Table of Contents - Teacher Created

Table of Contents

The Beginning of Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Amazing Face (I)¡ªSolving problems using order of operations

Amazing Face (II)¡ªSolving problems using order of operations

Name That Term¡ªDefining algebraic terms

¡°Express¡± Yourself¡ªTranslating phrases into algebraic expressions

Lipstick Lady¡ªIdentifying expressions

Writer¡¯s Dilemma¡ªUsing variables and evaluating expressions

A Really ¡°Pig¡± Show¡ªIdentifying properties of multiplication and addition

Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

A Sensible Solution¡ªComparing and ordering integers

¡°Spl-Integers¡±¡ªAdding integers

A Military Matter¡ªAdding and subtracting integers

Puzzling Problem¡ªMultiplying and dividing integers

Too Fast!¡ªMultiplying and dividing integers

One-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Lovesick¡ªSolving equations using the addition or subtraction steps

A Croaking Crook¡ªSolving equations using the inverse operation

The Wacky Werewolf¡ªSolving equations using the inverse operation

Factors and Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Follow the Divisibility Road¡ªUsing the divisibility rules while evaluating expressions

Time for a Treat¡ªIdentifying prime numbers while reviewing basic operations with integers

A Penny for Your Thoughts¡ªFinding the prime factorization of numbers

Surprise Dish¡ªFinding the prime factorization of numbers

From a Lawyer¡¯s Lips¡ªFinding the greatest common factor among monomials

The Bacon Company¡ªFinding the least common multiple among monomials

Term Search¡ªFamiliarizing oneself with common algebraic terms

A ¡°Sharking¡± Discovery¡ªSimplifying and identifying equivalent fractions

Rational Numbers (+ and -) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

The Problem with Pachyderms¡ªAdding and subtracting mixed numbers

¡°Stair¡± Crazy¡ªSolving equations involving addition and subtraction of rational numbers

Rabbit Riddle¡ªCompleting mathematical sequences

Rational Numbers (x and ¡Â ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Pilot Puzzle¡ªMultiplying positive and negative decimals

Duck Cookies¡ªMultiplying and dividing fractions

A Dating Disaster¡ªSolving multiplication and division equations

Reggae Frog¡ªWriting numbers in scientific notation

Multi-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Words of Wisdom¡ªSolving two-step equations

Go, Team, Go!¡ªSolving equations with variables on both sides of the equal sign

Baby Genius¡ªSolving multi-step equations

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Table of Contents (cont.)

Graphing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

You Are What You Drink¡ªComparing solutions from equations and inequalities as graphed on a

number line

Write Your Own Riddle¡ªFinding coordinates in the Cartesian Coordinate System

Smile!¡ªGraphing coordinates in the Cartesian Coordinate System

You Can Lead Them to Water...¡ªGraphing coordinates in the Cartesian Coordinate System

Largest Migrating Mammal¡ªGraphing coordinates in the Cartesian Coordinate System

Crisscross¡ªGraphing linear equations

A Canine Question¡ªSolving systems of equations by graphing linear equations

A Crossword Puzzle of Graphing Terms¡ªReviewing terminology associated with graphing

Proportion and Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

A Funny Feline¡ªSetting up ratios in fractional form

The Very Best¡ªSolving proportions

Fractions, Decimals, and Percents¡ªChanging fractions to decimals to percents

Don¡¯t Ruffle the Bird¡¯s Feathers¡ªChanging fractions to decimals to percents

Chow Time¡ªSolving percent problems

Pet-Pal Parlor¡ªFinding percent increase and percent decrease

Data and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

The Young Vampire¡ªOrganizing data in a frequency table and a chart

No Rest for the Weary¡ªCalculating the mean from a set of data

Doggy Diagnosis¡ªCalculating the mean, median, and mode from given data sets

The Land Down Under¡ªOrganizing data in a stem and leaf plot

Disguising Data Definitions¡ªIdentifying statistical terms

Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Heard It Through the Grapevine¡ªSolving permutations, combinations, and factorials

Probably Probability¡ªDetermining the probability of a simple event

Know the Terms¡ªBecoming familiar with statistical and probability terminology

Introduction to Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

What¡¯s Left?¡ªIdentifying geometrical terms

Food for Thought¡ªIdentifying angle relationships

The Square Team¡ªIdentifying angle relationships when parallel lines are cut by a transversal

