whole number multiplication multiplication is addition of...
TRANSCRIPT
January 24, 2011
At a certain store eggs can be brought in cartons of one, two, four and eight as shown. Describe the packaging for 5,8,12,15 eggs
In binary what is the base ten value of the binary numbers
1110 1010 1001 1111
In a certain market apple are sold in boxes of 1,3,9,27. What is the packaging for 38 apples.
How would you write thirty nine in base 3?
Whole Number MultiplicationThe Meaning of Multiplication
How many Fish?
Repetative Addition
4 312 This is
multiplicationsentence
Multiplication is Addition of sets
Commutative Property
Working with arrays Any multiplication problem is a grid
January 24, 2011
Teaching the multiplication tableMultiplication by zero
Remove the soccer balls and fill in
N X 0=0
Properties of Multiplication
· Commutative Property
· Distributive Property
· Associative Property
Commutative Property
a x b = b x a
Distributive Property
January 24, 2011
Associative Propertya x (b x c)=(a x b) x ca x (b x c)=(bxc) x a
Multiplication by tens or multiples of ten
Two Digit Multiplication
Build 10 x 10
Build 10 x 11
Build 10 x 12
Build 11 x 12
Build 13 x 12
Build 15 x 16
Two Digit Multiplication
Build 10 x 10
Build 10 x 11
Build 10 x 12
Build 11 x 12
Build 13 x 12
Build 15 x 16
Two Digit Multiplication
Build 10 x 10
Build 10 x 11
Build 10 x 12
Build 11 x 12
Build 13 x 12
Build 15 x 16
Two Digit Multiplication
Start with a flat and add on row and/or column at a time
Build 13 x 12
January 24, 2011
Problem: How Much is 25 X 13?With base 10 blocks; relate to
algorithmWhat multiplication problem is this?What is the answer?
Answer: 22 x 17
What multiplication problem is this?What is the answer?
Answer: 22 x 17 14 140 20 200
1 Which is the correct way of using base ten blocks and the area approach to find the answer to 12 x16
A A
B B
A B
180
January 24, 2011
Expanded Numerals
Step Method
Getting to the Algorithm Getting to the Algorithm
2 Which of the following shows the distributive (commutative, associative) property of multiplication
A 3x5=3x(3+2)=3x3+3x2
B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8
C 3x2=2x3
D# of sets with a # in each set, how many in all
E All of the above
Division of Whole Numbers
If Multiplication is repetative addition then division is?
63
In division total number in all is known and either box on left is unknown
63 7=
Distributive Example
637 ?
Subtractive Example
63? 7
January 24, 2011
Division by Zero 63/0 =?
63
3 Which of the following is an example of the distributive definition of division?
AWe have 5 baskets with 3 balls in each. How many balls in all?
BWe have 20 balls. How many baskets do we need if we want 5 in each basket
CWe have 20 balls and 4 baskets. How many can we put in each basket
D Both b and cE Both a and b
4 Which of the following is an example of the subtractive definition of division?
A
We have 5 baskets with 3 balls in each. How many balls in al
B
We have 20 balls. How many baskets do we need if we want 5 in each baske
C
We have 20 balls and 4 baskets. How many can we put in each basket
D Both b and c
E Both a and b
Long Division
100
10 1
· How many in each group· How many did you use alltogether· How many are left on the board
100
10 1
Distribute the 100’s (10's,1's) & stopLong Division with Base10
372/3
January 24, 2011
Distribute the 100’s & stop· How many in each group· How many did you use alltogether· How many are left on the board
· How many in each group· How many did you use alltogether· How many are left on the board
Distribute the 10’s and stop· How many in each group· How many did you use alltogether· How many are left on the board
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Multiplication and Division on the number line
Example: 5 x 3
20 4
-1 0-2-3-4-5 1 2 3 4 5
January 24, 2011
-1 0-2-3-4-5 1 2 3 4 510 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
· How many in each group· How many did you use alltogether· How many are left on the board
5 How much is 7 divided by zero?
A 7
B 0
C cannot be done
Dcan only be doen on a calculator
E 1
6 Which of the following illustrates 10 divided by zero?
A
We have 10 baskets, no apples in each, how many apples alltogether?
B
We have no apples, in each of 10 baskets. How many apples in all?
C We have no apples
D
We have 10 apples. How many baskets do we need to distribute them if we cannot put any in each basket?
E
We have 10 baskets, how can we distrute zero apples evenly among the 10 baskets?