Transcript ppMultpart1
Warm up Problem: Without doing any calculation, explain why 35 base 7 > 35 base 6. 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. Meanings for Multiplication • Repeated addition: 3 • 4 = 4 + 4 + 4 = 12 4 • 3 = 3 + 3 + 3 + 3 = 12 4 feet • Area: 4 • 2 = 2 feet Meanings for Multiplication • Measured Units: 5 times x units long • Cartesian Product: combinations e.g., 3 shirts, 5 pair pants Shirt 1 JBRKC Shirt 2 JBRKC Shirt 3 JBRKC Meanings for Multiplication • Arrays: 3 • 5 Meanings for Multiplication • Rate: 8 miles per hour for 5 hours: 8 • 5 = 40 miles 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!! Exploration 3.13 • Use Egyptian Duplation for 14 • 41. Exploration 3.13 • 14 • 41: 41 82 164 328 656 Now: 14 • 41 = (2 + 4 + 8) • 41 = 82 + 164 + 328 = 574 Exploration 3.13 • Use Egyptian Duplation for 65 • 17. Exploration 3.13 • Do this one with your partner: 65 • 17 65 130 260 520 1040 65 • 17 = 65 • (1 + 16) = 65 + 1040 = 1105 Exploration 3.13 • Lattice Multiplication--this is used today in certain schools. Kids love this! • 45 • 28 4 5 0 8 1 0 2 3 2 4 0 8 1 2 6 0 Exploration 3.13 • With a partner, can you explain what is going on in Lattice Multiplication? • If so, can you explain why it works? Exploration 3.13 • You try Lattice Multiplication for 27 • 13 2 7 1 3 Exploration 3.13 • Cross Product. • Read this with your partner three times. • Now, do it together. 8 • 6 = 4 tens 8 ones 8 • 50 = 40 tens = 4 56 hundreds x 4 8 40 • 6 = 24 tens = 2 hundreds 4 tens 40 • 50 = 20 hundreds = 2 thousands 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??? Homework for Monday • Read Textbook section 3.3 • Do Textbook problems pp. 186-187: 1, 12 • Exploration 3.13 Do #1 and #2 Warm Up • Can you explain what is going on here? 15 • 24 = 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.