper and label each model if needed. List all factors and describe the factors with a
written description.
(1)
Rory has a collection of 21 guitars. He has placed his guitars in equal groups. In what ways
can Rory arrange his guitars?
(2)
Enrique is arranging 9 posters to create a rectangle on the wall? If it does not matter where
each poster is placed within the rectangle, how can he put his posters on the wall?
(3)
Clementina has 6 dimes. How many different ways can she arrange her dimes if she places
them in equal groups?
(4)
Sherry has 16 CDs that she wants to put into equal stacks. What are the different stacks she
can make?
(5)
A marching drill team has 36 members. Identify all the different ways the members line up in
equal rows on the football field.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Centimeter Grid
©2012, TESCCC
Unit: 06 Lesson: 01
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Divisibility Rules – Notes
A number is divisible by a given number when it can be divided by that number and there is no remainder.
A number is divisible by
2→
3→
If the sum of the digits of the number is divisible by
3. Example: 621 → 6 + 2 + 1 = 9; 9 ÷ 3 = 3
4→
If the last 2 digits of the number are divisible by 4.
Example: 132 → 32 ÷ 4 = 8
5→
If the last digit of the number is a 0 or a 5.
6→
If the number is divisible by BOTH a 2 and a 3.
Example 132 is even, so it is divisible by 2. And 1
+ 3 + 2 = 6; 6 ÷ 3 = 2.
9→
10 →
©2012, TESCCC
If the number is even. Even numbers have a 0, 2,
4, 6, or 8 in the ones place.
If the sum of the digits of the number is divisible by
9.
Example: 621 → 6 + 2 + 1 = 9; 9 ÷ 9 = 1
If the last digit of the number is 0.
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Am I a Factor? Table KEY
Find all the factor pairs for 30. Then list all the factors of 30.
(1)
Try
Am I a Factor? Explain
Factor Pair
1
Yes, 1 is a factor of every whole number.
1 and 30
2
Yes, because 30 is an even number.
2 and 15
3
Yes, because 3 + 0 = 3; and 3 ÷ 3 = 1.
3 and 10
4
No, because 30 is not divisible by 4.
--
5
Yes, because 30 ends in 0.
5 and 6
6
Yes, because 30 is divisible by both 2 and 3.
6 and 5
7
No – Answers may vary.
8
No – Answers may vary.
9
No – Answers may vary.
10
Yes, because 30 ends in 0.
10 and 3
After which number could you stop trying to find factors? Explain.
After the 6, because at 6, the factor pairs start repeating.
(2)
What are the factors of 30?
1, 2, 3, 5, 6, 10, 15, and 30
(3)
Which divisibility rule was the most helpful in finding the factors of 30?
Answers may vary.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Am I a Factor? Table
Find all the factor pairs for 30. Then list all the factors of 30.
Try
Am I a Factor? Explain
Factor Pair
1
2
3
4
5
6
7
8
9
10
(1)
After which number could you stop trying to find factors? Explain.
(2)
What are the factors of 30?
(3)
Which divisibility rule was the most helpful in finding the factors of 30?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Am I a Factor? Practice KEY
Find all the factor pairs for 36. Then list all the factors of 36.
(1)
Try
Am I a Factor? Explain
Factor Pair
1
Yes, 1 is a factor of every whole number.
1 and 36
2
Yes, because 36 is an even number.
2 and 18
3
Yes, because 3 + 6 = 9; and 9 ÷ 3 = 3.
3 and 12
4
Yes, because 4 x 9 = 36 (basic fact).
4 and 9
5
No, because it does not end in 5 or 0.
--
6
Yes, because 36 is divisible by both 2 and 3;
OR because 6 x 6 = 36.
6 and 6
7
No, because 7 x 5 = 35 and the next basic fact
is 7 x 6 = 42.
--
8
No, because 8 x 4 = 32 and the next basic fact
is 8 x 5 = 40.
--
9
Yes, because 3 + 6 = 9; 9 ÷ 9 = 1.
9 and 4
10
No, because 36 does not end in 0.
--
After which number could you stop trying to find factors? Explain.
After the 9, because at 9, the factor pairs start repeating.
(2)
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18, and 36
(3)
Which divisibility rule was the most helpful in finding the factors of 36?
Answers may vary.
©2012, TESCCC
04/08/13
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Am I a Factor? Practice
Find all the factor pairs for 36. Then list all the factors of 36.
