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Chapter 3
Pages: 97 143
Assignments:
Due DateSectionPages#Homework Assignments3-1101 10222+1#12 48 (every other even), #50, #51, #54*, #55, #56 76 (evens)3-2106 10720+1#18 22 (evens), #24 48 (every other even), #50, #52, #54, #57*, #58, #59, #60, #62, #66, #68, #723-3113 11421+3#12 32 (every other even), #34 44 (evens), #48*, #50*, #51*, #52 56 (evens), #58 60 (all), #62 66 (evens)3-4118 11921+3#12 34 (every other even), #36 46 (evens), #48*, #49*, #51*, #52 68 (evens)3-5123 12430+2#14 48 (evens), #51*, #52*, #53, #54 74 (evens)3-6129 13017+0#8 22 (evens), #28, #29, #30 42 (evens)3-7134 13619+1#10 30 (evens), #33, #38, #40, #44*, #45, #46 52 (evens)141Practice Test
Prerequisite Knowledge:
Basic operations with whole numbers, decimals, and fractions with common denominators
Estimating and rounding
Evaluating, simplifying, and solving numeric and algebraic expressions and equations
Prerequisite Skills:
Using a calculator
Study Guide:
Getting Started (pg 97)
Algebra Tiles Activity (pg 108 109; section 3-2)
Practice Quiz #1 (pg 107)
Translating Verbal Problems into Equations (pg 125; section 3-6)
Practice Quiz #2 (pg 130)
Perimeter & Area Activity (pg 137; section 3-7)
Section 3-1
Objectives:
Use the Distributive Property to write equivalent numerical and algebraic expressions
Use the Distributive Property to make multiplying numbers easier
Vocabulary:
Equivalent Expressions expressions that are equal or have the same value (e.g. 3 + 2 + 1 = 1 + 2 + 3)
Concepts:
The Distributive Property states that to multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses (i.e. a(b + c) = (b + c)a = ab + ac; e.g. 3(4 + 2) = 3 4 + 3 2 = 12 + 6 = 18)
The Distributive Property can also be modeled with rectangles, as shown below.
Method 1: Separate the boxes. Multiply the length by the width for each rectangle to find each area. Then add the two areas together.
Method 2: Put the boxes together. Multiply the width by the sum of the lengths.
Examples:
Use the Distributive Property to write an equivalent expression. Evaluate if possible.
4(5 + 8) =
(6 + 9)2 =
2(x + 4) =
(y + 3)6 =
4(x 2) =
-2(n 3) =
Rewrite each product so it is easy to compute mentally. Then find the answer.
8 14 =
7 22 =
16 12 =
North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person, and wet suit rentals cost $15 each. If a family of four goes on a rafting trip and each family member rents a wet suit, write an expression in Distributive Property form to represent the cost of the trip, and use that expression to find the total cost of the trip.
Classwork:
Check for Understanding (pg 100) #2 #8 evens, #10 and #11
Section 3-2
Objectives:
Use the Distributive Property to simplify algebraic expressions
Vocabulary:
Term each part of an algebraic expression when the parts are separated by plus or minus signs (e.g. in 3x 6y + 1 + x 2y, 3x, -6y, 1, x, and -2y are terms)
Coefficient the number in front of a variable (e.g. in 3x, 3 is the coefficient; in xy, 1 is the coefficient)
Constant a number by itself (without a variable next to it)
Like Terms terms that contain the same combination of variables but may have different coefficients (e.g. in 3x 6y + 1 + x 2y, 3x and x are like terms, and -6y and -2y are like terms)
Simplest Form when an algebraic expression has no parentheses or like terms
Simplify to get an algebraic expression into simplest form; this may include using distributive property to get rid of parentheses or combining like terms
Concepts:
If there is a variable in an expression and it doesnt have a number in front of it, the coefficient of that variable is 1.
If a minus sign is used to separate terms, use the double-dash rule to make it an addition sign.
Examples:
Identify terms, like terms, coefficients, and constants in the expression below:
4x x + 2y 3 + 4xy + -5y
Simplify each expression:
5x + 4x =
8n + 4 + 4n =
6x + 4 5x 7 =
y + 2(x + 3y) =
2x 2(y + 5x) =
3x + 7(5 x) =
Classwork:
Check for Understanding (pg 105) #3 #15 odds, #16
Section 3-3
Objectives:
Solve equations by using the Addition and Subtraction Properties of Equality
Vocabulary:
Inverse Operations (or Opposite Operations) operations (like add, subtract, multiply, and divide) that undo each other
Equivalent Equations equations that have the same answer or solution (e.g. x + 4 = 7 and x = 3 are equivalent equations because the answer for both is 3)
Concepts:
Addition undoes subtraction and vice versa. Multiplication undoes division and vice versa. These pairs of operations are called inverses.
