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Collaborating Teachers. Grades 4-5 October 9, 2013 Factors and Multiples & Distributive Property. Tile Activity. Count out 12 tiles. Arrange them so that they form a rectangle. Tile Activity. Count out 12 tiles. Arrange them so that they form a rectangle. - PowerPoint PPT PresentationTRANSCRIPT
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Collaborating Teachers
Grades 4-5October 9, 2013
Factors and Multiples & Distributive Property
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Tile Activity
• Count out 12 tiles.• Arrange them so that they form a rectangle.
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Tile Activity
• Count out 12 tiles.• Arrange them so that they form a rectangle.
• What multiplication sentence could you write about your rectangle?
• Where in your figure do you see the numbers in your multiplication sentence?
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Tile Activity
Suppose you made this rectangle.
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Tile Activity
What multiplication sentence could you write about your rectangle?
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Tile Activity
What multiplication sentence could you write about your rectangle?
3 x 4 = 12 (for example)
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Tile Activity
Where in your figure do you see the numbers in the math sentence?
3 x 4 = 12
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Tile Activity
3 x 4 = 12
3
4
1 2 3 4
5 6 7 8
9 10 11 12
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Tile Activity
3
4
1 2 3 4
5 6 7 8
9 10 11 12
We say that the numbers 3 and 4 are factors of 12. The number 12 is a multiple of 3 and a multiple of 4.
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Tile Activity
• Can you write a division sentence about your rectangle?
• Where are the factors and multiples in your number sentence?
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Tile Activity
12 ÷ 3 = 4, for example.
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Tile Activity
12 ÷ 3
3
4
1 2 3 4
5 6 7 8
9 10 11 12
We say that the numbers 3 and 4 are factors of 12. The number 12 is a multiple of 3 and a multiple of 4.
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Tile Activity
• What other rectangle can you make with 12 tiles?
• What factors and multiples does your new rectangle illustrate?
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Tile Activity
• Use your 12 tiles make a rectangle with a length of 7.
• Does it work?• Is 7 a factor of 12?• Is 12 a multiple of 7?• What if you try to use your 12 tiles to make a
rectangle with a length of 5? Do you think it will work? Why?
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Tile Activity
• What are ALL the rectangles you can make with 12 tiles?
• What are ALL the factors of 12?
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Tile Activity
• On another day, do a similar activity with 20 tiles, 24, 30, 36, 48. Try the same activity with 13 tiles.
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Factor and Multiple Games Online
1) HoodaMath – Factor Feederwww.hoodamath.com/games/factorfeeder.html
2) nrich Factors and Multiples Gamewww.nrich.maths.org/5468
3) BBC.UK – The Legend of Dick and Domwww.bbc.co.uk/bitesize/ks2/maths/number/factors_multiples/play
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More Factor and Multiple Games Online
4) Johnnie’s Math Page – Ghost Multiples, Egg Multiples, and more
www.jmathpage.com/JIMSMultiplicationfactorsandmultiples.html
5) Math Playground - Pumpkin Multiples and morewww.mathplayground.com/multiples.html
6) Count On- Octopus factorswww.counton.org/games/map-numbers/octopus
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? ? ?
• How can you help your students build fluency with factors and multiples?
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Distributive Property of Multiplication over Addition
Let’s begin with some mental math. Solve these problems and remember what strategy you used:
8 x 243 x 569 x 53
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Distributive Property of Multiplication over Addition
Did your strategy incorporate the distributive property?
8 x 243 x 569 x 53
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Distributive Property of Multiplicationover Addition
Can you apply the distributive property to this problem?
32 x 15
Video 5.2 from Number Talks: Helping Children Build Mental Math and Computation Strategies by Sherry Parrish5th grade teacher Lee Ann Davidson
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Video 5.2
How did the students break the numbers apart?
Is this the distributive property?
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Introducing the Distributive Property Meaningfully
• Using tiles, show how you would model:4 x 3 – Choose one color of tile.4 x 8 – Choose a different color of tile.4 x (3 + 8)
In your representation, how is the four distributed over the three and eight?How could you use these examples to build students’ understanding of the distributive property?
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4 x 3
4 x 3
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(4 x 3) + (4 + 8)
(4 x 3) + (4 x 8)
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3 + 8
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4(3 + 8)
4(3 + 8)
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Modeling with base 10 blocks
Use base 10 blocks to model the following:3 x 14What mental math strategy could be represented by
your base 10 blocks?
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3 x 143 x 14
3 x 14 = (3 x 10) + (3 x 4) Now show 7 x 22 with base 10 blocks.
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7 x 22
7 x 22 =
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7 x 22
7 x 22 = ( 7 x 20 + (7 x 2) = 140 + 14 = 154
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Or: 7 x 22
7 x 22 =
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7 x 22
7 x 22 = (7 x 10) + (7x 12) = 70 + 84 = 154
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Try 11 x 12
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11 x 12
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11 x 12
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11 x 12
11 x 12 = (10 x 10) + (10 x 1) + (2 x 10) + ( 2 x 1)= 100 + 10 + 20 + 2 = 132
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3 Methods for Multiplying
11 11 11x 12 x 12 x 12
12 22 2 120 110 20132 132 10 100
Which one would you use? 132How do the other methods work?
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11 x 12
110 + 22 = 132
11X 12 22 110 132
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11 x 12
110 + 22 = 132
11X 12 22 110 132
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11 x 12
120 + 12 = 132
11X 12 12120132
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11 x 12
120 + 12 = 132
11X 12 12120132
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11 x 12
100 + 10 + 20 + 2 = 132
11X 12 2 20 10 100 132
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11 x 12
100 + 10 + 20 + 2 = 132
11X 12 2 20 10 100 132
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? ? ?
• How can you help your students make sense of the distributive property of multiplication over addition?
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Using the Distributive Property to Divide
• 84 ÷ 6• 6 x ? = 84
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Using the Distributive Property to Divide
• 84 ÷ 6• 6 x ? = 84• 60 + 24 = 84
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Using the Distributive Property to Divide
• 84 ÷ 6• 6 x ? = 84• 60 + 24 = 84• 60 ÷ 6 = 10• 24 ÷ 6 = 4
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Using the Distributive Property to Divide
• 84 ÷ 6• 6 x ? = 84• 60 + 24 = 84• 60 ÷ 6 = 10• 24 ÷ 6 = 4• 84 ÷ 6 = 10 + 4 = 14
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Try this problem!
• 144 ÷ 9
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Two strategies for 144 ÷ 9
144 ÷ 9144 ÷ 9
9 x ? = 144 9 x ? = 144
144 = 72 + 72144 = 90 + 54
72 ÷ 9 = 890 ÷ 9 = 10
72 ÷ 9 = 854 ÷ 9 = 6
144 ÷ 9 = 8 + 8 = 16 144 ÷ 9 = 10 + 6 = 16
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Two online videos
Khan Academy – an explanation of the distributive property with a helpful visual model.
https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_propertyLearnzillion – Approaches the distributive
property as a strategy for difficult facts. www.learnzillion.com
/lessons/966-use-the-distributive-property-of-multiplicaion-to-solve-unfamiliar-facts