CL Grade 6 Alignment to OAS. Page 1 of 29

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1 CL Grade 6 Alignment to OAS Cluster 6.N.1 Read, write, and represent integers and rational numbers expressed as fractions, decimals, percents, and ratios; write positive integers as products of factors; use these representations in realworld and mathematical situations 6.N.2 Add and subtract integers in order to solve real-world and mathematical problems Standard Description Course Module Topic 6.N N N N N N N N N.2.3 Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of zero in each situation Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and = Explain that a percent represents "parts out of 100" and ratios "to 100" Determine Equivalencies among fractions, decimals, and percent. Select among these representations to solve problems. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents Determine the greatest common factors and least common multiples. Use Common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property Estimate solutions to addition and subtraction of integers problems in order to assess the reasonableness of results Illustrate addition and subtraction of integers using a variety of representations Add and Subtract integers; use efficient and generalizable procedures including but not limited to standard algorithms 4: Moving Beyond Signed Numbers 4: Moving Beyond Positive Quantities 1: Signed Numbers 2: Positive Rational Numbers 1: Signed Numbers 2: Relating Quantities 2: Percents 2: Relating Quantities 2: Percents 2: Operating with Signed Numbers de6 2: Operating with Signed Numbers de6 2: Operating with Signed Numbers de6 MIDDLE SCHOOL MATH SOLUTION TEXTBOOK 1: Factors and Area 1: Factors and Area 1: Adding and Subtracting Rational Numbers 1: Adding and Subtracting Rational Numbers 1: Adding and Subtracting Rational Numbers (Module Number followed by page number ) 1: Human Number Line (M4-7) 2: Magnificent Magnitude (M4-23) 3: What's In a Name (M4-35) 1: Thinking Rationally (M1-71) 1: Human Number Line (M4-7) 2: Magnificent Magnitude (M4-23) 3: What's In a Name (M4-35) 1: We Are Family! (M2-109) 2: Warming the Bench (M2-123) 3: The Forest for the Trees (M2-137) 1: We Are Family! (M2-109) 2: Warming the Bench (M2-137) 4: Searching for Common Ground (M1-39) 5: Composing and Numbers (M1-51) 4: Searching for Common Ground (M1-39) 5: Composing and Numbers (M1-51) 1: Math Football (M2-7) 4: What's the Difference (M2-49) 1: Math Football (M2-7) 2: Walk the Line (M2-17) 3: Two Color Counters (M2-31) 4: What's the Difference (M2-49) 5: All Mixed Up (M2-69) 1: Math Football (M2-7) 2: Walk the Line (M2-17) 3: Two Color Counters (M2-31) 4: What's the Difference (M2-49) 5: All Mixed Up (M2-69) 1: Introduction to Negative Numbers 5: Negative Numbers and the Four Quadrants 1: Integers 2: Representing Integers on Number Lines 2: Ratios, Rates, and 3: Introduction to Percents Percent 1: Percent Models 2: Ratios, Rates, and 3: Introduction to 2: Fraction, Decimal, Percent Percents Percent Comparisons 1: Writing Equivalent Fractions using Equivalent Fractions Part-To-Whole Models Fraction Addition and 2: Using the Solver with Unlike 6th Grade RTI Subtraction Denominators Mixed Number 2: Adding and Subtracting with Addition and Unlike Denominators Subtraction 4: Exploring the Distributive Property 3: Numeric and Algebraic with Numeric Expressions 1: Number Properties Expressions 5: Using the Distributive Property with Numeric Expressions 1: Adding and Subtracting Negative 3: Rational Number Integers 1: Integer Operations Operations 2: Using Number Lines to Add and Subtract Integers 1: Adding and Subtracting Negative 3: Rational Number Integers 1: Integer Operations Operations 2: Using Number Lines to Add and Subtract Integers Page 1 of 29

2 CL Grade 6 Alignment to OAS Cluster 6.N.3 Understand the concept of ratio and its relationship to fractions and percents and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Standard Description Course Module Topic 6.N.3.1 Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different 2: Relating Quantities 1: Ratios 6.N.3.2 Determine the unit rate for ratios 2: Relating Quantities 6.N N N N.4.2 Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations Use multiplicative reasoning and representations to solve ratio and unit rate problems Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers. Use the estimates to assess the reasonableness of results in the context of the problem. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships 3: Unit Rates and Conversions 2: Relating Quantities 2: Percents 2: Relating Quantities 1: Ratios 3: Unit Rates and Conversions 2: Positive Rational Numbers (Module Number followed by page number ) 1: It's All Relative (M2-7) 2: Going Strong (M2-25) 6: One is Not Enough (M2-85) 2: What is the Best Buy? (M2-185) 3: Seeing Things Differently (M2-199) 1: We Are Family (M2-109) 2: Warming the Bench (M2-123) 3: The Forest for the Trees (M2-137) 3: Oh, Yes, I Am the Muffin Man (M2-37) 4: A Trip to the Moon (M2-57) 5: They're Growing (M2-69) 2: Did you Get the Part? (M1-83) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse (M1-131) 3: Decimals and Volume 3: Breaking the Fourth Wall (M1-2: Positive Rational Numbers 143) 4: Dividend in the House (M1-165) 2: Did you Get the Part? (M1-83) 2: Ratios, Rates, and Percents 2: Ratios, Rates, and Percents 2: Ratios, Rates, and Percents 1: Ratio and Rate Reasoning 1: Ratio and Rate Reasoning 3: Introduction to Percent 1: Ratio and Rate Reasoning 3: Yours is to Reason Why! (M1-93) 1: Fraction Division 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Decimals and Volume 3: Breaking the Fourth Wall (M1-2: Positive Rational Numbers 1: Many Ways to Measure (M2-165) 2: Introduction to Unit Rates (M2-143) 4: Dividend in the House (M1-165) 2: Did you Get the Part? (M1-83) 2: