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Find the value of each expression mentally.
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).
| 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 . . . |
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. If a player chooses a starting number that doesn’t have any uncovered factors or multiples, their turn ends and they don't get any points for the round. Students play 10 rounds, or as many rounds as time allows. The player with the higher score wins.
“In today’s lesson, we used the terms factors and multiples to describe numbers within 100.”
Display the following prompts:
“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:
Math Community
After the Cool-down, ask students to individually reflect on the following question: “Which one of the norms did you feel was most important in your work today, and why?” Students can write their responses on the bottom of their Cool-down paper, on a separate sheet of paper, or in a math journal.
Tell students that as their math community works together over the course of the year, the group will continually add to and revise its “Doing Math” and “Norms” actions and expectations.
We used what we learned about factors, multiples, and prime and composite numbers between 1 and 100 to play games and solve problems.
We learned that numbers can share factors and multiples. Example:
Knowing about factors and multiples helped us answer questions such as: