1. Multiplication tables Create a multiplication table in Alphabitia.

2. Alphabitia Multiplication Table

3. Warm-up Place the digits 1, 2, 3, 6, 7, 8 in the boxes to obtain: Greatest sum Least sum Greatest difference Least difference

4. What makes a good answer? 457 − 29 Explain the mistake. 338 Incomplete answer: He was supposed to cross out the 5 and make it a 4. This does not explain mathematically why it is wrong. It only says what the mechanical mistake was, assuming the standard algorithm. Better answer: The student recognized that since he could not take 9 units from 7 units that he needed to get more units for the minuend. However, when the ten was regrouped to give him 10 units for a total of 17 units and leaving 8 units in the difference, he forgot that there are only 4 tens left after regrouping. Four tens and 17 units is the same as 5 tens and 7 units.

5. Multiplication with blocks. Use the base 10 blocks to show 43 21

6. 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

7. 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

8. Meanings for Multiplication Arrays: 3 5

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

10. Terminology and Notation 5 7 = 35 7multiplicand × 5multiplier 35product

11. Properties of Multiplication

12. 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!!

13. Exploration 3.13 Use Egyptian Duplation for 14 41.

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

15. Exploration 3.13 Use Egyptian Duplation for 65 17.

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

17. 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

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

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

20. Exploration 3.13 You try Lattice Multiplication for 27 13 1313 2 7 1313 2 1 6 72 3 5 1

21. Homework for Thursday Read Textbook section 3.3 Do Textbook problems pp. 187-189: 12, 14, 18, 19b,d, 21, 42, 50 Exploration 3.13 Do #1 and #2