Try
Am I a Factor? Explain
Factor Pair
1
2
3
4
5
6
7
8
9
10
(1)
After which number could you stop trying to find factors? Explain.
(2)
What are the factors of 36?
(3)
Which divisibility rule was the most helpful in finding the factors of 36?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Find the Factor Practice KEY
(1)
Complete the table to find all the factor pairs for 12.
Try
Am I a Factor? Explain
Factor Pair
1
Yes, 1 is a factor of every whole number.
1 and 12
2
Yes, because 12 is an even number.
2 and 6
3
Yes, because 1 + 2 = 3; and 3 ÷ 3 = 1.
3 and 4
4
Yes, because 4 x 3 = 12 is a basic fact.
4 and 3
5
No, because 12 does not end in 0 or 5.
--
6
Yes, because 12 is divisible by both 2 and 3.
6 and 2
7
No, because 7 x 1 = 7 and the next basic fact is 7 x 2 = 14.
--
8
No, because 8 x 1 = 8 and the next basic fact is 8 x 2 = 16.
--
9
No, because 1 + 2 = 3; 3 is not divisible by 9.
--
10
No, because 12 does not end in 0.
--
The factors of 12 are: 1, 2, 3, 4, 6, 12
(2)
Complete the table to find all the factor pairs for 32.
Try
Am I a Factor? Explain
Factor Pair
1
Yes, 1 is a factor of every whole number.
1 and 32
2
Yes, because 32 is an even number.
2 and 16
3
No, because 3 + 2 = 5; and 5 is not divisible by 3.
--
4
Yes, because 4 x 8 = 32 is a basic fact.
4 and 8
5
No, because 32 does not end in 0 or 5.
--
6
No, because 32 is not divisible by BOTH 2 and 3.
--
7
No, because 7 x 4 = 28 and the next basic fact is 7 x 5 = 35.
--
8
Yes, because 8 x 4 = 32 is a basic fact.
8 and 4
9
No, because 3 + 2 = 5; 5 is not divisible by 9.
--
10
No, because 32 does not end in 0.
--
The factors of 32 are: 1, 2, 4, 8, 16, 32
©2012, TESCCC
03/07/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Find the Factor Practice
(1)
Complete the table to find all the factor pairs for 12.
Try
Am I a Factor? Explain
Factor Pair
1
2
3
4
5
6
7
8
9
10
The factors of 12 are:
(2)
Complete the table to find all the factor pairs for 32.
Try
Am I a Factor? Explain
Factor Pair
1
2
3
4
5
6
7
8
9
10
The factors of 32 are:
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Rainbow Practice KEY
Write all the factors of each number in the diagrams shown. Connect the pairs of factors as shown.
(1)
(2)
25
1
(3)
5
25
(4)
28
1
2
4
50
7
14
28
1
2
5
10
25
50
Use the space bellow to find the factors of 48. Use a rainbow diagram and describe how you found all the factors.
(5)
48
1
2
3
4
6
8
12
16
24
48
Possible description: I started counting from 1 to find the numbers that 48 was divisible by. I
found that 1, 2, 3, 4, and 6 were all factors of 48. The only factors after 6 were paired with the
first four factors.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Rainbow Practice
Write all the factors of each number in the diagrams shown. Connect the pairs of factors as shown.
(1)
(2)
25
1
(3)
25
(4)
28
1
50
28
1
50
Use the space below to find the factors of 48. Use a rainbow diagram and describe how you found all the factors.
(5)
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Common Factor Practice Part 1 KEY
A math team has 24 female members and 30 male members. The coach wants to arrange the members in
equal groups of all males or all females. In what ways can the coach arrange the groups?
(1)
List all the factors of each number.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
(2)
Circle the common factors:
.
(3)
So the math team can be arranged in equal groups of 1, 2, 3, or 6.
(4)
What is the largest number of students that can be in one equal group? How do you know? 6, because
both 24 and 30 can be divided equally by 1, 2, 3, or 6, but 6 is the largest divisor these numbers
have in common.
32 people at a bird sanctuary signed up for hiking and 20 people signed up for kayaking. They will be
divided into smaller groups. In what ways can these groups be arranged?
(5)
List all the factors of each number.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 20: 1, 2, 4, 5, 10, 20
(6)
Circle the common factors:
.
(7)
So the bird sanctuary groups can be arranged in equal groups of 1, 2, or 4.
