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: I can use Cuisenaire rods to discover multiples of one-digit numbers in the range 1-100.

Language Objective: I can describe the patterns seen in multiples of one-digit numbers in the range 1-100.

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.

Common Misconception:

Students easily confuse multiples and factors. Use the alliterations "few factors" and "many multiples" to help students remember which is which.

Lesson Outline:

🚀Launch

Students will think about how to solve the following problem and will then record possible answers.

5.4 launch 1.PNG

Discuss a few of the possible answers. Explain that Cuisenaire rods can be used to model this problem.

Teacher Note: When discussing multiples of a specific number, the first number in the multiplication equation changes to show how many iterations of the second number (which stays constant) are in the equation. Help students understand this by completing the Explore activity.

🤔Explore

Students will answer the following questions about this diagram:

a. How many multiples (groups) of 2 are seen? (zero)

b. Can you write this as a multiplication fact? (0 × 2 = 0)

c. 0 is a multiple of 2.

Questions You Can Ask

Showing students a single 2-unit rod, ask the following questions:

a. How many groups of 2 are seen? (one)

b. Can you write this as a multiplication fact? (1 × 2 = 2)

c. What number is a multiple of 2? (2 is a multiple of 2.)

Teachers should model and explain what multiples are and how to find them. Cuisenaire rods can help students who might need a hands-on, concrete example. Steps 6-10 of Advantage Math can walk you through this discussion.

💬Discuss

Students will use the following diagram to help them solve the word problem.

Modeling this with counters or drawing a picture is preferred if students are in person. Advantage Math steps 12-15 will lead you through this activity. To try this independently, encourage students to find four multiples of 5.

5.4 discuss 2-1.PNG

✅Exit Ticket

Before giving the Exit Ticket, explain to students that there are an infinite number of multiples for any number but a finite number of factors. There is an activity included in Advantage Math that will allow students to discover patterns on a hundreds chart. (There is a hundreds chart included below if you would like to invite students to try it out.) Make sure to read through Advantage Math steps 17-19.

100s Chart.pdf

Additional Resources:

Student Resources:

Math Playground: Pumpkin Multiples Game

Nrich: Factors and Multiples Game

Differentiation:

Challenge: For students who need a challenge, invite them to list as many multiples as possible up to 100 rather than limiting them to five multiples of the given number on the independent practice page, .

Struggling: For students struggling to complete the hundreds chart for each multiple, invite them to work with a competent peer who can give immediate feedback.