Pg Algebraic Expressions and the Order of Operations Copyright © 2012 by Reynolds Industries. All rights Reserved

Vocabulary and Key Concepts Define each: Variable- Algebraic Expression- Simplify- Evaluate- Order of operations-

Algebraic Expressions: Give me an example of an Algebraic Expression:

Example 1: Suppose your after-school job pays $8 an hour. You work a different number of hours a week. Define a variable. Write an algebraic expression for your weekly earnings.

Example 2: (Evaluate) Evaluate n – 5 for n = 27.

Part 2: Order of Operations PEMDAS! Work inside grouping symbols. Multiply and divide in order from left to right. Add and subtract in order from left to right.

Example 3: Evaluate n + (13 – n) 5 for n = 8.

Example 4: A fitness club charges $100 activation fee and $33 for each month. Write an expression to model the total cost and then evaluate the expression for 1 to 6 months of membership.

Problem Set Pg 8-9 Exercises #’s 1 – 9, 18 – 26, 31 – 34, and all

Pg Use a problem-solving plan Copyright © 2012 by Reynolds Industries. All rights Reserved

Key Concepts A problem solving plan: Read to understand the problem. Plan how to solve the problem, and then solve it. Look back and check to see if your answer makes sense.

Example 1: An air-traffic controller needs to find the difference between the altitudes of two airplanes. Airplane A is 3,800 ft above the clouds. Airplane B is at an altitude of 5,500 ft above the ground. The clouds are at 12,000 ft altitude. What is the difference in the altitudes of Airplane A and Airplane B.

Example 2: In a local school-committee election, a total of 250 votes were cast for two candidates. Candidate A won the election by 10 votes. How many votes did Candidate A receive?

Problem Set Pg 14 Exercises #’s 1, 2, 4, 6 and 8

Pg Integers and Absolute Values Copyright © 2012 by Reynolds Industries. All rights Reserved

Vocabulary and Key Concepts Opposites- two numbers who are the same distance away from zero. Ex. -5, and 5 Integers- are whole numbers and their opposites. …-3,-2, -1, 0, 1, 2, 3… Absolute Value- is the distance away from zero on a number line. Represented by two bars. |x|

Example 1: Graph the points 5, -4, -2, and 0 on a number line.

Example 2: Find the absolute value. |6||-6|

Example 3: Evaluate each expression for the given value. |a| for a = -2 3|c| for c = -3.5

Example 4: Order from least to greatest. -2, 3, -6, -17

Example 5: (Real world) Which continent has the lowest recorded temperature? Explain.

Problem Set Pg 18 – 20 #’s 2, 8, 16, 18, 24, 26, 40, 44, 46, 54, and 61 – 67

Pg Adding and Subtracting Integers Copyright © 2012 by Reynolds Industries. All rights Reserved

Key Concepts Adding Integers Rules: (Think number line) Same Sign: The sum of the two positive integers is positive. The sum of two negative integers is negative. Adding and keep sign!! Ex or -6 + (-11) = Different Signs: Find the absolute value of each. Subtract the lesser absolute value from the greater. The sum has the sign of the integer with the greater absolute value. Subtract and keep sign from larger absolute value!! Ex = or 8 + (-3) =

Example 1: Add A) 3 + (-5)B) -5 + (-6) C) (-17)D)

Key Concepts Subtracting Integers Rules: To subtract an integer, add its opposites. Ex. 5 – 7 or 5 – (-7)

Example 2: Which content has the lowest recorded temperature? Explain.

Example 3: (Real World) A group of archaeologists leaves a site in Jordan and descends 647 m to the shore of the Dead Sea. Their initial elevation was 251 m above sea level. What is the elevation of the Dead Sea?

Problem Set Pg #’s 2-36 evens, and all

Pg Multiplying and Dividing Integers Copyright © 2012 by Reynolds Industries. All rights Reserved

Key Concepts Multiplying Two Integers: Same Sign: The product of two integers with the same sign is positive Ex or -6(-11) = Different Signs: The product of two integers with different signs is negative. Ex = or 8(-3) =

Key Concepts Dividing Two Integers: (Exact same as multiplication) Same Sign: The quotient of two integers with the same sign is positive Ex. 8/2 or -12/(-6) = Different Signs: The quotient of two integers with different signs is negative. Ex. -10/5 = or 8/(-4) =

Example 1: Simplify. A) 3(-5)B) -55/(-11) C) 32/(-16)D) -168

Example 2: (Real life) A hiker descended 360 feet in 40 minutes. What was the hiker’s average change in elevation per minute?

A little gimmick.

Problem Set Pg #’s 2-30 evens

Pg Using Integers with Mean, Median, and Mode Copyright © 2012 by Reynolds Industries. All rights Reserved

Vocabulary and Key Concepts Measure of Central Tendency- is a single central value that summarizes a set of data. Mean- the average. (the meanest process) Median- is the middle value when list is in numerical order. (middle of the road) Mode- the item that occurs the most. (mode, most) Range- the difference between the greatest and least value. Outlier- a data item that is either much larger or smaller than the rest of the data. (out there!)

Example 1: Find the mean, the median, the mode, and the range of the scores.

Example 2: (Outlier) Find the absolute value. |6||-6|

Example 3: (Best measure) Evaluate each expression for the given value.

Problem Set Pg 36 #’s 2, 7, 14, 16 – 21, and 23(Tricky)

Pg Powers and Exponents Copyright © 2012 by Reynolds Industries. All rights Reserved

Vocabulary and Key Concepts Factor- an integer that divides another integer with a remainder of 0. Exponent- tells how many times a number, or base, is used as a factors. Base- is the number that is being used as factors. Power- is an expression using a base and an exponent. 2 5

Example 1: Write using exponents. a) b) 44xxy

Example 2: Simplify each expression. a) (-5) 4 b) -5 4

Review Order of Operations

Example 3: Simplify. a) 26 – (25) 2 b)

Example 4: Evaluate each expression for x = -2. a) 5x 3 b) (5x) 3

Problem Set Pg 42 #’s 2-40 evens

Pg Properties of Numbers Copyright © 2012 by Reynolds Industries. All rights Reserved

Key Concepts Commutative Properties of Addition and Multiplication (order) ArithmeticAlgebra = a + b = b + a 7·12 = 12·7 a·b = b·a Associative Properties of Addition and Multiplication (grouping) ArithmeticAlgebra (4 + 3) + 7 = 4 + (3 + 7) (a + b) + c = a + (b + c) (4·7)·3 = 4·(7·3) (a·b)·c = a·(b·c)

Key Concepts Identity Properties of Addition and Multiplication ArithmeticAlgebra = = 7 a + 0 = 0 + a = a 8·1 = 1·8 = 8 a·1 = 1·a = a

Example 1: Identify each property. a) 14 + ( ) = 14 + ( ) b) 14 + ( ) = ( ) + 16

Example 2: Use mental math and these properties to simplify. A) B)26 + (-12) + 34 C) -5·7·8D) -4·356·(-25)

Key Concepts Distributive Property ArithmeticAlgebra 3(2 + 7) = 3·2 + 3·7 a(b + c) = ab + ac (2 + 7)3 = 2·3 + 7·3 (b + c)a = ba+ ca 5(8 – 2) = 5·8 – 5·2 a(b – c) = ab – ac (8 – 2)5 = 8·5 – 2·5 (b – c)a = ba – ca

Example 3: Find the product. A)5 ( k – 4)B)(n + 14) (-8)

Example 4: Simplify: A) 27· ·12B)105· 8 – 5·8

Problem Set Pg 49 #’s 2-38 evens