Ratios, Rates, and Percents 1: Fraction and Decimal Operations 2: Problem Solving using Ratio and Rate 2: Decimal Operations 3: Yours is to Reason Why! (M1-93) 1: Fraction Division 1: Understanding Ratio 4: Fractional Rates 5: Comparing Rates 3: Determining a Part Given a Percent and a Whole 4: Determining a Whole Given a Percent and a Part 2: Equivalent Ratios 3: Multiple Representations of Ratios 1: Problem Solving with Equivalent Ratios and Rates Using Ratio Tables 1: Representing Fraction Division 2: Interpreting Remainders with Models 3: Developing the Fraction Division Algorithm 4: Exploring Decimal Facts 5: Multiplying and Dividing Decimals 4: Multiplying and Dividing Rational Numbers 6.N.4 Multiply and divide decimals, fractions, and mixed numbers; solve realworld and mathematical problems with rational numbers 6.N.4.3 Multiply and divide fractions and decimals using efficient and generalizable procedures 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Decimals and Volume 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 2: Positive Rational 2: Did You Get the Part? (M1-83) Numbers 3: Yours is to Reason Why! (M1-93) 1: Fraction and Decimal Operations 2: Decimal Operations 1: Fraction Division 6: Decimal Products and Quotients 2: Interpreting Remainders Using Models Page 2 of 29

3 CL Grade 6 Alignment to OAS Cluster numbers 6.A.1 Recognize and Represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs, and rules to solve realworld and mathematical problems 6.A.2 Use properties of arithmetic to generate MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Standard Description Course Module Topic 6.N A A A.1.3 Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry and data requiring arithmetic with decimals, fractions, and mixed numbers Plot integer and rational-valued ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality is true or false Generate equivalent expressions and evaluate expressions involving 3: Determining Unknown Quantities 4: Moving Beyond the Four Quadrants (Module Number followed by page number ) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Decimals and Volume 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 1: Expressions 2: Into the Unknown (M3-23) 2: 3: Graphing Quantitative 2: The Four Quadrants 5: Describing Variability 2: Numerical of Quantities 4: Moving Beyond the Four Quadrants 3: Determining Unknown Quantities 4: Moving Beyond Positive Quantities 3: Determining Unknown Quantities Summaries of Data 2: The Four Quadrants 3: Graphing Quantitative 3: Play it in Reverse (M3-119) 4: Getting Real (M3-135) 1: Every Graph Tells a Story (M3-155) 3: Planes, Trains, and Paychecks (M3-193) 4: Triathlon Training (M3-207) 2: It's a Bird, It's a Plane It's a Polygon on the Plane (M4-57) 3: There are Many Paths (M4-87) 2: Box It Up (M5-87) 3: March MADness (M5-105) 1: Four is Better Than One (M4-57) 2: It's a Bird, It's a Plane...It's a Polygon on the Plane (M4-73) 3: There are Many Paths (M4-87) 1: Every Graph Tells a Story (M3-155) 2: The Power of a Horizontal Line (M3-183) 3: Planes, Trains, and Paychecks (M3-193) 4: Triathlon Training (M3-207) 4: One Step 5: Negative Numbers and the Four Quadrants 4: One Step 2: Decimal Operations 5: Multiplying and Dividing Decimals 4: Problem Solving with One-Step 2: Area 3: Problem Solving with Decimals 2: Calculating Area of Various Figures 3: Solving Area Problems 4: Calculating Area of Composite Figures 1: Calculating Volume of Right Prisms 3: Volume and Surface 2: Using Volume of Right Prisms Area 3: Calculating Surface Area of Right Prisms 1: Measures of Central Mode Tendency 3: Mean Absolute Deviation 2: The Coordinate Plane 4: Problem Solving with One-Step 5: Negative Numbers and 3: Multiple 2: The Four Quadrants 3: There are Multiple Paths (M4-87) the Four Quadrants Representations 1: Expressions 2: 3: Graphing Quantitative 1: Factors and Area 2: Into the Unknown (M3-23) 3: Are They Saying the Same Thing? (M3-53) 5: DVDs and Songs (M3-67) 1: First Among Equals (M3-87) 3: Play it in Reverse (M3-119) 4: Getting Real (M3-135) 1: Every Graph Tells a Story (M3-155) 2: The Power of a Horizontal Line 1: Taking Apart Numbers and Shapes (M1-7) 1: Fraction and Decimal Operations 6: Geometric Measurement 7: Measures of Central Tendency and Data Displays 3: Numeric and Algebraic Expressions 4: One Step 2: Algebraic Expressions 2: Solving One-Step 3: Solving One-Step Inequalities 1: Number Properties 1: Calculating Mean, Median, and 3: Measuring the Effects of Changing Data Sets 1: Calculating Mean Absolute Deviation 1: Exploring Symmetry on the Coordinate Plane 2: Identifying and Interpreting Ordered Pairs 3: Plotting Points 1: Patterns and One-Step 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with Decimals 1: Solving One-Step using Multiple Representations in Four Quadrants 1: Evaluating Multi-step Expressions 2: Evaluating Expressions with Multiple Variables 3: Using Substitution to Identify Solutions to 1: Graphing Inequalities with Positive Rational Numbers 1: Commutative and Associative Properties 2: Order of Operations Page 3 of 29

