6th Grade Math Curriculum Map (as articulated through Diocese of Tucson ACE Collaborative Curriculum Design 2012) Unit 1: Rational Numbers and the Number Line 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.NS.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits,positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.7. Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. b. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. d. Distinguish comparisons of absolute value from statements about order. Duration: 4 weeks Prentice Hall Mathematics Course 1: Sections 4-1 Divisibility and Mental Math, 4-4 Greatest Common Factor, 4-7 Least Common Multiple, 11-1 Exploring Integers, 11-2 Comparing and Ordering Integers, Envision - Topics 5-1 Factors, Multiples, and Divisibility, 5-2 Prime Factorization, 5-3 Greatest Common Factor 7-2 Least Common Multiple, 1-2 Comparing and Ordering Whole Numbers, 1-3 Comparing and Ordering Decimals, 10-1 Understanding Integers, 10-2 Comparing and Ordering Integers, 10-3 Rational Numbers On the Number Line, 6-1 Fractions and Division, 6-2 Fractions and Decimals, 6-4 Decimals Forms of Fractions and Mixed Numbers Khan Academy Activities - Distributive Property, Greatest Common Divisor, Least Common Multiple, Negative Number Word Problems, Decimals On A Number Line 3, Fractions On A Number Line, Integers On A Number Line, Number Line 3, Absolute Value Word Problems, Finding Absolute Value, Comparing Absolute Value, Ordering Negative Numbers, Comparing Positive and Negative Numbers On The Number Line
Unit 2: Coordinate Plane 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. 6.NS.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Duration: 2 Week Prentice Hall Mathematics Course 1: Section 11-8 Graphing On the Coordinate Plane Envision - Topics 10-9 Graphing On the Coordinate Plane Khan Academy Activities - Graphing Points and Naming Quadrants, Points On The Coordinate Plane, Reflecting Points, Coordinate Plane Word Problems In All Four Quadrants
Unit 3: Adding, Subtracting, Multiplying and Dividing Decimal Numbers 6.NS.2. Fluently divide multi-digit numbers using the standard algorithm. 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Duration: 3 Weeks Prentice Hall Mathematics Course 1: Sections 1-7 Adding and Subtracting Decimals, 1-8a Modeling Decimal Multiplication, 1-8 Multiplying Decimals, 1-8b Technology: Multiplying and Dividing Decimals by 10, 100, or 1,000, 1-9 Dividing Decimals Envision:Topic 3-1 Estimating Sums and Differences of Decimals, 3-2 Adding and Subtracting Decimals, 3-3 Estimating Products and Quotients of Decimals, 3-4 Multiplying Decimals, 3-5 Dividing By Whole Numbers, 3-6 Dividing Whole Numbers by Decimals, 3-7 Dividing Decimals Khan Academy Activities: Multi-Digit Division, Adding Decimals 2, Subtracting Decimals 2, Adding and Subtracting Decimal Word Problems, Multiplying Decimals 3, Dividing Decimals 4
Unit 4: Introduction to Algebra: Algebraic Expressions 6.EE.1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 6.EE.3. Apply the properties of operations to generate equivalent expressions. 6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Duration: 3 weeks Prentice Hall Mathematics Course 1: Sections 4-2 Exponents, Sections 3-2, 3-3aq Modeling Expressions Activity Lab, 3-3 Writing Algebraic Expressions, 3-8 The Distributive Property Envision:Topics 2-1 Using Variables to Write Expressions, 2-2 Properties of Operations,2-3 Order of Operations, 2-6 Evaluating Expressions, 2-7 Using Expressions to Describe Patterns, 2-8 Problem Solving: Making a Table, 4-3 Problem Solving: Draw a Picture and Write an Equation, 4-5 Problem Solving: Draw a Picture and Write an Equation Khan Academy: Positive and Negative Exponents, Evaluating Expressions With Exponents, Evaluating Expressions With Exponents Word Problems, Writing Expressions With Exponents, Writing Expressions With Exponents Word Problems, Evaluating Expressions With Variables Word Problems, Writing Expressions 1, Writing Expressions 2, Evaluating Expressions With Variables Word Problems, Writing Expressions With
Variables Word Problems, Identifying Parts of Expressions, Evaluating Expressions in 1 Variable, Evaluating Expressions in 2 Variable, Order of Operations, Combining Like Terms, Equivalent Form of Expressions 1, Constructing and Solving Equations in Real World 1, Inequalities in 1 Variable. Unit 5: Algebra: Equations and Inequalities 6.EE.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. Duration: 5 weeks Prentice Hall Mathematics Course 1: 3-4 Using Number Sense to Solve One-Step Equations, 3-5 Solving Addition Equations, 3-6 Solving Subtraction Equations, 3-7a Modeling Division Equations Activity Lab, 3-7 Solving Multiplications and Division Equations, GSP Writing Equations to Solve Word Problems, 12-1 Solving Two-Step Problems, 12-1 b Algebra Thinking Using Equation Language, 12-2 Inequalities, 12-3 Solving One-Step Inequalities, 12-3 b Data Analysis: Applying Inequalities Lab Activity Envision: 4-2 Solving Addition and Subtraction Equations, 4-3 Draw A Picture and Write An Equation, 4-4 Solving Multiplication and Division Equations, 4-5 Draw a Picture and Write An Equation, 15-1 Equations with
