Math Series Course 1 (Grade 6)

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Common Core State Standards Math Series Course 1 (Grade 6) The Carnegie Learning Math Series Course 1 is all new and written specifically for the CCSS for Grade 6.

Course 1 focuses on developing number sense; comparing quantities using ratios, rates, and percents; algebraic thinking; geometry; and statistical thinking. Textbook Chapters 1.

Prime Factorization and the Fundamental Theorem of Arithmetic Least Common Multiple Calculating LCM by Listing Multiples Calculating LCM in Real-World Problems MATHia Software Sections Greatest

Decimals Fraction Representations Creating Part-to-Whole from Fractions Creating Number Line from Fractions Equivalent Fractions Writing Equivalent Fractions using Part-to-Whole Writing Equivalent

Fraction Addition and Subtraction Using Part-to-Whole with Like Denominators Using Number Lines with Like Denominators Using Part-to-Whole with Unlike Denominators Using Number Lines with Unlike

Adding/Subtracting Like Denominators (Solver) Adding/Subtracting Unlike Denominators (Solver) Fraction Multiplication and Division Multiplying Fractions using Area Dividing Fractions using Converting

to Decimals using Equivalent Fractions Decimal Addition and Subtraction Adding/Subtracting using Place-Label Values Adding/Subtracting using Regrouping Adding Three Decimals Decimal Multiplication

1 Common Core State Standards Math Series Course 1 (Grade 6) The Carnegie Learning Math Series Course 1 is all new and written specifically for the CCSS for Grade 6. This course contains complete alignment, coverage, and support for the Standards for Mathematical Content and Practice. Course 1 focuses on developing number sense; comparing quantities using ratios, rates, and percents; algebraic thinking; geometry; and statistical thinking. Textbook Chapters 1. Factors, Multiples, Primes, and Composites 2. Prime Factorization and the Fundamental Theorem of Arithmetic Least Common Multiple Calculating LCM by Listing Multiples Calculating LCM in Real-World Problems MATHia Software Sections Greatest Common Factor Calculating GCF by Listing Factors Calculating GCF in Real-World Problems 3. Fractions 4. Decimals Fraction Representations Creating Part-to-Whole from Fractions Creating Number Line from Fractions Equivalent Fractions Writing Equivalent Fractions using Part-to-Whole Writing Equivalent Fractions using Number Line Writing Simplified Fractions using Part-to-Whole Writing Simplified Fractions using Number Line Comparing Fractions using Part-to-Whole Comparing Fractions using Symbols Fraction Addition and Subtraction Using Part-to-Whole with Like Denominators Using Number Lines with Like Denominators Using Part-to-Whole with Unlike Denominators Using Number Lines with Unlike Denominators Using the Solver with Unlike Denominators Mixed Numbers and Improper Fractions Converting Mixed Numbers to Improper Fractions Converting Improper Fractions to Mixed Numbers Adding/Subtracting Like Denominators (Solver) Adding/Subtracting Unlike Denominators (Solver) Fraction Multiplication and Division Multiplying Fractions using Area Dividing Fractions using Converting Division to Multiplication Multiplying and Dividing Fractions (Solver) Fraction and Decimal Conversions Converting Decimals to Fractions Converting Special Fractions to Decimals Converting Fractions to Decimals using Equivalent Fractions Decimal Addition and Subtraction Adding/Subtracting using Place-Label Values Adding/Subtracting using Regrouping Adding Three Decimals Decimal Multiplication and Division Multiplying Decimals Dividing Decimals by Whole Numbers Dividing Decimals by Decimals Converting Fractions to Decimals using Division 5. Ratios 6. Percents Ratios Writing Ratios Equivalent Ratios and Rates Representing Equivalent Ratios/Rates using Double Number Lines Representing Equivalent Ratios/Rates using Tables Representing Equivalent Ratios/Rates using Graphs Unit Rates Comparing Rates Fraction, Decimal, and Percent Conversions Converting Common Percents Converting Percents Less Than 100 Converting Percents Greater Than 100 Problem Solving with Ratios and Rates Solving Problems using Tables Solving Problems using Double Number Lines Solving Problems using Graphs 4

