Math Grade 8 Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Grade Grade Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-8001 888 \|xiBAHBDy01221kzU Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Algebra Skills Integers & Exponents The Real Numbers Plane Geometry Perimeter & Ar ea Ratios, Rates & Pr oportions Applying Percents Organizing & Displaying Data Arithmetic & Sequences Systems of Equations

• An algebraic expression is a mathematical phrase consisting of variables, numbers, and operations. • Solve for a variable in terms of other variables. • Algebraic expressions are used to write formulas that show relationships between quantities. • Find the area of a triangle with a base of 5 inches and height of 8 inches. • To evaluate an algebraic expression, substitute the given numbers for the variables and solve to find the value for the formula. The area of a triangle is one half its base times its height. A = 20 in 2 Solve for y A = b • h 1 2 A = • 5 • 8 1 2 A = • 40 1 2 x -8 -4 0 4 8 4 3 2 1 0 y x y -5 -4 -3 -2 -1 -9 -8 -7 -6 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 0 x y -5 -4 -3 -2 -1 -9 -8 -7 -6 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 0 x + 4y = 8 4y = – x + 8 4y = -x + 8 4 4 4 – x – x A = b • h 1 2 y = x + 2 1 4 y = x + 2 1 4 8 in. 5 in. Algebraic Expressions Solving Equations Graphing a Solution • Equations and inequalities are used to solve many real-world problems. • In order to make a profit, revenue (R) has to be greater than cost (C). A video game manufacturer must spend $12,500 for research and development and $15 per game to produce. How many games would the manufacturer have to sell at $40 per game to make a profit? Solving Inequalities 200 300 400 500 600 700 x 500 > R C > > > 40x 12,500 + 15x 25x 12,500 > 25x 12,500 – 15x – 15x 25 25 - - Example: Example: © Copyright NewPath Learning. All Rights Reserved. 93-4801 www.newpathlearning.com Algebra Skills

\|xiBAHBDy01515kzU • An algebraic expression is • Solve for a variable in terms of other variables. • Algebraic expressions are used to • Find the area of a triangle with a base of 5 inches and height of 8 inches. • To evaluate an algebraic expression, substitute the given numbers for the variables and solve to find the value for the formula. A = 20 in 2 Solve for y A = b • h 1 2 A = • 5 • 8 1 2 A = • 40 1 2 x y x y -5 -4 -3 -2 -1 -9 -8 -7 -6 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 -1 -2 -3 -4 -5 -6 -7 -8 -9 0 x + 4y = 8 4y = – x + 8 4y = -x + 8 4 4 4 – x – x y = x + 2 1 4 y = x + 2 1 4 8 in. 5 in. Algebraic Expressions Solving Equations Graphing a Solution • Equations and inequalities are used to solve many real-world problems. • In order to make a profit, revenue (R) has to be greater than cost (C). A video game manufacturer must spend $12,500 for research and development and $15 per game to produce. How many games would the manufacturer have to sell at $40 per game to make a profit? Solving Inequalities 200 300 400 500 600 700 x 500 > R C > > > 40x 12,500 + 15x 25x 12,500 > – 15x – 15x - - Example: The area of a triangle is one half its base times its height. A = b • h 1 2 Example: Key Vocabulary Terms • algebraic expression • area • equation • greater than (>) • inequality • operation • solution • variable . . © Copyright NewPath Learning. All Rights Reserved. 93-4801 www.newpathlearning.com Algebra Skills