Subtraction Property of Equality you can subtract the same number from both sides of an equation without changing the solution (i.e. if a = b, then a c = b c)
Addition Property of Equality you can add the same number to both sides of an equation without changing the solution (i.e. if a = b, then a + c = b + c)
If youre adding or subtracting a number on one side of an equation, do the opposite on the other.
Examples:
Find the solutions to the problems below:
x + 8 = -5 x =
16 + x = 14 x =
x + 4 = -3 x =
y 7 = -25 y =
y 3 = -14 y =
3 y = -14 y =
The Matrix earned $225 million at the box office. That is $38 million more than Matrix Reloaded earned. Write an algebraic equation and solve it to find out how much Matrix Reloaded earned at the box office.
What value of x makes x 1 = 8 a true statement?
A. 9 B. 7 C. -7 D. -9
Classwork:
Check for Understanding (pg 113) #1 #11 odds
Section 3-4
Objectives:
Solve equations by using the Division and Multiplication Properties of Equality
Concepts:
Division Property of Equality you can divide both sides of an equation by the same number without changing the solution (i.e. if a = b, then a c = b c)
Multiplication Property of Equality you can multiply both sides of an equation by the same number without changing the solution (i.e. if a = b, then a c = b c)
Examples:
Find the solutions to the problems below:
5x = -30 x =
7x = -56 x =
8a = -48 a =
-3b = 27 b =
12c = -48 c =
EMBED Equation.3 y =
EMBED Equation.3 y =
a 8 = -4 a =
Sam Clemens can read 20 pages of a book in one hour. How long will it take him to read a 280-page book?
Joe Jackson spent a total of $112 on boxes of baseball cards. If he paid $14 per box, how many boxes did he buy?
Classwork:
Check for Understanding (pg 117) #1 #9 odds, #10
Section 3-5
Objectives:
Solve algebraic equations with two or more operations
Concepts:
To solve an equation with two or more operations, work PEMDAS backwards. Undo any adding or subtracting first, multiplication or division second, exponents next, and finally parentheses.
Examples:
Solve the algebraic equations below:
2x + 1 = 9 x =
5x 2 = 13 x =
3x 4 = 17 x =
3 = n 5 + 8 n =
5 x = 7 x =
b 3b + 8 = 18 b =
20 z = 11 z =
3n + n 4 = 12 n =
Classwork:
Check for Understanding (pg 122) #4 #12 evens
Section 3-6
Objectives:
Write verbal/written sentences as equations and solve these equations
Concepts:
more than = add (+)
less than = subtract ()
is = equals (=)
more math words can be found on page 11 in your textbook
Examples:
Translate each sentence below into an equation then solve:
Six more than twice a number is -20
Eighteen is six less than four times a number
The quotient of a number and 5, increased by 8, is equal to 14
Twice a number, increased by 5, equals -25
Four times a number minus 8 = 28
When five is added to the product of a number and 8, the result is 12
Classwork:
Check for Understanding (pg 128) #3 #7
Section 3-7
Objectives:
Solve problems by using formulas
Solve problems involving perimeters and areas of rectangles
Vocabulary:
Formula an equation that shows a relationship among certain quantities. A formula usually contains more than one variable.
Concepts:
If possible, always draw a sketch and label it
Common formulas:
Distance = Rate (or Speed) Time (d = rt)
Perimeter of Rectangle = 2 Length + 2 Width (P = 2L 2W)
Area of Rectangle = Length Width (A = L W)
Examples:
If you travel 135 miles in 3 hours, what is your average speed in miles per hour?
A rectangle has a width of 15 cm and a length of 20 cm. Find its perimeter and area.
The perimeter of a rectangle is 60 feet. Its width is 9 feet. Find its length.
One large rectangle is divided into 3 smaller rectangles. The largest rectangle of the three is 12 meters long and 6 meters wide. Underneath it, side-by-side, lie the other 2 rectangles. One of these measures 8 meters long and has an area of 32 meters squared. Its width is x. Find x as well as the area of the last smaller rectangle, and the perimeter of the large rectangle that contains the 3 rectangles. First draw a sketch of what you think this scene would look like. Then find the values indicated above.
Sketch
Answers
Classwork:
Check for Understanding (pg 133) #3 #9 odds
Technology Notes
To reference a list in a formula:
Press STAT ( Edit
Input desired values into L1
Use the arrow keys to highlight L2
Input the desired formula, using L1 for the variable
Press ENTER
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