2 Textbook Chapters MATHia Software Sections 7. Introduction to Expressions 8. Algebraic Expressions 9. Inequalities and Equations 10. Integers 11. The Cartesian Coordinate Plane 12. Units of Measure 13. Area 14. Introduction to the Third Dimension 15. Collecting and Displaying Data 16. Analyzing and Interpreting Data Order of Operations with Numeric Expressions Modeling Using the Distributive Property (Base Ten Algebra Tiles) Using Number Properties to Simplify Expressions Simplifying Numeric Expressions Squares and Cubes Calculating Perfect Squares/Square Roots Calculating Perfect Cubes and Cube Roots Picture Algebra and Equations Reviewing Picture Algebra Using Picture Algebra with Multiplication Using Picture Algebra with Addition/Subtraction Wirting Multiplication Equations Writing Addition Equations Writing Subtraction Equations Writing Equations Patterns and Expressions Modeling with Multiplication Modeling with Addition and Subtraction Modeling with Operations Point Plotting in First Quadrant Reading First Quadrant Points Pan Balances and One-Step Linear Equations Using Pan Balances with Shapes Using Pan Balances with Shapes Representing Variables and Constants Translating between Pan Balances and Equations Using Pan Balances to Solve Problems Solving Equations Displayed as Pan Balances Solving One-Step Linear Equations Patterns and One-Step Equations Modeling with Multiplication Modeling with Addition/Subtraction Modeling with Operations Problem Solving with One-Step Equations Modeling Operations Given Integers Modeling Operations Given Decimals Negative Numbers and Number Lines Identifying Integers from Number Lines Creating Number Lines for Integers One-Step Unit Conversions Converting within Systems with One-Step Equations Converting between Systems with One-Step Equations Multiple-Step Unit Conversions Converting within Systems with Multiple Steps Converting between Systems with Multiple Steps Perimeter and Area Finding Perimeter/Area of Squares and Rectangles Finding Perimeter/Area of Parallelograms Finding Perimeter/Area of Triangles Categorical Data Displays Creating Bar Graphs Reading Bar Graphs and Pie Charts Numerical Data Displays Creating Stem-and-Leaf Plots Creating Dot Plots Creating Histograms Reading Stem-and-Leaf Plots, Dot Plots, & Histograms Measures of Center Plotting First Quadrant Points Reading First Quadrant Points in Context Plotting First Quadrant Points in Context First Quadrant Graphs Graphing using Point Plotting Distributive Property Modeling using the Distributive Property Using the Distributive Property (Solver) Expression Evaluation Integers Evaluating One-Step Expressions Evaluating Two-Step Expressions Expression Evalution Fractions and Decimals Evaluating One-Step Expressions Evaluating Two-Step Expressions Evaluating Multi-Step Expressions Evaluating Expressions with Multiple Variables Variable Expression Simplification Combining Like Terms using Combining Like Terms Using Properties to Simplify Simplifying Variable Expressions (no type in) Simplifying Variable Expressions (type in) Checking Solutions to Linear Equations Solving with Addition/Subtraction Solving with Multiplication/Division Solving One-Step Equations Linear Inequalities Graphing Inequalities Solving Linear Inequalities Ordering Integers Absolute Value Using Absolute Value as a Distance Plotting Points in Four Quadrants Reading Points in Four Quadrants Plotting Points in Four Quadrants Reading Points in Context (Four Quadrants) Plotting Points in Context (Four Quadrants) Four Quadrant Graphs Graphing using Point Plotting Finding Perimeter/Area of Trapezoids Finding Area of Composite Figures Volume of Prisms Finding Volume of Prisms with Fractional Side Lengths Finding Volume of Prisms with Whole Number Side Lengths Surface Area Finding Surface Area of Prisms Finding Surface Area of Pyramids Finding Mean, Median, Mode, and Range Determining Appropriate Measures Measure the Effects of Changing Data Sets Finding a Data Value Given a Mean Data Distributions Deviation and Mean Absolute Deviation Box and Whisker Plots Identifying Key Characteristics from Data Sets Interpreting Box-and-Whisker Plots 5

