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Chapter 6 Division Concepts and Facts Click the mouse or press the space bar to continue. Division Concepts and Facts 6 Lesson 6-1 Relate Division to Subtraction Lesson 6-2 Relate Multiplication to Division Lesson 6-3 Problem-Solving Strategy: Choose an Operation Lesson 6-4 Divide by 2 Lesson 6-5 Divide by 5 Lesson 6-6 Problem-Solving Investigation: Choose a Strategy Lesson 6-7 Divide by 10 Lesson 6-8 Division Properties 6-1 Relate Division to Subtraction Five-Minute Check (over Chapter 5) Main Idea and Vocabulary California Standards Example 1: Use Models to Divide Example 2: Repeated Subtraction Understand Division 6-1 Relate Division to Subtraction • I will divide using subtraction. • division • divide 6-1 Relate Division to Subtraction Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Preparation for Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-1 Relate Division to Subtraction Colm and his brothers have 24 shirts in their closet. They are sizes small, medium, or large. There is an equal number of each size. How many shirts of each size are there? 6-1 Relate Division to Subtraction Using counters, divide 24 counters equally into 3 groups until all the counters are gone. 8 8 8 There are 8 counters in each group. So, 24 ÷ 3 = 8. Answer: There are 8 shirts of each size. 6-1 Relate Division to Subtraction Corbin and her sisters have 36 sweaters in their drawer. They are yellow, pink, green, red, blue, and purple. There is an equal number of each color. How many sweaters of each color are there? A. 7 sweaters B. 6 sweaters C. 3 sweaters D. 8 sweaters 6-1 Relate Division to Subtraction Coach Green wants to put her 21 softball players into equal groups of 3. How many equal groups can she form? Use repeated subtraction to find 21 ÷ 3. 6-1 Relate Division to Subtraction One Way: Number Line Start at 21. Count back by 3s until you reach 0. How many times did you subtract? 6-1 Relate Division to Subtraction Another Way: Paper and Pencil 21 18 15 12 9 6 3 –3 –3 –3 –3 –3 –3 –3 18 15 12 9 6 3 0 Subtract groups of 3 until you reach 0. How many groups did you subtract? Answer: So, 21 ÷ 3 = 7. Coach Green can form 7 equal groups. 6-1 Relate Division to Subtraction A classroom game requires teams of 4 students. In a class of 24 students, how many teams will there be? A. 6 teams B. 7 teams C. 5 teams D. 8 teams 6-2 Relate Multiplication to Division Five-Minute Check (over Lesson 6-1) Main Idea and Vocabulary California Standards Example 1: Relate Multiplication to Division Example 2: Write a Fact Family Relate Multiplication to Division 6-2 Relate Multiplication to Division • I will divide using related multiplication facts. • dividend • quotient • divisor • fact family 6-2 Relate Multiplication to Division Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-2 Relate Multiplication to Division Use the array of cherries to write related multiplication and division sentences. 6-2 Relate Multiplication to Division One Way: Multiplication number number number of rows in each row in all 2 × 4 = 8 factor factor product 6-2 Relate Multiplication to Division Another Way: Division number number number in in all of rows each row 8 ÷ 2 = 4 dividend divisor quotient 6-2 Relate Multiplication to Division Answer: The related multiplication and division sentences are 2 × 4 = 8 and 8 ÷ 2 = 4. 6-2 Relate Multiplication to Division Use the array of stars to choose related multiplication and division facts. A. 4 ÷ 3 = 1, 3 × 4 = 12 B. 4 × 4 = 16, 3 ÷ 3 = 1 C. 3 × 4 = 12, 12 ÷ 4 = 3 D. 3 × 3 = 9, 9 ÷ 3 = 3 6-2 Relate Multiplication to Division Use the numbers 5, 6, and 30 to write the related multiplication and division sentences for this array. Answer: 5 × 6 = 30 6 × 5 = 30 30 ÷ 5 = 6 30 ÷ 6 = 5 Notice each fact uses the same three numbers. 