Multiplication tables Create a multiplication table in Alphabitia

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 − 29 338 Explain the mistake. • 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 = 12 4 • 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 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 hr = 40 miles

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. 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 You try Lattice Multiplication for 27 • 13 2 7 2 1 3 7 2 6 3 5 7 2 1 1 1 3

Homework for Thursday • Read Textbook section 3. 3 • Do Textbook problems pp. 187 -189: 12, 14, 18, 19 b, d, 21, 42, 50 • Exploration 3. 13 Do #1 and #2