1. Using the methods that you were taught inUsing the methods that you were taught in elementary school, compute the followingelementary school, compute the following on paper.on paper. Using the methods that you were taught inUsing the methods that you were taught in elementary school, compute the followingelementary school, compute the following on paper.on paper. 267133+42267133+42 1. 212 - 45- 45212 2. 216 x 24 =216 x 24 = 3. 846 ÷ 35 = 4.

2. The traditional, rote approach to teaching algorithms fosters beliefs such as the following: mathematics consists mostly of symbols on paper; mathematics consists mostly of symbols on paper; following the rules for manipulating those symbols is of prime importance; following the rules for manipulating those symbols is of prime importance; mathematics is mostly memorization; mathematics is mostly memorization; mathematics problems can be solved in no more than 10 minutes — or else they cannot mathematics problems can be solved in no more than 10 minutes — or else they cannot be solved at all; speed and accuracy are more important in mathematics than understanding; speed and accuracy are more important in mathematics than understanding; there is one right way to solve any problem; there is one right way to solve any problem; different (correct) methods of solution sometimes yield contradictory results; and different (correct) methods of solution sometimes yield contradictory results; and mathematics symbols and rules have little to do with common sense, intuition, or the real world. mathematics symbols and rules have little to do with common sense, intuition, or the real world.

3. Active Learning Fact Families in Arrays. (2-dimensional models) 1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 2 NSN 13 Product is 12. What are the possible arrays?

4. You can teach multiplication facts using arrays to give students a second perspective on these relationships For example – how many different ways can you make 48?

8. Rafi had 12 cookies on a plate. If he ate them 3 at a time, how many times could he go back for cookies? Addition: 3 + 3 + 3 + 3 = 12 Solution: 4 times Subtraction: 12 - 3 - 3 - 3 - 3 = 0 Solution: 4 times Multiplication: 4 (trips) x 3 = 12 Solution: 4 times Division: 12  3 = 4 Solution: 4 times

9. Working With ‘Different’Algorithms: 1.Help children develop a strong understanding of the operations. 2. Develop efficient strategies for fact retrieval. 3. Provide practice in the selection and use of these strategies.

10. What Algorithms do you know and use?

11. Product of 8 x 7 Lattice Method of Multiplication 427 3 8 5 6

12. Repeat for the rest of the lattice Lattice Method of Multiplication 427 3 1 2 0 6 2 1 8 3 2 1 6 5 6

13. Add along the diagonals created by the slanted lines Lattice Method of Multiplication 427 3 1 2 0 6 2 1 8 3 2 1 6 5 6 Carry-Over

14. Egyptian Method

15. Russian-Peasant Method

16. ‘ Carry ’ … 1.Trade 2.Regroup 3.‘ squish ’ ‘ Borrow ’ … 1.Trade 2.Regroup 3.‘ nab ’

17. Math Trick – Multiplication of two-digit numbers

19. Patterns in Arrays …. Number Fact Families x 12345678910 1123456789 22468 1214161820 336912151821242730 4481216202428323640 55101520253035404550 66121824303642485460 77142128354249566370 88162432404856647280 99182736455463728190 10 2030405060708090 100

20. Now expand to a 20 X 20 multiplication array! [Hint: use the patterns] x 1234567891011121314151617181920 112345678910 22468 1214161820 336912151821242730 4481216202428323640 55101520253035404550 66121824303642485460 77142128354249566370 88162432404856647280 99182736455463728190 10 2030405060708090100 11 12 13 14 15 16 17 18 19 20

21. Think Pattern - Multiplication Tables Think Turnarounds 5 x 7 = 7 x 5 Commutative Property Think Distributive Property Follow equality 9 x 14 = 9 x (10 + 4) 9 x 14 = 9 x 10 + 9 x 4

25. X 151025 1410 2832 1812 2772

26. How: 1.Make a set of cards numbered 1-25. 2.Shuffle and deal 5 cards face up. 3.Select a ‘ Target Card ’. 4.Goal: use operations (any order) to have the 5 cards equal the target value. 215178312 =