# Lesson 7

Find Factors and Multiples

## Warm-up: Number Talk: Division (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat for each expression.

### Student Facing

Find the value of each expression mentally.

• $$12 \div 3$$
• $$30 \div 3$$
• $$60 \div 3$$
• $$72 \div 3$$

### Activity Synthesis

• “How does knowing the first and third quotients help you find the last quotient?” (Since $$12 + 60=72$$ , we can add the answers to those quotients to get the answer to the last problem.)
• “Who can restate _____'s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone approach the expression in a different way?”
• “Does anyone want to add on to_____’s strategy?”

## Activity 1: Factor and Multiple Statements (15 minutes)

### Narrative

The purpose of this activity is for students to find factors and multiples of a given number and make statements that use the terms “factors” and “multiples.” This work prompts students to use language precisely (MP6).

Students can generate many different statements for each number and use the given number in either of the two blanks in the sentence stem. They then share their statements with their partner and explain why their sentences make sense. As they do so, students practice constructing viable arguments and attending to the reasoning of others (MP3).

MLR8 Discussion Supports. Use multi-modal examples to show the meaning of factor and multiple. Invite students to use verbal descriptions along with gestures, drawings, or concrete objects to show factors of 10 and multiples of 10.

### Launch

• Groups of 2
• “We are going to practice using the words ‘factor’ and ‘multiple’ in preparation for a game we’ll play. Take some time to complete the statements on your own.”
• 3–5 minutes: independent work time

### Activity

• “Now share your statements with your partner. Be sure to ask each other questions as you explain your statements.”
• 3–5 minutes: partner discussion

### Student Facing

1. Complete a statement using the word “factor” and a statement using the word “multiple” for each number.
number factor multiple
10

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

7

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

50

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

16

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

number factor multiple
35

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

20

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

19

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

6

____ is a factor of ____ because . . .

____ is a multiple of ____ because . . .

2. As you compare statements with your partner, discuss one thing you notice and one thing you wonder.

### Activity Synthesis

• “What was your favorite statement you came up with? Why was it your favorite?”

## Activity 2: Introduce Find the Number, Factors and Multiples (20 minutes)

### Narrative

The purpose of this activity is for students to practice finding factors and multiples of numbers and using the vocabulary. Students can play multiple rounds of the game as time allows and should be encouraged to use the ideas from the previous activity, if needed. This game is Stage 2 of the center Find the Number. In this stage, students find factors and multiples for a given number. The gameboard is a square grid with the numbers 1–100.

To start, one player chooses an even number less than 50. The other player covers either a factor or multiple of that number. Students take turns covering either a multiple or factor of the previous number. When there are no factors or multiples left to cover, the player who covered the last number gets a point. Students take turns choosing the starting number. Students play 10 rounds, or as many rounds as time allows. The player with the most points wins.

Engagement: Develop Effort and Persistence. Invite students to generate a list of shared expectations and possible language to use during group work, especially when playing a game that has a winner. Encourage students to discuss how they might support their partner’s learning or collaborate to find solutions, even though they are on opposing teams. Record responses on a display and keep visible during the activity.
Supports accessibility for: Language, Social-Emotional Functioning

### Required Materials

Materials to Gather

Materials to Copy

• Find the Number Stage 2 Directions and Gameboard

### Launch

• Groups of 2
• Give each group of 2 students the blackline master and centimeter cubes.
• “We are going to play a game called Find the Number. Take a few minutes to read the directions.”
• 2 minutes: independent work time
• “What questions do you have about the game?”
• If needed, play an example round.

### Activity

• 10–15 minutes: partner game time
• Monitor for students who strategically choose numbers to win the round.

### Activity Synthesis

• “What was your strategy for choosing numbers as you played the game?” (I wanted to keep the round going as long as possible, so I liked choosing numbers that I knew had a lot of factors. I tried to find a number that was prime that I could use so that my partner would have a harder time choosing a number.)

## Lesson Synthesis

### Lesson Synthesis

“In today’s lesson, we used the terms factors and multiples to describe numbers within 100.”

Display the following prompts:

• “How do you know if _____ is a factor of a number?”
• “How do you know if a number is a multiple of ______?”

“With your partner, take turns using each number 1, 2, 5, and 10 to ask and answer the prompts. For example: The first partner asks: ‘How do you know if 2 is a factor of a number?’ and the second partner responds. The second partner then asks: ‘How do you know if a number is a multiple of 2?’ and the first partner responds.”

Share and record responses. Highlight these observations:

• The number 1 is a factor of every number and every number is a multiple of 1.
• The number 2 is a factor of every even number and each even number is a multiple of 2.
• A number is a multiple of 5 when the last digit of the number is 5 or 0.
• The number 10 is a factor of a number when the last digit of the number is 0.
• A number is a multiple of 10 if its last digit is 0.

## Student Section Summary

### Student Facing

In this section, we used what we learned about factors, multiples, and prime and composite numbers between 1–100 to play games and solve problems.

We learned that numbers can share factors and multiples. For example:

• The number 2 is a factor of 6 and and also a factor of 8.
• The number 24 is a multiple 6 and also a multiple of 8.

Knowing about factors and multiples helped us answer questions such as:

• “Can we put 24 chairs in 6 equal rows? What about 7 equal rows or 8 equal rows?”
• “If there are 20 lockers in a row and a student touches every fourth locker, how many lockers would they touch? Which locker numbers would they touch?”