Foundations of Algebra

Foundations of Algebra

Correlation to the Archdiocese of Cincinnati 2020 Graded Course of Study for Mathematics

Grade 8

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Foundations of Algebra Grade 8 Correlation to the Archdiocese of Cincinnati 2020 Graded Course of Study for Mathematics

STANDARD 1 ? THE NUMBER SYSTEM (NS)

Grade 8 Standard & Benchmark Description

Foundations of Algebra, Grade 8

M.NS.8.1 Know that there are numbers that are not rational, and approximate them by rational numbers.

M.NS.8.1.1 Know that real numbers are either rational or irrational. Understand informally that every number has a decimal expansion which is repeating, terminating, or is non-repeating and non-terminating.

Chapter 1 Rational Numbers 1-1 The Rational Numbers--TE pp. 2?3B; SB pp. 2?3 / PB pp. 1?2 1-2 The Rational Numbers on a Number Line--TE pp. 4?5B; SB pp. 4?5 / PB pp. 3?4

Chapter 2 Real Numbers 2-5 Irrational Numbers--TE pp. 44?45B; SB pp. 44?45 / PB pp. 47?48

M.NS.8.1.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e,g., 2 falls between 9 and 10). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Chapter 2 Real Numbers 2-4 Estimate Square Roots--TE pp. 42?43B; SB pp. 42?43 / PB pp. 45?46

2-5 Irrational Numbers--TE pp. 44?45B; SB pp. 44?45 / PB pp. 47?48

2-7 The Real Number System--TE pp. 48?49B; pp. SB 48?49 / PB pp. 51?52t

STANDARD 2 ? EXPRESSIONS AND EQUATIONS (EE)

Grade 8 Standard & Benchmark Description

Foundations of Algebra, Grade 8

M.EE.8.1 Work with radicals and integer exponents.

M.EE.8.1.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3-5 = 3-3 = 1/33 = 1/27.

Chapter 1 Rational Numbers 1-12 Integral Exponents--TE pp. 24?25B; SB pp. 24?25 / PB pp. 23?24

1-13 Powers and Exponents--TE pp. 26?27B; SB pp. 26?27 / PB pp. 25?26

M.EE.8.1.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number.

Chapter 2 Real Numbers 2-3 Perfect Squares and Square Roots--TE pp. 40?41B; SB pp. 40?41 / PB pp. 43?44 2-4 Estimate Square Roots--TE pp. 42?43B; SB pp. 42?43 / PB pp. 45?46

continued

TE = Teacher's Edition SB = SourceBook PB = Practice Book ? 800 221 5175

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Foundations of Algebra Grade 8 Correlation to the Archdiocese of Cincinnati 2020 Graded Course of Study for Mathematics

STANDARD 2 ? EXPRESSIONS AND EQUATIONS (EE)

Grade 8 Standard & Benchmark Description

Foundations of Algebra, Grade 8

M.EE.8.1 Work with radicals and integer exponents.

M.EE.8.1.3 Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.

M.EE.8.1.4 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 108; and the population of the world as 7 x 109; and determine that the world population is more than 20 times larger.

M.EE.8.1.5 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

M.EE.8.1.6 Use scientific notation and choose units of appropriate size for measurements of vary large or very small quantities, e.g., use millimeters per year for seafloor spreading. Interpret scientific notation that has been generated by technology.

Chapter 12 Three-Dimensional Geometry 12-5A Perfect Cubes and Cube Roots--Online 12-5B Use Cube Root Symbols--Online

Chapter 2 Real Numbers 2-3 Perfect Squares and Square Roots--TE pp. 40?41B; SB pp. 40?41 / PB pp. 43?44 2-4 Estimate Square Roots--TE pp. 42?43B; SB pp. 42?43 / PB pp. 45?46 2-6 Square Roots as Irrational Numbers--TE pp. 46?47B; SB 46?47 / PB pp. 49?50

Chapter 12 Three-Dimensional Geometry 12-5A Perfect Cubes and Cube Roots--Online 12-5B Use Cube Root Symbols--Online

Chapter 2 Real Numbers 2-1 Scientific Notation--TE pp. 36?37B; SB pp. 36?37 / PB pp. 39?40 2-2 Multiply and Divide in Scientific Notation--TE pp. 38?39B; SB pp. 38?39 / PB pp. 41?42

Chapter 2 Real Numbers 2-2 Multiply and Divide in Scientific Notation--TE pp. 38?39B; SB pp. 38?39 / PB pp. 41?42

Chapter 2 Real Numbers 2-2 Multiply and Divide in Scientific Notation--TE pp. 38?39B; SB pp. 38?39 / PB pp. 41?42

TE = Teacher's Edition SB = SourceBook PB = Practice Book ? 800 221 5175

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Foundations of Algebra Grade 8 Correlation to the Archdiocese of Cincinnati 2020 Graded Course of Study for Mathematics

STANDARD 2 ? EXPRESSIONS AND EQUATIONS (EE)

Grade 8 Standard & Benchmark Description

Foundations of Algebra, Grade 8

M.EE.8.2 Understand the connections between proportional relationships, lines, and linear equations.

