Multiplication tables

Create a multiplication table in Alphabitia.

Alphabitia Multiplication Table

Warm-up

Place the digits 1, 2, 3, 6, 7, 8 in the boxes to obtain:

• Greatest sum• Least sum • Greatest difference• Least difference

What makes a good answer?

457 − 29 Explain the mistake.

338• Incomplete answer: He was supposed to cross out the 5 and

make it a 4.

• This does not explain mathematically why it is wrong. It only says what the mechanical mistake was, assuming the standard algorithm.

• Better answer: The student recognized that since he could not take 9 units from 7 units that he needed to get more units for the minuend. However, when the ten was regrouped to give him 10 units for a total of 17 units and leaving 8 units in the difference, he forgot that there are only 4 tens left after regrouping. Four tens and 17 units is the same as 5 tens and 7 units.

Multiplication with blocks.

Use the base 10 blocks to show

43 • 21

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 hr = 40 mileshrmi

Terminology and Notation

5 • 7 = 35

7 multiplicand

× 5 multiplier

35 product

Properties of Multiplication

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 3.1314 • 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 • 1765130260520104065 • 17 = 65 • (1 + 16) = 65 + 1040 = 1105

Exploration 3.13Lattice 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

You try Lattice Multiplication for 27 • 13

1

3

2 7

1

3

2 7

216

72

3 5 1

Homework for Thursday

• Read Textbook section 3.3

• Do Textbook problems

pp. 187-189: 12, 14, 18, 19b,d, 21, 42, 50

• Exploration 3.13

Do #1 and #2