Number Properties

Number PropertiesEssential Question: How can you

select the representation that models one of the arithmetic properties (commutative, associative, or distributive)? 

SPI: 0606.1.4) /CC.6EE.3 /CC.6EE.4 / CC.6.EE.2

Investigation

What is the value of this expression?5 + 2 + 4= ?

What is the value of this expression?4 + 5 + 2= ?

Explain why the value you determined is the same for both expressions.

The order in which numbers are added or multiplied does not change the sum or product.

Examples: Numbers: 13 + 6 = 19 10 x 7 = 70

6 + 13 = 19 7 x 10 = 70

Letters: A + B = B + A

Pictures: + = +

Stop and Jot….

How can you prove that order doesn't matter when adding or multiplying?

Check your Understanding:https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-exp-pattern-topic/cc-3rd-grade-properties-patterns/v/order-doesn-t-matter-when-purely-multiplying#

!

Commutative Property

Will the communicative property work for division and subtraction? Prove or disprove it…

Associative Property

The way in which numbers are grouped does not change the sum or product.

Examples: Numbers: (7 + 2) + 9 = 18 (12 x 2) x 4 = 96

7 + (2 + 9) = 18 12 x (2 x 4) = 96

Letters: (A + B) + C = A + (B +C)

Pictures:

( + ) + = + (

+ )

Does the commutative and associative property work for operations involving subtracting and dividing? Explain your reasoning using words and examples.

Check your Understanding: No; Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2

Stop and Jot….Example: Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2Example: Commutative Property (changing order): 6 - 4 = 2 where as 4 – 6 = -2

Distributive Property

Distribute

6 x (10 + 4) = (6 x 10) + (6 x 4)

60 + 24

= 84

Order of Operations

6 x (10 + 4) =

6 x (14)

= 84

To multiply a sum by a number, multiply each addend by the number outside the parentheses

Factoring It Out by Place ValueTo use Mental Math

Examples: Numbers:

54 x 2 = 50 x 2 +4 x 2

100 + 8 108

Distributive Property

Distributive Property

Letter:

Picture: x ( + ) = ( x ) + ( x )

A x (B + C) = (A x B) + (A x C)

How can you use the Distributive Property to multiply mentally?

Check your Understanding:6 ● 99 = ?

6 ● 90 + 6 ● 9 Use the distributive property to break down the problem by place value.

540 + 54

594 OR

6 (100 -1) = 6 (100) – 6 (1) Mental math by breaking down the numbers.

6 (99) = 600 – 6 100 – 1 = 99

594 = 594

Stop and Jot….

Guided Practice Name the property and explain why. 2 x 15 = 15 x 2 4 x (2 + 1) = (4 x 2) + (4 x 1) (3 x 6) x 2 = 3 x (6 x 2)

Fill in the blank. Name the property. 8 + (5 + 3) = (8 + __) + 3 6 x 7 = __ x 6 4 X (7 x __) = (4 x __) x 9 8 x (2 + __) = (8 x __) + ( __ x 4) __ x 15 = __ x 12

Commutative; changing order

Distributive; distributing 4

Associative; changing groups

Associative; 5

Commutative; 7

Associative; 9; 7

Distributive; 4; 2; 8

Commutative; 12; 15

Exit Ticket

Let x, y, and z represent three different numbers. Use them to write equations showing each property.

commutative, associative, and distributive property

Record answers on Exit Ticket

Represent EACH property with a definition, numbers, letters, and pictures (symbols). (commutative, associative, distributive)

EACH property needs its own sheet of paper

Be creative, use graphics, but make sure content is accurate!!!

View grading rubric.

Properties Project

Commutative Property - Changing order……

Letters A + B = B + A

Numbers96 + 14 = 14 + 96

Picture or Symbols

+ = +

Project Example

Don’t use my example!! Be creative and design your

own!!

Additional Resources

Interactive Game: http://ltcconline.net/greenl/java/BasicMath/numberProperties.htm

Number Property Video:http://www.youtube.com/watch?v=7HFRH_M1nAc