Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 73111
Using Rectangles to Find Prime and Composite Numbers
In this lesson, students will be using rectangles to find prime and composite numbers. Students will draw different rectangles for the area of a given
set of numbers. They will determine the factor pairs for each number in the given set and use them to discover the meaning of prime and
composite numbers.
Note: This lesson only addresses subpart a and c of the standard MAFS.4.OA.2.4.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Suggested Technology: Document Camera
Instructional Time: 1 Hour(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: factor, prime, composite, rectangle, area
Resource Collection: FCR-STEMLearn Mathematics General
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will find all factor pairs for a given set of whole numbers in the range 1-100.
Students will determine whether each of the numbers in the given set is prime or composite.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to find a factor pair for a whole number in the range of 1-100.
Students should be familiar with the following vocabulary: factor, multiple, product, rectangle.
Students should be able to create an area model for a multiplication problem.
Guiding Questions: What are the guiding questions for this lesson?
1. What is a factor?
2. Do you see a pattern as you work? What is it? Can it help you?
3. We said some things in mathematics are always true. Can one of those relationships or structures help here?
4. Can you think of a rule or property that could help us?
Teaching Phase: How will the teacher present the concept or skill to students?
Hook:
Write the following numbers and question on the board: 3, 18, 25, 8, and 13 How they can categorize these numbers?
Ask students to record any way they can think of to categorize these numbers.
Give students 2-3 minutes to think of and record an answer. Students will record their answers on individual white boards, in their math journals, or on notebook
paper. At the end of the given time, ask all students to hold up their answers. (Possible answers: odd/even, single/double digit, big/small…) Teacher can use a class roster or this Checklist to monitor students who have appropriate answers as listed above. If there are answers that are way off base, the
teacher will know to give them extra attention during the guided practice and/or independent portions of the lesson.
Direct Instruction:
page 1 of 4 Begin the lesson by using the answers to the hook question.
I noticed that the majority of the class categorized these numbers into odd and even groups.
Some students used odd/even numbers, single/double­digit numbers… Tell students they will be categorizing numbers into composite and prime groups. At the end of the lesson, they will be expected to complete a chart and use words
to explain/justify their answers.
Write the number 10 on the ¼” graph paper. Use the document camera to project your drawing for the whole class to see. (If you do not have a document camera,
you can use chart paper, overhead projector or another method to show your work to all students.)
How many different rectangles can I draw that uses 10 squares?
Remember we are finding rectangles with an area of 10.
Draw a 1x10 rectangle and a 10x1 rectangle.
Are these rectangles different?
Students should understand that they are the same rectangle. Make sure they understand that they can only include one for their answer.
I know that 1 and 10 are factors of 10. What other factors can I think of for a product of 10? What number multiplied by another number equals 10?
Draw a 2x5 rectangle. Explain that 2 and 5 are factors of 10. If there are no other factors, that problem is finished.
Students will now split into partners for further practice on this skill. Create pairs of students with either their face partner (the student facing them) or their
shoulder partner (the student next to them).
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Give each student a sheet of 1” graph paper and small bag of previously divided crackers. The teacher will explain to students that they will receive a product. They must work with their partner to create as many different rectangles for that number on
the graph paper with the crackers and explain/justify their answer. (Tell students not to eat the crackers. Students can eat the crackers at the end of the lesson.)
The teacher will tell students to start with the number 9. The teacher will circulate around to each group. Ask questions to allow the students an opportunity to
verbalize their thinking.
Why did you create a 1x9 rectangle?
How many rectangles were you able to create for this number?
Direct students’ attention to the projection of your rectangles made with crackers from the document camera. If you do not have a way to project this, you could
have students gather around a table or desk to see your paper and crackers.
Who would like to share what rectangles your group created?
I made a 1x9 rectangle. Why did you do that? I know that 1x9=9.
I made a 3x3 square. Some students may say that you asked for rectangles, but you can remind them that a square is a special type of rectangle.
Are there any other factors of 9? No.
Give students the number 5 with the same directions. Walk around and ask students similar questions to allow them to verbalize their thinking.
I noticed that you finished that problem quickly.
Why did you finish so quickly?
