Modelling Division

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LESSON Modelling Division 8 Explore You will need 18 counters. Arrange 18 counters into groups of 6. How many groups are there? Record your work with pictures and numbers. Arrange 15 counters into 3 equal groups. How many counters are in each group? Record your work. Show and Share Share your work with another pair of classmates. How did you find out how many groups? How did you find out how many counters in each group? Connect Janet has 12 pencils. Janet arranges the pencils into groups of 4. How many groups are there? Put 4 pencils in each group. Count how many groups. There are 3 groups of 4. This is division by grouping. 168 LESSON Focus Use grouping and sharing to divide.You write: 12 4 = 3 This is a division sentence. number of number in number of pencils each group groups You say, "12 divided by 4 is 3." Now Janet arranges the pencils into 6 equal groups. How many pencils are in each group? Share the pencils among 6 groups. Count how many pencils are in each group. There are 6 groups of 2. This is division You write: 12 6 = 2 by sharing. number of number of number in pencils groups each group You say, "12 divided by 6 is 2." Practice Use counters when they help. 1. Find the number of groups. Then write a division sentence. The first one is done for you. a) Make groups of 2. b) Make groups of 1. c) Make groups of 4. 5 groups of 2 10 ÷ 2 = 5 1692. Find the number in each group. Then write a division sentence. a) Make 2 equal b) Make 3 equal c) Make 1 group. groups. groups. 3. Kathryn has 24 stickers. She shares them equally among 6 people. How many stickers does each person get? 4. Omar puts 21 stamps in equal groups. 1 He puts more than 1 stamp in each group. 3 What is the greatest number of groups Omar can make? How many stamps would be in each group? How do you know? 5. Write a story problem for each situation. Solve the problem. a) You know the number of groups. You need to find out how many are in each group. b) You know how many are in Numbers Every Day each group. You need to find out Mental Math how many groups. In each pair, which product is greater? How can you tell without multiplying? Reflect or 7 X 2 or Describe two kinds of division problems. 5 X 1 or 4 X 1 Give an example of each kind. 3 X 0 or 5 X 0 170 ASSESSMENT Focus I Question 4LESSON 9 Using Arrays to Divide Explore You will need 16 counters. There are 16 children in the gym. They line up in equal rows. How many children could be in each row? How many different ways can you find? Use counters to model each way. Record each model. Numbers Every Day Show and Share Number Strategies Share your answers with another 30 is: pair of classmates. tens and ones How many different ways could the 1 ten and ones children line up in equal rows? groups of 5 Write a division sentence for each way. ones LESSON Focus I Use arrays to divide. 171Connect There are 8 drum dancers. They will dance onto the stage in equal rows. How many dancers could be in each row? Make an array to show each way. Write a division sentence for each way. 2 rows of 4 4 rows of 2 1 row of 8 8 rows of 1 JJJJ 1 = 8 1 row of 8 dancers 8÷ 2 = 4 2 rows of 4 dancers 4 = 2 4 rows of 2 dancers 8 = 1 8 rows of 1 dancer Practice Use counters when they help. 1. Copy each division sentence. Use the array to complete the sentence. a) 12 ÷ 2 = b) 20 ÷ 4 = 1722. Write a division sentence for each array, a) b) c) 3. Use counters. Make an array for each division sentence. a) 12 ÷ 3 = 4 ÷ c) 25 ÷ 5 = 5 d) 42 ÷ = 4. Copy and complete each division sentence. a) 12 ÷ 4 = b) 21 ÷ 7 = c) 10 ÷ 5 = d) 36 ÷ 6 = 5. The choir sings on stage. a) There are 24 chairs in 6 equal rows. How many chairs are in each row? b) Suppose there are 24 chairs in 4 equal rows. How many chairs are in each row? Draw an array to show each answer. 6. There are 12 drummers and 15 horn players. 3 a) Can they form equal rows of 2? How do you know? b) Can they form equal rows of 3? How do you know? c) What other equal rows can they form? Show your work. 7. Write a story problem that you can solve by drawing an array to divide. Solve your problem. Show your work. Reflect How can you use an array to divide? Use words and pictures to explain. ASSESSMENT Focus I Question 6 173LESSON Dividing by 2, by 5, and by 10 10 Explore ** You will need 31 counters. Thirty children are working on a project. How many children will be in each group if there are: 5 equal groups? 10 equal groups? 2 equal groups? Show your work. Suppose 31 children work on the project. Can they make: 5 equal groups? 10 equal groups? 2 equal groups? How do you know? Show your work. Show and Share Share your work with another pair of classmates. How did you find how many children were in each equal group? How did you know you could not make equal groups with 31 children? 174 LESSON Focus I Identify numbers that can be divided by 2, by 5, or by 10.Connect There are 20 children in Mr. Carlson's class. Can Mr. Carlson make 5 equal groups? 2 equal groups? How many children will be in each group? You can use an array to model the groups. **** **** **** **** Mr. Carlson can make Mr. Carlson can make 5 groups of 4 children. 