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Prime Factorization — Guided Notes, Doodle Math, Color by Number, Application
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Overview
Ever wondered how every time you swipe your credit card, buy something online, or tell a secret with a messaging app, your data is protected from hackers?
Prime factorization powers the cryptography that keeps you safe.
Use this artistic, real-life lesson plan to teach your students about prime factorization. Students will learn material with artistic guided notes, practice and check for understanding with doodle math and mazes, and wrap up with the real life application of prime factorization for cryptography.
- Grades: 4th Grade, 5th Grade, 6th Grade
- Topic: Factors, Multiples & Divisibility
- Standards: CCSS 4.OA.B.4, CCSS 6.EE.A.1
- Type: Lesson Plans
Get the Lesson Materials
Prime Factorization — Guided Notes, Doodle Math, Color by Number, Application
$3.99
Learning Objectives
After this lesson, students will be able to:
Differentiate between prime numbers and composite numbers
Use factor trees to decompose a composite number into the products of its prime factors
Represent prime factorization using exponents (i.e. 125 = 5^3)
Describe how prime factorization is used in the real world for cryptography
Prerequisites
Before this lesson, students should be familiar with:
Basic multiplication and division skills
Understanding of the concepts of factors and multiples
Basic understanding of fractions and decimals (optional, but helpful)
Length
1 hour
Materials
Pencils
Colored pencils or markers
Printouts of Prime Factorization 4-in-1 Lesson
Key Vocabulary
Prime factorization
Composite numbers
Prime numbers
Least common denominator
Cryptography
Curriculum Standards
CCSS 4.OA.B.4
Find all factor pairs for a whole number in the range 1-100. 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 one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
CCSS 6.EE.A.1
Write and evaluate numerical expressions involving whole-number exponents.
Exclusions
This lesson plan practices 2 and 3 digit numbers. See extensions for more practice.
Procedures
Hook and Guided Notes
As a hook, ask students how computers keep them safe from hackers when they swipe their credit card or send a message on their phone. It all has to do with prime factorization! Refer to the last page of the guided notes as well as the FAQs below for ideas.
Use the guided notes to introduce the concept of prime numbers, composite numbers, and prime factorization itself. Refer to the FAQ below for a walk through on this, as well as ideas on how to respond to common student questions.
Introduce the steps to factor composite numbers. Then show students how to compute the prime factorization of 120 using a factor tree (120 = 2 x 2 x 2 x 3 x 5).
Lastly, explain how 120 = 2 x 2 x 2 x 3 x 5 can be represented in exponent form as 120 = 2^3 x 3 x 5.
Check for Understanding
Have students work through the problems on the check for understanding page, either collaboratively or independently.
Walk around and spot-check student answers on the check for understanding activity.
Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.
Practice
Have students practice prime factorization using the maze activity. Walk around to answer student questions.
Fast finishers can dive into the Doodle Math activity. You can assign it as homework for the remainder of the class.
Real-World Application
Bring the class back together, and introduce the concept of cryptography.
Have students wrap class by writing down writing down ways they might use prime factorization in everyday life.
And best of all—the materials for the above are included in our Prime Factorization 4-in-1 Lesson. Just print and go for an amazing lesson.
Extensions
Additional practice with up to 4 digit numbers
A fun, no-prep way to practice prime factorization is our Prime Factorization with Exponents Doodle Math activity (sold separately) — it's a fresh take on color by number or color by code. It includes three levels that help students practice finding the factors of 2-, 3- and 4-digit numbers. Each answer unlocks patterns that they can doodle onto an image.
There's also a special Earth Day version of the activity (sold separately), perfect for spring.
FAQs
Prime numbers have two factors only: 1 and itself.
Composite numbers have at least 3 or more factors. They can be divided evenly by at least one integer besides 1 or itself; for instance, 4 can be divided into smaller integers: 8 ÷ 2 = 4, so 4 is not a prime number because it can still be reduced further into smaller numbers.
Prime factorization is the process of expressing a number as a product of its prime factors.
Here's an example of prime factorization: 12 = 2 x 2 x 3.
Prime factorization is also known as prime decomposition or integer factorization.
Cryptography is the practice of secure communication in the presence of third parties. It involves creating mathematical algorithms that can be used to encrypt and decrypt messages, making them unreadable to anyone who does not have the key to unlock them.
Prime factorization is used for finding the least common denominator, solving problems in probability, and powering cryptography:
Finding the least common denominator.
This is necessary when adding or subtracting fractions. Prime factorization can be used to determine a number's prime factors, which can then be used to find the least common denominator.
Solving problems in probability.
Probability problems often require counting the number of ways a certain combination can happen using permutations and combinations. Prime factorization can help determine how many factors a number has, which is crucial in calculating probability.
Powering cryptography.
Cryptography relies on the difficulty of factoring large numbers. This makes it much less likely for someone to come up with their own encryption key based on your data unless they have access to a lot more computing power than you do.
Prime factorization is truly the backbone of our modern society.
Students can compute prime factorization by creating a factor tree. For students that need a visual walk through, I find this Khan Academy video helpful:
Here's the steps to create a factor tree:
First, you'll want to start by writing down your number (the number you want to find the prime factors of) in the center circle and drawing two branches coming off of it.
Then divide your number by one of its factors that you think may be prime—I usually just start with 2 and work my way up—and write down those two numbers at the ends of each branch.
Repeat the process with those numbers until either both endpoints are prime or they break down into another set of numbers whose product equals the original number.
I always circle the prime number at the endpoint so that it's clear when I've stopped.
Here's some examples that you can walk through with your students:
Prime factorization of 24
24 = 2 x 2 x 2 x 3
Prime factorization of 36
36 = 2 x 2 x 3 x 3
Prime factorization of 48
48 = 2 x 2 x 2 x 2 x 3
Prime factorization of 72
72 = 2 x 2 x 2 x 3 x 3
Prime factorization of 100
100 = 2 x 2 x 5 x 5
The prime factorization of a number includes only the prime numbers that are multiplied together to get the original number. Any non-prime factors such as 0, 1, composite numbers are not included in the prime factorization.
Prime factorization is written in the form of prime numbers multiplied together to get the original number. For example, the prime factorization of 24 is 2 × 2 × 2 × 3, and the prime factorization of 100 is 2 × 2 × 5 × 5.
This can be condensed using exponent form, where the prime factorization of 24 can be written as 2³ × 3, and the prime factorization of 100 can be written as 2² × 5². This condensed form is useful for calculations involving large numbers.