3 Carnegie Learning Math Series Course 1 is composed of 16 chapters. In the pages that follow, you will see a scope & sequence that includes information on each chapter as well as each lesson contained within those chapters. Course 1 Chapter Sequence 1. Factors, Multiples, Primes, and Composites 2. Prime Factorization and the Fundamental Theorem of Arithmetic 3. Fractions 4. Decimals 5. Ratios 6. Percents 7. Introduction to Expressions 8. Algebraic Expressions 9. Inequalities and Equations 10. Integers 11. The Cartesian Coordinate Plane 12. Units of Measure 13. Area 14. Introduction to the Third Dimension 15. Collecting and Displaying Data 16. Analyzing and Interpreting Data 6

4 The Middle School Math Series: Course 1 scope & sequence gives you information about each lesson. Lesson title Key math objective The Common Core State Standard that is addressed in that lesson Key terms that are introduced within the lesson Problem types that will be found within the lesson (see page 30 for more information on problem types) 1 Factors, Multiples, Primes, and Composites This chapter reviews factors, multiples, primes, composites, and divisibility rules. the 1.1 Collection Connections Factors and Multiples 4.OA.4 arrays, factor pair, factor, Commutative Property of Multiplication, distinct factors, perfect square, multiple, divisible 1.2 and More Physical of Factors and Multiples 4.OA.4 6.NS.4 area model, set, Venn diagram 1.3 Sifting for Prime Numbers Investigating Prime and Composite Numbers 4.OA.4 prime number, composite number, multiplicative identity 1.4 Divisibility Rules! Investigating Divisibility Rules 4.OA.4 divisibility rules 2 Prime Factorization and the Fundamental Theorem of Arithmetic This chapter demonstrates how least common multiples and greatest common factors are used to solve real- world problems. 2.1 The Think Tank Prime Factorization and Factor Trees 6.NS.4 6.EE.1 prime factorization, Associative Property of Multiplication, factor tree, power, base, exponent, Fundamental Theorem of Arithmetic 2.2 Together Again 2.3 Happenings at Harvest Day 2.4 Common Factors or Common Multiples? Investigating Multiples and Least Common Multiples Investigating Factors and Greatest Common Factors 6.NS.4 common multiple, least common multiple (LCM) 6.NS.4 common factor, greatest common factor (GCF), relatively prime numbers Using GCF and LCM to Solve Problems 6.NS.4 3 Fractions This chapter begins with a review of how to model parts of a whole and various fractional representations. Students create their own fraction strips and use them to model operations with fractions. The focus then shifts to the relationship between multiplication and division to understand the procedures for dividing fractions. An emphasis is placed on estimation skills throughout the chapter. 3.1 Flags and Fractions Modeling Parts of a Whole 4.NF.1 fraction, numerator, denominator 3.2 You Mean Three Can Be One? Fractional Representations 5.NF Rocket Strips Dividing a Whole into Fractional Parts 3.4 Getting Closer Benchmark Fractions 4.NF.1 4.NF.2 unit fraction, equivalent fractions benchmark, fractions, inequality 3.5 What's My Cut Equivalent Fractions 4.NF.1 simplest form, Multiplicative Identity Property 3.6 Trail Mix Adding and Subtracting Fractions with Like and Unlike Denominators 4.NF.3b 4.NF.3d 5.NF.1 5.NF.2 common, denominator, least common denominator (LCD) 3.7 Trail Mix Extravaganza Improper Fractions and Mixed Numbers 4.NF.3c 5.NF.1 mixed number, improper fractions 3.8 Pizzas By the Slice- - or the Rectangle! Parts of Parts 5.NF.4a 5.NF.4b 5.NF Yours Is to Reason Why! Parts in a Part reciprocal, multiplicative inverse, Multiplicative Inverse Property 3.10 Divide Your Time Well, and Your Trail Mix, and Your Mixed Number Division 7

