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 real-world and mathematical situations 6.N.1.1 6.N.1.2 6.N.1.3 6.N.1.4 6.N.1.5 6.N.1.6 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. 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 4: Moving Beyond Signed Positive 1: Signed 2: Positive 1: Signed 2: Percents 2: Percents 1: Human Number Line (M4-7) 2: Magnificent Magnitude (M4-23) 3: What s In a Name (M4-35) 1: Thinking ly (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 (M1-51) 4: Searching for Common Ground (M1-39) 5: Composing and (M1-51) 5: Negative and the Four 6 th Grade RTI 3: Numeric and Algebraic 1: Integers 3: Introduction to Percent 3: Introduction to Percent Equivalent Fractions Fraction Addition and Subtraction Mixed Number Addition and Subtraction 1: Number Properties 1: Introduction to Negative 2: Representing Integers on Number Lines 1: Percent Models 2: Fraction, Decimal, Percent Comparisons 1: Writing Equivalent Fractions using Part-To- Whole Models 2: Using the Solver with Unlike Denominators 2: Adding and Subtracting with Unlike Denominators 4: Exploring the Distributive Property with Numeric 5: Using the Distributive Property with Numeric Grade 6 Middle School Math Solution: Alignment to OAS 1
6.N.2 Add and subtract integers in order to solve real-world and mathematical 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 6.N.2.1 6.N.2.2 6.N.2.3 6.N.3.1 Estimate solutions to addition and subtraction of integers 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 Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different 6.N.3.2 Determine the unit rate for ratios 6.N.3.3 6.N.3.4 Apply the relationship between ratios, equivalent fractions and percents to solve in various contexts, including those involving mixture and concentrations Use multiplicative reasoning and representations to solve ratio and unit rate 2: Operating with Signed 2: Operating with Signed 2: Operating with Signed 1: Adding and Subtracting 1: Adding and Subtracting 1: Adding and Subtracting 1: Ratios 3: Unit Rates and Conversions 2: Percents 1: Ratios 3: Unit Rates and Conversions 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: 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) 1: Many Ways to Measure (M2-165) 2: Introduction to Unit Rates (M2-185) 3: Seeing Things Differently (M2-199) 3: Number 3: Number 1: Integer 1: Integer 1: Ratio and Rate Reasoning 1: Ratio and Rate Reasoning 3: Introduction to Percent 1: Ratio and Rate Reasoning 2: Problem Solving using Ratio and Rate Reasoning 1: Adding and Subtracting Negative Integers 2: Using Number Lines to Add and Subtract Integers 1: Adding and Subtracting Negative Integers 2: Using Number Lines to Add and Subtract Integers 1: Understanding Ratio 4: Fractional Rates 5: Comparing Rates 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 2: Problem Solving with Equivalent Ratios and Rates Using Double Number Lines 3: Problem Solving with Equivalent Ratios and Rates Using Graphs Grade 6 Middle School Math Solution: Alignment to OAS 2
6.N.4 Multiply and divide decimals, fractions, and mixed numbers; solve real-world and mathematical with rational numbers 6.N.4.1 6.N.4.2 6.N.4.3 Estimate solutions to 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 Multiply and divide fractions and decimals using efficient and generalizable procedures 2: Positive 3: and Volume 2: Positive 3: and Volume 2: Positive 3: and Volume 2: Did you Get the Part? (M1-83) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse (M1-131) 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 2: Did you Get the Part? (M1-83) 3: Yours is to Reason Why! (M1-93) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 2: Did you Get the Part? (M1-83) 3: Yours is to Reason Why! (M1-93) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 1: Fraction and Decimal 1: Fraction and Decimal 1: Fraction Division 2: Decimal 1: Fraction Division 2: Decimal 1: Representing Fraction Division 2: Interpreting Remainders with Models 3: Developing the Fraction Division Algorithm 4: Exploring Decimal Facts 5: Multiplying and Dividing 4: Multiplying and Dividing 6: Decimal Products and Quotients Grade 6 Middle School Math Solution: Alignment to OAS 3
