5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 1. 19, 31, 43, 55,…. 2. 78, 64, 50, 36,…. 3. 3.4, 4.1, 4.8,

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5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 1. 19, 31, 43, 55,…. 2. 78, 64, 50, 36,…. 3. 3.4, 4.1, 4.8, 5.5, …. 4. 3 4 , 1 1 12 , 1 5 12 , 1 3 4 , …

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 1. 19, 31, 43, 55,….

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 1. 19, 31, 43, 55,…. +12 +12 +12 Each term is found by adding 12 to the previous term. The next three terms are 67, 79, 91

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 2. 78, 64, 50, 36,….

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 2. 78, 64, 50, 36,…. -14 -14 -14 Each term is found by adding -14 to the previous term. The next three terms are 22, 8, - 6

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 3. 3.4, 4.1, 4.8, 5.5, ….

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 3. 3.4, 4.1, 4.8, 5.5, …. +.7 +.7 +.7 Each term is found by adding 0.7 to the previous term. The next three terms are 6.2, 6.9, 7.6

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 4. 3 4 , 1 1 12 , 1 5 12 , 1 3 4 , …

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes. 4. 3 4 , 1 1 12 , 1 5 12 , 1 3 4 , … 9 12 , 13 12 , 17 12 , 21 12 , + 4 12 + 4 12 + 4 12 Each term is found by adding 1 3 to the previous term. The next three terms are 2 1 12 , 2 5 12 , 2 3 4 ,

Lesson 7.5.3 Properties of Operations Tuesday, May 12 Lesson 7.5.3 Properties of Operations

Properties of Operations Objective: To identify and use mathematical properties to simplify algebraic expressions.

Properties of Operations A property is a statement that is true for any number.

Properties of Operations Commutative Property (CP) - The order in which two or more numbers are added or multiplied does not change the sum or product. e.g. 9 + 7 = 7 + 9 e.g. 3 · 2 = 2 · 3 a + b = b + a a · b = b · a Notice with CP, the order changes.

Properties of Operations Associative Property (AP) - The way in which three numbers are grouped when they are added or multiplied does not change the sum or product. e.g. 9 + (7+ 5) = (9 + 7) + 5 3 · (2 · 4)= (3 · 2) · 4 a + (b+ c) = (a + b) + c a · (b · c) = (a · b) · c Notice with AP, the order does not change.

Properties of Operations Identity Properties (IP) - The sum of an addend and zero is the addend. The product of a factor and one is the factor. IP of Addition IP of Multiplication e.g. 9 + 0 = 9 3 · 1 = 3 a + 0 = a a · 1 = a

Properties of Operations Name the property shown in the statement. 2 · (5 · n) = (2 · 5) · n

Properties of Operations Name the property shown in the statement. 2 · (5 · n) = (2 · 5) · n Associative Property (notice how the terms are in the same order)

Properties of Operations Name the property shown in the statement. 42 + x + y = 42 + y + x

Properties of Operations Name the property shown in the statement. 42 + x + y = 42 + y + x Commutative Property (notice how the terms are in a different order)

Properties of Operations Name the property shown in the statement. 3x + 0 = 3x

Properties of Operations Name the property shown in the statement. 3x + 0 = 3x Identity Property of Addition

Properties of Operations Name the property shown in the statement. a + (b + 12) = (b + 12) + a

Properties of Operations Name the property shown in the statement. a + (b + 12) = (b + 12) + a Commutative Property

Properties of Operations Name the property shown in the statement. 3m · 0 · 5m = 0

Properties of Operations Name the property shown in the statement. 3m · 0 · 5m = 0 Identity Property of Multiplication

Properties of Operations Name the property shown in the statement. 16 + (c + 17) = (16 + c) + 17

Properties of Operations Name the property shown in the statement. 16 + (c + 17) = (16 + c) + 17 Associative Property

Properties of Operations You may wonder if any of the properties apply to subtraction or division. If you can find a counterexample, an example that shows that a conjecture is false, the property does not apply.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. ? 15 ÷ 3 = 3 ÷ 15 State the conjecture.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. ? 15 ÷ 3 = 3 ÷ 15 State the conjecture. 5 ≠ 1 5 The conjecture is false, since we found a counterexample. Division is not commutative.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. The difference of two different whole numbers is always less than both of the numbers.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. The difference of two different whole numbers is always less than both of the numbers. 8 – 2 = 6 State the conjecture. 6 < 2 The conjecture is false, since we found a counterexample.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative.

Properties of Operations State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative. ? (12 – 5) -3 = 12 – (5 - 3) State the conjecture. 4 ≠ 10 The conjecture is false, since we found a counterexample. Subtraction is not associative.

Properties of Operations Simplify each expression. ( 7 + g ) + 5

Properties of Operations Simplify each expression. ( 7 + g ) + 5 What is the operation?

Properties of Operations Simplify each expression. ( 7 + g ) + 5 We can only add or subtract like terms. Which are the like terms?

Properties of Operations Simplify each expression. ( 7 + g ) + 5 We can only add or subtract like terms. Which are the like terms? 7, 5

Properties of Operations Simplify each expression. ( 7 + g ) + 5 7 + g + 5 12 + g

Properties of Operations Simplify each expression. (m · 11) · m

Properties of Operations Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is 1 · 11 · 1?

Properties of Operations Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is 1 · 11 · 1 = 11

Properties of Operations Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is m · m ?

Properties of Operations Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is m · m = m² What is the product?

Properties of Operations Simplify each expression. (m · 11) · m 11m · m 11m²

Properties of Operations Simplify each expression. 4 · (3c · 2)

Properties of Operations Simplify each expression. 4 · (3c · 2) 4 · 6c 24c

Properties of Operations Simplify each expression. 3x · (x · 7)

Properties of Operations Simplify each expression. 3x · (x · 7) 3x · 7x 21x²

Properties of Operations Simplify each expression. 9c + (3c + 8)

Properties of Operations Simplify each expression. 9c + (3c + 8) 9c + 3c + 8 12c + 8

Properties of Operations Simplify each expression. (5n · 9 ) · 2n

Properties of Operations Simplify each expression. (5n · 9 ) · 2n 45n · 2n 90n²

Properties of Operations Simplify each expression. 15 + (12 + 8a)

Properties of Operations Simplify each expression. 15 + (12 + 8a) 15 + 12 + 8a 27 + 8a

Properties of Operations Simplify each expression. (2 · 4m) · 5m

Properties of Operations Simplify each expression. (2 · 4m) · 5m 8m · 5m 40m²

Properties of Operations Darien ordered a soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the bill.

Properties of Operations Darien ordered a soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the bill. 1.15 + 3.85 = 5 2.75 + 8.50 = 11.25 5 + 11.25 = 16.25

Properties of Operations The times of each leg of a relay race for four runners are shown. Use mental math to find the total time for the relay team.

Properties of Operations The times of each leg of a relay race for four runners are shown. Use mental math to find the total time for the relay team. 11.8 + 11.2 = 23 12.4 + 12.6= 25 23 + 25 = 48

Properties of Operations Agenda Notes No Homework – Homework Practice 7.5.3 Due by the end of the period Circle all answers and show all work Chapter 7.5 Quiz Friday, May 15