Integers Exponents Example Rule If the signs of the integers are the same, add the absolute values. The sum will have the same sign as the integers you are adding. If the signs of the integers are different, subtract the absolute values. The difference will have the same sign as the integer with the larger absolute value. 6 + 4 = 10 -6 + (-4) = -10 -6 + 4 = -2 6 + (-4) = 2 • Integers are a set of whole numbers and their opposites. • Positive integers are whole numbers greater than zero. • Negative integers are whole numbers less than zero. • The integer 0 is neither positive nor negative. • Integers have either a positive (+) or negative (–) sign, except zero, which has no sign. • An exponent tells how many times to multiply a number, called the base, by itself. Scientific Notation • Scientific notation is used to express very large or very small numbers. Adding Integers Example Rule If the factors have different signs, the product is negative. If the factors have the same sign, the product is positive. If one factor is zero, the product is zero. -7 x 4 = -28 -4 x 0 = 0 5 x -3 = -15 6 x 2 = 12 -8 x -9 = 72 Multiplying Integers Example Rule To subtract an integer, add its opposite by changing the subtraction sign to addition and changing the sign of the second integer. Subtracting Integers 6 – (-2) = 6 + 2 = 8 6 – 2 = 6 + (-2) = 4 Example Property Properties of Exponents a x • a y = a x + y 50 = 1 ; (-5)0 = 1 42 • 43 = 42 + 3 = 45 Example Rule If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals zero. -12 ÷ 4 = -3 15 ÷ (-3) = -5 32 ÷ 4 = 8 -21 ÷ (-3) = 7 = 0 = 0 Dividing Integers 0 9 0 -8 a 0 = 1 , if a = 0 a x = a x – y, if a = 0 a y 25 = 25 – 2 = 2 3 22 Example Definition Negative Exponents a-x = , if a = 0 a x 1 64 1 (-4)-3 = = = (-4)3 1 (-4) (-4) (-4) 1 • • 5-2 = = = 5 2 1 25 1 5•5 1 5 = 5 x 5 x 5 = 125 3 base exponent scientific notation standard form 2.58 x 10 2,580,000 6 0.00012 1.2 x 10 -4 © Copyright NewPath Learning. All Rights Reserved. 93-4802 www.newpathlearning.com Integers & Exponents

Example Rule If the signs of the integers are the same, add the absolute values. The sum will have the same sign as the integers you are adding. If the signs of the integers are different, subtract the absolute values. The difference will have the same sign as the integer with the larger absolute value. • Integers are • Positive integers are • Negative integers are • The integer 0 is neither positive nor negative . • Integers have either a or sign, except zero, which none. • An exponent tells how many times to multiply a number, called the base, by itself. Scientific Notation • Scientific notation is used to express very large or very small numbers. Adding Integers Example Rule If the factors have different signs, the product is negative. If the factors have the same sign, the product is positive. If one factor is zero, the product is zero. Multiplying Integers Example Rule To subtract an integer, add its opposite by changing the subtraction sign to addition and changing the sign of the second integer. Subtracting Integers Example Property Properties of Exponents a x • a y = a x + y Example Rule If the dividend and divisor have different signs, the quotient is negative. If the dividend and divisor have the same signs, the quotient is positive. Zero divided by any integer equals zero. Dividing Integers a 0 = 1 , if a = 0 a x = a x – y, if a = 0 a y Example Definition Negative Exponents a-x = , if a = 0 a x 1 scientific notation standard form 2,580,000 0.00012 Integers Exponents . . . Key Vocabulary Terms • absolute value • difference • dividend • divisor • exponent • factor • integer • negative integer • positive integer • quotient • scientific notation • sum © Copyright NewPath Learning. All Rights Reserved. 93-4802 www.newpathlearning.com Integers & Exponents \|xiBAHBDy01670qzZ

• Numbers used in everyday life are real numbers. • Real numbers are used to measure quantities such as temperature, speed of a car or volume of liquid in a cup. • Real numbers are classified as either rational or irrational. Properties of Real Numbers Rational Numbers Irrational Numbers Property Property Addition Addition Multiplication Multiplication Associative Commutative Identity Inverse Distributive a + b = b + a a + 0 = a a • 1 = a a • b = b • a a + (b + c) = (a + b) + c a + (-a) = 0 (-a) + a = 0 a • (b • c) = (a • b) • c (b + c) a = ba + ca or If a = 0, then a • = 1 or a 1 a 1 • a = 1 b a • The Density Property is an important property of real numbers. It states that between any two real numbers there’s another real number. • Rational numbers can be written as a ratio of two integers, such as , where b is not zero. • Rational numbers can also be written as a decimal that is either a terminating or repeating decimal. • Real numbers that are not rational are irrational. • Irrational numbers cannot be written as ratios. • The decimal form of irrational numbers neither repeats nor terminates. • any number that has a position on a number line Ratio Form Decimal Form 0.27272727.... or (0.2727) 0.375 3.141592654....... 2.718281828....... 1.4142135....... 4.0 8 3 11 3 16 2 e Integers -3, -2, -1, 0, 1, 2, 3 Whole numbers 0, 1, 2, 3... Natural numbers 1, 2, 3, 4, 5... Real Numbers Examples: Examples: and a (b + c) = ab + ac Irrational Numbers Rational Numbers • non-terminating, non-repeating decimals • any square root that is not a perfect root © Copyright NewPath Learning. All Rights Reserved. 93-4803 www.newpathlearning.com The Real Numbers

