Lesson 1 – 1

Problems 1 and 2 What is an algebraic expression for the word phrase? a. 32 more than a number n n + 32 b. 58 less a number n n - 58 c. 8 times a number n 8n d. The quotient of a number n and 5 n ÷ 5

Problem 3 What is an algebraic expression for the word phrase? a. 3 more than twice a number x 3 + 2x b. 9 less than the quotient of 6 and a number x (6/x) – 9 c. The product of 4 and the sum of a number x and 7 4(x + 7)

Problem 4 What word phrase can you use to represent the algebraic expression? a. x The sum of a number x and 8.1. b. 10x + 9 c. n/3 The quotient of a number n and 3 d. 5x – 1

Problem 5 The table below shows how the height above the floor of a house of cards depends on the number of levels. What is the a rule for the height? Give the rule in words and as an algebraic expression. Number of LevelsHeight (in) 2(3.5 ∙ 2) (3.5 ∙ 3) (3.5 ∙ 4) + 24 n?

Got It? 5 Suppose you draw a segment from any one vertex of a regular polygon to the other vertices. A sample for a regular hexagon is shown below. Use the table to find a pattern. What is a rule in words and as an algebraic expression. # of Sides of Polygon # of Triangle 44 – 2 55 – 2 66 – 2 n?

Lesson 1 – 2

Problem 1 What is the simplified from of the expression? a ∙ 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 ∙ 10 = 10,000,000 b. (0.2) ∙ 0.2 ∙ 0.2 ∙ 0.2 ∙ 0.2 = c. (⅚) 3 ⅚ ∙ ⅚ ∙ ⅚= 125/216

Problem 2 What is the simplified form of each expression? a. (6 – 2) 3 ÷ ÷ 2 64 ÷ 2 = 32 b. 2 4 – – = ==

Got it? 2 What is the simplified form of each expression? a. 5 ∙ 7 – 4 2 ÷ 2 b. 12 – 25 ÷ 5 c – 2

Problem 3 What is the value of the expression for x = 5 and y = 2? x 2 + x – 12 ÷ y – 12 ÷ – 12 ÷ – 3 27

Problem 3 What is the value of the expression for x = 5 and y = 2? (xy) 2 (5 ∙ 2) Look at “Got it?” 3c on page 12.

Problem 4 What is an expression for the spending money you have left after depositing 2/5 of your wages in savings? Evaluate the expression for weekly wages of $40, $50, $75, and $100. wages minus 2/5 of wages w – 2/5 ∙ w Wages (w)w – 2/5 wTotal Spending $ $4040 – 2/5(40)24 $5050 – 2/5(50)30 $7575 – 2/5(75)45 $ – 2/5(100)60

Homework Lesson 1-1 #10 – 38 evens Lesson1-2 #10 – 36 evens

Lesson 1 – 3

Principal of Square Roots radical symbol → √ a ← radicand

Problem 1

Problem 2 Estimate √386 by finding the two closest perfect squares = = = 400 √361√386√

Got it? 2 What is the value of √34 to the nearest integer? 5 2 = = 36 √25√34√ √34 is between 5 and 6.

Vocabulary Review Set: collection of objects All of Maroon Five’s CD’s Element of a set: an individual object that is in a set The song “Misery” Subset: a group of elements that are in the set. The album “Hands All Over”

Number Families  Counting Numbers: 1, 2, 3, 4, 5, …  Whole Numbers: 0, 1,2 3, 4, 5,… What’s the difference between the two families?

Review Whole Numbers Both Whole and Counting Counting Numbers

Number Families  Integers: …,-4, -3, -2, -1, 0, 1, 2, 3, 4,…  Rational Numbers: Anything that can be made into a fraction. ½, 5/8, 0.35, -4/-2, 3/1, 0

Review Rational Numbers Both Rational and Integers Integers ½ /

Picture Rational Integers Whole Numbers Counting Numbers

Vocabulary Review Inequalities <Less than >Greater than ≤Less than or equal to ≥Greater than or equal to

Problem 5 and Got it? 5 What is the order of √4, 0.4, -2/3, √2, and -1.5 from least to greatest? -1.5, -2/3, 0.4, √2, √4 What is the order of 3.5, -2.1, √9, -7/2, √5 from least to greatest? -7/2, -2.1, √5, √9, 3.5

Lesson 1 – 4

Properties of Real Numbers PropertyAlgebraExample Commutative Property of Addition and Multiplication a + b = b + a a ∙ b = b ∙ a = ∙ 6 = 6 ∙ 12 Associative Property of Addition and Multiplication (a + b) + c = a + (b + c) (a ∙ b) ∙ c = a ∙ (b ∙ c) (7 + 9) + 4 = 7 + (9 + 4) (5 ∙ 2) ∙ 10 = 5 ∙ (2 ∙ 10) Identity Property of Addition and Multiplication a + 0 = a a ∙ 1 = a = ∙ 1 = 82 Zero Property of Multiplication a ∙ 0 = 0-51 ∙ 0 = 0 Multiplication Property of ∙ a = -a-1 ∙ 9 = ∙ (-4) = 4

Problem 1 What property is illustrated by each statement? a. 42 ∙ 0 = 0 Zero property of Multiplication b. (y + 25) + 28 = y + ( ) Associative Property of Addition c. 10x + 0 = 10x Identity Property of Addition d. 4x ∙ 1 = 4x Identity Property of Multiplication

Problem 2 A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink and popcorn? Use mental math. $ ($ $1.25) $ $11.40 Got it? 2. A can holds 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math.

Problem 3 Simplify each expression. a. 5(3n) (5 ∙ 3)n 15n b. (4 + 7b) + 8 (4 + 8) + 7b b

Counterexample - An example showing that a statement is false. Statement: All students are right handed. Counterexample: Ethan is left handed and is a student.

Problem 4 Is the statement true or false? IF it is false, give a counterexample. a. For all real numbers a and b, a ∙ b = b + a False. 5 ∙ 3 ≠ b. For all real numbers a, b, and c, (a + b) + c = b + (a + c) True.

Homework Lesson 1-3 #12 – 48 multiplies of four Lesson 1-4 #8 – 30 evens

Page 29

Lesson 1 – 5

Lesson Check Use the number line to find each sum (-1) (-3) – (-5) – What is the sum of a number and its opposite? 8. Your friend says that since –a is the opposite of a, the opposite of a number is always negative. Describe and correct the error.

“Always, Sometime, or Never” Turn to page 37. Get with a partner and complete Activity 1, 2 and 3 We will correct this as a class in 15 minutes.

Lesson 1 – 6

Jeopardy Problem 1Problem 2Problem 3Problem 4 8(12)√40048 ÷ 320 ÷ ¼ -7 ∙ 1.1-√ ÷ (-13)9/10 ÷ (-4/5) -(3/7) ∙ (9/10)√(121/16)(63/-21) Find the value of x/y if x = -2/3 and y = -¼ 6(-¼)-√(1/9)-8.1 ÷ 9 Find the value of x/y if x = 2/7 and y = -20/21 (1.2) 2 ±√0.25(-121)/11 Find the value of x/y if x = 3/8 and y = ¾

Homework Lesson 1-5 #10 – 45 multiplies of five Lesson 1-6 #10 – 45 multiplies of five

Lesson 1 – 7

Problem 1 What is the simplest form of each expression? a. 3(x + 8) 3x + 3(8) 3x + 24 b. (5b – 4)(-7) (5b)(-7) – (4)(-7) -35b – (-28) -35b + 28

Got it? 1 a. 5(x + 7) b. 12(3 – ¼ t) c. ( c)3 d. (2y – 1)(-y)

Problem 2 What sum or difference is equivalent to (7x + 2)/5 (1/5)(7x + 2) (1/5)(7x) + (1/5)(2) 7/5x + 2/5

Got it? 2 a (-8) b c. 9 + (-11) d (-2)

Problem 3 What is the simplified form of –(2y – 3x)? a. 2y + 3x b. -2y + (-3x) c. -2y + 3x d. 2y – 3x

Problem 4 Deli sandwiches cost $4.95 each. What is the total cost of 8 sandwiches? Use mental math. 8(4.95) = 8(5 – 0.05) 8(5) - 8(0.05) 40 – $39.60

Constant vs. Coefficient 6a 2 + (-5ab) + 3b + (-12) Coefficient Constant Like Terms, Variables and Like Terms Terms 7a and -3a4x 2 and 12x 2 6ab and -2axy 2 and x 2 y Variable Factors Like Terms? a and a x 2 and x 2 xy 2 and x 2 yab and a yes no

Problem 5 – Combining Like Terms What is the simplified form of each expression? a. 8x 2 + 2x 2 (8 + 2)x 2 10x2 b. 5x – 3 – 3x + 6y + 4 5x – 3x + 6y – x + 6y + 1

Lesson 1 – 8

Problem 1 Is the equation true, false or open? Open sentence: contains one or more variables a = TRUE b. 7 ∙ 8 = 54 FALSE c. 2x – 14 = 54 OPEN

Problem 2 Is x = 6 a solution to the equation 32 = 2x + 12? 32 = 2(6) = ≠ 24 No, 6 is not a solution of the equation.

Problem 4 What is the solution of each equation. Use mental math. a. x + 8 = 12 x = 4; = 12 b. a/8 = 9 a = 72; 72/8 = 9 Got it? What is the solution of 12 – y = 3?

Problem 5 What is the solution of 5n + 8 = 48? Use a table. When n = 8, 5n + 8 = 48, so 8 is the solution. n5n + 8Value of 5n (5) (6) (7) (8) + 848

Problem 6 What is the estimate of the solution of -9x – 5 = 28? Use a table. 28 is between 22 and 31, so the solution is between -3 and -4 x-9x – 5Value of -9x – 5 -9(-1) – (-2) – (-3) – (-4) – 531

Lesson Check 1. Is y = -9 a solution of y + 1 = 8? 2. What is the solution of x – 3 = 12? 3. Give an example of an open ended equation using one variable and division.

Homework Lesson 1-7 #12 – 64 multiplies of eight Lesson 1-8 #8 – 36 multiplies of four

Lesson 1 – 9

Problem 1 Is (3,10) a solution of the equation y = 4x? y = 4x 10 = 4(3) 10 ≠ 12 NO Got it? 1:Is the ordered pair a solution of the equation y = 4x? a. (5,20) b. (-5,-20) c. (-20,-5) d. (1.5,6)

Problem 2 Turn to page 62 and look at Problem 2. Complete the “Got it?” worksheet.

Problem 3 Turn to page 63 and look at Problem 3

Homework Lesson 1-9 #8 – 34 evens

Choose 2 Tasks and create a cross word puzzle from 20 vocabulary words