Warm - up Just-In Power point Just the Facts Guided Practice Developing Story Independent Practice Questions and Answers Math Properties

Just In (warm up) Which problem situation matches the equation below? ( x) = 90 5 A) The weights of four packages are 80 ounces, 95 ounces, 86 ounces, and 100 ounces. Find x, the sum of the weights of the four packages. B) Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on his cell phone. Find x, the average time Juan talked on his phone. C) Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the grade Courtney needs on her fifth quiz to have an average of 90. D) The heights of four trees in a park are 80 feet, 95 feet, 86 feet, and 100 feet. Find x, the average height of the trees.

Just In (warm up key) Which problem situation matches the equation below? ( x) = 90 5 A The weights of four packages are 80 ounces, 95 ounces, 86 ounces, and 100 ounces. Find x, the sum of the weights of the four packages. False, x is the missing weight of the package B Juan talked 80 minutes, 95 minutes, 86 minutes, and 100 minutes on his cell phone. Find x, the average time Juan talked on his phone. False, the average time have already been identified as 90 C Courtney’s first four quiz grades were 80, 95, 86, and 100. Find x, the grade Courtney needs on her fifth quiz to have an average of 90. True, in order to calculate the average, base on five items one number is missing D The heights of four trees in a park are 80 feet, 95 feet, 86 feet, and 100 feet. Find x, the average height of the trees. False, x is the missing value that related o the others numbers not a combine amount of what is already given.

Developing Story Just the Facts Hello Everyone, classrooms across the district are learning about the properties of math. Properties are statements that are true for all numbers. During today’s math lesson, we will explore the characteristics for each property and create a model of its function in order to demonstrate the purpose and action of each. Who can name and elaborate on the math properties?

Commutative The order in which two numbers are added or multiplied does not change the sum or product. Just the facts Associative Property Commutative Property Distributive Property Identity Property Math Properties Travel back and forth to spread out To connect or combine When zero is added to a number, it does not change its sum. When I is multiplied to a factor, it does not affect the product.

Identity Property The identity property of zero. states the number 0 can be added to any real number without changing its value. Workmat Just the facts = 8 (positive integers) a + 0 = a (algebraic notation) (negative integers) = -4 Examples: (decimals) = 2.2 (fractions) 3/4 + 0 = 3/4 a + 0 = a

The multiplicative identity for the set of all real numbers is 1 (one). Any real number can be multiplied by the number 1 without changing its value. Identity Property Just the facts Workmat -8 * 1 = -8 (negative integers) (positive integers) 8 * 1 = 8 (fractions) 2/5 * 1 = 2/5 (decimals) 2.2 * 1 = 2.2 (algebraic notation) a * 1 = a

Commutative Property of Addition No matter he order in which you add two numbers, the sum is always the same. Workmat Just the facts a + b = b + a = Let’s create a model this property. model order a different way a + b = b + a

Commutative Property of Addition a + b Different _ _ _ _ _ b + a workmat model oredr + = 13 +

workmat Commutative Property of Multiplication Just the facts The order in which two numbers are multiplied does not change its product. Let’s use our algebra tiles to model this property. a * b = b * a Order different way Factors will vary

Associative Property of Addition The way in which three numbers are grouped when added or multiplied does not change the sum or product. (a + b) + c = a + (b + c) Just the facts (a*b) * c = c = (b * a) (a * b) * c = c = (b * c) (6 + 3) + 4 = 6 + (3 + 4) (5*3) * 6 = 6 = (3 *5) Associative of Addition Property Associative of Multiplication Property () When you add three numbers together, the sum will be the same no matter how the numbers are grouped. No matter how you group the numbers when you multiply, the answer will always be the same product.

Associative Property of Addition Which expression can be written as (1 + r) + s Just the facts A 1 * + ( r + s ) B 1 * ( r * s ) C 1 + ( r * s ) D 1 + ( r + s ) Justify your response ()

A change in the way multiplied numbers are grouped does not affect the product. a x (b x c)b x (a x c) workmat Associate Property of Multiplication Just the facts Associate- connect or combine. (b*c) * a (9*2) * 6 Show a different group )( a* (b* c) 2* (6* 9)

Distributive Property The Distributive Property allows the choice of multiplication followed by addition or addition followed by multiplication. Just the facts a (b + c) = ab + ac 3 (x+1) and 3x + 3 are equivalent x x x x x x

Distributive Property Write an equivalent expression for 3(x+2) Picture Model using tiles A(B+C) = AB + AC Equivalent Representation 3x + 6 X X X Just the facts 3 * x + 3 * 2

Distributive Property 3(X - 2) Just the facts Try this using your algebra tiles Describe in your own words, the distributive property. Support your description with examples, and draw a model to illustrate the property. x x x

Distributive Property Model using algebra tiles (2+5)3 Jared deposited $5 into his saving account. Six months later, his account balance had doubled. If his balance was b dollars, which of the following would be equivalent to his new balance of 2(b+5) dollars? F 2b + 5 H b + 10 G 2b + 7 J 2b + 10 Just the facts Can you apply your new info and solve this problem ? Let’s try 7 * 3

Developing Story (Guided practice) 1. Which is an example of the Associative Property? A = 8 C = B = 9 + (8+2) D 5 * (12 +3) = 5 * * 3 2. Which property of 3(4+8) = (3*4) + (3*8) an example of? A Associative C Distributive B Commutative D Identity 3. Define in your own words and write an example of each property A Commutative B Identity C Distributive D Associative

Developing Story (Guided practice key) 1. Which is an example of the Associative Property? A = 8 C = B = 9 + (8+2) D 5 * (12 +3) = 5 * * 3 2. Which property of 3 * (4+8) = (3*4) + (3*8) an example of? A Associative C Distributive B Commutative D Identity 3. Define in your own words and write an example of each property: Answers will vary A Commutative- When you add numbers, regardless of the order, the sum is the same = = 12 B Identity - The sum of 0 and any number is the number. The product of 1 and any number is the number. 6+0=6 a+0=a 6*1=6 a*1=a C Distributive- To multiply the sum of two numbers, you can first add, then multiply. Or you can first do each multiplication, then add. 4 x (5+2) or 4 x x 2 4 x 7 D Associative – multiply numbers, regardless of how they are grouped. Example (4 x36)x19 = 4 x(36 x 19)