1. Breakout Session March 2012 Van De Walle and all others

2. Moving from a strategy to drill 1.Make strategies explicit in the classroom 2.Drill established strategies 3.Individualize 4.Practice strategy selection

3. Strategies for Addition Facts Facts so far after +0, 1, 2, doubles, and near doubles, +8, +9 +0123456789 00123456789 112345678910 223456789 11 33456789101112 445678910111213 5567891011121314 66789101112131415 778910111213141516 8891011121314151617 99101112131415161718 Only 6 facts left!

4. 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)

5. 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

6. Check for Understanding

7. Strategies for Multiplication Facts “Multiplication facts can and should be mastered by relating new facts to existing knowledge” Van De Walle, pg. 88

8. Strategies Doubles Fives Facts Zeros and Ones Nifty Nines Helping Facts

9. x0123456789 00000000000 10123456789 2024681012141618 30369121518212427 404812162024283236 5051015202530354045 6061218243036424854 7071421283542495663 8081624324048566472 9091827364554637281 After twos, fives, zeros, ones and nines… Only 15 facts left!

10. 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.

11. 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.)

12. 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?

13. 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?

15. Associative Property 7 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.

16. 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

17. So What About Division?

18. 24 ÷ 6, 24/6, 24, 6 24 The symbolism for division: 6

19. 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?

20. Division Facts An interesting question: “When students are working on a page of division facts, are they practicing division or multiplication?”

22. 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!