Warm up Problem: Without doing any calculation, explain why

1

• Warm up Problem Without doing any calculation,
  explain why
• 35 base 7 35 base 6.

2
Musical Chairs!

• Change your table groups.
• One person may remain at each table. The
  remaining students move to another tableeach
  going to a different new table. All tables
  should have groups that have no more than one
  person from a previous group.

3
Meanings for Multiplication

• Repeated addition
• 3 4 4 4 4 12
• 4 3 3 3 3 3 12
• Area 4 2

4
Meanings for Multiplication

• Measured Units 5 times x units long
• Cartesian Product combinations e.g., 3
  shirts, 5 pair pants

5
Meanings for Multiplication

• Arrays 3 5

6
Meanings for Multiplication

• Rate 8 miles per hour for 5 hours
• 8 5 40 miles

7
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!!

8
Exploration 3.13

• Use Egyptian Duplation for 14 41.

9
Exploration 3.13

• 14 41
• 41
• 82
• 164
• 328
• 656
• Now 14 41 (2 4 8) 41
• 82 164 328 574

10
Exploration 3.13

• Use Egyptian Duplation for 65 17.

11
Exploration 3.13

• Do this one with your partner 65 17
• 65
• 130
• 260
• 520
• 1040
• 65 17 65 (1 16) 65 1040 1105

12
Exploration 3.13

• Lattice Multiplication--this is used today in
  certain schools. Kids love this!
• 45 28

13
Exploration 3.13

• With a partner, can you explain what is going on
  in Lattice Multiplication?
• If so, can you explain why it works?

14
Exploration 3.13

• You try Lattice Multiplication for 27 13

15
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
16
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???

17
Homework for Monday

• Read Textbook section 3.3
• Do Textbook problems pp. 186-187 1, 12
• Exploration 3.13
• Do 1 and 2

18
Warm Up

• Can you explain what is going on here?
• 15 24

19
Class Notes--Vidoes

• In general, watch the videos, and try to
  noticea) what is the child doing?b)
  mathematically, what is going on?c)
  mathematically, why is it correct or incorrect.