whole number multiplication multiplication is addition of...

8
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 Multiplication The Meaning of Multiplication How many Fish? Repetative Addition 4 3 12 This is multiplication sentence Multiplication is Addition of sets Commutative Property Working with arrays Any multiplication problem is a grid

Upload: others

Post on 04-Aug-2020

12 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 2: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 3: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 4: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 5: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 6: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 7: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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

Page 8: Whole Number Multiplication Multiplication is Addition of setsgkolodiy/3123/notebook/ch4notebook.pdfmultiplication A 3x5=3x(3+2)=3x3+3x2 B 3x2x4=(3x2)x4=6x4=3x(2x4)=3x8 C 3x2=2x3 D

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?