(8)
What is the largest number of people that can be in one equal group? How do you know? 4, because
both 32 and 20 can be divided equally by 1, 2, or 4, but 4 is the largest divisor these numbers have
in common.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Common Factor Practice Part 1
A math team has 24 female members and 30 male members. The coach wants to arrange
the members in equal groups of all males or all females. In what ways can the coach
arrange the groups?
(1)
(2)
List all the factors of each number.
Circle the common factors:
.
(3)
So the math team can be arranged in equal groups of ________________.
(4)
What is the largest number of students that can be in one equal group? How do you
know?
32 people at a bird sanctuary signed up for hiking and 20 people signed up for kayaking.
They will be divided into smaller groups. In what ways can these groups be arranged?
(5)
List all the factors of each number.
(6)
Circle the common factors:
.
(7)
So the bird sanctuary groups can be arranged in equal groups of _____________.
(8)
What is the largest number of people that can be in one equal group? How do you know?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Common Factor Practice Part 2 KEY
Find the common factors of each set of numbers. Show your work.
(1)
12, 18, 30
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
(2)
21, 28, 35
Factors of 21: 1, 3, 7, 21
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 35: 1, 5, 7, 35
Find the common factors of each set of numbers. Show your work.
(3)
6, 15
Factors of 6: 1, 2, 3, 6
Factors of 15: 1, 3, 5, 15
(4)
24, 40, 56
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
(5)
12, 18, 30 and 54
Factors of 12:
Factors of 18:
Factors of 30:
Factors of 54:
(6)
1,
1,
1,
1,
2,
2,
2,
2,
3,
3,
3,
3,
4,
6,
5,
6,
6,
9,
6,
9,
12
18
10, 15, 30
18, 27, 54
Carrie has 3 book shelves that can hold 12, 24, and 60 books. The cases have shelves holding the same
number of books. What is the greatest number of books on each shelf? How do you know?
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
By finding the common factors of all three numbers, I know that the greatest number of books that
will fit on each shelf of the bookcases is 12. 12 is the largest divisor these numbers have in
common. I can check this as follows: Bookcase 1 = 12 and 12 ÷ 12 = 1; Bookcase 2 = 24 and 24 ÷ 12
= 2; and Bookcase 3 = 60 and 60 ÷ 12 = 5.
©2012, TESCCC
04/02/13
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Common Factor Practice Part 2
Find the common factors of each set of numbers. Show your work.
(1)
12, 18, 30
(2)
21, 28, 35
Find the common factors of each set of numbers. Show your work.
(3)
6, 15
(4)
24, 40, 56
(5)
12, 18, 30 and 54
(6)
Carrie has 3 book shelves that can hold 12, 24, and 60 books. The cases have shelves
holding the same number of books. What is the greatest number of books on each shelf?
How do you know?
©2012, TESCCC
04/02/13
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime and Composite KEY
Directions:
A. Find the factor pairs for each number, 1-20. You may use centimeter grid paper to make area models if
needed, or choose another method to find the factor pairs.
B. Record each number's factor pairs and how many factor pairs it has.
C. Cross out the number 1 because it is neither prime nor composite.
D. Color the numbers in the number column that have exactly 1 factor pair with two different factors PINK.
E. Color the numbers in the number column that have 2 or more factor pairs YELLOW.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
©2012, TESCCC
Factors of Rectangles
1x1
1x2
1x3
Number of
Rectangles Made
1x8
2x4
1x9
3x3
1 x 10
2x5
1 x 11
1 x 12 2 x 6 3 x 4
1 x 13
1 x 14 2 x 7
1 x 15 3 x 5
1 x 16 2 x 8 4 x 4
1 x 17
1 x 18 2 x 9 3 x 6
1 x 19
1 x 20 2 x 10 4 x 5
1
1
1
2
1
2
1
2
2
2
1
3
1
2
2
3
1
3
1
3
04/08/13
page 1 of 2
1x4
2x2
1x5
1×6
3×2
1x7
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime and Composite KEY
Use the chart you created to answer the following questions:
(1)
Which numbers have only 1 factor pair (PINK)? These numbers are PRIME numbers.
Prime numbers have exactly 2 different factors, 1 and itself. List the prime numbers from the chart here.
2, 3, 5, 7, 11, 13, 17, 19
(2)
Which numbers have 2 or more factor pairs (YELLOW)? These numbers are COMPOSITE numbers.
