Standards:

4.OA.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.

Objectives:

Math Objective: Using Cuisenaire rods, I can demonstrate finding factors and can label a number as a prime or composite.

Language Objective: I can use mathematical language to discuss the discovery of factors and what they mean.

Vertical Alignment:

3.OA.7 Fluently multiply and divide.

4.OA.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.

Not addressed again until 6th grade.

Common Misconception:

Many students overlook that the number itself and 1 are factors for any given number.

Lesson Outline:

🚀Launch:

Students will explain their thinking in the following problem:

5.1 explore 1.PNG

After students have attempted the question, choose several ideas from students and discuss them as a class. Work as a class to model the problem as you do the 🤔Explore section.

🤔Explore A1

Remote: Students will watch the video below, explaining what Cuisenaire rods are. HERE is a link to digital Cuisenaire rods.

They will then answer the following questions:

1. Find the brown rod. How many units it is worth?

2: What rod is half of the brown rod?

3: How did you figure this out?

4: What patterns did you discover?

In Class: This part is best done in class so students can discover by handling the Cuisenaire rods themselves. See Advantage Math for a full explanation of this portion of lesson (#3-5)

🤔Explore A2

This portion would be best done in class. If this is not possible, record yourself or do a video call that explains what factors are and models how to find them finding Cuisenaire rods. (Steps 7-14 of Advantage Math Lesson Outline)

Students are asked to use the following models to think about the pizza problem again. Students should then submit a video explaining if the models helped them revise their thinking or solidify their answer.

5.1 factor rod model with factors-1.PNG 5.1 factor explanation-1.PNG

💬Discuss

Students will look at the following model of the factors of 9 and describe what they think a factor is. This can be used as a good formative assessment before teaching prime and composite numbers.

Factors of 9.PNG

🚀Launch B

Students will make observations about the following models and hopefully notice the difference in the number of factors between 7 and 9.

Factors of 9.PNG Factors of 7.PNG

🤔Explore B

Students will use the following model to answer these questions.

What number and its factors does this model? (6)
What are the factors of 6? (1,2,3,6)
Is the number composite or prime? (Composite)

💬Discuss B

Students will use the Cuisenaire rods to find another prime number.

✅Exit Ticket

Students will do a word problem that uses factors and reflect on how they feel about the concept.

Additional Resources:

Differentiation:

Challenge: For students who need a challenge, invite them to create a model of the factors for any multiple 10–100. This is more difficult because they will have to use combinations of Cuisenaire rods of different values to represent an equal group. See below for an example of the factors of 36:

5.1 factors of 36.PNG

Struggling:

For students who are struggling, consider giving them their own set of Cuisenaire rods so they can copy and contribute to the work that is being done in the small group during the lesson. Students will have more opportunity to have a hands-on experience with the concept if they don't have to share manipulatives.

Teacher Resource #1: Factors and Multiples: Math is Fun.com

Student Resource #1: Factor Game