• Numbers used in everyday life are . • Real numbers are used . • Real numbers are classified as either rational or irrational . Properties of Real Numbers Rational Numbers Irrational Numbers Property Property Addition Addition Multiplication Multiplication Associative Commutative Identity Inverse Distributive • The Density Property is an important property of real numbers. It states that . • Rational numbers can be written as • Rational numbers can also be written as • Real numbers that are not rational are irrational. • Irrational numbers cannot be written as ratios. • The decimal form of irrational numbers neither repeats nor terminates. • Real Numbers Key Vocabulary Terms • associative property • commutative property • decimal • distributive property • identity property • integers • inverse property • irrational numbers • natural numbers • non-terminating decimal • ratio • rational numbers • real numbers • square root • terminating decimal • whole number . . . . . . Irrational Numbers Rational Numbers • • © Copyright NewPath Learning. All Rights Reserved. 93-4803 www.newpathlearning.com The Real Numbers \|xiBAHBDy01690ozX

7 days 1 week (wk) You multiply integers just as you do whole numbers, except that you determine the sign of the product using these rules. • Parallel lines are two lines that are always the same distance apart and will never intersect. • Perpendicular lines are lines that meet at right angles (90º). • A transversal line is a line that crosses at least two other lines. Angles marked in green are congruent to each other. Angles marked in blue are congruent to each other. • Any angle marked in green is supplementary to any angle marked in blue. Points, Lines & Planes Angles Parallel & Perpendicular Lines Polygons Triangles Two Parallel Lines Intersected by a Transversal right angle D G H E F I A plane is a two- dimensional surface that extends infinitely in all directions. A right angle forms a square corner and measures 90º. Complementary angles are angles whose sum is 90º. Supplementary angles are angles whose sum is 180º. A triangle is a three-sided polygon. Types of triangles include acute, right, obtuse, equilateral, isosceles and scalene. A polygon is a closed plane figure with three or more sides and angles. An acute angle measures less than 90º. An obtuse angle measures greater than 90º. A ray is part of a line with one endpoint and goes on forever in the other direction. A line segment is part of a line between two endpoints. A line is a straight collection of points that extend in two opposite directions without end. A point is a location in space. AB CD • point A • point B AB CD AB CD A B D C A B D A B C A B D C Line Segment Line Ray Plane Point Plane m or Plane ABC m C A B 90º m AED + CEB = 90º m AED + DEB = 180º 55º 35º A E D C B º + mº + nº = 90º º mº m n t nº Number of sides ( n ) Sum of angle measures 180º ( n – 2 ) Polygon Quadrilateral Triangle 180º 3 4 5 6 7 8 360º 540º 720º 900º 1080º Pentagon Hexagon Heptagon Octagon rhombus nº nº nº nº hexagon (6 congruent angles) nº nº nº nº nº nº n = 120º 6nº = 720º 6nº = 180º (4) 6nº = 180º (6 – 2) = 6nº 6 6 720º 120º 120º 60º 60º 120º 120º 60º 60º m n © Copyright NewPath Learning. All Rights Reserved. 93-4804 www.newpathlearning.com Plane Geometry

