1. Multiplication and division
October 22-27

2. 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

3. 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?

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

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

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

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

8. 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?

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

10. Contexts for division
Repeated subtraction/measurement
Partitioning

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

12. 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.

13. 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?

14. 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?