Mystery Name¡ªFinding the degrees of missing angle measurements in triangles

Vacation Destination¡ªIdentifying corresponding parts of congruent triangles

All Aboard!¡ªWriting true conditional statements

Area and Perimeter

Shop ¡¯Til You Drop¡ªCalculating the areas and perimeters of polygons

Speedy the Squirrel¡ªCalculating the areas of triangles and parallelograms

Check, please!¡ªCalculating the areas of trapezoids

A Painful Problem¡ªCalculating the areas and circumferences of circles

Corny Acorns¡ªCalculating the surface areas of prisms

Student Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Answer Key. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

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Brain Teasers

A Penny for Your Thoughts

Directions: Find the prime factorization for each number surrounding the penny. Then complete the

statement below by filling in the blanks. To fill in a blank, look at the prime factorization written

below it, and insert the matching letter from the penny.

E) 80

C) 40

T) 92

I) 144

A) 64

S) 108

H) 580

M) 216

N) 200

K) 630

O) 70

W) 56

Finish the Statement: A man who constantly says, ¡°A penny for your thoughts¡± . . .

______

24 x 32

______

22 x 33

______

26

______ _________ ______

23 x 7 22 x 5 x 29 2 x 5 x 7

______

23 x 52

__________

2 x 5 x 7

______

23 x 5

______

23 x 33

______

26

______

23 x 52

______

23 x 33

______ __________ ______

26

2 x 32 x 5 x 7 24 x 5

______

24 x 5

______

23 x 52

______

22 x 3 3

______ ______.

22 x 23 22 x 33

Focus: Finding the prime factorization of numbers

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Student Guide

? Vertical, Complementary, and Supplementary Angles

Vertical angles are formed when two lines intersect. The angles opposite each other are called vertical

angles, and they are congruent.

Example:

(5x ¨C 1)¡ã

Solution: (5x ¨C 1)¡ã = (3x + 11)¡ã

(2x)¡ã = 12¡ã

x¡ã = 6¡ã

(3x +11)¡ã

The first angle is 5(6) ¨C 1 = 29¡ã.

The second angle is 3(6) + 11 = 29¡ã.

Complementary angles are two angles whose sum is 90¡ã.

Example:

Solution: (3x + x)¡ã = 90¡ã

(4x)¡ã = 90¡ã

x¡ã = 22.5¡ã

(3x)¡ã

(x)¡ã

The larger angle is 3x = 3(22.5) = 67.5¡ã.

The smaller angle is x = 22.5¡ã.

Solution: (2x ¨C 5)¡ã + (3x + 30)¡ã = 180¡ã

(5x + 25)¡ã = 180¡ã

(5x)¡ã = 155¡ã

x¡ã = 31¡ã

Supplementary angles are two angles whose sum is 180¡ã.

Example:

(3x + 30)¡ã

(2x ¨C5)¡ã

The larger angle is (3x + 30)¡ã = 3(31) + 30 = 123¡ã.

The smaller angle is (2x ¨C 5)¡ã = 2(31) ¨C 5 = 57¡ã.

? Angles Formed by a Transversal and Parallel Lines

When dealing with angles formed by a transversal and parallel lines, note the following rules:

? Alternate interior angles are congruent. ( ¡Ï3 ? ¡Ï5, ¡Ï4 ? ¡Ï6)

? Alternate exterior angles are congruent. ( ¡Ï1 ? ¡Ï7, ¡Ï2 ? ¡Ï8)

? Vertical angles are congruent. ( ¡Ï1 ? ¡Ï3, ¡Ï2 ? ¡Ï4, ¡Ï5 ? ¡Ï7, ¡Ï6 ? ¡Ï8)

? Interior angles on the same side are supplementary. ( ¡Ï4 + ¡Ï5 = 180¡ã, ¡Ï6 + ¡Ï3 = 180¡ã)

? Exterior angles on the same side are supplementary. ( ¡Ï1 + ¡Ï8 = 180¡ã, ¡Ï2 + ¡Ï7 = 180¡ã)

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