5 the 4 Decimals This chapter begins with a comprehensive review of decimals. are used to develop the conceptual understanding of operations with decimals. Estimation is emphasized throughout. 4.1 Minty- Fresh Coins? Introduction to Decimals 5.NBT.1 5.NBT.3.a decimal 4.2 You Be the Judge Comparing, Ordering, Estimating, and Rounding Decimals 5.NBT.3.a 5.NBT.3.b 5.NBT.4 benchmark decimal, round 4.3 The Ancient Spaniards Didn't Count the Thumbs Fraction- Decimal Equivalents 4.NF.6 terminating decimal, repeating decimal 4.4 When Less Is Better Adding and Subtracting Decimals 6.NS I Just Spent One Week Going to Work! Multiplying Decimals 6.NS Organized Estimation Long Division of Whole Numbers 6.NS.2 6.NS.3 dividend, divisor, quotient 4.7 Los Angeles Commute Didn't Top the List? Dividing Decimals 6.NS.2 6.NS.3 5 Ratios This chapter focuses on the concept of ratios and the ratio relationship between two quantities. Ratio reasoning is developed through the use of tables, double number lines, and graphs. Rate and ratio reasoning is used to solve various real- world problems. 5.1 Mixing Paint Introduction to Ratios ratio 5.2 What's in a Name? Ratio Representations 5.3 I'd Like to Solve the Puzzle Writing Equivalent Ratios rate, scaling up, scaling down 5.4 The Most Important Meal of the Day Modeling Ratios double number line 5.5 A Trip to the Moon Using Tables to Represent Equaivalent Ratios 6.RP.2 6.RP.3.a 5.6 Graphing Out Equivalence Using Graphs to Represent Equaivalent Ratios 6.RP.3.a 5.7 Water Is a Precious Resource Using Multiple Ratio Representations to Solve Problems 6.RP.3.a 5.8 What Is the Better Buy? Introduction to Unit Rates 6.RP.2 6.RP.3.a unit rate 6 Percents This chapter extends ratio reasoning to include percents. Estimation and benchmark percents are emphasized to continue the development of number sense. Various strategies are presented to help students think about efficiency when solving problems. 6.1 Percents Can Make or Break You! Introduction to Percents 6.2 Wacky Weather! Estimating Percents 6.3 It's All in the Follow- Through Determining the Percent of a Number percent benchmark percents 6.4 Mi Mi Mi Mi Mi Mi Mi! Determine the Part, Whole, or Percent of Percent Problems 6.5 Practical Percents Practice! Using Percents in Real- World Situations commission, gratuity 7 Introduction to Expressions This chapter reviews numerical expressions that lead to algebraic expressions. A variable is introduced as a representation of a quantity that varies. An emphasis is placed on writing and representing expressions in multiple ways. 7.1 There's a Reason Behind the Rhyme Order of Operations 6.EE.1 conventions, numerical expression, evaluate, operations, parentheses, order of operations 7.2 Getting to the Root of It Exploring Squares, Cubes, and Roots 6.NS.3 6.EE.1 square of a number, perfect squares, square root, radical, radicand, perfect cube, cube of a number, cube root, index 7.3 Things That Vary Understanding Variables 6.NS.3 variable, algebraic expression, equation 7.4 What's My Number? Writing Algebraic Expressions numerical, coefficient, constant, evaluate an algebraic expression 7.5 Different Ways Multiple Representations of Algebraic Expressions multiple representations 7.6 There's More Than One Way Using Mulitple Representations of Problems 8

