1. Week 7 What does the distribution property of multiplication mean? That is, what does 19 73 = (16 + 2 + 1) 73 = 16 73 + 2 73 + 1 73 Tell us about multiplication? Write a sentence or two explanation of what distribution means (mathematically) for this example. *Don’t forget to sign in!*

2. Agenda D2L Comment Finish Exploration 3.13 Class Notes Videos Area models Assign homework

3. Link the pictorial models Suppose I want to multiply 3 4.

4. Link the pictorial models Suppose I want to multiply 3 40. This is much harder to draw, but it can be done. Do you see 3 40 = ?

5. Link the pictorial models As the numbers get bigger, it is harder to draw in all the little dots. But the area model will work well: 3 40: 3 40

6. Area Model Let’s look a little closer: Let this be a unit square--that is, a square that measures 1 unit on each side. Then, this is a representation for 7 15. 7 15

7. Area Model Look at this more closely: This is the same as 7 10 + 7 5 7 10 and 7 5 are partial products.

8. Area Model This idea works for more: 32 14 Identify the partial products: 10 + 10 + 10 + 2 10 + 4

9. 32 14 Do you see 4 2? 4 30? 10 2? 10 30? Add the partial products.

10. Area Model You try: 46 23 Use the base 10 blocks or draw a picture. Now, can you explain where these products are in the diagram? 46 23 = (46 20) + (46 3) or = (23 40) + (23 6)

11. Compare models Can you explain how this is related to the lattice multiplication model you did for Exploration 3.13? Can you explain how this area model is related to the standard multiplication algorithm? Can you explain how this area model is related to the four students’ models from the video on Friday?

13. Ryshawn and Nicholas 20 4+ 9 4

14. Jemea 30 12 - 12

15. Thomas 17 36 = ((17 10) 3)+ (6 10) + (6 7)

16. Homework See course webpage for homework. For Wednesday, print off division worksheet and bring to class.