\|xiBAHBDy01681mzV • Parallel lines are _____________ ______________________________ ______________________________. • Perpendicular lines are _______ ______________________________ ______________________________. • A transversal line is a ______________________________ ______________________________. Points, Lines & Planes Angles Parallel & Perpendicular Lines Polygons Triangles Two Parallel Lines Intersected by a Transversal D G H E F I A plane is a two- dimensional surface that extends infinitely in all directions. Complementary angles are angles whose sum is . Supplementary angles are angles whose sum is . A triangle is __________ ______________________. Types of triangles include _______________ _______________________ __________________ ______________. A polygon is a closed plane figure with three or more sides and angles. A ray is part of a line with one endpoint and goes on forever in the other direction. A line segment is part of a line between two endpoints. A line is a straight collection of points that extend in two opposite directions without end. A point is a location in space. Line Segment Line Ray Plane Point 90º m AED + CEB = m AED + DEB = 35º A E D C B º + mº + nº = 90º m n t º mº nº Number of sides ( n ) Sum of angle measures 180º ( n – 2 ) Polygon Quadrilateral Triangle Pentagon Hexagon Heptagon Octagon nº nº nº nº nº nº nº nº nº nº n = m n Key Vocabulary Terms • acute angle • complementary angle • congruent • line • line segment • obtuse angle • parallel lines • perpendicular lines • plane • point • polygon • ray • right angle • supplementary angle • transversal Find the measure of angle n. Draw a point. Draw a line. Draw a line sement. Draw a ray. Draw a plane. 120º 60º 120º 60º ___º ___º ___º ___º ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ © Copyright NewPath Learning. All Rights Reserved. 93-4804 www.newpathlearning.com Plane Geometry

A = 1 2 h (b 1 + b 2) A = 1 2 4 (5 + 8 ) 3.14 (4 )2 = A = 1 2 b • h A = 1 2 (9 )(6 ) = A = Triangle Trapezoid Circle Perimeter Area • Perimeter is the distance around a figure. • Area is the number of square units inside the boundary of a two-dimensional figure. • The area of a triangle is one-half of the base length times the height. • The area of a circle is times the square of the radius. • The area of a trapezoid is one-half the height (h) times the sum of the base lengths b 1 and b 2. • To find the perimeter, add all side lengths. or substitute 12 for b and 8 for h. P = 9 + 10 + 2 + 7 + 3 + 4 + 2 + 2 + 2 + 5 = 46 units P = 8 + 8 + 12 + 12 = 40 units P = 2 (12) + 2 (8) P = 2 b + 2 h = 24 + 16 y x (-4, -2) (-4, 3) (4, 3) (4, -2) 10 8 12 9 2 2 2 2 4 3 7 5 = 40 units Rectangle Rectangle base (b) height (h) A = b • h = 8 • 5 = 40 units2 A = b • h = 8 • 5 = 40 units2 Parallelogram • If a triangular section is cut and placed on the opposite side of a parallelogram, it forms a rectangle. • Therefore, a parallelogram has the same area as a rectangle with the same base length and height. 8 (b) 5 (h) 8 (b) 5 (h) 8 (b) 5 (h) 26 units2 27 units2 50.24 units2 r 2 9 (b) 6 (h) 8 (b 2) 4 (h) 5 (b 1) radius (r) center diameter 4 © Copyright NewPath Learning. All Rights Reserved. 93-4805 www.newpathlearning.com Perimeter & Area

A = 1 2 h (b 1 + b 2) A = A = 1 2 b • h A = A = A Triangle Trapezoid Circle Perimeter Area • Perimeter is . • Area is the number of square units inside the boundary of a two-dimensional figure. • The area of a triangle is one-half of the base length times the height. • The area of a circle is times the square of the radius. • The area of a trapezoid is one-half the height (h) times the sum of the base lengths b 1 and b 2. • To find the perimeter, all side lengths. or substitute 12 for b and 8 for h. P = 9 + 10 + 2 + 7 + 3 + 4 + 2 + 2 + 2 + 5 = 46 units P = 8 + 8 + 12 + 12 = 40 units P = P = 2 b + 2 h y x ( -4 , -2 ) ( -4 , 3 ) ( 4 , 3 ) ( 4 , -2 ) 10 8 12 9 2 2 2 2 4 3 7 5 Rectangle Rectangle base (b) height (h) A = b • h = 8 • 5 = 40 A = b • h Parallelogram • If a triangular section is cut and placed on the opposite side of a parallelogram, it forms a • Therefore, a parallelogram has the same area as a rectangle with the same base length and height. 8 (b) 5 (h) r 2 9 (b) 6 (h) 8 (b 2) 4 (h) 5 (b 1) radius (r) center diameter 4 Key Vocabulary Terms • area • base • circle • height • length • parallelogram • perimeter • rectangle • trapezoid • triangle • width = 8 • 5 = 40 . © Copyright NewPath Learning. All Rights Reserved. 93-4805 www.newpathlearning.com Perimeter & Area \|xiBAHBDy01680pzY

