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

Warm up Problem: Without doing any calculation, explain why 35 base 7 > 35 base 6. HW pp. 150-151. 35 + 25 = 62 in base ____ 135 + 444 = 601 in base ____ 31 a = 25 b Find different numbers for a and b so this statement is true. HW pp. 166-168. 7c. 76 7d. 70

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

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

  2. HW pp. 150-151 • 35 + 25 = 62 in base ____ • 135 + 444 = 601 in base ____ • 31a = 25b Find different numbers for a and b so this statement is true.

  3. HW pp. 166-168 • 7c. 76 7d. 70 - 48 - 48 38 38 7f. 700 - 482 228

  4. HW pp. 166-168 • 20.

  5. HW pp. 166-168

  6. Number line problems

  7. 4 feet 2 feet Meanings for Multiplication • Repeated addition: 3 • 4 = 4 + 4 + 4 = 12 4 • 3 = 3 + 3 + 3 + 3 = 12 • Area: 4 • 2 =

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

  9. Meanings for Multiplication • Arrays: 3 • 5

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

  11. 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!!

  12. Exploration 3.13 • Use Egyptian Duplation for 14 • 41.

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

  14. Exploration 3.13 • Use Egyptian Duplation for 65 • 17.

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

  16. 4 5 2 8 0 8 1 0 3 2 4 0 1 2 6 0 Exploration 3.13 • Lattice Multiplication--this is used today in certain schools. Kids love this! • 45 • 28

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

  18. 1 3 2 7 Exploration 3.13 • You try Lattice Multiplication for 27 • 13

  19. Exploration 3.13 • Cross Product. • Read this with your partner three times. • Now, do it together. 5 6x 4 8 8 • 6 = 4 tens 8 ones8 • 50 = 40 tens = 4 hundreds40 • 6 = 24 tens = 2 hundreds 4 tens40 • 50 = 20 hundreds = 2 thousands

  20. 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???

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

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

  23. 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.

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