Download Chapter 3: Multiplication, Part 1

Warm up Problem: Without doing
any calculation, explain why
35 base 7 > 35 base 6.
HW pp. 150-151
• 35 + 25 = 62
• 135 + 444 = 601
in base ____
in base ____
• 31a = 25b
Find different
numbers for a and b so this statement
is true.
HW pp. 166-168
• 7c.
7f.
76
- 48
38
700
- 482
228
7d.
70
- 48
38
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
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.