6 th Grade Using Properties to Generate Equivalent

Objective • To be able to apply the properties of operations to generate equivalent

Essential Question • How can I use properties to generate equivalent expressions? Copyright ©

Zero Property of Multiplication – the product of 0 and a number is always

Use the Zero Property of multiplication to solve these problems • 8 n =

Vocabulary • Identity property (for addition) – the sum of zero and any number

Solve These • • • 5+0= 0 + (3 + c) = 27 +

Vocabulary Identity property for multiplication – the multiplication of any number and one equals

Use the Identity Property of multiplication to solve these problems • 1 n =

Vocabulary • Commutative property (for multiplication) – the product stays the same when the

In multiplication, you can move the numbers back and forth any way you want

Commutative Property • • • 5 • 4 = 20 10 x 4 =

Solve these problems using the Commutative Property c • 8 • c = ___

Solve these equivalent expressions using the commutative property n=4 • n • 7=7 •

Vocabulary Associative Property – the addition or multiplication of a set of numbers is

Vocabulary Parentheses – the enclosing symbols ( ) which indicate that the terms within

Vocabulary Parentheses – ( ) are also called grouping symbols. (4 • 3) +

Associative Property The Associative Property is like a man and woman getting married. First,

Before marriage they are counted separately. After the marriage they are considered as one.

These numbers are all separate. • 4 • 5 • 9 • 3= •

The numbers with parentheses around them are counted as one number. (4 x 5)

Therefore, the operations inside the parentheses must be done first. • (4 x 5)

The numbers are associated together. Copyright © 2013 by Monica Yuskaitis 24

Associative Property of Multiplication • 5 (4 x 6) = (5 x 4) x

Use the Associative Property to find the missing factor. 5 x 7) x 6

Making Equivalent Expressions • • x + x +x = 4 x add with

Review and copy notes for 1. 3 Copyright © 2013 by Monica Yuskaitis 28

The Distributive Property Copyright © 2013 by Monica Yuskaitis 1. 4 29

When you distribute things you spread them out. Before Copyright © 2013 by Monica

When you distribute things you spread them out. After Copyright © 2013 by Monica

Vocabulary • Distributive Property of Multiplication – When one of the factors of a

Distributive Property • You are spreading the multiplication out over the addition. 6 x

Let’s see how the Distributive Property works First let’s look at regular multiplication. 12

Let’s see how the Distributive Property works 2 x 6 = 12 Let’s break

Let’s see how the Distributive Property works 2 Note! x 6 = 12 (2

You can use the Distributive Property to help with Multiplication Facts you’ve forgotten. 6

You can use the Distributive Property to help with Multiplication Facts you’ve forgotten. 7

Using the Distributive Property Start with Change to 7 x (4 + 5) =

Find the missing number using the Distributive Property • 4 x 9 = •

Find the missing number using the Distributive Property • 5 x 8 = •

Find the missing numbers using the Distributive Property • n x 7 = •

Find the missing numbers using the Distributive Property x • 9= 4 = x

Find the missing numbers using the Distributive Property p • 43 = p •

Find the missing numbers using the Distributive Property 24 n = n(12 + 12

Find the missing numbers using the Distributive Property x(y + z) = xy +

Tip You can use the Distributive Property of Multiplication when you multiply a difference

Problem Solving Copyright © 2013 by Monica Yuskaitis 48 48

The New Floor Copyright © 2013 by Monica Yuskaitis 49

Problem Solving Steps What information do you need? What is the problem asking you

Find the number of one foot tiles needed to cover the kitchen floor that

Let me present you with this bouquet! Copyright © 2013 by Monica Yuskaitis 52

Slides: 52

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Objective • To be able to apply the properties of operations to generate equivalent expressions using: – Zero Property – Identity Property – Commutative Property – Associative Property – Distributive Property Copyright © 2013 by Monica Yuskaitis 2

In multiplication, you can move the numbers back and forth any way you want and still come out with the same answer. This is called the commutative property. 6 x 9 = 54 9 x 6 = 54 6 x 9=9 x 6 Use this commutative property to help you solve problems. Copyright © 2013 by Monica Yuskaitis 12

Solve these equivalent expressions using the commutative property n=4 • n • 7=7 • 4 m=5 • mx 2=2 x 5 z=9 • z • 3=3 • 9 g = 11 • g x 6 = 6 x 11 s = 20 • s • 4 = 4 • 20 c = 32 • c x 8 = 8 x 32 Copyright © 2013 by Monica Yuskaitis 15

Vocabulary Associative Property – the addition or multiplication of a set of numbers is the same no matter how the numbers are grouped. (4 x 3) x 9 = 108 4 x (3 x 9) = 108 Copyright © 2013 by Monica Yuskaitis 16

Associative Property The Associative Property is like a man and woman getting married. First, they are each counted separately, then after they are married they are counted as one, even though they are still separate people. Copyright © 2013 by Monica Yuskaitis 19

Associative Property of Multiplication • 5 (4 x 6) = (5 x 4) x 6 • (7 • 6) • 8 = 7 • (6 • 8) • a • (bc) = (ab) • c The grouping of the factors does not change the product. Copyright © 2013 by Monica Yuskaitis 25

Making Equivalent Expressions • • x + x +x = 4 x add with variables 4 y – 3 y = 1 y subtract with variables 2(3 x) = 6 x multiplying with variables 24 x ÷ 8 = 3 x dividing with variables Copyright © 2013 by Monica Yuskaitis 27

Vocabulary • Distributive Property of Multiplication – When one of the factors of a product is written as a sum, 6 x (4 + 3), multiplying each addend before adding does not change the product (6 x 4) + (6 x 3). 6 x (4 + 3) = 6 x 7 = 42 6 x (4 + 3) = (6 • 4)+(6 • 3) = 24 + 18 = 42 Copyright © 2013 by Monica Yuskaitis 32

Let’s see how the Distributive Property works 2 x 6 = 12 Let’s break the 6 apart this time. 2 x (2 + 4) = Now multiply the 2 times each separate number. (2 x 2) + (2 x 4) = Copyright © 2013 by Monica Yuskaitis 35

Using the Distributive Property Start with Change to 7 x (4 + 5) = (7 x 4) + (7 x 5) = 6 • (7 + 3) = (6 • 7) + (6 • 3) = 5(6 + 2) = (5)(6) + (5)(2) = a x (b + c) = (a x b) + (a x c) = c • (d + f) = (c • d) + (c • f) = x(y + z) = xy + xz = Copyright © 2013 by Monica Yuskaitis 39

Problem Solving Steps What information do you need? What is the problem asking you to find out? Is the answer going to be larger or smaller? What strategies will you use? What operations will you use? How many steps are there and in what order must you do them? Analysis Representation How will you solve the problem? Did you check your answer? Does your answer make sense? Resolution Copyright © 2013 by Monica Yuskaitis 50

Find the number of one foot tiles needed to cover the kitchen floor that measures 8 ft by 23 ft. Use the distributive property to solve the problem. · 8 23 = 8 (20 + 3) ( 8 20) + (8 3) · · 160 + 24 184 sq ft or 1842 ft Copyright © 2013 by Monica Yuskaitis 51