4 CL Grade 6 Alignment to OAS Cluster arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive and negative numbers 6.A.3 Use and inequalities to represent real-world and mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context. 6.GM.1 Calculate areas of squares, parallelograms, and triangles to solve realworld and mathematical problems MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Standard Description Course Module Topic and evaluate expressions involving 6.A A A GM GM GM.1.3 positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems Represent real-world or mathematical situations using expressions, equations, and inequalities involving variables and rational numbers Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = q and px=q where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm Develop and use formulas for the area of triangles Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real- 3: Determining Unknown Quantities 3: Determining Unknown Quantities 4: Moving Beyond the Four Quadrants 3: Determining Unknown Quantities 4: Moving Beyond Positive Quantities 4: Moving Beyond Positive Quantities 4: Moving Beyond Positive Quantities 1: Expressions 1: Expressions 2: 3: Graphing Quantitative (Module Number followed by page number ) 2: Into the Unknown (M3-23) 3: Second Verse, Same as the First (M3-35) 4: Are They Saying the Same Thing? (M3-53) 5: DVDs and Songs (M3-67) 1: First Among Equals (M3-87) 2: Bar None (M3-107) 3: Play it in Reverse (M3-119) 4: Getting Real (M3-135) 1: Every Graph Tells a Story (M3-155) 2: The Power of a Horizontal Line (M3-183) 3: Planes, Trains, and Paychecks (M3-193) 4: Triathlon Training (M3-207) 2: The Four Quadrants 3: There are Many Paths (M4-87) 2: 3: Graphing Quantitative 1: Factors and Area 2: The Four Quadrants 1: Factors and Area 2: The Four Quadrants 1: Factors and Area 2: The Four Quadrants 1: Matter (M3-7) 3: Numeric and Algebraic 3: Second Verse, Same as the First Expressions (M3-35) 4: Are they Saying the Same Thing? (M3-53) 2: Bar None (M3-107) 3: Play it in Reverse (M3-119) 4: Getting Real (M3-135) 2: The Power of a Horizontal Line (M3-183) 3: Planes, Trains, and Paychecks (M3-193) 4: Triathlon Training (M3-207) 2: All About that Base and Height (M1-15) 3: Slicing and Dicing (M1-29) 2: It's a Bird, It's a Plane It's a Polygon on the Plane (M4-57) 2: All About that Base and Height (M1-15) 3: Slicing and Dicing (M4-57) 2: It's a Bird, It's a Plane It's a Polygon on the Plane (M4-57) 2: All About that Base and Height (M1-15) 3: Slicing and Dicing (M1-29) 2: It's a Bird, It's a Plane It's a Polygon on the Plane (M4-57) 6: Geometric Measurement 6: Geometric Measurement 4: One Step 4: One Step 4: One Step 6: Geometric Measurement 3: Equivalent Algebraic with Algebraic Expressions Expressions 3: Solving One-Step Inequalities 4: Problem Solving with One-Step 1: Reasoning with Expressions and 2: Solving One-Step 4: Problem Solving with One-Step 2: Area 2: Area 2: Area 1: Modeling Equivalent Algebraic Expressions 2: Exploring the Distributive Property 3: Simplifying Algebraic Expressions (No Type In) 4: Simplifying Algebraic Expressions (Type In) 1: Graphing Inequalities with Positive Rational Numbers 1: Patterns and One-Step 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with Decimals 1: Using Picture Algebra with Addition, Subtraction, and Multiplication 2: Using Picture Algebra with 1: Solving One-Step with a Balance 1: Patterns and One-Step 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with Decimals 1: Developing Area Formulas 2: Calculating Area of Various Figures 3: Solving Area Problems 4: Calculating Area of Composite Figures 1: Developing Area Formulas 2: Calculating Area of Various Figures 3: Solving Area Problems 4: Calculating Area of Composite Figures 1: Developing Area Formulas 2: Calculating Area of Various Figures 3: Solving Area Problems 4: Calculating Area of Composite Figures Page 4 of 29

5 CL Grade 6 Alignment to OAS Cluster 6.GM.2 Understand and use the relationships between angles in geometric figures 6.GM.3 Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems 6.GM.4 Use translations, reflections, and rotations to establish congruency and understand symmetries 6.D.1 Display and Analyze Data MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Standard Description Course Module Topic 6.GM M GM GM GM GM GM GM D D.1.2 Solve problems using the relationships between angles formed by intersecting lines 5: Constructing and Measuring Develop and use the fact that the sum of the interior angles of a 1: Transforming triangle is 180* to determine Geometric Objects missing angle measures in a triangle de6 Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units Solve problems in various realworld and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units Predict, describe, and apply translations, reflections, and rotations to a two-dimensional figure Recognize that translations, reflections, and rotations preserve congruency and use them to show that two figures are congruent Use distances between two points that are either vertical or horizontal to each other to solve real-world and mathematical problems about congruent two-dimensional figures Identify and describe line(s) of symmetry in two-dimensional shapes Calculate mean, median, and mode for a set of real-world data Explain and justify which measure of central tendency would provide the most descriptive information for a given set of data de6 2: Relating Quantities 2: Relating Quantities 1: Transforming Geometric Objects de6 1: Transforming Geometric Objects de6 4: Expanding Number Systems de6 1: Transforming Geometric Objects de6 (Module Number followed by page number ) 1: Angles and Triangles 2: Special Delivery (M5-19) 5: 1: Angle Properties 3: Line and Angle 3: Unit Rates and Conversions 3: Unit Rates and Conversions 1: Rigid Motion Transformations 1: Rigid Motion Transformations 2: Pythagorean Theorum 1: Rigid Motion Transformations 5: Describing Variability 2: Numerical of Quantities Summaries of Data 5: Describing Variability 2: Numerical of Quantities Summaries of Data 1: Pulling a One-Eighty (M1-167) 1: Many Ways to Measure (M2-165) 6: Geometric 1: Many Ways to Measure (M2-165) Measurement 2: Slides, Flips, and Spins (M1-17) 3: Lateral Moves (M1-39) 4: Mirror, Mirror (M1-53) 5: Half Turns and Quarter Turns (M1-67) 6: Every Which Way (M1-83) 1: Patty Paper, Patty Paper (M1-7) 2: Slides, Flips, and Spins (M1-17) 3: Lateral Moves (M1-39) 4: Mirror, Mirror (M1-53) 5: Half Turns and Quarter Turns (M1-67) 6: Combining Rigid Motions (M1-83) 3: Pythagoras Meets Descartes (M4-87) 1: Slides, Flips, and Spins (M1-17) 2: Mirror, Mirror (M1-53) 1: In the Middle (M5-71) 4: You Chose Wisely (M5-117) 4: Geometric Transformations 7: Measures of Central Tendency and Data Displays 7: Measures of Central Tendency and Data Displays 1: Ratio and Rate Reasoning 1: Transformations of Figures on the Coordinate Plane 1: Calculating Angles 2: Classifying Angles and Determining Unknown Measures 1: Converting Within Systems 1: Translating Plane Figures 2: Rotating Plane Figures 3: Reflecting Plane Figures 5: Performing One Transformation 6: Performing Multiple Transformations See Glossary-Line(s) of Symmetry, Symmetry, and Reflections 1: Measures of Central 1: Calculating Mean, Median, and Tendency Mode 1: Measures of Central 2: Determining Appropriate Measure Tendency Page 5 of 29