6.N.4 (cont d) 6.N.4.4 Solve and interpret real-world and mathematical including those involving money, measurement, geometry and data requiring arithmetic with decimals, fractions, and mixed numbers the Four 5: Describing Variability of 2: Positive 3: and Volume 1: 2: 3: Graphing Quantitative 2: Numerical Summaries of Data 2: Did You Get the Part? (M1-83) 3: Yours is to Reason Why! (M1-93) 1: Length, Width, and Depth (M1-115) 2: Which Warehouse? (M1-131) 3: Breaking the Fourth Wall (M1-143) 4: Dividend in the House (M1-165) 2: Into the (M3-23) 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: Fraction and Decimal and 6: Geometric Measurement 7: Measures Tendency and Data Displays 1: Fraction Division 2: Decimal 4: Problem Solving with 2: 3: Volume and Surface 1: Measures Tendency 3: Mean Absolute Deviation 2: Interpreting Remainders Using Models 5: Multiplying and Dividing 3: Problem Solving with 2: Calculating of Various Figures 3: Solving Problems 4: Calculating of Composite Figures 1: Calculating Volume of Right Prisms 2: Using Volume of Right Prisms 3: Calculating Surface of Right Prisms 1: Calculating Mean, Median, and Mode 3: Measuring the Effects of Changing Data Sets 1: Calculating Mean Absolute Deviation Grade 6 Middle School Math Solution: Alignment to OAS 4
6.A.1 Recognize and Represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs, and rules to solve real-world and mathematical 6.A.1.1 6.A.1.2 6.A.1.3 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 the Four Positive 3: Graphing Quantitative 1: 2: 3: Graphing Quantitative 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) 3: There are Multiple Paths (M4-87) 2: Into the (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 (M3-183) 3: Planes, Trains, and Paychecks (M3-193) 4: Triathlon Training (M3-207) 5: Negative and the Four and 5: Negative and the Four 3: Numeric and Algebraic and 2: The Coordinate Plane 4: Problem Solving with 3: Multiple Representations 2: Algebraic 2: Solving One- Step 3: Solving 1: Exploring Symmetry on the Coordinate Plane 2: Identifying and Interpreting Ordered Pairs 3: Plotting Points 1: Patterns and 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with 1: Solving One- Step using Multiple Representations in Four 1: Evaluating Multi-step 2: Evaluating with Multiple Variables 3: Using Substitution to Identify Solutions to 1: Graphing with Positive Grade 6 Middle School Math Solution: Alignment to OAS 5
6.A.2 Use properties of 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 and use the idea of maintaining equality to solve equations. Interpret solutions in the original context. 6.A.2.1 6.A.3.1 Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical Represent real-world or mathematical situations using expressions, equations, and inequalities involving variables and rational numbers the Four 1: 1: 2: 3: Graphing Quantitative 1: Taking Apart and Shapes (M1-7) 1: Matter (M3-7) 3: Second Verse, Same as the First (M3-35) 4: Are they Saying the Same Thing? (M3-53) 2: Into the (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) 3: There are Many Paths (M4-87) 3: Numeric and Algebraic and 1: Number Properties 3: Equivalent Algebraic 3: Solving 4: Problem Solving with 1: Commutative and Associative Properties 2: Order of 3: Simplifying Numeric 4: Exploring the Distributive Property with Numeric 5: Using the Distributive Property with Numeric 1: Modeling Equivalent Algebraic 2: Exploring the Distributive Property with Algebraic 3: Simplifying Algebraic (No Type In) 4: Simplifying Algebraic (Type In) 1: Graphing with Positive 1: Patterns and 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with Grade 6 Middle School Math Solution: Alignment to OAS 6
6.A.3 (cont d) 6.A.3.2 Use number sense and properties of operations and equality to solve real-world and mathematical 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 2: 3: Graphing Quantitative 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) and and 1: Reasoning with and 2: Solving One- Step 4: Problem Solving with 1: Using Picture Algebra with Addition, Subtraction, and Multiplication 2: Using Picture Algebra with Multiplication, Total Given 3: Using Picture Algebra with Addition and Subtraction, Total Given 4: Patterns and One Step 1: Solving with a Balance 2: Representing 4: Solving with Addition and Subtraction (No Type In) 5: Solving with Multiplication and Division (No Type in) 6: Solving (Type In) 1: Patterns and 2: Problem Solving Using Multiple Representations in the First Quadrant 3: Problem Solving with Grade 6 Middle School Math Solution: Alignment to OAS 7