Ratios & Rates Geometric Proportions Using Conversion Factors Ordering Ratios Equivalent Ratios Numerical Proportions corresponding angles • Numerical Proportions compare two numbers. • Cross products are used to find a missing quantity in a proportion. • A ratio is a comparison of two quantities measured in the same units. • Ratios are used to solve proportions, to find dimensions in similar figures and to determine distances in travel maps. • To order ratios, convert them to decimals or fractions. • Order them from least to greatest: 0.875, 1.20, 1.33 and 1.5 • A conversion factor is a ratio that represents the same quantity but uses different units. The ratios of 1,200 ft per minute into miles per hour and are equivalent. • Rates are used to compare quantities measured with different units. • A unit rate has a denominator of 1. Zoe rode her bike 6 miles in 48 minutes. Example: Convert: • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • The triangles are similar since their corresponding sides are equivalent. • A cross product is the product of the numerator in one ratio and the denominator in the other ratio. Cross Product Rule • When two ratios are equal, then the cross products, a•d and b•c, are equal. 3 6 1 2 = a b c d = 5 10 1 2 1 2 = = = = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm • An equation with two equal ratios is called a proportion. 5 ÷ 10 10 ÷ 10 5 10 5 10 25 50 25 50 = , = 5 • 5 10 • 5 3:2 1.5 = = = • • = 4:3 1.33 = = 7:8 0.875 = = 6:5 1.20 3 2 4 3 7 8 1,200 ft 1,200 • 60 mi 13.63 mi/h 5,280 h 1 min 1,200 ft 5,280 ft 1 min 60 min 1 mi 1 h 6 5 = 6 mi 48 min. 48 min. 6 mi Rate or = 0.125 mi 1 min. 8 min. 1 mi Unit Rate or corresponding sides © Copyright NewPath Learning. All Rights Reserved. 93-4806 www.newpathlearning.com Ratios, Rates & Proportions

\|xiBAHBDy01683qzZ Ratios & Rates Geometric Proportions Using Conversion Factors Ordering Ratios Equivalent Ratios Numerical Proportions • Numerical Proportions compare numbers. • Cross products are used to find a missing quantity in a proportion. • A ratio is a comparison of • Ratios are used to • To order ratios, convert them to decimals or fractions. • Order them from least to greatest: 0.875, 1.20, 1.33 & 1.5 • A conversion factor is a ratio that represents the same quantity but uses different units. The ratios of 1,200 ft per minute into miles per hour and are equivalent. • Rates are used to • A unit rate has a denominator of 1 . Zoe rode her bike 6 miles in 48 minutes. Example: Convert: • Geometric proportions compare two similar figures. • Similar figures have equal corresponding angles and corresponding sides that are in proportion. • A cross product is the product of the numerator in one ratio and denominator in the other ratio. 3 6 = 5 10 1 2 = = = = 3 5 6 10 = 5 • 6 = 30 3 • 10 = 30 • An equation with two equal ratios is called a proportion. 5 ÷ 10 10 ÷ 10 5 10 5 10 = , = 5 • 5 10 • 5 3:2 = = = • • = 4:3 = = 7:8 = = 6:5 3 2 4 3 7 8 6 5 = Rate or = Unit Rate or . . . G I H 3 cm 6 cm 4 cm K J L 24 cm 12 cm 16 cm . • The triangles are since their corresponding sides are equivalent. . • corresponding angle • corresponding side • cross product numerator • denominator • equation • equivalent ratio • geometric proportion Key Vocabulary Terms • numerical proportion • proportion • rate • ratio • similar figures • unit rate © Copyright NewPath Learning. All Rights Reserved. 93-4806 www.newpathlearning.com Ratios, Rates & Proportions