6 CL Grade 6 Alignment to OAS Cluster 6.D.2 Use to solve real-world and mathematical problems; represent probabilities using fractions and decimals MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Standard Description Course Module Topic 6.D D D D.2.3 Create and analyze box and whisker plots observing how each segment contains one quarter of the data Represent possible outcomes using a probability continuum from impossible to certain Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by use of tree diagrams, tables or pictorial representations Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there 5: Describing Variability 2: Numerical of Quantities 4: Analyzing Probabilities de6 Populations and 4: Analyzing 4: Analyzing Populations and Probabilities de6 Populations and Probabilities de6 Summaries of Data 1: Introduction to 1: Introduction to 2: Compound 1: Introduction to 2: Compound (Module Number followed by page number ) 2: Box It Up (M5-87) 1: Rolling, Rolling, Rolling (M4-7) 1: Rolling, Rolling, Rolling (M4-7) 2: Give the Models a Chance (M4-23) 3: Toss the Cup (M4-33) 4: A Simulating Conversation (M4-47) 1: Evens or Odds (M4-73) 2: Three Girls and No Boys? (M4-89) 3: Pet Shop Probabilities (M4-101) 4: On a Hot Streak (M4-113) 3: Toss the Cup (M4-33) 4: A Simulating Conversation(M4-47) 1: Evens or Odds (M4-73) 4: On a Hot Streak (M4-113) 7: Measures of Central 1: Constructing Box Plots Tendency and Data 4: Box Plots Displays 2: Interpreting Box Plots 6: Data Comparisons and 2: Introduction to 1: Determining Probabilities 1: Determining Probabilities 6: Data Comparisons and 2: Introduction to 3: Calculating Compound Probabilities 6: Data Comparisons and 2: Introduction to 2: Comparing Experimental and Theoretical Probabilities Page 6 of 29

7 CL Grade 7 Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic Know that every rational number (Module Number followed by Page Number) can be written as the ratio of two 2: Operating with 2: Multiplying ands 7.N.1.1 2: Be Rational (M2-103) integers or as a terminating or Signed Numbers Dividing Rational Numbers repeating decimal. 7.N.1 Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals 7.N N.1.3 Compare and order rational numbers expressed in various forms using the symbols >, <, or = Recognize and generate equivalent expressions of rational numbers, including equivalent fractions de7 4: Moving Beyond Positive Quantities 2: Operating with Signed Numbers 1: Signed Numbers 1: Human Number Line (M4-7) 5: Negative Numbers and the Four Quadrants 1: Equal Groups (M2-89) 2: Be Rational (M2-103) 2: Multiplying ands 3: Building a Wright Brothers' Flyer Dividing Rational Numbers (M2-113) 4: Properties Schmoperties (M2-125) 1: Integers 2: Representing Integers on Number Lines 7.N.2.1 Estimate solutions to multiplication and division of integers in order to assess the reasonableness of results 2: Operating with Signed Numbers 2: Multiplying ands 1: Equal Groups (M2-89) Dividing Rational Numbers 2: Be Rational (M2-103) 7.N.2 Calculate with integers, with and without positive integer exponents, to solve real-world and mathematical problems; explain the relationship between absolute value of a rational number and the distance of that number from zero 7.N N N N.2.5 Illustrate multiplication and division of integers using a variety of representations Solve real-world and mathematical problems involving addition, subtraction, multiplication, and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms Raise integers to positive integer exponents Solve Real world and mathematical problems involving calculations with rational numbers and positive integer exponents de7 de7 2: Operating with Signed Numbers 2: Operating with Signed Numbers 3: Determining Unknown Quantities 3: Determining Unknown Quantities 2: Operating with Signed Numbers 2: Multiplying ands 1: Equal Groups (M2-89) 2: Be Rational (M2-103) 3: Rational Number Dividing Rational Numbers 4: Properties Schmoperties (M2- Operations 125) 2: Walk The Line (M2-17) 1: Adding and Subtracting 3: Two-Color Counters (M2-31) Rational Numbers 4: What's the Difference (M2-49) 5: All Mixed Up (M2-69) 1: Equal Groups (M2-89) 3: Rational Number 2: Be Rational! (M2-103) Operations 2: Multiplying ands 3: Building a Wright Brothers' Flyer Dividing Rational Numbers (M2-113) 4: Properties Schmoperties (M2-125) 1: Expressions 1: Matter (M3-7) 3: Rational Number Operations 1: Expressions 1: Matter (M3-7) 3: Building a Wright Brothers' Flyer 2: Multiplying ands (M2-113) 3: Rational Number Dividing Rational Numbers 4: Properties Schmoperties (M2- Operations 125) 1: Integer Operations 3: Multiplying and Dividing Integers 1: Adding and Subtracting Integers 2: Using Number Lines to Add and 1: Integer Operations Subtract Integers 3: Multiplying and Dividing Integers 4: Using Order of Operations to Simplify Numeric Expressions (No 1: Integer Operations Type In) 5: Using Order of Operations to Simplify Numeric Expressions (Type In) 4: Using Order of Operations to Simplify Numeric Expressions (No 1: Integer Operations Type In) 5: Using Order of Operations to Simplify Numeric Expressions (Type In) Page 7 of 29