Students should be able to tell you that there is only one rectangle.
Record rectangles on the white board/SmartBoard for students. Direct their attention to the board.
When we made area models for 9, we had 2 solutions.
When we made area models for 5, we had 1 solution.
Draw and label each rectangle. (1x9, 1x3 for 9 and 1x5 for 5)
Students should take out their notebooks to write notes. Tell students that these two numbers can be labeled as either prime or composite. Have the students write
down the following notes:
Composite number: a whole number that can be divided evenly by numbers other than 1 and itself
Ex. 9 (Draw a 1x9 and 3x3 rectangle. There is more than 1 rectangle, more than one factor pair. This number is composite.)
Prime number: a whole number that can be divided evenly by only 1 and itself
Ex. 5 (Draw a 1x5 rectangle. There is only 1 rectangle, one factor pair. This number is prime.)
Write another example on the board using the number 27. Ask the students how many different rectangles with an area of 27 could I draw? Call on students for
their answers.
You said to draw a rectangle 1x27, why did you say that? You know that 1 and 27 are factors of 27.
Are there any other rectangles we could draw?
Continue on with the discussion until all rectangles are drawn 1x27, 3x9.
Ask students if this number would be prime or composite and how they know.
If students are struggling to understand this concept, have them complete a couple more examples with the crackers and their 1” graph paper. (Use the numbers 6
and 13.) The teacher will continue to think aloud and guide the students through the problems with questioning and discussion.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will now separate from their partners and work individually. Pass out a piece of ¼” graph paper to each student. Explain to students that they will be doing the same activity, but this time they will be drawing the rectangle to show the area of each number. Remind students that
rectangles of the same size rectangles do not get recorded twice.
Students should find different rectangles for the following set of numbers: 15, 7, 12, 24, 16, 19, and 25. Remind students that they should label each rectangle with
the factor pairs.
After students have drawn all the rectangles for each number, students should record their answers in a chart. The Graph Worksheet file has a chart that can be
projected, copied onto the board and/or photocopied.
Teacher will circulate around the room asking students to explain and justify their responses on their paper. Teacher should be looking for students’ use of
academic vocabulary (factors, product, area, prime, composite), correct area models
Can the students explain why they drew a certain rectangle?
Do they have an understanding of prime and composite numbers.
Can they explain the meaning of the two terms and distinguish the difference in their own words?
page 2 of 4 After about 15­20 minutes, direct students’ attention to the front boardorLCD projector. Ask students to share their answers for a few numbers. For 15, I drew a 1x15 and a 3x5 rectangle because I know that 15 has 4 factors.
Continue sharing and recording for the whole class. Students who did not quite finish can complete their drawings.
Complete table as a whole group.
Ask the students what they conclude about the number of rectangles and whether the number is prime or composite. They should be able to state that 1 rectangle
(1 factor pair) is a prime number and more than 1 rectangle (more than one factor pair) is drawn for a composite number.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Ask students to write down the steps they took in their math notebooks to find out if a number was prime or composite.
Give students about 2-3 minutes to organize their thoughts in their math notebooks.
At the end of the 3 minutes, state aloud the steps that were taken.
With each number, we thought of the factors that made each product.
We drew different rectangles.
If a number only had 1 rectangle, we knew that the factors were 1 and itself. That number was prime.
If a number had more than one rectangle, we knew there were other factors than 1 and itself. That number was composite.
Students will complete an exit slip and turn into teacher at the end of the class period. Students will also need another sheet of ¼” graph paper to attach to their
exit slip.
Teacher will use a rubric on the bottom of the exit slip to evaluate each student and use data to drive future lessons. Students who did not perform well at the end
of the lesson can be pulled into a small group the following day to reteach concepts that are still unclear.
Summative Assessment
Students should be able to use the drawings of their rectangles to explain and justify why a number is either prime or composite.
Teachers will use an exit slip, a paper that will be turned into the teacher at the end of the lesson, to assess each student.
The teacher will ask each student to draw as many different rectangles that contain 3, 18, 25, and 13 squares. Each rectangle must be labeled with the factor pairs
and include a written explanation stating whether each number is prime or composite. If any additional information is known about a number, students can also
include that in their written response.