Composite numbers have more than 2 factors. List the composite numbers from the chart here.
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20
(3)
Write all the factors of each number. Then circle either PRIME or COMPOSITE next to each number.
7
1, 7
PRIME
COMPOSITE
14
1, 2, 7, 14
PRIME
COMPOSITE
21
1, 3, 7, 21
PRIME
COMPOSITE
25
1, 5, 25
PRIME
COMPOSITE
17
1, 17
PRIME
COMPOSITE
31
1, 31
PRIME
COMPOSITE
19
1, 19
PRIME
COMPOSITE
9
1, 3, 9
PRIME
COMPOSITE
35
1, 5, 7, 35
PRIME
COMPOSITE
18
1, 2, 3, 6, 9, 18
PRIME
COMPOSITE
30
1, 2, 3, 5, 6, 10, 15, 30
PRIME
COMPOSITE
28
1, 2, 4, 7, 14, 28
PRIME
COMPOSITE
©2012, TESCCC
04/08/13
page 2 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime and Composite
Directions:
A. Find the factor pairs for each number, 1-20. You may use centimeter grid paper to make area models if
needed, or choose another method to find the factor pairs.
B. Record each number's factor pairs and how many factor pairs it has.
C. Cross out the number 1 because it is neither prime nor composite.
D. Color the numbers in the number column that have exactly 1 factor pair with two different factors PINK.
E. Color the numbers in the number column that have 2 or more factor pairs YELLOW.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
©2012, TESCCC
Factor Pairs
1×6
3×2
04/08/13
Number of
Factor Pairs
2
page 1 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime and Composite
Use the chart you created to answer the following questions:
(1)
Which numbers have only 1 factor pair (PINK)? These numbers are PRIME numbers.
Prime numbers have exactly 2 different factors, 1 and itself. List the prime numbers from the chart here.
(2)
Which numbers have 2 or more factor pairs (YELLOW)? These numbers are COMPOSITE numbers.
Composite numbers have more than 2 factors. List the composite numbers from the chart here.
(3)
Write all the factors of each number. Then circle either PRIME or COMPOSITE next to each
number.
©2012, TESCCC
7
____________________
PRIME
COMPOSITE
14
____________________
PRIME
COMPOSITE
21
____________________
PRIME
COMPOSITE
25
____________________
PRIME
COMPOSITE
17
____________________
PRIME
COMPOSITE
31
____________________
PRIME
COMPOSITE
19
____________________
PRIME
COMPOSITE
9
____________________
PRIME
COMPOSITE
35
____________________
PRIME
COMPOSITE
18
____________________
PRIME
COMPOSITE
30
____________________
PRIME
COMPOSITE
28
____________________
PRIME
COMPOSITE
04/08/13
page 2 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Trees to Find Prime and Composite Numbers KEY
Use factor trees to determine whether the given numbers are prime or composite. Circle or
underline the correct type of number. Explain your reasoning.
(1) 18
(2) 63
(3) 29
18
63
29
2
x
9
7
x
3 x 3
Prime
Composite
9
3 x 3
Prime
Composite
Prime
Composite
Explain:
Answers may vary but
should include: 18 has
factors other than one and
itself (2 and 9)
Explain:
Answers may vary but
should include: 63 has
factors other than one and
itself ( 7 & 9)
Explain:
Answers may vary but
should include: 29 has only
2 factors, one and itself
(4) 53
(5) 77
(6) 81
77
53
7
81
x 11
9
x
9
3 x 3 3 x 3
Prime
Composite
Explain:
Answers may vary but
should include: 53 has only
2 factors, one and itself
©2012, TESCCC
Prime
Composite
Explain:
Answers may vary but
should include: 77 has
factors other than one and
itself (7 and 11)
04/08/13
Prime
Composite
Explain:
Answers may vary but
should include: 81has
factors other than one and
itself (9 and 9)
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factor Trees to Find Prime and Composite Numbers
Use factor trees to determine whether the given numbers are prime or composite. Circle or
underline the correct type of number. Explain your reasoning.
(1) 18
(2) 63
(3) 29
Prime
Composite
Prime
Composite
Prime
Explain:
Explain:
Explain:
(4) 53
(5) 77
(6) 81
Prime
Explain:
©2012, TESCCC
Composite
Prime
Explain:
Composite
Prime
Composite
Composite
Explain:
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Sieve of Eratosthenes KEY
(1)
(2)
(3)
(4)
(5)
Cross off the 1.