8 CL Grade 7 Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic 7.A.1 Understand the concept of proportionality in realworld and mathematical situations, and distinguish between proportional and other relationships 7.A.2 Recognize proportional relationships in realworld and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols, and graphs; solve problems involving proportional relationships and interpret results in the original context 7.N A A A A A.2.3 Explain the relationship between absolute value of a rational number and the distances of that number from zero on a number line. Use the symbol for absolute value. Describe that the relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx; distinguish proportional relationships from other relationships, including inversely proportional relationships xy=k or y = k/x Recognize the graph of a proportional relationship is a line through the origin and the coordinates (1,r) where both r and the slope are the unit rate (constant of proportionality, k) Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations Solve multi-step problems involving proportional relationships involving distance-time, percent increase or decrease, discounts, tips, unit pricing, similar figures, and other real-world and mathematical situations Use proportional reasoning to solve real-world and mathematical problems involving ratios de7 4: Moving Beyond Positive Quantities 1: Thinking Proportionally 1: Thinking Proportionally 1: Thinking Proportionally 1: Thinking Proportionally 1: Thinking Proportionally (Module Number followed by Page Number) 1: Signed Numbers 2: Magnificent Magnitude (M4-23) 3: Proportionality 3: Proportionality 3: Proportionality 4: Proportional 2: Fractional Rates 1: Circles and Ratios 1: How Does Your Garden Grow (M1-91) 2: Complying with Title IX (M1-109) 4: Minding Your Ps and Qs (M1-139) 1: How Does Your Garden Grow (M1-91) 3: Fish-Inches (M1-127) 4: Minding Your Ps and Qs (M1-139) 1: How Does Your Garden Grow (M1-91) 2: Complying with Title IX (M1-109) 3: Fish-Inches (M1-127) 4: Minding Your Ps and Qs (M1-139) 1: Markups and Markdowns (M1-161) 2: Perks of Work (M1-177) 3: No Taxation without Calculation (M1-197) 4: More Ups and Downs (M1-209) 5: Pound for Pound, Inch for Inch (M1-223) 1: Making Punch (M1-51) 2: Eggzactly (M1-59) 3: Tagging Sharks (M1-69) 1: Pi: The Ultimate Ratio (M1-7) 5: Negative Numbers and the Four Quadrants 1: Integers 3: Using Absolute Value 1: Introduction to Direct Variation 3: Representing 1: Proportional Proportional 3: Representing 1: Proportional Proportional 3: Representing 1: Proportional Proportional by 2: Proportional Reasoning and Percents 2: Proportional Reasoning 3: Problem Solving and Percents with Percents using Proportional 5: 2: Scale Drawings 1: Problem Solving using Ratio and Rate Reasoning 1: Proportional 2: Proportional Reasoning 2: Writing Direct Variation 3: Converting between Proportions and Direct Variation 4: Modeling Direct Variation 5: Determining Characteristics of Direct Variation Graphs 1: Introduction to Direct Variation 2: Writing Direct Variation 3: Converting between Proportions and Direct Variation 4: Modeling Direct Variation 5: Determining Characteristics of Direct Variation Graphs 1: Using Proportions to Solve Percent Problems 2: Solving Percent Problems 1: Calculating Percent Change and Final Amounts 2: Using Percents and Percent Change 1: Using Scale Drawings 2: Using Scale Factor 1: Problem Solving with Equivalent Ratios and Rates using Tables 2: Problem Solving with Equivalent Ratios and Rates using Double Number Lines 3: Problem Solving with Equivalent Ratios and Rates Using Graphs 1: Solving Proportions using Equivalent Ratios 2: Solving Proportions using Means and Extremes Page 8 of 29

9 CL Grade 7 Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic 2: Fractional Rates (Module Number followed by Page Number) 1: Making Punch (M1-51) 2: Eggzactly (M1-59) 3: Tagging Sharks (M1-69) 7.A A.3.1 Use proportional reasoning to assess the reasonableness of solutions Write and solve problems leading to linear equations with one variable in the form px+q=r and p(x+q) = r, where p, and q are non-negative rational numbers 1: Thinking Proportionally 3: Reasoning Algebraically 3: Proportionality 4: Proportional 2: Two-Step 4: How Does Your Garden Grow? (M1-91) 5: Complying with Title IX (M1-109) 6: Fish-Inches (M1-127) 7: Minding Your Ps and Qs (M1-139) 1: Markups and Markdowns (M1-161) 2: Perks of Work (M1-177) 3: No Taxation without Calculation (M1-197) 4: More Ups and Downs (M1-209) 5: Pound for Pound, Inch for Inch (M1-223) 1: Picture Algebra (M3-53) 2: Expressions that Play Together (M3-65) 3: Formally Yours (M3-77) 4: Two-Step 2: Picture Algebra 3: Solving Two-Step 1: Using Picture Algebra with 2: Modeling Two-Step 2: Solving with Multiplication (No Type In) 3: Solving with Multiplication (Type In) 4: Solving with Division (No Type In) 5: Solving with Division (Type In) 6: Solving Two-Step 7.A.3 Represent and solve linear equations 7.A A.3.3 Represent, write, solve, and graph problems leading to linear inequalities with one variable of the form x + p >q and x+p<q, where p and q are nonnegative rational numbers Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers de7 3: Determining Unknown Quantities 3: Reasoning Algebraically 3: Reasoning Algebraically 2: 2: Two-Step 2: Two-Step 3: Multiple Representations of 1: First Among Equals (M3-87) 4: One-Step 4: Be Greater Than (M3-95) 1: Picture Algebra (M3-53) 2: Expressions that Play Together (M3-65) 3: Formally Yours (M3-77) 4: Be Greater Than (M3-95) 1: Put It On the Plane (M3-125) 2: Stretches, Stacks, and Structure (M3-139) 3: Deep Flight I (M3-155) 4: Two-Step 4: Two-Step 3: Solving One-Step Inequalities 2: Picture Algebra 2: Picture Algebra 3: Solving Two-Step 4: Problem Solving with Two-Step and Inequalities 1: Graphing Inequalities with positive Rational Numbers 2: Solving One-Step Linear Inequalities 1: Using Picture Algebra with 2: Modeling Two-Step 3. Solving with Multiplication (No Type In) 4: Solving with Multiplication (Type In) 5: Solving with Division (No Type In) 6: Solving with Division (Type In) 7: Solving Two-Step " 1: Using Picture Algebra with 2: Modeling Two-Step 2: Solving with Multiplication (No Type In) 3: Solving with Multiplication (Type In) 4: Solving with Division (No Type In) 5: Solving with Division (Type In) 6: Solving Two-Step 1: Using Linear and Inequalities 2: Solving Problems with Integers 3: Solving Problems with Decimals and Fractions Page 9 of 29

