1. Making Sense of Algorithms for Multidigit Multiplication and Division Juli K. Dixon, Ph.D. University of Central Florida

2. Making Sense of Multiplication Now Consider 12 x 15

3. Making Sense of Multiplication Mutliply 4 x 27 using strategies based on multiplication rather than division.

4. Making Sense of Multiplication Now Consider 12 x 15 How might you solve this with mental computation?

5. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies

6. Making Sense of Multiplication How might students invent strategies for 12 x 29?

7. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies Base-ten Blocks

8. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies Base-ten Blocks Partial Products

9. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies Base-ten Blocks Partial Products How does it help us prepare for Algebra?

10. “Say, I think I see where we went off. Isn’t eight times seven fifty-six?”

11. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies Base-ten Blocks Partial Products How does it help us prepare for Algebra? Consider (x + 2)(x + 5)

12. Making Sense of Multiplication Now Consider 12 x 15 Solve it with: Invented Strategies Base-ten Blocks Partial Products Traditional Algorithm

13. Define, “demonstrating understanding of the standard algorithm.”

14. The context is important. Consider a “sharing” problem.

15. Making Sense of Division Consider 532 ÷ 14. How can we make sense of this in a measurement context?

16. Making Sense of Division Consider 532 ÷ 14. How can we make sense of this in a measurement context? Repeated subtraction takes too long.

17. Making Sense of Division Consider 532 ÷ 14. How can we make sense of this in a measurement context? Repeated subtraction takes too long. Consider Partial Quotients.

18. Making Sense of Division Consider 532 ÷ 14. How can we make sense of this in a measurement context? Repeated subtraction takes too long. Consider Partial Quotients. But what happens when we get to decimals?