Warm up Problem: Without doing Warm up Problem: Without doing any calculation, explain whyany calculation, explain why
35 base 7 > 35 base 6.35 base 7 > 35 base 6.
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.
HW pp. 166-168• 7c. 76 7d. 70
- 48 - 48
38 38
7f. 700
- 482
228
HW pp. 166-168
• 20.
HW pp. 166-168
• Number line problems
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
Meanings for Multiplication
• Measured Units: 5 times x units long
• Cartesian Product: combinations e.g., 3 shirts, 5 pair pants
Shirt 1 Shirt 2 Shirt 3
J B R K C J B R K C J B R K C
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 82164328656
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
65130260520104065 • 17 = 65 • (1 + 16) = 65 + 1040 = 1105
Exploration 3.13• Lattice Multiplication--this is used today
in certain schools. Kids love this!
• 45 • 28
2
8
4 5
0 8 1 0
3 2 4 0
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
1
3
2 7
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 ones8 • 50 = 40 tens = 4 hundreds40 • 6 = 24 tens = 2 hundreds 4 tens40 • 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.