Circle the 2, and shade every number that is evenly divisible by 2.
Circle the 3, and shade every number that is evenly divisible by 3.
Circle the 5, and shade every number that is evenly divisible by 5.
Circle the 7, and shade every number that is evenly divisible by 7.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Sieve of Eratosthenes
(1)
(2)
(3)
(4)
(5)
Cross off the 1.
Circle the 2, and shade every number that is evenly divisible by 2.
Circle the 3, and shade every number that is evenly divisible by 3.
Circle the 5, and shade every number that is evenly divisible by 5.
Circle the 7, and shade every number that is evenly divisible by 7.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Sign of the Primes KEY
Exactly 107 of the squares below contain prime numbers. Shade in each of these 107 squares.
2
7
6
19
59
9
89
48
41
65
23
13
5
22
61
53
79
87
11
12
3
28
15
71
84
10
97
99
37
80
83
44
17
63
47
35
71
94
29
82
31
67
27
7
51
95
5
53
41
63
97
60
61
18
19
24
89
4
71
98
50
13
86
3
69
64
47
32
83
35
59
70
17
39
73
33
67
93
23
12
31
2
25
11
37
81
29
68
7
30
5
17
83
88
13
2
3
9
11
31
43
92
79
61
57
74
90
89
5
46
37
71
97
30
31
73
3
51
67
87
29
55
11
76
9
70
46
83
15
69
43
4
17
95
53
20
41
49
2
80
7
24
29
13
75
59
21
67
84
18
19
63
41
40
5
58
83
6
73
8
31
77
99
59
81
93
36
3
48
98
13
88
89
12
47
68
2
90
11
27
61
42
37
71
78
35
94
17
97
18
43
19
67
25
79
3
23
86
7
5
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Sign of the Primes
Exactly 107 of the squares below contain prime numbers. Shade in each of these 107 squares.
2
7
6
19
59
9
89
48
41
65
23
13
5
22
61
53
79
87
11
12
3
28
15
71
84
10
97
99
37
80
83
44
17
63
47
35
71
94
29
82
31
67
27
7
51
95
5
53
41
63
97
60
61
18
19
24
89
4
71
98
50
13
86
3
69
64
47
32
83
35
59
70
17
39
73
33
67
93
23
12
31
2
25
11
37
81
29
68
7
30
5
17
83
88
13
2
3
9
11
31
43
92
79
61
57
74
90
89
5
46
37
71
97
30
31
73
3
51
67
87
29
55
11
76
9
70
46
83
15
69
43
4
17
95
53
20
41
49
2
80
7
24
29
13
75
59
21
67
84
18
19
63
41
40
5
58
83
6
73
8
31
77
99
59
81
93
36
3
48
98
13
88
89
12
47
68
2
90
11
27
61
42
37
71
78
35
94
17
97
18
43
19
67
25
79
3
23
86
7
5
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime Problem Solving KEY
Solve. Explain your answers.
(1)
Corey’s jersey number is a prime number that is also an even number. What number is
on Corey’s jersey?
2; 2 is the only even prime number.
(2)
Pedro’s classroom number is the least 2-digit prime number that has all prime numbers
for digits. What is Pedro’s classroom number?
23; explanations may vary.
(3)
Meredith’s street address is a composite number less than 10 that can be formed by
multiplying 2 different prime numbers. What is Meredith’s street address?
6; 2 and 3 are the only two prime numbers whose product is less than 10
(2 x 3 = 6).
(4)
The sum of my ones digit and tens digit is 10. My tens digit is less than my ones digit
and both my digits are prime. I am a prime number. What number am I?
37; explanations may vary.
(5)
I am a number between 70 and 100. My ones digit is 1 more than my tens digit. I am a
prime number. What number am I?
89; explanations may vary.
(6)
Below are the t-shirts of two teams:
TEAM A
12
4
TEAM B
11
21
2
63
19
53
How would you describe the numbers chosen for TEAM A? TEAM B?
TEAM A are composite numbers and TEAM B are prime numbers.
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Prime Problem Solving
Solve. Explain your answers.
(1)
Corey’s jersey number is a prime number that is also an even number. What number is
on Corey’s jersey?