6-2 Relate Multiplication to Division Use the numbers 6, 9, and 54 to choose the related multiplication and division sentences. A. 6 × 9 = 54, 9 × 6 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9 B. 6 × 6 = 36, 9 × 9 = 81, 54 ÷ 9 = 6, 54 ÷ 6 = 9 C. 54 × 6 = 326, 54 × 9 = 546, 9 ÷ 3 = 3, 6 ÷ 3 = 2 D. 6 × 9 = 54, 6 × 9 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9 6-3 Problem-Solving Strategy: Choose an Operation Five-Minute Check (over Lesson 6-2) Main Idea California Standards Example 1: Problem-Solving Strategy 6-3 Problem-Solving Strategy: Choose an Operation • I will choose an operation to use to solve a problem. 6-3 Problem-Solving Strategy: Choose an Operation Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 6-3 Problem-Solving Strategy: Choose an Operation Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-3 Problem-Solving Strategy: Choose an Operation Lakita’s doctor saw patients for 5 hours today. During this time, the doctor saw 20 patients. How many patients did the doctor see each hour if she saw the same number? 6-3 Problem-Solving Strategy: Choose an Operation Understand What facts do you know? • The doctor saw patients for 5 hours. • She saw 20 patients in all. What do you need to find? • The number of patients the doctor saw each hour. 6-3 Problem-Solving Strategy: Choose an Operation Plan Think about what is happening. You have a group of 20 patients. You want to know how many patients the doctor saw each hour in the 5 hours. You should use division. 6-3 Problem-Solving Strategy: Choose an Operation Solve Divide 20 ÷ 5. total number number of number of of patients hours patients 20 ÷ 5 = 4 Answer: So, the doctor saw 4 patients each hour. 6-3 Problem-Solving Strategy: Choose an Operation Check You can use multiplication to check division. Since 5 × 4 = 20, it makes sense that 4 patients would have been seen each hour. 6-4 Divide by 2 Five-Minute Check (over Lesson 6-3) Main Idea California Standards Example 1: Make Equal Groups 6-4 Divide by 2 • I will divide by 2. 6-4 Divide by 2 Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 6-4 Divide by 2 Arlo and his brother have 18 water toys in their pool. If they share the toys equally, how many will each child get? To share equally between 2 people means to divide by 2. You can write a related fact to find 18 ÷ 2 or 2 18. 2× = 18 6-4 Divide by 2 9 Answer: So, 18 ÷ 2 = 9 or 2 18. Each person will get 9 toys. Check The number line shows that 18 divided into groups of 2 is 9. 6-4 Divide by 2 Tiffany and her cousin have 16 bracelets in the jewelry box. If they share them equally, how many will each child get? A. 9 bracelets B. 7 bracelets C. 8 bracelets D. 6 bracelets 6-5 Divide by 5 Five-Minute Check (over Lesson 6-4) Main Idea California Standards Example 1: Real-World Example Example 2: Real-World Example 6-5 Divide by 5 • I will learn to divide by 5. 6-5 Divide by 5 Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 6-5 Divide by 5 Raul stacked 30 boxes on 5 empty shelves in a storage room. Each shelf had the same number of boxes on it. How many boxes were on each shelf? You need to find 30 ÷ 5. 6-5 Divide by 5 One Way: Use Models There are 30 counters and 5 counters are in each group. There are 6 equal groups. 6-5 Divide by 5 Another Way: Repeat Subtraction 30 25 20 15 10 5 –5 –5 –5 –5 –5 –5 25 20 15 10 5 0 Subtract groups of 5 until you reach 0. Count the number of groups you subtracted. 6-5 Divide by 5 6 Answer: So, 30 ÷ 5 = 6 or 5 30. There are 6 boxes on each shelf. 6-5 Divide by 5 Tim put 32 cans on 4 shelves in a grocery store. Each shelf has the same number of cans on it. How many cans are on each shelf? A. 9 cans B. 6 cans C. 8 cans D. 7 cans 6-5 Divide by 5 Niran has a scrapbook for his baseball cards. He has 25 cards. If 5 cards will fit on a page, how many pages can he fill? Write a related multiplication fact to find 25 ÷ 5. 25 ÷ 5 = 5× = 25 5 × 5 = 25 5 Answer: So, 25 ÷ 5 = 5 or 5 25. Niran can fill 5 pages. 6-5 Divide by 5 Check The model show that 25 ÷ 5 = 5. 