Transcript X 12 - Math Garden

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.
• What multiplication sentence could you write
about your rectangle?
• Where in your figure do you see the numbers
in your multiplication sentence?
Tile Activity
Suppose you made this rectangle.
Tile Activity
What multiplication sentence could you write about
your rectangle?
Tile Activity
What multiplication sentence could you write about
your rectangle?
3 x 4 = 12 (for example)
Tile Activity
Where in your figure do you see the numbers in the
math sentence?
3 x 4 = 12
Tile Activity
3 x 4 = 12
3
1
2
3
4
5
6
7
8
9
10
11
12
4
Tile Activity
3
1
2
3
4
5
6
7
8
9
10
11
12
4
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.
Tile Activity
• Can you write a division sentence about your
rectangle?
• Where are the factors and multiples in your
number sentence?
Tile Activity
12 ÷ 3 = 4, for example.
Tile Activity
12 ÷ 3
3
1
2
3
5
6
7
8
9
10
11
12
4
4
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.
Tile Activity
• What other rectangle can you make with 12
tiles?
• What factors and multiples does your new
rectangle illustrate?
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?
Tile Activity
• What are ALL the rectangles you can make
with 12 tiles?
• What are ALL the factors of 12?
Tile Activity
• On another day, do a similar activity with 20
tiles, 24, 30, 36, 48. Try the same activity with
13 tiles.
Factor and Multiple Games Online
1) HoodaMath – Factor Feeder
www.hoodamath.com/games/factorfeeder.html
2) nrich Factors and Multiples Game
www.nrich.maths.org/5468
3) BBC.UK – The Legend of Dick and Dom
www.bbc.co.uk/bitesize/ks2/maths/number/factors
_multiples/play
More Factor and Multiple Games Online
4) Johnnie’s Math Page – Ghost Multiples, Egg
Multiples, and more
www.jmathpage.com/JIMSMultiplicationfactorsand
multiples.html
5) Math Playground - Pumpkin Multiples and more
www.mathplayground.com/multiples.html
6) Count On- Octopus factors
www.counton.org/games/map-numbers/octopus
• How can you help your students build fluency
with factors and multiples?
Distributive Property of Multiplication
over Addition
Let’s begin with some mental math. Solve
these problems and remember what strategy
you used:
8 x 24
3 x 56
9 x 53
Distributive Property of Multiplication
over Addition
Did your strategy incorporate the distributive
property?
8 x 24
3 x 56
9 x 53
Distributive Property of Multiplication
over 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 Parrish
5th grade teacher Lee Ann Davidson
Video 5.2
How did the students break the numbers apart?
Is this the distributive property?
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?
4x3
4x3
(4 x 3) + (4 + 8)
(4 x 3)
+
(4 x 8)
3+8
4(3 + 8)
4(3 + 8)
Modeling with base 10 blocks
Use base 10 blocks to model the following:
3 x 14
What mental math strategy could be represented by
your base 10 blocks?
3 x 14
3 x 14
3 x 14 =
(3 x 10) + (3 x 4)
Now show 7 x 22 with base 10 blocks.
7 x 22
7 x 22 =
7 x 22
7 x 22 = ( 7 x 20 + (7 x 2) = 140 + 14 = 154
Or: 7 x 22
7 x 22 =
7 x 22
7 x 22 =
(7 x 10) + (7x 12) = 70 + 84 = 154
Try 11 x 12
11 x 12
11 x 12
11 x 12
11 x 12 = (10 x 10) + (10 x 1) + (2 x 10) + ( 2 x 1)
= 100 + 10 + 20 + 2 = 132
3 Methods for Multiplying
11
x 12
12
120
132
11
x 12
22
110
132
Which one would you use?
How do the other methods work?
11
x 12
2
20
10
100
132
11 x 12
11
X 12
22
110
132
110 + 22 = 132
11 x 12
11
X 12
22
110
132
110 + 22 = 132
11 x 12
11
X 12
12
120
132
120
+ 12 = 132
11 x 12
11
X 12
12
120
132
120
+ 12 = 132
11 x 12
100 + 10 + 20 + 2 = 132
11
X 12
2
20
10
100
132
11 x 12
100 + 10 + 20 + 2 = 132
11
X 12
2
20
10
100
132
• How can you help your students make sense
of the distributive property of multiplication
over addition?
Using the Distributive Property to Divide
• 84 ÷ 6
• 6 x ? = 84
Using the Distributive Property to Divide
• 84 ÷ 6
• 6 x ? = 84
• 60 + 24 = 84
Using the Distributive Property to Divide
•
•
•
•
•
84 ÷ 6
6 x ? = 84
60 + 24 = 84
60 ÷ 6 = 10
24 ÷ 6 = 4
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
Try this problem!
• 144 ÷ 9
Two strategies for 144 ÷ 9
144 ÷ 9
9 x ? = 144
144 = 72 + 72
72 ÷ 9 = 8
72 ÷ 9 = 8
144 ÷ 9 = 8 + 8 = 16
16
144 ÷ 9
9 x ? = 144
144 = 90 + 54
90 ÷ 9 = 10
54 ÷ 9 = 6
144 ÷ 9 = 10 + 6 =
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_property
Learnzillion – Approaches the distributive property
as a strategy for difficult facts.
www.learnzillion.com/lessons/966-use-thedistributive-property-of-multiplicaion-to-solveunfamiliar-facts