# Prime Factor

## Curriculum Goal

#### Junior: Number Sense

• Represent composite numbers as a product of their prime factors, including through the use of factor trees

## Context

• Students use factor trees and multiplication facts to identify prime factors of composite numbers.
• Students should be familiar with factors, prime factors, prime numbers, and composite numbers
• This activity is inspired by the board game “Prime Climb”.

## Materials

• Prime Climb Prompt Sheet (Appendix A)
• Worksheet (Appendix B)
• Prime Climb Challenge Slides (Appendix C)
• Pencil crayons or markers (red, orange, green, blue and purple)

## Lesson

Introduction

• Before starting the activity provide students with an overview of the terms they will be engaging with. Ask students: What are factors? What are prime numbers? What are prime factors? What are composite numbers?
 Term Definition Example Factor A number you multiply with another number to get a product Factors of 6: 1, 2, 3, and 6 1 × 6, 6 × 1, 2 × 3, and 3 × 2 Prime Numbers Has two factors Can only be divided by one and the number itself 2, 3, 5, 7, 11, etc. E.g., 5 is divisible by 1 and 5 Prime Factors Are numbers you multiple with another number to get a product that can   only be divided by one and the number itself Prime Factors of 6: 2 and 3 The numbers 2 and 3 can both only be divided by one   and the number itself making them prime 2 × 3 and 3 x 2 Composite Numbers Has more than two factors Can be divided by all its factors 4, 6, 8, 9, etc. E.g., 6 is divisible by 1,2,3, and 6

Lesson

• Project the Prime Climb prompt sheet (Appendix A). Tell students: Look at circles one to 20 and write down what you notice and wonder about the different colours and number of sections in each circle. What do you think the different colours represent? What do you think the sections in each circle represent?
• As students share what they notice, record their ideas so the class can see them. Pay particular attention to any ideas on prime numbers, composite numbers, and prime factors.
• Ensure students understand the relationship between the colours/patterns in the circles.
• Each circle has a white center indicating that each number is divisible by 1
• Prime numbers are one solid colour and only have one section (e.g., 1, 2, 3, 5, 7, 11, 13, 17, 19)
• Composite numbers have two or more sections (e.g., 4, 6, 8, 9, 10, etc.)
• Ask students to share the knowledge they already have: Who can share a prime number? Who can share a composite number? What are the factors? How do you know?
• Continue by projecting Appendix B. Work on the first challenge collaboratively.
• Tell students that in the left column, they will identify factors before creating a factor tree, which is used to determine the prime factors of a number greater than one. Emphasize that a factor tree is not complete until the composite numbers are broken down to their prime factors. Remind students that there may be more than one way to get to the answer.
• Ask students: What are the factors of the number 36? What does the factor tree look like? What are the prime factors? Is the number prime or composite? How do you know? What does the factor circle look like?
• Prompt students to start with the number 36. Tell students: 1 × 36 = 36. What are two other numbers that we can multiple together to get a product or total of 36?
• If students are unsure of how to start this process ask them: Two multiped by what number equals 36? When the number 18 is shared draw two lines like the ones in blue above and write 2 at the bottom of one and 18 at the bottom of the other.
• Ask students: Are either of these numbers prime? Why or why not? Students should share that two is a prime number as it can only be divided by one and itself.
• Instruct students to circle the two as it is a prime number.
• Repeat the same instructions until you reach two prime numbers.
• Tell students to write all the prime numbers horizontally which should be circled at the bottom of the box where it says “Prime factors:” with a space left in between each value.
• Continue by asking students: What do these numbers represent? Allow a couple of students to share they ideas before telling students to multiple these four terms together. Students should find that when the prime factors of a number are multiplied together the product is that number.
• Tell students to add multiplication symbols in the spaces they left between the prime factors.
• Proceed by asking students: Is 36 a prime or composite number? Students should share that 36 is a composite number as it has more than two factors.
• Ask students: Since we know the prime factors of the number 36 are 2, 2, 3, and 3, how many sections will our circle have? Students should share that this circle will have four sections as the number 36 has four prime factors.
• Continue by asking: Now that we know our factor circle has four sections what colour will these sections be? Students should share that since two of the prime factors were multiples of two, two of the sections will be orange and since two of the prime factors were multiples of three two of the sections will be green.
• Project Appendix A to allow students to compare their answer to the factor circle provided.
• Advance to the next challenge when it seems appropriate.

Conclusion

• Tell students that they will now select two number in between twenty and sixty to carry out the same procedures they completed for the former challenges.

When students have independently grasped the idea of the challenges section students into group of 4 to determine the factor tree and circle for numbers between 60 and 99.

## Look Fors

• Are students able to differ between factors and multiples?
• Are students able to use mental math multiplication to identify prime factors in prime and composite numbers?
• What language are students using to describe the patterns they notice in the numbers?