Download Homework— Due Monday, 9/24/07

Musical Chairs!
• Change your table groups.
• One person may remain at each table.
The remaining students move to another
table—each going to a different new table.
All tables should have groups that have no
more than one person from a previous
group.
Homework—
Due Monday, 9/24/07
Exploration 3.13
Do #1 b and c, 2 b and c, and 3 b, c, and d.
Also, in the Class Notes Packet, do Children’s
Thinking Activity 1 (pp. 1-3).
Write your answers directly in the
packet if you wish
Multiplication terms
4  3  12
multiplier:
multiplicand:
product:
factors:
multiple:
4
3
12
4 and 3 are factors of 12
12 is a multiple of 4
12 is a multiple of 3
Multiplication Models
• Repeated addition
3333
• Area
• Cartesian product
a1
a2
a3
Units
• For addition and subtraction
3 hours plus 5 miles
• For multiplication
8 miles per hour for 5 hours:
how many miles?
8 mi • 5 hr = 40 mi
» hr
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?
• With your partner, see if you can do
14 • 41. Do not use a calculator!!
Exploration 3.13
•
•
•
•
•
•
•
•
14 • 41:
41
82
164
328
656
Now: 14 • 41 = (2 + 4 + 8) • 41 =
82 + 164 + 328 = 574
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
Exploration 3.13
• You try Lattice Multiplication for 27 • 13
Exploration 3.13
• Cross Product.
• Read this with your partner three times.
• 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???
Multiplication
Properties
• Identity
• Zero
• Commutative
• Associative
Multiplication
Properties continued:
Distributive property
combines multiplication and addition or
subtraction
The area model and the standard
multiplication algorithm
Expanded vs compacted
Expanded
Compacted
Multiplication-the area model
• How could Jemea’s strategy be
represented using the rectangular area
model?
10
10
+
4
+
10
+ 10
+
2
Does this look familiar?
53  46  (50  3)( 40  6)
 50  40  50  6  3  40  3  6