6.GM.1 Calculate areas of squares, parallelograms, and triangles to solve real-world and mathematical 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 6.GM.1.1 6.GM.1.2 6.GM.1.3 6.GM.2.1 6.M.2.2 6.GM.3.1 6.GM.3.2 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-world mathematical Solve using the relationships between angles formed by intersecting lines Develop and use the fact that the sum of the interior angles of a triangle is 180* to determine missing angle measures in a triangle Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units Solve in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units Course 3* Positive Positive Positive 5: Constructing and Measuring 1: Transforming Geometric Objects 1: Angles and Triangles 3: Line and Angle 3: Unit Rates and Conversions 3: Unit Rates and Conversions 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 6: Geometric Measurement 2: Special Delivery (M5-19) 5: Geometry 1: Pulling a One-Eighty (M1-167) 1: Many Ways to Measure (M2-165) 1: Many Ways to Measure (M2-165) 6: Geometric Measurement 2: 2: 2: 1: Angle Properties 1: Ratio and Rate Reasoning 1: Developing Formulas 2: Calculating of Various Figures 3: Solving Problems 4: Calculating of Composite Figures 1: Developing Formulas 2: Calculating of Various Figures 3: Solving Problems 4: Calculating of Composite Figures 1: Developing Formulas 2: Calculating of Various Figures 3: Solving Problems 4: Calculating of Composite Figures 1: Calculating Angles 2: Classifying Angles and Determining Measures 1: Converting Within Systems Grade 6 Middle School Math Solution: Alignment to OAS 8
6.GM.4 Use translations, reflections, and rotations to establish congruency and understand symmetries 6.D.1 Display and Analyze Data 6.GM.4.1 6.GM.4.2 6.GM.4.3 6.GM.4.4 6.D.1.1 6.D.1.2 6.D.1.3 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 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 Create and analyze box and whisker plots observing how each segment contains one quarter of the data Course 3* Course 3* Course 3* Course 3* 1: Transforming Geometric Objects 1: Transforming Geometric Objects 4: Expanding Number Systems 1: Transforming Geometric Objects 5: Describing Variability of 5: Describing Variability of 5: Describing Variability of 1: Rigid Motion Transformations 1: Rigid Motion Transformations 2: Pythagorean Theorem 1: Rigid Motion Transformations 2: Numerical Summaries of Data 2: Numerical Summaries of Data 2: Numerical Summaries of Data 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) 2: Box It Up (M5-87) 4: Geometric Transformations 1: Transformations of Figures on the Coordinate Plane 1: Translating Plane Figures 2: Rotating Plane Figures 3: Reflecting Plane Figures 5: Performing One Transformation 6: Performing Multiple Transformations See MATHia Glossary-Line(s) of Symmetry, Symmetry, and Reflections 7: Measures Tendency and Data Displays 7: Measures Tendency and Data Displays 7: Measures Tendency and Data Displays 1: Measures Tendency 1: Measures Tendency 4: Box Plots 1: Calculating Mean, Median, and Mode 2: Determining Appropriate Measure 1: Constructing Box Plots 2: Interpreting Box Plots Grade 6 Middle School Math Solution: Alignment to OAS 9
6.D.2 Use to solve real-world and mathematical ; represent probabilities using fractions and decimals 6.D.2.1 6.D.2.2 6.D.2.3 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 might be differences between the two results. 4: Analyzing Populations and 4: Analyzing Populations and 4: Analyzing Populations and 1: Introduction to 1: Introduction to 2: Compound 1: Introduction to 2: Compound 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 (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) 6: Data Comparisons and 6: Data Comparisons and 6: Data Comparisons and 2: Introduction to 2: Introduction to 2: Introduction to 1: Determining 1: Determining 3: Calculating Compound 2: Comparing Experimental and Theoretical Grade 6 Middle School Math Solution: Alignment to OAS 10