M.EE.8.2.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Chapter 6 Linear Functions and Inequalities 6-9 Direct Variation--TE pp. 172?173B; SB pp. 172?173 / PB pp. 191?192

Chapter 7 Ratio and Proportion 7-1 Ratios, Rates, and Unit Rates--TE pp. 188?189B; SB pp. 188?189 / PB pp. 211?212 7-3 Conversion Factors and Measurement Systems-- TE pp. 192?193B; SB pp. 192?193 / PB pp. 215?216 7-5 Direct Proportions--TE pp. 196?197B; SB pp. 196?197 / PB pp. 219?220 7-5A Proportions and Unit Rates--Online 7-5B Graph Proportional Relationships--Online

M.EE.8.2.2 Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Chapter 7 Ratio and Proportion 7-5C Compare Proportional Relationships--Online

M.EE.8.2.3 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Chapter 6 Linear Functions and Inequalities 6-6 Linear Functions: Standard Form and SlopeIntercept Form--TE pp. 166?167B; SB pp. 166?167 / PB pp. 185?186 6-9 Direct Variation--TE pp. 172?173B; SB pp. 172?173 / PB pp. 191?192

Chapter 10 Geometric Measures and Coordinate Geometry

10-7 Coordinate Plane and Polygons--TE pp. 278? 279B; SB pp. 278?279 / PB pp. 313?314

M.EE.8.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

M.EE.8.3.1 Solve linear equations in one variable.

Chapter 3 Expressions and Equations 3-3 Equations--TE pp. 68?69B; SB pp. 68?69 / PB pp. 75?76

TE = Teacher's Edition SB = SourceBook PB = Practice Book ? 800 221 5175

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Foundations of Algebra Grade 8 Correlation to the Archdiocese of Cincinnati 2020 Graded Course of Study for Mathematics

STANDARD 2 ? EXPRESSIONS AND EQUATIONS (EE)

Grade 8 Standard & Benchmark Description

Foundations of Algebra, Grade 8

M.EE.8.3 Analyze and solve linear equations and pairs of simultaneous linear equations.

M.EE.8.3.2 Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers.)

Chapter 3 Expressions and Equations 3-3 Equations--TE pp. 68?69B; SB pp. 68?69 / PB pp. 75?76

3-10A Identify Equations with One, Many, or No Solutions--Online

3-10B Solve Equations with One, Many, or No Solutions--Online

M.EE.8.3.3 Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Chapter 1 Rational Numbers 1-15 Problem-Solving Strategy: Make a Drawing--TE pp. 30?31B; SB pp. 30?31 / PB pp. 29?30

Chapter 3 Expressions and Equations 3-3 Equations--TE pp. 68?69B; SB pp. 68?69 / PB pp. 75?76 3-4 One-Step Addition and Subtraction Equations-- TE pp. 70?71B; SB pp. 70?71 / PB pp. 77?78 3-5 One-Step Multiplication and Division Equations-- TE pp. 72?73B; SB pp. 72?73 / PB pp. 79?80 3-6 Model Two-Step Equations--TE pp. 74?75B; SB pp. 74?75 / PB pp. 81?82 3-7 Two-Step Equations--TE pp. 76?77B; SB pp. 76?77 / PB pp. 83?84 3-8 Multistep Equations with Grouping Symbols--TE pp. 78?79B; SB pp. 78?79 / PB pp. 85?86 3-9 Multistep Equations with Variables on Both Sides--TE pp. 80?81B; SB pp. 80?81 / PB pp. 87?88 3-10 Multistep Equations: Fractions and Decimals--TE pp. 82?83B; SB pp. 82?83 / PB pp. 89?90 3-14 Problem-Solving Strategy: Guess and Test--TE pp. 90?91B; SB pp. 90?91 / PB pp. 97?98

Chapter 6 Linear Functions and Inequalities 6-14 Problem-Solving Strategy: Reason Logically--TE pp. 182?183B; SB pp. 182?183 / PB pp. 201?202

Chapter 7 Ratio and Proportion 7-2 Proportions--TE pp. 190?191B; SB pp. 190?191 / PB pp. 213?214 7-12 Problem-Solving Strategy: Solve a Simpler Problem--TE pp. 210?211B; SB pp. 210?211 / PB pp. 233?234

continued

TE = Teacher's Edition SB = SourceBook PB = Practice Book ? 800 221 5175

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