6 the 8 Algebraic Expressions This chapter develops an understanding of the Distributive Property through real- world situations, manipulatives, and analysis of student work. An emphasis is placed on extending and applying properties of operations to generate equivalent expressions, and to determine when two expressions are equivalent. 8.1 The Parts of Cars You Don't See! Relationships between Quantities sequence, term 8.2 Tile Work Simplifying Algebraic Expressions 6.EE.4 Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication 8.3 Blueprints to Floor Plans to Computers Using the Distributive Property to Simplify Algebraic Expressions 6.EE.4 Distributive Property of Multiplication over Addition, Distributive Property of Multiplication over Subtraction, Distributive Property of Division over Addition, Distributive Property of Division over Subtraction 8.4 Are They Saying the Same Thing? Multiple Representations of Equivalent Expressions 6.EE.4 equivalent expressions 8.5 Like and Unlike Combining Like Terms 6.EE DVDs and Songs: Fun with Expressions Using Algebraic Expressions to Analyze and Solve Problems 9 Inequalities and Equations This chapter introduces algebraic equations and inequalities. A pan balance model is used to develop the conceptual understanding of solving equations involving one step. Equations, tables, and graphs are used to represent and solve real- world problems. 9.1 Call to Order Inequalities 6.NS.7.a 6.EE.8 inequality, solution, set of an inequality, graph of an inequality, ray 9.2 Opposites Attract to Maintain a Balance Solving One- Step Equations Using Addition and Subtraction one- step equation, Properties of Equality for Addition and Subtraction, solution, inverse operations 9.3 Statements of Equality Redux Solving One- Step Equations Using Multiplication and Division Properties of Equality for Multiplication and Division 9.4 There Are Many Ways Representing Situations in Multiple Ways 9.5 Measuring Short Using Multiple Representations to Solve Problems 9.6 Variables and More Variables The Many Uses of Variables in Mathematics homonyms 9.7 Quantities that Change Independent and Dependent Variables 6.EE.9 independent quantity, dependent quantity, independent variable, dependent variable 10 Integers This chapter develops the concept of negative numbers and moves toward the broader understanding of the rational number system including order and absolute value What, Me Negative? Introduction to Negative Integers 10.2 Number Sets Number Systems 6.NS.5 6.NS.6.a 6.NS.7.b 6.NS.6.a negative numbers, infinity, negative sign, positive sign, ellipses, integers Density Property, fractional numbers, rational numbers 10.3 Ordering and Absolute Value Ordering the Rational Numbers 6.NS.6.a 6.NS.7.c 6.NS.7.d absolute value 10.4 Elevators, Making Money Redux, and Water Level Solving Problems with Rational Numbers 6.NS.5 6.NS.6.a 6.NS.7.c 6.NS.7.d 9

