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.