WIXLIB

California Math Textbook to Curriculum Map Alignment for CC Grade 6from 0 on the number line; interpret absolute value as magnitude fora positive or negative quantity in a real-world situation.For example, for an account balance of –30 dollars, write –30 30 to describe the size of the debt in dollars.d. Distinguish comparisons of absolute value from statements about 6.NS.7d- IQL 5-2, 5-2, 5-3order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.6.NS.8. Solve real-world and mathematical problems by graphingpoints in all four quadrants of the coordinate plane. Include use ofcoordinates and absolute value to find distances between points withthe same first coordinate or the same second coordinate.6.NS.8- 5-7, IQL 5-7, 9-56.NS.8Illustrative MathematicsDistances between PointsMathematics Assessment ProjectFractions, Decimals and Percents,Adding and Subtracting DirectedNumbers, Evaluating StatementsAbout Number Operations,A Measure of Slope FAL (6.NS.5-8)(s/a)2 Solve realworld andmathematicalproblems involvingarea, surface area,and volume.6.G.1. Find the area of right triangles, other triangles, specialquadrilaterals, and polygons by composing into rectangles ordecomposing into triangles and other shapes; apply these techniquesin the context of solving real-world and mathematical problems.6.G.1- IQL 9-1, 9-1, IQL 92, 9-2, IQL 9-3, 9-3, Ch.9PSI, 9-4, 9-5, IQL 9-6, 9-66.G.2. Find the volume of a right rectangular prism with fractionaledge lengths by packing it with unit cubes of the appropriate unitfraction edge lengths, and show that the volume is the same as wouldbe found by multiplying the edge lengths of the prism. Apply theformulas V l w h and V b h to find volumes of right rectangularprisms with fractional edge lengths in the context of solving realworld and mathematical problems.6.G.2- IQL 10-1, 10-1,Ch.10 PSI,LAUSD Secondary MathematicsNovember 19, 2014 DraftPage 6

California Math Textbook to Curriculum Map Alignment for CC Grade 6Grade 6- Unit 3Understanding Expressions and EquationsCritical Area: Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations,evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they usethe properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make theequation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations.Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x y) to describe relationshipsbetween quantities.CLUSTERSApply and extendpreviousunderstandings ofarithmetic toalgebraicexpressionsCOMMON CORE STATE STANDARDS6.EE.1. Write and evaluate numerical expressions involving wholenumber exponents.CA MATH6.EE.1- 6-1, 6-2ADDITIONAL RESOURCES6.EE.1Illustrative MathematicsThe Djinni’s Offer, Seven to theWhat?!?, G Sierpinski's Carpet6.EE.2. Write, read, and evaluate expressions in which letters standfor numbers.a. Write expressions that record operations with numbers andwith letters standing for numbers. For example, express thecalculation “Subtract y from 5” as 5 – y.b. Identify parts of an expression using mathematical terms(sum, term, product, factor, quotient, coefficient); view oneor more parts of an expression as a single entity. Forexample, describe the expression 2 (8 7) as a product oftwo factors; view (8 7) as both a single entity and a sum oftwo terms.c. Evaluate expressions at specific values of their variables.Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, includingthose involving whole-number exponents, in the conventionalorder when there are no parentheses to specify a particularorder (Order of Operations). For example, use the formulas V s3 and A 6 s2 to find the volume and surface area of acube with sides of length s 1/2.LAUSD Secondary Mathematics6.EE.2a- IQL 6-1, 6-3, IQL6-4, 6-4, Ch.6 PSI, 6-7, 8-1,8-26.EE.2b- IQL 6-1, IQL 6-4,6-76.EE.2Illustrative MathematicsRectangle Perimeter 1, Distance toSchool6.EE.2c-6-3, 6-4, 8-1, 8-2November 19, 2014 DraftPage 7

