Multiplication and division October 22-27

Multiplication Within your group develop a strategy for multiplication of integers using manipulatives or drawing pictures. You are not allowed to use the standard algorithm. Apply the strategy to the following problems or explain why it can’t be done: 4  5 10  15 12  15 123  14

Discussion Which properties of multiplication and place value did you use? How does your algorithm relate to the standard algorithm? How will you teach multiplication to kids? Look at the Lattice algorithm. Why does it work? What do you think about it?

Models for multiplication Repeated addition Rectangular array Cartesian product Note: these are also different ways to define multiplication.

Properties of multiplication Closure Commutative Associative Identity How does this relate to addition? How are addition and multiplication related?

Distributive property Use blocks or a picture to explain to a student why 35 x 67 is not equal to 30 x 60 + 5 x 7. Work on “Understanding the Standard Multiplication Algorithm.”

Strategies We will watch videos of children solving multiplication problems. Write down your thoughts in the handout I will provide.

Division Think about how you can use manipulatives to divide. Use base 10 blocks to divide 432 by 3. Look at scaffolding. What do you think about this as a strategy? Work on “Mental Division.” Which properties of multiplication and division are you using?

Defining division Missing factor approach: a/b = c if and only if a = bc.

Contexts for division Repeated subtraction/measurement Partitioning

Properties of division Which properties does division share with multiplication? How is division related to subtraction?

Children’s strategies We will look at some videos of children doing division problems. Jot down your thoughts in the handout that I will provide.

Long division Long division is very complicated. Let us spend some time looking at what is really going on here. For example, let’s say we are dividing 461 by 3. When we say “3 goes into 4 once,” what are we really saying? When we “pull down the 6,” what is going on? Try to use blocks to help you make sense of the algorithm. How do we regroup here?

WASL problems The sum of two whole numbers is 63.  The difference between the numbers is less than 10.  Find as many solutions as you can.     Jeff has less than 30 marbles. When he puts them in piles of 3 he has no marbles left over. When he puts them in piles of 2 he has 1 left. When he puts them in piles of 5 he has 1 left. How many does he have?  Willard Van Winkle (distant cousin of Rip) woke up slowly and looked around. "These things don't exist," he said, "wait a minute. ..." Suddenly a voice said, "No, wait 6,000,000 minutes!" And so it was - Willard had in fact been asleep for 6,000,000 minutes, having fallen asleep on January 1, 1990 at 8 PM. What time did Willard wake up?