Post on 19-Dec-2015
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.
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
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
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?