California Math Textbook to Curriculum Map Alignment for CC Grade 66.EE.3. Apply the properties of operations to generate equivalent6.EE.3- 6-5, IQL 6-6,expressions. For example, apply the distributive property to the6-6, 6-7expression 3 (2 x) to produce the equivalent expression 6 3x;apply the distributive property to the expression 24x 18y toproduce the equivalent expression 6 (4x 3y); apply properties ofoperations to y y y to produce the equivalent expression 3y.6.EE.4. Identify when two expressions are equivalent (i.e., when thetwo expressions name the same number regardless of which value issubstituted into them). For example, the expressions y y y and 3yare equivalent because they name the same number regardless ofwhich number y stands for.6.EE.3Illustrative MathematicsAnna in D.C.6.EE.4Illustrative MathematicsEquivalent Expressions,Rectangle Perimeter 26.EE.4- IQL 6-7, 6-7Mathematics Assessment ProjectLaws of Arithmetic, Investigating:Consecutive Sums FAL (6.EE.1-4)6.EE.5Illustrative MathematicsLog Ride6.EE.5. Understand solving an equation or inequality as a process ofanswering a question: which values from a specified set, if any, makethe equation or inequality true? Use substitution to determine whethera given number in a specified set makes an equation or inequalitytrue.6.EE.5- 7-1, IQL7-2, 7-2,IQL 7-3, 7-3, IQL 7-4, 7-4,IQL 7-5, 7-5, IQL 8-5, 8-5,IQL 8-7, 8-76.EE.6. Use variables to represent numbers and write expressionswhen solving a real-world or mathematical problem; understand thata variable can represent an unknown number, or, depending on thepurpose at hand, any number in a specified set.6.EE.6-6-3, 6-4, 8-2, 8-6,8-76.EE.7. Solve real-world and mathematical problems by writing andsolving equations of the form x p q and px q for cases in whichp, q and x are all nonnegative rational numbers.6.EE.7- IQL 7-2, 7-2, IQL6.EE.77-3, 7-3, Ch.7 PSI, IQL 7-4, Illustrative Mathematics7-4, IQL 7-5, 7-5Firefighter Allocation, Morning Walk,Anna in D.C., Fruit Salad6.EE.8. Write an inequality of the form x c or x c to represent aconstraint or condition in a real-world or mathematical problem.Recognize that inequalities of the form x c or x c have infinitelymany solutions; represent solutions of such inequalities on number6.EE.8- IQL 8-5,8-5, 8-6,IQL8-7, 8-7LAUSD Secondary MathematicsInside Mathematicsboxes (6.EE.4-5)6.EE.6Illustrative MathematicsPennies to heaven6.EE.8Illustrative MathematicsFishing Adventures 1November 19, 2014 DraftPage 8

California Math Textbook to Curriculum Map Alignment for CC Grade 6line diagrams.Represent andanalyze quantitativerelationshipsbetween dependentand independentvariables.(s/a)2 Solve realworld andmathematicalproblems involvingarea, surface area,and volume.Mathematics Assessment ProjectInterpreting Equations,Evaluating Statements About NumberOperations FAL (6.EE.5-8)6.EE.9Illustrative MathematicsChocolate Bar Sales6.EE.9.Use variables to represent two quantities in a real-worldproblem that change in relationship to one another; write an equationto express one quantity, thought of as the dependent variable, in termsof the other quantity, thought of as the independent variable. Analyzethe relationship between the dependent and independent variablesusing graphs and tables, and relate these to the equation. For example,in a problem involving motion at constant speed, list and graphordered pairs of distances and times, and write the equation d 65tto represent the relationship between distance and time.6.EE.9- 8-1, 8-2, 8-3,8-4, Ch.8 PSI6.G.1. Find the area of right triangles, other triangles, specialquadrilaterals, and polygons by composing into rectangles ordecomposing into triangles and other shapes; apply these techniquesin the context of solving real-world and mathematical problems.6.G.1- IQL 9-1, 9-1, IQL9-2, 9-2, IQL 9-3, 9-3,Ch.9 PSI, 9-4, 9-5, IQL 96, 9-66.G.2. Find the volume of a right rectangular prism with fractionaledge lengths by packing it with unit cubes of the appropriate unitfraction edge lengths, and show that the volume is the same as wouldbe found by multiplying the edge lengths of the prism. Apply theformulas V l w h and V b h to find volumes of right rectangularprisms with fractional edge lengths in the context of solving realworld and mathematical problems.6.G.2- IQL 10-1, 10-1,Ch.10 PSI6.G.4. Represent three-dimensional figures using nets made up ofrectangles and triangles, and use the nets to find the surface area ofthese figures. Apply these techniques in the context of solving realworld and mathematical problems.6.G.4- Ch.10 PSI, IQL 103,, 10-3, IQL 10-4, 10-4,IQL 10-5, 10-5LAUSD Secondary MathematicsInside Mathematicsgym, tuffles (6.EE.6 and 9)Mathematics Assessment ProjectModeling: Car Skid MarksFAL (6.EE.9)November 19, 2014 DraftPage 9

