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

Making Sense of Multiplication Now Consider 12 x 15

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

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

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

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

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

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

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?

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

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)

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

Define, “demonstrating understanding of the standard algorithm.”

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

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

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

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.

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?