(2)
Pedro’s classroom number is the least 2-digit prime number that has all prime numbers
for digits. What is Pedro’s classroom number?
(3)
Meredith’s street address is a composite number less than 10 that can be formed by
multiplying 2 different prime numbers. What is Meredith’s street address?
(4)
The sum of my ones digit and tens digit is 10. My tens digit is less than my ones digit
and both my digits are prime. I am a prime number. What number am I?
(5)
I am a number between 70 and 100. My ones digit is 1 more than my tens digit. I am a
prime number. What number am I?
(6)
Below are the t-shirts of two teams:
TEAM A
12
4
TEAM B
11
21
2
63
19
53
How would you describe the numbers chosen for TEAM A? TEAM B?
©2012, TESCCC
08/03/12
page 1 of 1
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factors and Primes Practice KEY
What term could be used to describe the numbers in each problem listed below? Explain your
answer.
(1)
2 x 15, 1 x 30, 5 x 6, 3 x 10
factors or factor pairs of 30
(2)
40:
24:
1
1
2
2
4
3
5
4
8
6
10
8
20
12
40
24
factors and common factors for 40 and 24
What term could be used to describe the shaded numbers in the table? Explain your answer.
2
(3)
3
4
5
6
7
8
9
10
11
12
13
14
composite numbers
What term could be used to describe the numbers in the table that are not shaded? Explain
your answer.
2
(4)
3
4
5
6
7
8
9
10
11
12
13
14
prime numbers
For each composite number, write the word “composite”. For each prime number, write the
word “prime”.
(5)
29
prime
(6)
13
prime
(7)
9
composite
(8)
26
composite
©2012, TESCCC
04/08/13
page 1 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factors and Primes Practice KEY
Make a list to find all the factors of each number. Then underline all the factors that are prime
for each number.
(9)
45: 1, 3, 5, 9, 15, 45
(10)
91: 1, 7, 13, 91
(11)
28: 1, 2, 4, 7, 14, 28
(12)
54: 1, 2, 3, 6, 9, 18, 27, 54
List all the factors of each number and then find the common factors.
(13)
24 and 35
(14)
Factors of 10: 1, 2, 5, 10
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 35: 1, 5, 7, 35
(15)
10, 25 and 100
Factors of 25: 1, 5, 25
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
12, 35, and 42
(16)
15, 21, 24, 60
Factors of 15:
Factors of 21:
Factors of 24:
Factors of 60:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 35: 1, 5, 7, 35
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
1,
1,
1,
1,
3,
3,
2,
2,
5,
7,
3,
3,
15
21
4, 6, 8, 12, 24
4, 5, 6, 10, 12, 15, 20, 30, 60
Select and write a prime number greater than 10 in the spaces provided below. Draw a picture
and explain how you know each number you have chosen is prime.
11
(17) ________
(18) ________
Many answers are possible.
A sample is shown:
Many answers are possible.
The array shows that 11 has
only 2 factors: 1 and 11.
©2012, TESCCC
04/08/13
page 2 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factors and Primes Practice
What term could be used to describe the numbers in each problem listed below? Explain your
answer.
(1)
2 x 15, 1 x 30, 5 x 6, 3 x 10
(2)
40:
24:
1
1
2
2
4
3
5
4
8
6
10
8
20
12
40
24
What term could be used to describe the shaded numbers in the table? Explain your answer.
2
(3)
3
4
5
6
7
8
9
10
11
12
13
14
What term could be used to describe the numbers in the table that are not shaded? Explain
your answer.
2
(4)
3
4
5
6
7
8
9
10
11
12
13
14
For each composite number, write the word “composite”. For each prime number, write the
word “prime”.
(5)
29
(6)
13
(7)
9
(8)
26
©2012, TESCCC
04/08/13
page 1 of 2
Grade 5
Mathematics
Unit: 06 Lesson: 01
Factors and Primes Practice
Make a list to find all the factors of each number. Then underline all the factors that are prime
for each number.
(9)
45:
(10)
91:
(11)
28:
(12)
54:
List all the factors of each number and then find the common factors.
(13)
35 and 24
(14)
10, 25 and 100
(15)
12, 35, and 42
(16)
15, 21, 24, 60
Select and write a prime number greater than 10 in the spaces provided below. Draw a picture
and explain how you know each number you have chosen is prime.
(17) ________
©2012, TESCCC
(18) ________
04/08/13
page 2 of 2