10 CL Grade 7 Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic (Module Number followed by Page Number) 7.A.4 Use order of operations and properties of operations to generate equivalent numerical and algebraic expressions containing rational numbers and grouping symbols; evaluate such expressions 7.A A.4.2 Use Properties of operations (limited to associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and : See supplemental materials on whole number exponents Carnegie de7 : See supplemental materials on Carnegie de7 Apply understanding of order of operations and grouping symbols when using calculators and other technologies 2: Operating with Signed Numbers 3: Determining Unknown Quantities 3: Determining Unknown Quantities 3: Reasoning Algebraically 2: Multiplying ands 3: Building a Wright Brothers' Flyer (M2-113) 3: Rational Number Dividing Rational Numbers 4: Properties Schmoperties (M2- Operations 125) 1: Matter (M3-7) 2: Into the Unknown (M3-23) 1: Expressions 3: Second Verse, Same as the First 4: Two-Step (M3-35) 4: Are They Saying the Same Thing? (M3-53) 3: Rational Number 1: Expressions 1: Matter (M3-7) Operations 1: No Substitute for Hard Work - (M3-7) 3: Rational Number 1: Algebraic Expressions 2: Mathematics Gymnastics - (M3-19) Operations 3: All My Xs - (M3-33) 4: Using Order of Operations to Simplify Numeric Expressions (No 1: Integer Operations Type In) 5: Using Order of Operations to Simplify Numeric Expressions (Type In) 1: Factoring Linear Expressions 2: Using Order of Operations to Simplify Algebraic Expressions (No 1: Variable Expressions Type In) 3: Using Order of Operations to Simplify Algebraic Expressions (Type In) 4: Using Order of Operations to Simplify Numeric Expressions (No 1: Integer Operations Type In) 5: Using Order of Operations to Simplify Numeric Expressions (Type In) 4: Using Order of Operations to Simplify Numeric Expressions (No 1: Integer Operations Type In) 5: Using Order of Operations to Simplify Numeric Expressions (Type In) 7.GM.1Develop and Understand the concept of surface area and volume of rectangular prisms 7.GM.1.2 Using a variety of tools and strategies, develop the concept that volume of a rectangular prism with rational-valued edge lengths can be found by counting the total number of same-sized units cubes that fill a shape without gaps or overlap. Use appropriate measurements such as cm^3 de7 de7 3: Decimals and Volume 1: Factors and Area 1: Length, Width, and Depth (M1-115) 2: All About that Base and Height (M1-15) 6: Geometric Measurement 6: Geometric Measurement 3: Volume and Surface Area 2: Area 1: Calculating Volume of Right Prisms 1: Developing Area Formulas 2: Calculating Area of Various Figures 7.GM.2 Determine the area of trapezoids and area and perimeter of composite figures 7.GM.3 Use reasoning with proportions and ratios to determine measurements justify formulas, and solve real-world and 7.GM.4 Analyze the 7.GM GM GM.4.3 Find the Area and perimeter of composite figures to solve realworld and mathematical problems Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations Graph and describe translations and reflections of figures on a coordinate plane and determine the coordinates of the vertices of the figure after the transformation de7 de7 de7 1: Transforming Geometric Objects 1: Thinking Proportionally 1: Transforming Geometric Objects 1: Factors and Area 1: Circles and Ratio 2: Similarity 4: Proportional 1: Rigid Motion Transformations 3: Slicing and Dicing (M1-51) 2: That's a Spicy Pizza (M1-19) 3: Circular Reasoning (M1-33) 1: Pinch-Zoom (M1-109) 2: Rising, Running, Stepping, Scaling (M1-125) 3: From Here to There (M1-141) 5: Pound for Pound, Inch for Inch (M1-223) 3: Lateral Moves (M1-39) 4: Mirror Mirror (M1-53) 6: Geometric Measurement 4: Geometric Transformations 2: Area 3: Circles 1: Transformations on the Coordinate Plane 5: 2: Scale Drawings 4: Geometric Transformations 1: Transformations on the Coordinate Plane 4: Calculating Area of Composite Figures 1: Calculating Circumference and Area of Circles 4: Dilating Plane Figures 1: Using Scale Drawings 2: Using Scale Factor 1: Translating Plane Figures 3: Reflecting Plane Figures 5: Performing One Transformation Page 10 of 29

11 CL Grade 7 Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic 7.GM.4 Analyze the effects of dilations, translations, and reflections on the attributes of twodimensional figures on and off the coordinate plane 7.D.1 Display and analyze data in a variety of ways 7.D.2 Calculate probabilties and reason about probabilities using proportions to solve real-world and mathematical problems 7.D D D D D.2.3 Design simple experiments, collect data and calculate measures of central tendency and spread (range). Use these quantities to draw conclusions about the data collected and make predictions Use Reasoning with proportions to display and interpret data in circle graphs and histogram. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions, and decimals between 0 and 1 Calculate the probability as a fraction of a sample space or as a fraction of area. Express Probabilities as percents, decimals, or fractions Use proportional reasoning to draw conclusions about and predict relative frequencies based on de7 de7 5: Describing Variability 2: Numerical Summaries of Quantities of Data 5: Describing Variability 1: The Statistical Process of Quantities 4: Analyzing Populations and Probabilities 4: Analyzing Populations and Probabilities 4: Analyzing Populations and Probabilities 1: Introduction to 2: Compound 1: Introduction to 2: Compound 1: Introduction to (Module Number followed by Page Number) 1: In the Middle (M5-71) 2: Box it Up (M5-87) 1: What's Your Question (M5-7) 3: Using Histograms to Display Data (M5-47) 1: Rolling, Rolling, Rolling (M4-7) 2: Give Models a Chance (M4-23) 3: Toss the Cup (M4-33) 4: A Simulating Conversation (M4-47) 1: Evens or Odds (M4-73) 2: Three Girls and No Boys (M4-89) 1: Rolling, Rolling, Rolling (M4-7) 2: Give Models a Chance (M4-23) 3: Toss the Cup (M4-33) 4: A Simulating Conversation (M4-47) 1: Evens or Odds (M4-73) 2: Three Girls and No Boys (M4-89) 3: Toss the Cup (M4-33) 2: Compound 1: Evens or Odds (M4-73) 7: Measures of Central Tendency and Data Displays 7: Measures of Central Tendency and Data Displays 6: Data Comparisons and 6: Data Comparisons and 6: Data Comparisons and 1: Measures of Central 1: Calculating Mean, Median, Mode, Tendency 2: Displays of Numerical Data 2: Introduction to 2: Introduction to 1: Introduction to and Range 3: Creating and Interpreting Histograms 1: Determining Probabilities 1: Determining Probabilities 1: Determining Probabilities Page 11 of 29

12 CL Pre-Algebra Alignment to OAS Cluster Standard Description Course Module Topic PA.N.1 Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts. PA.A.1 Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions PA.N.1.1 PA.N.1.2 PA.N.1.3 PA.N.1.4 PA.N.1.5 PA.A.1.1 PA.A.1.2 Develop and apply the properties of integer exponents, including a^0 = 1, to generate equivalent numerical and algebraic expressions Express and compare approximations of very large and very small numbers using scientific notation Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation Classify Real Numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational. Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 4000 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable Use Linear to represent and explain real-world and mathematical situations 5: Applying Powers 5: Applying Powers 5: Applying Powers 4: Expanding Number Systems 4: Expanding Number Systems 3: Determining Unknown Quantities de8 MIDDLE SCHOOL MATH SOLUTION TEXTBOOK 2: Developing Function Foundations 2: Developing Function Foundations 1: Exponents and Scientific Notation 1: Exponents and Scientific Notation 1: Exponents and Scientific Notation 1: The Real Number System 1: The Real Number System 3: Graphing Quantitative 3: Introduction to 3: Introduction to (Module Number followed by page number) 1: It's a Generational Thing (M5-7) 2: Show What You Know (M5-29) 7: Exponents 1: Properties of Whole Number Exponents 3: The Big and Small of It (M5-43) 7: Exponents 2: Scientific Notation 4: How Much Larger (M5-61) 2: Rational Decisions (M4-17) 3: What Are Those? (M4-31) 1: So Many Numbers, So Little Time (M4-7) 3: What are Those?! (M4-31) 1: Every Graph Tells a Story (M3-155) 3: One or More Xs to One Y (M2-205) 4: Over the River and Through the Woods (M2-223) 5: Comparing Apples to Oranges (M2-241) 3: Right Triangles 3: Right Triangles 2: Linear 2: Linear 1: Rational and Irrational Numbers 1: Rational and Irrational Numbers 1: Relations and 2: Linear Models 3: Graphs of Linear in Two- Variables 1: Using the Product Rule and the Quotient Rule 2: Using the Power to a Power Rule 3: Using the Product to a Power Rule and the Quotient to a Power Rule 4: Using Properties of Exponents with Whole Number Powers 5: Simplifying Expressions with Negative and Zero Exponents 1: Using Scientific Notation 2: Comparing Numbers using Scientific Notation 1: Introduction to Irrational Numbers 2: Graphing Real Numbers on a Number Line 3: Ordering Rational and Irrational Numbers 1: Exploring 1: Graphing Given an Integer Slope and Y-Intercept 2: Graphing Given a Decimal Slope and Y-Intercept 3: Modeling Linear in Standard Form 1: Graphing Linear Using a Given Method 2: Graphing Linear using a Chosen Method 1: Modeling Given Slope and a Point 3: Modeling Given Two Points 4: Writing of 4: Modeling Given an Initial Point a Line 5: Modeling Linear using Multiple Representations Page 12 of 29

13 CL Pre-Algebra Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic (Module Number followed by page number) PA.A.2 Recognize linear functions in realworld and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret the result in the original context PA.A.3 Generate equivalent numerical PA.A.1.3 PA.A.2.1 PA.A.2.2 PA.A.2.3 PA.A.2.4 PA.A.2.5 PA.A.3.1 Identify a function as linear if it can be expressed in the form y=mx+b or if its graph is a straight line Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another Identify, describe and analyze linear relationships between two variables Solve problems involving linear functions and interpret the results in the original context Use substitution to simplify and evaluate algebraic expressions 2: Developing Function Foundations 2: Developing Function Foundations 3: Reasoning Algebraically de8 2: Developing Function Foundations 1: Thinking Identify the graphical properties of Proportionally linear functions, including slope and de8 intercepts. Know that the slope equals the rate of change, and the y intercept is zero when the function represents a proportional relationship Predict the effect on the graph of a linear function when the slope or y- intercept changes. Use appropriate tools to examine these effects. 