More Than One Operation, 15-2 Patterns and Equations, 15-3 More Patterns and Equations, 15-4 Graphing Equations, 15-5 Graphing Equations with More Than One Operation, 15-6 Functions, Ch. 15 Enrichment, 15-7 Act It Out and Use Reasoning Khan Academy Activities: One Step Equations Intuition, One Step Equations, One Step Equations With Multiplication, Inequalities In One Variable 1, Inequalities On A Number Line, Solving Equations and Inequalities Through Substitution, Dependent and Independent Variables, Constructing and Solving Linear Equations Word Problems, Using Inequalities to Describe Real-World Contexts
Unit 6: Ratios, Rates and Proportions 6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b=0, and use rate language in the context of a ratio relationship. 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. c. Find a percent of a quantity as a rate per 100. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. AZ.6.NS.9. Convert between expressions for positive rational numbers, including fractions, decimals, and percents. 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Duration: 5 Weeks Prentice Hall Mathematics Course 1: Sections 7-1 Ratios, 7-1b Hands On Modeling Ratios Activity Lab, 7-2 Unit Rates, 7-3 Understanding Proportions, 7-4 Solving Proportions, 7-4b Hands On: Predicting Results Activity Lab, 7-6a Hands On: Modeling Percents, 7-6 Percents, Fractions, and Decimals, 7-6 Percents, Fractions, Decimals, 7-7 Finding the Percent of a Number, 6-3a Hands On: Fraction Division Activity Lab, 6-3 Dividing Fractions, 6-4 Dividing Mixed Numbers Envision: 12-1 Understanding Ratios, 12-2 Equal Ratios and Proportions, 12-3 Understanding Rates and Unit Rates, 12-4 Comparing Rates, 12-5 Distance, Rate and Time, 13-1 Using Ratio Tables, 13-2 Using Unit Rates, 13-3 Ways to Solve Proportions, 13-4 Writing to Explain, 14-1 Understanding Percents, 14-2 Fractions,
Decimals, and Percents, 9-1 Understanding Division of Fractions, 9-2 Dividing a Whole Number By a Fraction, 9-3 Dividing Fractions, 9-4 Estimating Quotients, 9-5 Dividing Mixed Numbers Khan Academy: Representing Ratios, Rate Problems 0.5, Ratio Word Problems, Finding Percents, Percentage Word Problems 1, Solving Ratio Problems With Tables, Units, Dividing Fractions By Fractions and Whole Numbers Applications, Dividing Fractions By Fractions Word Problems, Dividing positive Fractions, Understanding Dividing Fractions By Fractions,
Unit 7: Area, Surface Area and Volume 6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Duration: 5 Weeks Prentice Hall Mathematics Course 1: 9-3 Perimeters and Area of Rectangles, 9-4a Hands On: Comparing Areas Activity Lab, 9-4 Area of Parallelograms and Triangles, 9-7a Hands On: Three-Dimensional Views Activity Lab, 9-7 Three-Dimensional Figures and Spatial Reasoning, 9-8 Surface Area of Prisms, 9-9a Hands On: Exploring Volume Activity Lab, 9-9 Volumes of Rectangular Prisms Envision: 17-2 Area of Rectangles and Irregular Figures, 17-3 Area of Parallelograms and Triangles, Ch. 17 Enrichment, 18-1 Solid Figures, 18-2 Surface Area, 18-3 Volume of Rectangular Prisms, 18-4 Volume of Triangular Prisms and Cylinders, 18-5 Use Objects and Reasoning Khan Academy: Area of Parallelograms, Area of Quadrilaterals and Polygons, Area of Trapezoids, Rhombi, and Kites, Area of Triangles, Area of Triangles 2, Finding Area by Composing and Decomposing Shapes, Volume With Fractions, Volume WIth Unit Cubes 2, Volume With Fractions Word Problems, Nets of 3D Figures, Surface Area, Surface Area Using Nets
Unit 8: Statistical Variability and Analyzing Statistical Data 6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box and whisker plots. 6.SP.5. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Duration: 3 Weeks Prentice Hall Mathematics Course 1: 2-1a Hands On: Exploring the Mean Activity Lab, 2-1 Finding the Mean, 2-2 Median and Mode, 2-3 Frequency Tables and Line Plots, 2-4 Bar Graphs and Line Graphs, 2-6 Stem-and-Leaf Plots, 2-7 Misleading Graphs and Statistics Envision: 19-1 Graphs Reading and Making Graphs, 19-3 Comparing Graphs, 19-5 Statistics Mean, Median, Mode, and Range, 19-6 Statistics Frequency Tables and Histograms, 19-7 Statistics Stem-and-Leaf Plots, 19-8 Statistics Appropriate Uses of Statistical Measures, 19-9 Statistics Samples and Surveys, 19-10 Using Statistics to Draw Conclusions
Khan Academy: Statistical Questions, Understanding the Mean, Mean, Median, and Mode, Analyzing Data With Box Plots, Describing Distributions With Center and Spread, Analyzing Data WIth Dot Plots, Creating Bar Charts, Creating Box and Whisker Plots, Creating Dot Plots, Reading Bar Charts 1, Reading Bar Charts 2, Reading Bar Charts 3, Reading Pictographs 1, Reading Pictographs 2, Exploring Mean and Median