25 divided into groups of 5 forms 5 groups. 5 groups of 5 = 25 6-5 Divide by 5 Heather has a photo album for her vacation. She has 63 photos. If 6 photos fit on each page, how many pages can she fill? A. 7 pages B. 8 pages C. 9 pages D. 10 pages 6-6 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 6-5) Main Idea California Standards Example 1: Problem-Solving Investigation 6-6 Problem-Solving Investigation: Choose a Strategy • I will choose the best strategy to solve a problem. 6-6 Problem-Solving Investigation: Choose a Strategy Standard 3MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 6-6 Problem-Solving Investigation: Choose a Strategy Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-6 Problem-Solving Investigation: Choose a Strategy KINAH: I want to plant a vegetable garden. I have 6 tomato plants, 5 pepper plants, and 5 zucchini plants. I want to put the plants into 4 equal rows. YOUR MISSION: Find how many plants should be planted in each row. 6-6 Problem-Solving Investigation: Choose a Strategy Understand What facts do you know? • Kinah has 6 tomato, 5 pepper, and 5 zucchini plants. • She wants to plant them in 4 equal rows. What do you need to find? • Find how many plants to put in each row. 6-6 Problem-Solving Investigation: Choose a Strategy Plan You need to look at how to arrange items. So, the draw a picture strategy is a good choice. 6-6 Problem-Solving Investigation: Choose a Strategy Solve The picture shows 6 + 5 + 5 or 16 plants. There are 4 equal groups of 4 plants. Since 16 ÷ 4 = 4, Kinah needs to plant 4 plants in each row. 6-6 Problem-Solving Investigation: Choose a Strategy Check Look back at the problem. Since 4 × 4 = 16, you know that the answer is correct. 6-7 Divide by 10 Five-Minute Check (over Lesson 6-6) Main Idea California Standards Example 1: Real-World Example 6-7 Divide by 10 • I will learn to divide by 10. 6-7 Divide by 10 Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-7 Divide by 10 Standard 3MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 6-7 Divide by 10 Juanita arranged her 80 football cards into stacks of 10. How many stacks does she have? You need to find 80 ÷ 10. 6-7 Divide by 10 One Way: Use Repeated Subtraction 80 70 60 50 40 30 20 1 – 10 – 10 – 10 – 10 – 10 – 10 – 10 70 60 50 40 30 20 10 0 Subtract groups of 10 until you reach 0. Count the number of groups you subtracted. You subtracted 10 groups eight times. 6-7 Divide by 10 Another Way: Use a Related Fact Write a related multiplication fact to find 80 ÷ 10. You know that 10 × 8 = 80. 8 So, 80 ÷ 10 = 8 or 10 80. Answer: So, Juanita has 8 stacks. 6-7 Divide by 10 George put his 60 bananas into bunches of 10. How many bunches does he have? A. 10 bunches B. 8 bunches C. 6 bunches D. 5 bunches 6-8 Division Properties Five-Minute Check (over Lesson 6-7) Main Idea California Standards Key Concept: Division Properties 6-8 Division Properties • I will learn to use properties about using 1 and 0 in division. 6-8 Division Properties Standard 3NS2.6 Understand the special properties of 0 and 1 in division. Standard 3NS2.3 Use the inverse relationship of multiplication and division to compute and check results. 6-8 Division Properties Division Concepts and Facts 6 Five-Minute Checks Math Tool Chest Image Bank Understand Division Relate Multiplication to Division Division Concepts and Facts 6 To use the images that are on the following four slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation. Division Concepts and Facts 6 Division Concepts and Facts 6 Division Concepts and Facts 6 Division Concepts and Facts 6 Division Concepts and Facts 6 Lesson 6-1 (over Chapter 5) Lesson 6-2 (over Lesson 6-1) Lesson 6-3 (over Lesson 6-2) Lesson 6-4 (over Lesson 6-3) Lesson 6-5 (over Lesson 6-4) Lesson 6-6 (over Lesson 6-5) Lesson 6-7 (over Lesson 6-6) Lesson 6-8 (over Lesson 6-7) Division Concepts and Facts 6 (over Chapter 5) One tricycle has 3 wheels. Two tricycles have 6 wheels. How many wheels will there be on 6 tricycles? A. 16 wheels B. 18 wheels C. 9 wheels D. 12 wheels Division Concepts and Facts 6 (over Lesson 6-1) Divide. Use a number line or paper and pencil. 