Breakout Session

March 2012Van De Walle and all others

Moving from a strategy to drill

1. Make strategies explicit in the classroom

2. Drill established strategies3. Individualize4. Practice strategy selection

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!

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)

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 1014 – 9

– Count-up --- 9 + 1 makes 10 and 4 more makes 14

– Count-down --- 14 – 4 makes 10 and minus 1 more makes 9

Check for Understanding

Strategies for Multiplication Facts

“Multiplication facts can and should be mastered by

relating new facts to existing knowledge”

Van De Walle, pg. 88

Strategies

•Doubles•Fives Facts•Zeros and Ones•Nifty Nines•Helping Facts

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!

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.

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.)

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?

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?

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.

Reflection1. 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

So What About Division?

24 ÷ 6, 24/6, 24 , 6 24

The symbolism for division:

6

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?

Division Facts An interesting question:

“When students are working on a page of division facts,

are they practicing division or multiplication?”

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!