lesson objectives · web viewlesson 1 lesson objectives: use the order of operations to evaluate...

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Unit I

Algebra Review

Name:____________________ Period:__________

College Bound Math Teacher: _____________

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Lesson 1 Lesson Objectives: Use the order of operations to evaluate expressions Analyze and solve verbal problems that involve the order of operations Use proper calculator techniques to compute expressions

Who's correct?????????

When you evaluate an expression, you find its numerical value. What is the value of (1 + 3 x 2 - 4)? Without a set order of how to do things, what are some other possible outcomes?

To avoid confusion, mathematicians have agreed on a set of rules called the order of operations.

ParenthesesExponents

Multiplication/DivisionAddition/Subtraction

Why are multiplication/division and addition/subtraction on the same line? _______________________________________________________

What other symbols appear in expressions and where do they fall in the order of operations?

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Examples:4[25 – (5 – 2)2]

Evaluate if m = 9, n = 2, and p = 5

Practice:

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Lesson #1 Homework

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Lesson 2 Lesson Objectives:

Use the distributive property and combining like terms to simplify expressions Translate verbal phrases into algebraic expressions Use proper calculator techniques to compute expressions

Vocabulary ExamplesA term is a number, a variable, or a product or quotient of numbers and variables.Like-terms are terms that contain the same variables with the same exponents. An expression is a combination of terms.

An expression is in simplest form is when all like terms are combined and parentheses are removed.An equation relates two expressions with an equal sign.

The Distributive Property can be used to simplify expressions by removing parentheses.Examples:6(x2 + 3x – 5) -0.5(12 – 6x)

4(a2 + 3ab) -2(7 + x – 2x2)

14(j – 2) – 3j(4 – 7) 50(3a – b) – 20(b – 2a)

Practice:

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Writing expressions and equations is the process of translating into math symbols.

Math TranslatorAddition Subtraction

Multiplication Division

Equals

Words Variable (Unknown) Expression/Equation

Five years older than her brother

six dollars an hour times the number of hours

The difference between seven and a number

eight less than a number is 22

The product of -11 and the square of a number

The sum of x and its square is equal to y times z

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Homework #2

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Lesson 3 Lesson Objective: How do we solve multi-step equations?

Steps:1.____________________________________________________________________________

2.____________________________________________________________________________

3.____________________________________________________________________________

4.____________________________________________________________________________

Examples:

3x + 5 = 12 4y – 8 = 12 5m – 4 = -25

7x – 3x – 8 = 24 3(4m – 6) = 2(7m – 5) 8 – 3(4x – 11) = 15x + 1 – 7x 13 + 5(2x – 7) = 6x + 13

5x + 3(x + 4) = 28 4x – 3(x – 2) = 21 2x – 5(x – 9) = 27

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Homework #3

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Lesson 4 Lesson Objective: How do we solve absolute value equations?

The absolute value of a number is the _______________________ that number is from zero. Can distance be negative? Therefore absolute value cannot be negative. The symbol |x| is used to represent the absolute value of, x.

Evaluate: |-5| = _______ |5| = _________ |6 – 10| = __________

So if I was to ask |x| = 5, what would the value of x be? _______________

Solving Absolute Value Equations

1. Get the absolute value bars _________________________________________.2. Make sure that the absolute value is equal to a __________________ number ONLY!!! As we talked about

earlier, absolute value is NEVER negative!3. Create _________ equations.4. Solve both Equations5. Check to be sure your answers work.

Examples:1.) |t – 4| = 5 2.) 2|2x – 3| = 6

3.) 4.) -3|4x + 9| = 24

5.) -5|3x – 7| + 8 = -102 6.) 13 + 4|3 – 5x| = 5

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Homework #4

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Lesson 5 Lesson Objective: Solve inequalities

Solve each inequality and graph its solution

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Lesson 6Lesson Objective: Solve compound inequalities

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Homework #6: Compound Inequalities

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Lesson 7Lesson Objectives:Writing algebraic expressions from word problemsSolving algebraic expressions from word problems

The sum of two numbers is 90.The larger number is three more than twice the other.

Find the larger number.

Sometimes we will have MORE than one variable to define. We may have to define a variable and then USE that variable to define our other unknown(s).

Type I

1.) The sum of two numbers is 90. The larger number is three more than twice the other. Find the larger number.

Define your variable(s) Write your equation and solve:Let x =Let ________________=

2) A ribbon 56 centimeters long is cut into two pieces. One of the pieces is three times longer than the other. Find the lengths, in centimeters, of both pieces of ribbon.


3) In triangle ABC, the measure of angle B is 21 less than four times the measure of angle A, and the measure of angle C is 1 more than five times the measure of angle A. The measures of the angles of a triangle add up to 180 degrees. Find the measure, in degrees, of each angle.


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Let ________________=4) Jackie has $200 to spend. She buys a clock for $66, and wants to spend the rest on picture frames marked

at $15 each. How many picture frames can she afford?

Define your variable(s) Write your equation and solve:Let x =Let ________________=Let ________________=

Type II

1) The larger of two numbers exceeds six times the smaller by 10. If the larger number is 76 find the smaller.


What does “consecutive integers” mean?___________________________________________________________________________________________________________________________________________________

Give an example of 3 consecutive integers:_______________________________________________________

How would you write these as algebraic expressions?______________________________________________2) The sum of the ages of the three Romano brothers is 63. If their can be represented as consecutive

integers, what is the age of the middle brother?

3) Find three consecutive integers such that the sum of the first two integers is 24 more than the third.

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What does “consecutive EVEN integers” mean?___________________________ _________________________________________________________________________________________________________________

Give an example of 3 consecutive even integers:__________________________________________________

How would you write these as algebraic expressions?______________________________________________

4) The sum of three consecutive even integers is 126. Find the integers.

What does “consecutive ODD integers” mean?___________________________ _________________________________________________________________________________________________________________

Give an example of 3 consecutive odd integers:__________________________________________________

How would you write these as algebraic expressions?______________________________________________

5) The sum of four consecutive odd integers is -48. Find the integers.

6) Find three consecutive even integers such that the sum of the smallest and twice the second is 20 more than the third.

7) The perimeter of a rectangle is 40 feet. The length is 2 more than 5 times the width. Find the dimensions of the rectangle.

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(Optional) Homework #7: Word Problems

PRACTICE:1) The sum of three consecutive integers is 71 less than the smallest of the integers. Find the integers.

2) The sum of four consecutive odd integers is three more than five times the smallest. Find the integers.

3) Find four consecutive odd integers such that the sum of the first three exceeds the fourth by 18.

4) Is it possible to find three consecutive odd integers whose sum is 59? Why?

5) The sum of 3 numbers is 207. The second number is 8 times the first, while the third is 3 less than the first. Find the number.

Define your variable(s) Write your equation and solve:Let x =Let ________________=Let ________________=

6) The length of a rectangle is 2 less than twice the width. If the perimeter is 11m, find the length and width.


lesson objectives · web viewlesson 1 lesson objectives: use the order of operations to evaluate...

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