Teacher will collect the exit slips and assess if the students have mastered the learning objectives using the rubric at the bottom of the exit slip.
The teacher can form a small group of students to work with the following day for students who did not complete the exit slip successfully. Use the data received in
the exit slips to drive further teaching on this standard.
Formative Assessment
Teacher will use the answer to the hook question on white boards (or notebook paper) to get a better understanding of how the students in the class will categorize
numbers.
Use this checklist to help you record student responses and guide the discussion.
Teacher may need to guide students for a starting place.
When I look at these numbers, I know that I can categorize them into even and odd numbers.
Can you think of another way to categorize these numbers?
During the Guided Practice, circulate around the room and ask students questions to have them verbalize their thinking process. Examples of questions may
include:
What do you have to find out?
What have you already tried?
Where could you start?
Show me what you mean so I can see.
During Guided Practice, make sure you visit each partner group. If there are several students who are not understanding the activity, you may need to reteach
before moving on to Independent Practice.
At the end of the 15-20 minutes of Independent Practice, you can use the completed table as a measure of their understanding. Make note on the same checklist
you used at the beginning of the lesson.
Feedback to Students
The teacher can use the Guiding Questions to steer a student in the correct direction to solve a particular problem. The students can immediately apply the
feedback to their work.
Ask students How do you know that? When the student is explaining their answer, the teacher can better understand where the error is occurring, and at times, the
student can self-correct.
Some example questions to allow for improved performance: How do you know that there are no other different rectangles with an area of 15? Is this answer
reasonable? Does it make sense?
Student: I know the factors of 15 are 1x15, 3x5. I can’t think of any other ones. Teacher: What does this tell you about the number 15?
The exit slip includes a rubric to be completed by the teacher along with any comments. The exit slips can be used to drive future lessons.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Students who are having difficulty completing the individual task with multiple numbers in the given set can be given one number at a time. Teacher can make sure
the student is completing the task correctly before giving out another number.
Students who have difficulty writing on the 1/4" grid paper can continue to use 1" grid paper.
Extensions:
When students are quickly identifying prime and composite numbers and can explain/justify their reasoning, the teacher can introduce the concept of a square
number. Students can find other examples and use the 100 chart to explain a pattern. (Students may notice that all the square numbers make a diagonal from
upper left to lower right on the 100 chart. The teacher can question students on how they know this.)
If students know the definitions of prime and composite, ask them to explain if '1' is a composite or prime number. (Students may say that '1' is a prime number
because it is divisible by 1. Some may argue that '1' is itself as well. Teacher can clarify that '1' is a special number that is not prime or composite. A prime
page 3 of 4 number is defined as a number greater than 1.
If the students want or need extra practice they could play the game Factorize on the Internet.
Suggested Technology: Document Camera
Special Materials Needed:
1" grid paper
1/4" grid paper
Small, square shaped cracker (Teacher may want to separate a small amount, 15-20 crackers in small plastic bags or buy individually packaged crackers.)
100 chart
Math notebook/journal (Use the resource that students use on a daily basis to take notes.)
Individual dry-erase boards & markers (It is more convenient to use these boards, but notebook paper and pencil will be adequate.)
Further Recommendations:
1. This lesson could lead into a future lesson of using the Sieve of Eratosthenes to find prime and composite numbers.
2. Teacher could show students the YouTube Video on how to use the Sieve of Eratosthenes.
Additional Information/Instructions
By Author/Submitter
This lesson supports the following Standards for Mathematical Practice:
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 Model with mathematics.
MAFS.K12.MP.7.1 Look for and make use of structure.
This lesson only addresses subpart a and c of the standard MAFS.4.OA.2.4.
SOURCE AND ACCESS INFORMATION
Contributed by: Maria Israel
Name of Author/Source: Maria Israel
District/Organization of Contributor(s): Manatee
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.OA.2.4:
Description
Investigate factors and multiples.
a. Find all factor pairs for a whole number in the range 1–100.
b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the
range 1–100 is a multiple of a given one­digit number. c. Determine whether a given whole number in the range 1–100 is prime or composite.
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