Example: What is the sales tax on a $120 purchase, if the tax rate is 8.5%? • Percent means “out of each hundred.” It is a ratio that compares a number to 100. • Percents are often used in business, banking and everyday math problems to determine sales tax, interest, discounts and commissions. • Sales tax is a percent of the purchase price that a store collects. • Convert the tax rate to a decimal and multiply it by the purchase amount. • A discount is the amount by which the regular purchase price is reduced. • Simple interest is charged when you borrow money or paid when you invest your money. Cross multiply. Divide by 100 to isolate the variable. Cross multiply. Divide by 70 to isolate the variable. Divide by 0.15 to isolate the variable. Write the percent as a decimal. • To solve a problem with a percent, convert the percent to a decimal. • To convert a percent to a decimal, move the decimal point two decimal places to the left. Example: Example: Solving Problems with Percents Determining the Percent of a number Using Proportions Using Equations 35 is what percent of 70? 36 is 15% of what number? What is 57% of 80? 57% of 80 is 45.6 I = $40.50 I = P • r • t I = 600 • 0.045 • 1.5 Sales Tax = $10.20 0.085 x 120 = 10.20 Sale Price = 145 – 21.75 = 0.15 x 145 = x = $21.75 Sale Price = $123.25 Discount Simple Interest Sales Tax Converting Percent to a Decimal whole part whole part 57 100 m 80 = 4,560 100 100 100m = 57 • 80 100 • m = 45.6 m = 4,560 100m = 75% 0.75 35 is 50% of 70 m 100 35 70 = m • 70 100 • 35 = 36 0.15 • m = 36 15% • m = 50 m = 36 is 15% of 240 m 240 = 3,500 70m = 70 70 70m = 3,500 0.15 0.15 36 = 0.15 • m What is the interest paid on a $600 loan for 18 months at 4.5%? How much would you pay for an item if it is discounted 15% from its regular price of $145? Amount of Discount Amount of Discount Tax Rate Purchase Amount Discount Rate Regular Price = Amount of Discount Regular Price Sale Price – simple interest annual interest rate time in years principal substitute 1.5 years for 18 months substitute 0.045 for 4.5% x Sales Tax = © Copyright NewPath Learning. All Rights Reserved. 93-4807 www.newpathlearning.com Applying Percents

\|xiBAHBDy01664pzY Example: What is the sales tax on a $120 purchase, if the tax rate is 8.5%? • Percent means “_________________________.” It is a ratio that compares a number to . • Percents are often used in _______________ __________________________________________ _________________________________ _________________________________. • Sales tax is a __________ _______________________ _______________________. • Convert the tax rate to a decimal and multiply it by the purchase amount. • A discount is _______________________ _______________________. • Simple interest is ____________ _____________________________ _____________________________. Cross multiply. Divide by to isolate the variable. Cross multiply. Write the percent as a decimal. • To solve a problem with a percent, convert the percent to a decimal. • To convert a percent to a decimal, move the decimal point places to the . Example: Example: Divide by to isolate the variable. Divide by to isolate the variable. Solving Problems with Percents Determining the Percent of a number Using Proportions Using Equations 35 is what percent of 70? 36 is 15% of what number? What is 57% of 80? 57% of 80 is I = $ I = P • r • t I = 600 • 0.045 • 1.5 Sales Tax = $ Sale Price = – = 0.15 x = x = $21.75 Sale Price = $ Discount Simple Interest Sales Tax Converting Percent to a Decimal whole part whole part 57 100 m 80 = m = m = 75% 0.75 35 is % of 70 m 100 35 70 = m = 36 is 15% of What is the interest paid on a $600 loan for 18 months at 4.5%? How much would you pay for an item if it is discounted 15% from its regular price of $145? Amount of Discount Amount of Discount Tax Rate Purchase Amount Discount Rate Regular Price = Amount of Discount Regular Price Sale Price – simple interest annual interest rate time in years principal x Sales Tax = x = • • = = = • • = • = = = = 36 15% • m = • Key Vocabulary Terms • cross multiply • decimal • decimal point • discount • equation • interest • percent • proportion • ratio • tax • variable © Copyright NewPath Learning. All Rights Reserved. 93-4807 www.newpathlearning.com Applying Percents

