1. Warm up Problem: Without doing any calculation, explain why 35 base 7 > 35 base 6.

2. 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.

3. Meanings for Multiplication Repeated addition: 3 4 = 4 + 4 + 4 = 12 4 3 = 3 + 3 + 3 + 3 = 12 Area: 4 2 = 4 feet 2 feet

4. Meanings for Multiplication Measured Units: 5 times x units long Cartesian Product: combinations e.g., 3 shirts, 5 pair pants Shirt 1Shirt 2 Shirt 3 J B R K C J B R K C J B R K C

5. Meanings for Multiplication Arrays: 3 5

6. Meanings for Multiplication Rate: 8 miles per hour for 5 hours: 8 5 = 40 miles

7. 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? If so, can you explain why it works? With your partner, see if you can do 14 41; 65 17; 18 37. Do not use a calculator!!

8. Exploration 3.13 Use Egyptian Duplation for 14 41.

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

10. Exploration 3.13 Use Egyptian Duplation for 65 17.

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

12. Exploration 3.13 Lattice Multiplication--this is used today in certain schools. Kids love this! 45 28 2828 4 5 0 8 1 0 3 2 4 0 1 2 6 0

13. Exploration 3.13 With a partner, can you explain what is going on in Lattice Multiplication? If so, can you explain why it works?

14. Exploration 3.13 You try Lattice Multiplication for 27 13 1313 2 7

15. Exploration 3.13 Cross Product. Read this with your partner three times. Now, do it together. 5 6 x 4 8 8 6 = 4 tens 8 ones 8 50 = 40 tens = 4 hundreds 40 6 = 24 tens = 2 hundreds 4 tens 40 50 = 20 hundreds = 2 thousands

16. Exploration 3.13 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???

17. Homework for Monday Read Textbook section 3.3 Do Textbook problems pp. 186-187: 1, 12 Exploration 3.13 Do #1 and #2

18. Warm Up Can you explain what is going on here? 15 24 =

19. Class Notes--Vidoes In general, watch the videos, and try to notice: a) what is the child doing? b) mathematically, what is going on? c) mathematically, why is it correct or incorrect.