16 ÷ 8 A. 3 B. 6 C. 2 D. 8 Division Concepts and Facts 6 (over Lesson 6-1) Divide. Use a number line or paper and pencil. 9÷3 A. 3 B. 6 C. 1 D. 9 Division Concepts and Facts 6 (over Lesson 6-1) Divide. Use a number line or paper and pencil. 35 ÷ 7 A. 10 B. 5 C. 7 D. 12 Division Concepts and Facts 6 (over Lesson 6-1) Divide. Use a number line or paper and pencil. 24 ÷ 4 A. 6 B. 7 C. 12 D. 14 Division Concepts and Facts 6 (over Lesson 6-2) Write the fact family for the following set of numbers: 3, 8, 24. A. 8 × 3 = 24, 3 × 8 = 24, 24 ÷ 8 = 3, 24 ÷ 3 = 8 B. 8 × 3 = 24, 8 × 4 = 32, 24 ÷ 3 = 8, 32 ÷ 4 = 8 C. 24 × 3 = 8, 24 × 8 = 3, 8 ÷ 3 = 24, 3 ÷ 8 = 24 D. 8 + 3 = 11, 3 + 8 = 11, 11 – 8 = 3, 11 – 3 = 8 Division Concepts and Facts 6 (over Lesson 6-2) Write the fact family for the following set of numbers: 1, 5, 5. A. 5 × 1 = 5, 1 × 5 = 5, 5 ÷ 5 = 1, 1 ÷ 5 = 5 B. 5 × 1 = 5, 5 × 5 = 25, 5 ÷ 1 = 5, 25 ÷ 5 = 5 C. 1 × 5 = 5, 5 × 1 = 5, 5 ÷ 1 = 5, 5 ÷ 5 = 1 D. 5 × 1 = 1, 1 × 5 = 5, 5 ÷ 1 = 1, 5 ÷ 5 = 5 Division Concepts and Facts 6 (over Lesson 6-3) Solve. Gracia had 6 daises and 9 roses. How many flowers did Gracia have in all? A. 15 flowers B. 3 flowers C. 13 flowers D. 2 flowers Division Concepts and Facts 6 (over Lesson 6-3) Solve. Brian had 6 pots each with 2 lilacs. How many lilacs did Brian have? A. 10 lilacs B. 12 lilacs C. 9 lilacs D. 4 lilacs Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 18 ÷ 2 A. 9; 2 × 9 = 18 B. 2; 9 × 2 = 18 C. 18; 6 × 3 = 18 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 6÷2 A. 2; 2 × 3 = 6 B. 4; 2 × 4 = 8 C. 3; 2 × 3 = 6 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 12 ÷ 2 A. 6; 2 × 6 = 12 B. 6; 2 × 3 = 6 C. 10; 2 × 10 = 20 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 16 ÷ 2 A. 4; 4 × 4 = 16 B. 8; 2 × 8 = 16 C. 32; 2 × 16 = 32 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 10 ÷ 2 A. 10; 5 × 2 = 10 B. 5; 5 × 3 = 15 C. 5; 2 × 5 = 10 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 8÷2 A. 4; 2 × 4 = 8 B. 6; 2 × 4 = 8 C. 3; 2 × 3 = 6 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 14 ÷ 2 A. 9; 3 × 3 = 13 B. 7; 2 × 7 = 14 C. 12; 4 × 3 = 12 Division Concepts and Facts 6 (over Lesson 6-4) Divide. Write a related multiplication fact. 4÷2 A. 2; 2 × 2 = 4 B. 8; 2 × 4 = 8 C. 6; 3 × 4 = 12 Division Concepts and Facts 6 (over Lesson 6-5) Divide. Write a related multiplication fact. 25 ÷ 5 A. 5; 5 × 5 = 25 B. 10; 6 × 6 = 36 C. 15; 3 × 5 = 15 Division Concepts and Facts 6 (over Lesson 6-5) Divide. Write a related multiplication fact. 50 ÷ 5 A. 25; 5 × 5 = 25 B. 10; 10 × 5 = 50 C. 15; 3 × 5 = 15 Division Concepts and Facts 6 (over Lesson 6-5) Divide. Write a related multiplication fact. 5÷5 A. 10; 2 × 5 = 10 B. 5; 1 × 1 = 1 C. 1; 1 × 5 = 5 Division Concepts and Facts 6 (over Lesson 6-5) Divide. Write a related multiplication fact. 35 ÷ 5 A. 7; 5 × 7 = 35 B. 5; 5 × 6 = 30 C. 12; 3 × 4 = 12 Division Concepts and Facts 6 (over Lesson 6-6) Three men are standing in line. Mr. Smith is 3 inches taller than Mr. Sanchez. Mr. Jones is 2 inches shorter than Mr. Smith. Which man is shortest? A. Mr. Smith B. Mr. Sanchez C. Mr. Jones Division Concepts and Facts 6 (over Lesson 6-7) Divide 70 ÷ 10. A. 7 B. 10 C. 11 D. 70 Division Concepts and Facts 6 (over Lesson 6-7) Divide 30 ÷ 10. A. 10 B. 13 C. 3 D. 11 Division Concepts and Facts 6 (over Lesson 6-7) Divide 50 ÷ 10. A. 5 B. 10 C. 15 D. 20 Division Concepts and Facts 6 (over Lesson 6-7) Divide 20 ÷ 10. A. 2 B. 10 C. 15 D. 20 Division Concepts and Facts 6 (over Lesson 6-7) Divide 90 ÷ 10. A. 9 B. 15 C. 90 D. 100 Division Concepts and Facts 6 (over Lesson 6-7) Divide 100 ÷ 10. A. 1 B. 100 C. 0 D. 10 This slide is intentionally blank.

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