1. Musical Chairs! Change your table groups. One person may remain at each table. The remaining students move to another table—each going to a different new table. All tables should have groups that have no more than one person from a previous group.

2. Homework— Due Monday, 9/24/07 Exploration 3.13 Do #1 b and c, 2 b and c, and 3 b, c, and d. Also, in the Class Notes Packet, do Children’s Thinking Activity 1 (pp. 1-3). Write your answers directly in the packet if you wish

3. Multiplication terms multiplier: 4 multiplicand:3 product:12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

4. Multiplication Models Repeated addition Area Cartesian product a1a1 a2a2 a3a3

5. Units For addition and subtraction 3 hours plus 5 miles For multiplication 8 miles per hour for 5 hours: how many miles? 8 mi 5 hr = 40 mi » hr

6. Exploration 3.13 First, read through the Egyptian Duplation example. Focus on the Hindu-Arabic numerals. With a partner, can you explain what is going on here? With your partner, see if you can do 14 41. Do not use a calculator!!

7. Exploration 3.13 14 41: 41 82 164 328 656 Now: 14 41 = (2 + 4 + 8) 41 = 82 + 164 + 328 = 574

8. Exploration 3.13 Do this one with your partner: 65 17 65 130 260 520 1040 65 17 = 65 (1 + 16) = 65 + 1040 = 1105

9. Exploration 3.13 Lattice Multiplication--this is used today in certain schools. Kids love this! 45 28

10. Exploration 3.13 You try Lattice Multiplication for 27 13

11. Exploration 3.13 Cross Product. Read this with your partner three times. Think of 56 48 as (50 + 6)(40 + 8), and reread the directions. Can you follow it better? In algebra, we learned to multiply binomials: (x + a)(y + b) = xy + xb + ay + ab. (FOIL). Do you see it now???

12. Multiplication Properties Identity Zero Commutative Associative

13. Multiplication Properties continued: Distributive property combines multiplication and addition or subtraction

14. The area model and the standard multiplication algorithm

15. Expanded vs compacted ExpandedCompacted

16. Multiplication-the area model How could Jemea’s strategy be represented using the rectangular area model?

17. 10 + 10 + 10 + 2 10 + 4

18. Does this look familiar?