Identifying Multiples

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Esmond Preston Dennis
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$division, and equivalent fractions.$ Students also need to understand multiples to find least common multiples and greatest common factors.

4 20 Common Core State Standards Talk About It Discuss the Try It! activity. Ask: What is a factor? What is a multiple?

We needed to know if 24 is a multiple of 6. So you arranged 24 Color Tiles into rows of 6. Ask: What did you find out?

Ask: What would it mean if you weren t able to make all the rows full? Have students test whether 16 is a multiple of 6.

Have them write the multiplication sentence and a description of what the sentence means.

Spinner (BLM 13). Have one student spin the spinner to find one factor. Then have the other student pick a total from 10 81.

Have them write the multiplication sentence for the array if the number picked is a multiple of the number spun.

1 4 Objective Identifying Multiples An understanding of multiples is useful to students when they work with multiplication, division, and equivalent fractions. Students also need to understand multiples to find least common multiples and greatest common factors. Using concrete models to build arrays allows students to explore multiples visually and kinesthetically. 4.OA.4 20 Common Core State Standards Talk About It Discuss the Try It! activity. Ask: What is a factor? What is a multiple? Say: In the problem, we wanted to find out if Gian could take exactly 24 fruit cups to the meeting in packs of 6. We needed to know if 24 is a multiple of 6. So you arranged 24 Color Tiles into rows of 6. Ask: What did you find out? Elicit from students that since they were able to arrange the 24 tiles into 4 rows of 6, they know that 24 is a multiple of 6. Ask: What would it mean if you weren t able to make all the rows full? Have students test whether 16 is a multiple of 6. Solve It Reread the problem with students. Have students draw the array that shows 24 as a multiple of 6. Have them write the multiplication sentence and a description of what the sentence means. More Ideas For other ways to teach about identifying multiples Have students work in pairs and make a spinner using 2 9 Number Spinner (BLM 13). Have one student spin the spinner to find one factor. Then have the other student pick a total from Have students use Color Tiles or Two-Color Counters to see if they can make an array based on the numbers. Have them write the multiplication sentence for the array if the number picked is a multiple of the number spun. Have students pick a number of Color Tiles or Two-Color Counters and build as many arrays as they can, using all the tiles or counters. For example, for 24, they should build 1 24, 2 12, 3 8, 4 6, 6 4, 8 3, 12 2, and Have them write the multiplication sentence for each array. Formative Assessment Have students try the following problem. Which array shows that 9 is a multiple of 3? A. B. C. D.

Try It! 15 minutes Pairs Here is a problem about identifying multiples.

Fruit cups come in packs of 6. Can Gian take exactly 24 fruit cups to the meeting using packs of 6?

Distribute Color Tiles, paper, and pencils to students.

Say: Count out 24 Color Tiles for the number of students in the Science Club.

Remember that each pack has 6 cups. Students should begin to make rows of 6 tiles. 2.

How many rows can you make with 24 Color Tiles? Students should make 4 rows of 6 tiles.

2 Try It! 15 minutes Pairs Here is a problem about identifying multiples. Gian wants to take fruit cups for snacks to the Science Club meeting. The Science Club has 24 members. Fruit cups come in packs of 6. Can Gian take exactly 24 fruit cups to the meeting using packs of 6? Introduce the problem. Then have students do the activity to solve the problem. Distribute Color Tiles, paper, and pencils to students. Materials Color Tiles (30 per pair) paper (1 sheet per pair) pencils (1 per pair) 1. Say: Count out 24 Color Tiles for the number of students in the Science Club. Think of how you can make rows to show the packs of fruit cups that Gian will need. Remember that each pack has 6 cups. Students should begin to make rows of 6 tiles. 2. Ask: How many Color Tiles will you put in a row to represent a pack of fruit cups? How many rows can you make with 24 Color Tiles? Students should make 4 rows of 6 tiles. Watch that students make equal rows of 6 tiles. If students have one or two tiles left over, have them check that each row has 6 tiles and that they have a total of 24 tiles. 3. Ask: How many rows of 6 do you have? How many packs of fruit cups will Gian need? Do you have any tiles left over? What multiplication sentence does the model show? 21

3 Lesson 4 Name Answer Key Use Color Tiles. Build the array. Answer the questions. (Check students work.) 1. Is 18 a multiple of 6? yes Why or why not? 18 is a multiple of 6 because there can be 6 rows of 3 or 3 rows of Is 21 a multiple of 5? Why or why not? 21 is not a multiple of 5 because there is one tile left over. no Use Color Tiles. Make as many arrays as possible for the number. Draw your arrays Drawings can include 1 row of 25 and 5 rows of 5. Drawings can include 1 row of 16, 2 rows of 8, 8 rows of 2, and 4 rows of Drawings can include 1 row of 10, 2 rows of 5, 5 rows of 2. Drawings can include 1 row of Download student pages at hand2mind.com/hosstudent.

4 Answer Name Key Challenge! A class of 72 students is going on a field trip. There are vans for boys and vans for girls. The boys vans can each take 7 students, and the girls vans can each take 5 students. One group has 30 students, and the other has 42. Each van will be full. Using what you know about multiples, find which group is the boys and which is the girls. Then tell how many vans each group will need. Explain how you know. How many boys: How many boys vans: How many girls: How many girls vans: Challenge: There are 42 boys in 6 vans, because 42 is a multiple of 7. There are 30 girls in 6 vans because 30 is a multiple of 5. Download student pages at hand2mind.com/hosstudent. 23

5 Lesson 4 Name Use Color Tiles. Build the array. Answer the questions. 1. Is 18 a multiple of 6? Why or why not? 2. Is 21 a multiple of 5? Why or why not? Use Color Tiles. Make as many arrays as possible for the number. Draw your arrays

6 Name Challenge! A class of 72 students is going on a field trip. There are vans for boys and vans for girls. The boys vans can each take 7 students, and the girls vans can each take 5 students. One group has 30 students, and the other has 42. Each van will be full. Using what you know about multiples, find which group is the boys and which is the girls. Then tell how many vans each group will need. Explain how you know. How many boys: How many boys vans: How many girls: How many girls vans: 23

Penny, Nickel, and Dime

9 Objective Penny, Nickel, and Dime With an understanding of the penny and the nickel and the relationship between them, children expand their work with money to include the dime. They perform counting,