Mean (the largest value minus the smallest value) (the average of a set of numbers) (the middle value, or average of two middle values) Range (the number that occurs most often in a set of data) Mode Line Graph Bar Graph Frequency Table A frequency table shows the totals of the tally marks. Ranger Bike Tally Total Outdoor Starburst Mountain Total 19 10 2 4 3 Stem–and–Leaf Plot A stem-and-leaf plot shows data arranged by place value. 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) 5 0 8 1 5 6 9 2 1 2 3 4 5 0 1 2 3 4 5 6 10 20 30 40 50 10 10 20 30 40 50 20 30 40 50 10 10 20 30 40 50 20 30 40 50 Measures of Central Tendency Organizing Data Box–and–Whisker Plot Displaying Data Scatter Plots 99 – 57 = 42 57 & 99 57, 57, 62, 64, 67, 68, 75, 79, 80, 84, 89, 99, 99 = 75.4 • Central tendency is a way to describe a data set using one number. • A box-and-whisker plot is an easy way to view the distribution of data. • Smallest value: • First quartile: • Median: • Third quartile: • Largest value: smallest value (57) first quartile (63) third quartile (86.50) largest value (99) median (75) Order the data from smallest to largest value. 13 Median 75 Step 1 Step 2 Draw a number line and plot the values above. Draw the box-and-whiskers. Positive Correlation Negative Correlation 10 10 20 30 40 50 20 30 40 50 No Correlation 57, 57, 62, 64, 67, 68, 75, 79, 80, 84, 89, 99, 99 57 75 99 = 63 2 62 + 64 = 86.50 2 84 + 89 50 55 60 65 70 75 80 85 90 95 100 © Copyright NewPath Learning. All Rights Reserved. 93-4808 www.newpathlearning.com Organizing & Displaying Data

Mean (the largest value minus the smallest value) (the average of a set of numbers) (the middle value, or average of two middle values) Range (the number that occurs most often in a set of data) Mode Line Graph Bar Graph Frequency Table A frequency table shows the totals of the tally marks. Ranger Bike Tally Total Outdoor Starburst Mountain Total Stem–and–Leaf Plot A stem-and-leaf plot shows data arranged by place value. 15, 20, 28, 31, 35, 46, 49, 52 (arranged from least to greatest) Stem (tens digit) Leaf (ones digit) 0 1 2 3 4 5 6 10 20 30 40 50 10 10 20 30 40 50 20 30 40 50 10 10 20 30 40 50 20 30 40 50 Measures of Central Tendency Organizing Data Box–and–Whisker Plot Displaying Data Scatter Plots 99 – 57 = 42 57 & 99 57, 57, 62, 64, 67, 68, 75, 79, 80, 84, 89, 99, 99 = 75.4 • Central tendency is a way to ________________________________________________________. • A box-and-whisker plot is an easy way to view the distribution of data. • Smallest value: • First quartile: • Median: • Third quartile: • Largest value: Order the data from smallest to largest value. 13 Median 75 Step 1 Step 2 Draw a number line and plot the values above. Draw the box-and-whiskers. Positive Correlation Negative Correlation 10 10 20 30 40 50 20 30 40 50 No Correlation 57, 57, 62, 64, 67, 68, 75, 79, 80, 84, 89, 99, 99 50 55 60 65 70 75 80 85 90 95 100 Key Vocabulary Terms • bar graph • box-and-whisker plot • central tendency • data set • line graph • mean • median • mode • negative correlation • no correlation • number line • positive correlation • range • scatter plot • stem-and-leaf • table 2 62 + 64 2 62 + 64 © Copyright NewPath Learning. All Rights Reserved. 93-4808 www.newpathlearning.com Organizing & Displaying Data \|xiBAHBDy01679tz]

• A sequence is a set of numbers, called terms, in a specific order. • An arithmetic sequence is a sequence in which the difference between any two consecutive terms is constant. This difference which increases or decreases by a constant amount each term is called the common difference. • The common difference is either added or subtracted to each term to determine the next term. The common difference is: This geometric sequence has a common ratio of 2. Find the 12th term of the sequence Find the 12th term of the sequence Example: Example: Example: Example: • To determine the nth term (an) of an arithmetic sequence with a common difference (d), the following formula may be used: • A geometric sequence is a sequence in which each term after the first is multiplied by a constant to obtain the following term. • The constant multiplier is called the common ratio (r). • To determine the nth term (an) of a geometric sequence with a common ratio (r), the following formula may be used: Finding the nth Term of an Arithmetic Sequence Finding the nth Term of a Geometric Sequence 3 3 3 3 3 3, 6, 12, 15, 18... 15 – 12 = 3 9, 3, 6, 9, 12, 15, 18... an = a1 + (n – 1)d a12 = a1 + (12 – 1)3 a12 = 36 an = a1 r n - 1 3, 6, 12, 24, 48, 96... a 12 = 3 • 2 12 – 1 a 12 = 3 • 2 11 a 12 = 3 • 2,048 a 12 = 6,144 2 2 2 2 ratio 2 = 1 2 3, 6, 24, 48, 96... 12, Arithmetic Sequences Geometric Sequences © Copyright NewPath Learning. All Rights Reserved. 93-4809 www.newpathlearning.com Arithmetic & Geometric Sequences

