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					                                 Chapter 6
        Division Concepts and Facts
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    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
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    1. Exit this presentation.
    2. Open a chapter presentation using a
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       in editing mode and scroll to the Image
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    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
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