2 groups of 10 children. 20 can be divided into 20 can be divided into 5 groups of 4. 2 groups of 10. You say 20 is divisible by 5. 20 is divisible by 2. 20 is also divisible by 4. 20 is also divisible by 10. There are 23 children in Miss Dawson's class. Can Miss Dawson make groups of 5? Groups of 10? 23 is 4 groups of 5, 23 is 2 groups of 10, with 3 left over. with 3 left over. 23 is not divisible by 5. 23 is not divisible by 10. Miss Dawson cannot make Miss Dawson cannot make groups of 5. groups of 10. 175Practice 1. Divide. Use the array to help you. a) 8÷ 2 = b) 35 ÷ 5 = c) 50 ÷ 10 = 2. Find each missing number. a) 12 ÷ 2 = b) 5 ÷ 5 = c) 14 ÷ 2 = d) 35 ÷ 5 = e) 30 ÷ 10 = f) 6 ÷ 2 = g) 90 ÷ 10 = h) 20 ÷ 5 = 3. Divide. a) 12 ÷ 2 b) 2 c) 35 ÷ 5 d) 50 ÷ 10 e) 15 ÷ 5 f) 40 ÷ 10 g) 4 ÷ 2 h) 10 ÷ 5 4. Fourteen children work in groups of 2. How many groups are there? 5. Draw an array to show each division. a) 15 ÷ 2 b) 18 ÷ 5 c) 32 ÷ 10 d) 32 ÷ 5 6. Zoe bought 3 baskets of strawberries. Each basket held 10 strawberries. Zoe and 4 friends share the strawberries equally. How many strawberries does each person get? Show your work. Math Link Measurement CANTS To find how many dimes are in divide by 10. To find how many nickels are in divide by 5. 176 ASSESSMENT Focus I Question 6Use a copy of a hundred chart for 1 2 3 4 5 6 7 8 9 10 questions 7 to 9. 11 12 13 14 15 16 17 18 19 20 7. a) Colour blue the numbers 21 22 23 24 25 26 27 28 29 30 that are divisible by 2. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 b) What patterns do you see in 51 52 53 54 55 56 57 58 59 60 the ones digits? 61 62 63 64 65 66 67 68 69 70 c) How can you tell if a number 71 72 73 74 75 76 77 78 79 80 is divisible by 2? 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 8. a) Colour green the numbers that are divisible by 5. b) What patterns do you see in the ones digits? c) How can you tell if a number is divisible by 5? 9. a) Colour yellow the numbers that are divisible by 10. b) What patterns do you see? c) How can you tell if a number is divisible by 10? 10. Copy the Venn diagram below. Sort these numbers: 4, 12, 17, 24, 25, 30, 32, 45, 50 What is true about the numbers where the loops overlap? Divisible by 5 Divisible by 2 Numbers Every Day Number Strategies Reflect 6 Choose a number between 20 and 50. How can you use this result to find How can you tell, by looking, if the number is divisible by 2, 5, or 10? Use pictures and words Use words, pictures, or numbers to explain. to explain. 177LESSON Relating Multiplication 11 and Division Explore X 1 2 3 4 5 6 7 You will need 1-cm grid paper. 1 1 2 3 4 5 6 7 Choose any product from the 2 2 4 6 8 10 12 14 multiplication chart. 3 3 6 9 12 15 18 21 Keep the product secret. 4 4 8 12 16 20 24 28 Use grid paper. 5 5 10 15 20 25 30 35 Draw an array for the product. 6 6 12 18 24 30 36 42 Show the array to your partner. 7 7 14 21 28 35 42 49 Ask your partner to write a multiplication sentence and a division sentence for the array. Trade roles. Continue until each of you has made 5 different arrays. Record your work. Show and Share Show your work to another pair of classmates. How are the multiplication and division sentences for each array related? Connect Kamil used a different multiplication chart. XXXXXXXXXX chose the product 50. XXXXXXXXXX He made this array. XXXXXXXXXX XXXXXXXXXX There are 5 rows of 10. XXXXXXXXXX You can write this multiplication sentence: 5 X 10 = = 50 You can write this division sentence: 50 ÷ ÷ 5 = 10 178 LESSON Focus I Find related multiplication and division facts.You can also turn the array to show 10 rows of 5. There are 10 rows of 5. You can write this multiplication sentence: 10 X 5 = 50 You can write this division sentence: 50 ÷ 10 = 5 These four number sentences are related facts. 5 X 10 = 50 10 X 5 = 50 50 ÷ 10 = 5 50 ÷ 5 = 10 When you know one number fact, you can write related facts. Practice Use counters when they help. 1. Write a multiplication sentence and a division sentence for each picture. Part of the first one is done for you. a) b) 4 X 3 = 12 12 ÷ 3 = c) d) 1792 Use related facts to find each missing number. d) 6 X = 24 c) 7 X 7 = 49 ÷ 7 = 24 ÷ 6 = 42 ÷ 6 = 30 ÷ 6 = 3. Write the related facts for each set of numbers. b) 4,7,28 c) 7,5,35 d) 3,6, 18 a) 3,5, 15 4. Divide. How can you use multiplication facts to help you? a) 9 ÷ 3 b) 15 ÷ 3 c) 28 ÷ 4 d) 4 ÷ 4 e) 30 ÷ 6 f) 12 ÷ 6 g) 14 ÷ 7 h) 42 ÷ 7 5. Concentration ** Game Your teacher will give you a set of cards. Arrange the cards face down on a table. Take turns to choose 2 cards. If the cards represent related facts, keep them. The player with the most cards at the end of the game wins. 6. Mrs. Bowski tries to arrange her class into work groups. When she makes groups of 6 or of 4, she has 1 child left over. Mrs. Bowski has fewer than 30 children in her class. How many children might be in Mrs. Bowski's class? How do you know? Numbers Every Day Number Strategies Order each set of numbers Reflect from least to greatest. 87, 99, 42, 21, 55 Show 3 different ways to find 21 ÷ 7. 91, 26, 30, 80, 72 Use words, numbers, or pictures 47, 20, 53, 68, 63 to explain each way. 42, 18, 85, 57, 36 180 ASSESSMENT Focus I Question 6