7 11 The Cartesian Coordinate Plane 11.1 Four Quadrants Extending the Coordinate Plane 6.NS.6.b 6.NS.7.c 6.NS.8 x- axis, y- axis, origin, quadrant, ordered pair, Cartesian Coordinate Plane the This chapter extends plotting points to four quadrants and includes an introduction to coordinate geometry. Representations of algebraic expressions and equations are used to solve real- world problems Geometry and Graphs Graphing Geometric Figures 6.NS.6.b 6.NS.8 6.G Water, Water Everywhere Solving Problems with Multiple Representations 6.NS.5 6.NS.6.b 6.NS.8 6.EE Every Graph Tells a Story! Interpreting Graphs 6.EE.9 12 Units of Measure This chapter extends ratio reasoning to convert measurement units within and between customary and metric systems Customary to Whom? Customary Measurement 12.2 It's All Based on Powers of 10! Metric Measurement standard units of measure, measurement, convert meter (m), liter (L), gram (g), prefix 12.3 They're Saying the Same Thing? Moving between Measurement Systems 12.4 Is That Appropriate? Choosing Appropriate Measures 13 Area This chapter connects the knowledge related to the areas of rectangles and squares to determine the areas of triangles, parallelograms, trapezoids, and rhombi. Formulas are used to solve real- world problems The Language of Geometry Sketching, Drawing, Naming, and Sorting Basic Geometric Figures protractor, draw, compass, triangle, sketch, square, polygon, kite, construct, rhombus, equilateral triangle, isosceles triangle, scalene triangle, equiangular triangle, acute triangle, right triangle, obtuse triangle, quadrilateral, opposite sides, consecutive sides, rectangle, parallelogram, trapezoid, isosceles trapezoid, regular polygon, straightedge 13.2 Weaving a Rug Area and Perimeter of Rectangles and Squares 6.G Boundary Lines Area of Parallelograms and Triangles 6.G.1 altitude of a parallelogram, height of a parallelogram, altitude of a triangle, height of a triangle 13.4 The Keystone Effect Area of Trapezoids 6.G.1 bases of a trapezoid, legs of a trapezoid, altitude of a trapezoid, height of a trapezoid 13.5 Go Fly a Kite Area of Rhombi and Kites 6.G Street Signs Area of Regular Polygons 6.G.1 congruent polygons, apothem 14 Introduction to the Third Dimension This chapter develops an understanding of three- dimensional figures using nets made up of rectangles and triangles. Nets are then used to determine surface area. Estimation is emphasized prior to calculations and real- world problems are solved using volume and surface area formulas Cut, Fold, and Voila! Nets geometric solids, prototype, edge, face, vertex, net 14.2 More Cans in a Cube? The Cube 6.G.2 point, line segment, polygon, polyhedron, regular polyhedron, congruent, cube, unit cube, diameter, surface area, volume 14.3 Prisms Can Improve Your Vision! Prisms 14.4 Outside and Inside a Prism Surface Area and Volume of a Prism The Egyptians Were on to Something or Was It the Mayans? And the Winning Protype Is? Pyramids Identifying Geometric Solids in Everyday Occurances 6.G.2 6.G.2 prisms, bases of a prism, lateral faces, height of a prism, rectangular prism, right prism pyramid, vertex of a pyramid, height of a pyramid, slant height of a pyramid 15 Collecting and Displaying Data Explores the importance of statistics and variability. Various representations are used to summarize numerical data sets Why Do We Use Statistics? Designing Statistical Questions 6.SP.1 data, statistical question, population, sample, data analysis, parameter, statistic, survey, experiment 15.2 Dealing With Data Collecting Displaying, and Analyzing Data categorical data, quantitative data, discrete data, continuous data, bar graph, double bar graph, stacked bar graph, circle graph, key, frequency 15.3 At the Olympics Line Plots and Stem- and- Leaf Plots 6.SP.5.b dot plot, distribution, symmetric, skewed left, skewed right, clusters, gaps, stem- and- leaf plot, side- by- side stem- and- leaf plot 15.4 Building Up Using Histograms 15.5 Analyze This! Designing and Implementing an Experiment histogram, frequency table 10

8 y = kx k y = x 2012 Curricula Scope & Sequence the 16 Analyzing and Interpreting Data This chapter reviews the measures of center with an emphasis on which measure is the most appropriate to describe a data set. Box- and- whisker plots are used to display numerical data and investigate variation. Graphing calculators and spreadsheets are used to determine mean absolute deviation and to construct box- and- whisker plots In the Middle Analyzing Data Using Measures of Center 6.SP.3 measure of center, mode, median, mean, balance point 16.2 Which Measure of Center Should I Use? Determing When to Use the Mean, Median, or Mode 6.SP.5.b 6.SP.5.c 16.3 Picking a Player Calculating and Interpreting the Mean Absolute Deviation 6.SP.3 6.SP.5.c measures of variation or variability, deviation, absolute deviation, mean absolute deviation 16.4 Five- Number Summary Analyzing Data Using the Five- Number Summary 6.SP.5.b 6.SP.5.c range, quartiles (Q), interquartile range (IQR), five- number summary 16.5 Box It Up! Displaying and Analyzing Data Using Box- and- Whisker Plots 6.SP.5.b 6.SP.5.c box- and- whisker plot, outlier 11

Carnegie Learning Math Series Course 1, A Florida Standards Program. Chapter 1: Factors, Multiples, Primes, and Composites

. Factors and Multiples Carnegie Learning Math Series Course, Chapter : Factors, Multiples, Primes, and Composites This chapter reviews factors, multiples, primes, composites, and divisibility rules. List