2: Developing Function Foundations 3: Introduction to 3: Introduction to 2: Linear 3: Introduction to 3: Proportionality 1: From Proportions to Linear 2: Linear 4: Over the River and Through the Woods (M2-223) 4: Over the River and Through the Woods (M2-223) 5: Comparing Apples to Oranges (M2-241) 1: U.S. Shirts (M2-81) 2: At the Arcade (M2-93) 3: Dining, Dancing, Driving (M2-109) 4: Derby Day (M2-119) 5: What's the Point (M2-135) 6: The Arts Are Alive (M2-151) 4: Over the River and Through the Woods (M2-223) 5: Comparing Apples to Oranges (M2-241) 1: How Does Your Garden Grow? (M1-91) 3: Fish-Inches (M1-137) 1: Post-Secondary Proportions (M2-7) 2: Jack and Jill Went Up the Hill (M2-23) 3: Slippery Slopes (M2-43) 2: At the Arcade (M2-93) 4: Derby Day (M2-119) 2: Jack and Jill Went Up the Hill (M2-23) 1: Proportions to Linear 2: Developing Function 3: Slippery Slope (M2-43) Foundations 4: Up, Down, and All Around (M2-53) 2: Linear 4: Derby Day (M2-119) 3: Dining, Dancing, Driving (M2-2: Developing Function 109) 2: Linear Foundations 4: Derby Day (M2-119) 6: The Arts Are Alive (M2-151) 1: No Substitute for Hard Work 1: Algebraic Expressions (M3-7) 2: Linear 2: Linear 1: Proportional 4: Two-Step 2: Linear 2: Linear 1: Linear 4: Writing of 5: Modeling Linear using a Line 2: Linear Models 3: Graphs of Linear in Two- Variables Multiple Representations 1: Graphing Given an Integer Slope and Y-Intercept 2: Graphing Given a Decimal Slope and Y-Intercept 3: Modeling Linear in Standard Form 1: Graphing Linear Using a Given Method 2: Graphing Linear using a Chosen Method 1: Modeling Given Slope and a Point 3: Modeling Given Two Points 4: Writing of 4: Modeling Given an Initial Point a Line 5: Modeling Linear using 3: Representing Proportional by 2: The Coordinate Plane and Two-Step 1: Relations and Multiple Representations 5: Determining Characteristics of Direct Variation Graphs 1: Graphs of 4: Modeling Given an Initial Point 4: Writing of 5: Modeling Linear Using a Line Multiple Representations 2: Linear Models and the Distributive Property 4: Identifying Key Characteristics from Graphs 1: Modeling with Integer Rates of Change 2: Modeling with Fractional Rates of Change 3: Modeling using the Distributive Property over Division Page 13 of 29

14 CL Pre-Algebra Alignment to OAS MIDDLE SCHOOL MATH SOLUTION TEXTBOOK Cluster Standard Description Course Module Topic (Module Number followed by page number) equivalent numerical Justify steps in generating 1: Factoring Linear Expressions and algebraic equivalent expressions by 2: Using Order of Operations to expressions and use identifying the properties used, Simplify Algebraic Expressions (No algebraic properties to 2: Mathematics Gymnastics (M3- including the properties of 3: Reasoning 4: Two-Step Type In) evaluate expressions PA.A.3.2 1: Algebraic Expressions 19) 1: Variable Expressions operations (associative, Algebraically 3: Using Order of Operations to 3: All My Xs (M3-33 commutative, and distributive laws) Simplify Algebraic Expressions (Type de8 and the order of operations In) PA.A.4 Represent realworld and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context. PA.GM.1 Solve problems involving right triangles using the Pythagorean Theorem PA.A.4.2 PA.A.4.3 PA.GM.1.1 PA.GM.1.2 PA.GM.2.1 PA.GM.2.2 including grouping symbols Illustrate, write, and solve mathematical problems using linear equations with one variable with PA.A.4.1 one solution, infinitely many solutions, or no solutions. Interpret the solutions in the original context Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px+q > r and px+q<r, where p, q, and r are rational numbers Represent real-world situations using equations and inequalities in one variable Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurement. Calculate the surface area of a cylinder, in terms of Pi and using approximations for Pi, using decomposition or nets. Use appropriate units 3: Reasoning Algebraically de8 3: Reasoning Algebraically de8 4: Expanding Number Systems 4: Expanding Number Systems de8 3: Modeling Linear 2: Developing Function Foundations 5: Applying Powers 1: Solving Linear 2: Two-Step 2: Two-Step 2: Linear 2: Pythagorean Theorem 2: Pythagorean Theorem 4: Be Greater Than (M3-95) 4: Be Greater Than (M3-95) 1: Right Triangle Connection (M4-55) 2: Can That Be Right? (M4-75) 3: Pythagoras Meets Descartes (M4-87) 4: Catty Corner (M4-99) 3: Pythagoras Meets Descartes (M4-87) 3: Breaking the Fourth Wall (M1-3: Decimals and Volume 143) 2: Volume of Curved Figures 1: Strategic Solving (M3-7) 2: MP3s and DVDs (M3-17) 3: Tic-Tac-Bingo (M3-31) 1: U.S. Shirts (M2-81) 2: At the Arcade (M2-93) 3: Dining, Dancing, Driving (M2-109) 4: Derby Day (M2-119) 5: What's the Point (M2-135) 6: The Arts Are Alive (M2-151) 1: Drum Roll, Please! (M5-85) 4: Silos, Frozen Yogurt, and Popcorn (M5-123) 1: Linear 6: Systems of Linear 4: Two-Step 1: Linear 2: Linear 3: Right Triangles 3: Right Triangles 6: Geometric Measurement 1: Solving Linear 1: Exploring Two-Step 2: Solving Multi-Step 1: Solving with Integers (No Type In) 2: Solving with Integers (Type In) 1: Linear 3: Solving with One with Variables on Both Solution, Infinite, and No Solutions Sides 4: Sorting by Number of 4: Solving Two-Step Inequalities 2: Linear Models and the Distributive Property Solutions 1: Graphing Inequalities with Rational Numbers 2: Solving Two-Step Linear Inequalities 1: Modeling with Integer Rates of Change 2: Modeling with Fractional Rates of Change 3: Modeling using the Distributive Property over Division 4: Modeling Given an Initial Point 4: Writing of 5: Modeling Linear Using a Line Multiple Representations 2: The Pythagorean Theorem 2: The Pythagorean Theorem 1: Exploring the Pythagorean Theorem 2: Applying the Pythagorean Theorem 3: Problem Solving Using the Pythagorean Theorem 4: Calculating Distances on the Coordinate Plane 3: Volume and Surface 3: Calculating Surface Area of Right Area 8: Volume 1: Volume Prisms 1: Calculating Volume of Cylinders 2: Using Volume of Cylinders Page 14 of 29