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Breakout Session
March 2012
Van De Walle and all others
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Moving from a strategy to drill
1. Make strategies explicit in the classroom
2. Drill established strategies
3. Individualize
4. Practice strategy selection
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Strategies for Addition FactsFacts so far after +0, 1, 2, doubles, and
near doubles, +8, +9+ 0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9 10
2 2 3 4 5 6 7 8 9 10 11
3 3 4 5 6 7 8 9 10 11 12
4 4 5 6 7 8 9 10 11 12 13
5 5 6 7 8 9 10 11 12 13 14
6 6 7 8 9 10 11 12 13 14 15
7 7 8 9 10 11 12 13 14 15 16
8 8 9 10 11 12 13 14 15 16 17
9 9 10 11 12 13 14 15 16 17 18
Only 6 facts left!
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Strategies mentioned in the standards
• counting on****• making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 =
14) • decomposing a number leading to a ten (e.g.,
13 – 4 = 13 – 3 – 1 = 10 – 1 = 9) • using the relationship between addition and
subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4)
• creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)
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Strategies for Subtraction Facts
• Think-Addition– This strategy is most immediately applicable to
facts with sums of 10 or less – 64 subtraction facts fall into that category.
• Work up/down through 10
14 – 9 – Count-up --- 9 + 1 makes 10 and 4 more
makes 14– Count-down --- 14 – 4 makes 10 and
minus 1 more makes 9
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Check for Understanding
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Strategies for Multiplication Facts
“Multiplication facts can and should be mastered by
relating new facts to existing knowledge”
Van De Walle, pg. 88
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Strategies
•Doubles
•Fives Facts
•Zeros and Ones
•Nifty Nines
•Helping Facts
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x 0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9
2 0 2 4 6 8 10 12 14 16 18
3 0 3 6 9 12 15 18 21 24 27
4 0 4 8 12 16 20 24 28 32 36
5 0 5 10 15 20 25 30 35 40 45
6 0 6 12 18 24 30 36 42 48 54
7 0 7 14 21 28 35 42 49 56 63
8 0 8 16 24 32 40 48 56 64 72
9 0 9 18 27 36 45 54 63 72 81
After twos, fives, zeros, ones and nines…
Only 15 facts left!
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The Product Game
• Players choose markers• First player chooses two factors from
the game board and places a paper clip on each. They mark the product with his/her color.
• Player two moves one of the paper clips and forms a new product. Again mark with his/her color.
• Winner is player who has marked four sums in a row, column or diagonal.
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3.OA.5: Apply properties of operations as strategies to multiply and divide. (Note:
Students need not use formal terms for these properties.) (Commutative property of
multiplication.) (Associative property of multiplication.)
(Distributive property.)
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The Commutative Property
Taylor is in charge of making four stars for each of the bulletin boards in the school hallway. If there are five bulletin boards, how many stars will need to be made?
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4 x 5 = 5 x 4
• Is there a difference in the interpretations?
• Is there a way to solve using addition?
What about 8 x 2?
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Associative Property7 x 6 x 5=
• How did you solve? • The associative property allows you
to write the multiplication of three or more whole numbers without using parentheses.
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Reflection
1. How are the following two quotients related?
12 ÷ 3 = 4 and 3 ÷ 12 = 1/4
2. Compare the following relationships.
7 – 4 = 3 and 4 – 7 = -3
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So What About Division?
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24 ÷ 6, 24/6,
24 , 6 24
The symbolism for division:
6
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Understanding Division
Division can be thought of in at least 4 different ways. 24 divided by 6 can mean:
• How many times can 6 be subtracted from 24?
• 24 divided into 6 equal groups.• 24 divided into equal groups of size 6.• What number times 6 gives the
product of 24?
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Division Facts
An interesting question:
“When students are working on a page of division facts,
are they practicing division or multiplication?”
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Division “Near” Facts
Division problems that do NOT come out even are much more prevalent in computations and in real like than division facts or
division without remainders!
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