• A sequence is a _____________________ _____________________________________. • An arithmetic sequence is a sequence in which the difference between any two consecutive terms is . This difference which increases or decreases by a constant amount each term is called the . • The common difference is either or to each term to determine the next term. The common difference is: This geometric sequence has a common ratio of . Find the 12th term of the sequence Find the 12th term of the sequence Example: Example: Example: Example: • To determine the nth term (an) of an arithmetic sequence with a common difference (d), the following formula may be used: • A geometric sequence is a sequence in which each term after the first is multiplied by a constant to obtain the following term. • The constant multiplier is called the common ratio (r). • To determine the nth term (an) of a geometric sequence with a common ratio (r), the following formula may be used: Finding the nth Term of an Arithmetic Sequence Finding the nth Term of a Geometric Sequence 3, 6, 12, 15, 18... 15 – 12 = 3 9, 3, 6, 9, 12, 15, 18... an = a1 + (n – 1)d an = a1 r n - 1 3, 6, 12, 24, 48, 96... ratio = 3, 6, 24, 48, 96... 12, Arithmetic Sequences Geometric Sequences a12 = a12 = a12 = © Copyright NewPath Learning. All Rights Reserved. 93-4809 www.newpathlearning.com Arithmetic & Geometric Sequences Key Vocabulary Terms • arithmetic sequence • common difference • common ratio • constant • geometric sequence • sequence • term \|xiBAHBDy01666tz]

• In algebra, two or more equations, called a system of equations, can be solved together. • A system of equations is a set of two or more equations with the same number of variables. • A solution of a system of equations is a set of values that are solutions which satisfy all the equations. y = -3 x – 2 2 x + y = 12 2 x + y = 12 12 – 2 x = -8 + 2 x 12 = -8 + 4 x y = 12 – 2 x y = 12 – 2 (5) y = 12 – 10 y = 2 4 x – 2 y = 16 – 2 x – 2 x y = 2 x – 2 y = -3 x – 2 y = -3 x – 2 y = 2 x – 2 -2 = -2 y = 2 x – 2 Solving Systems of Equations Identifying Solutions The Graphical Method x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A system of equations can be solved by graphing all of the equations in the system. Is the ordered pair (0,-2) a solution of the system of equations below? • The solution of a system of equations is the point at which the lines intersect. • The solution set is (5,2) • The ordered pair (0,-2) is a solution of the system of equations. Solve the system of equations: Solve the system of equations: y = 2 x – 2 y = -3 x – 2 -2 = -3 (0) – 2 ? -2 = -2 -2 = 2 (0) – 2 + 2 x + 2 x + 8 + 8 4 x – 2 y = 16 -2 y = 16 – 4 x y = -8 + 2 x – 4 x – 4 x -2 -2 -2 • Solve both equations for y 20 = 4x 5 = x solution (0,-2) ? © Copyright NewPath Learning. All Rights Reserved. 93-4810 www.newpathlearning.com Systems of Equations

\|xiBAHBDy01687ozX • In algebra, two or more equations, called a , can be solved together. • A system of equations is ____________ _____________________________________ _____________________________________ . • A solution of a system of equations is _____________________________________ _____________________________________ . y = -3 x – 2 2 x + y = 12 2 x + y = 12 y = 4 x – 2 y = 16 y = 2 x – 2 y = -3 x – 2 y = -3 x – 2 y = 2 x – 2 y = 2 x – 2 Solving Systems of Equations Identifying Solutions The Graphical Method x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A system of equations can be solved by graphing all of the equations in the system. Is the ordered pair (0,-2) a solution of the system of equations below? • The solution of a system of equations is the point at which the lines intersect. • The solution set is Solve the system of equations: Solve the system of equations: 4 x – 2 y = 16 • Solve both equations for y = x Key Vocabulary Terms • algebra • equation • ordered pair • solution set • system of equations • variable © Copyright NewPath Learning. All Rights Reserved. 93-4810 www.newpathlearning.com Systems of Equations

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