California Math Textbook to Curriculum Map Alignment for CC Grade 6GRADE 6 – UNIT 4Geometry and Statistics and ProbabilityCritical Area: Description of the critical area: Building on and reinforcing their understanding of number, students begin to develop their ability to thinkstatistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The medianmeasures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if thetotal of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartilerange or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet bedistinguished by their variability.Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data werecollected. Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surfacearea, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, andrelating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areasof polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prismswith fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings andconstructions in Grade 7 by drawing polygons in the coordinate plane.CLUSTERS Developunderstanding ofstatisticalvariability.Summarize anddescribedistributions.COMMON CORE STATE STANDARDS6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in theanswers. For example, “How old am I?” is not a statistical question,but “How old are the students in my school?” is a statistical questionbecause one anticipates variability in students’ ages.CA MATH6.SP.1- IQL 11-1, Ch.11PSIADDITIONAL RESOURCES6.SP.1Illustrative MathematicsButtons: Statistical Questions,Identifying Statistical Questions 6.SP.2. Understand that a set of data collected to answer a statisticalquestion has a distribution which can be described by its center,spread, and overall shape.6.SP.2- 12-3, 12-46.SP.2Illustrative MathematicsPuppy Weights, Electoral College 6.SP.3. Recognize that a measure of center for a numerical data setsummarizes all of its values with a single number, while a measure ofvariation describes how its values vary with a single number.6.SP.3- IQL 11-1,11-1, 11-2, 11-36.SP.4. Display numerical data in plots on a number line, includingdot plots, histograms, and box plots.6.SP.4- 12-1, 12-2, 12-3,Ch.12 PSI, IQL 12-46.SP.5. Summarize numerical data sets in relation to their context,such as by:a. Reporting the number of observations.6.SP.5a- 12-1, 12-2, 12-4,LAUSD Secondary MathematicsMathematics Assessment ProjectMean, Median, Mode, and RangeFAL (6.SP.1-4)6.SP.4Illustrative MathematicsPuppy Weights, Puzzle TimesNovember 19, 2014 DraftPage 10

California Math Textbook to Curriculum Map Alignment for CC Grade 6IQL 12-4, IQL 12-6b. 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) andvariability (interquartile range and/or mean absolute deviation), aswell as describing any overall pattern and any striking deviationsfrom the overall pattern with reference to the context in which thedata were gathered.d. Relating the choice of measures of center and variability to theshape of the data distribution and the context in which the datawere gathered.6.SP.5b- 11-2,11-4,12-1,12-2, 12-3, IQL 12-4,IQL 12-66.SP.5c- 11-2, 11-3, 11-4,11-5, 12-1, 12-3, Ch.12PSI, IQL 12-4, IQL 12-66.SP.5.c6.SP.5d- 11-5, 12-4, IQL12-46.SP.5.dIllustrative MathematicsPuzzle TimesIllustrative MathematicsElectoral CollegeInside Mathematicsbaseball playersSolve real-world andmathematicalproblems involvingarea, surface area,and volume.6.G.1. Find the area of right triangles, other triangles, specialquadrilaterals, and polygons by composing into rectangles ordecomposing into triangles and other shapes; apply these techniquesin the context of solving real-world and mathematical problems.6.G.1- IQL 9-1, 9-1, IQL 92, 9-2, IQL 9-3, 9-3, Ch. 9PSI, 9-4, 9-5, IQL 9-6, 9-66.G.2. Find the volume of a right rectangular prism with fractionaledge lengths by packing it with unit cubes of the appropriate unitfraction edge lengths, and show that the volume is the same as wouldbe found by multiplying the edge lengths of the prism. Apply theformulas V l w h and V b h to find volumes of right rectangularprisms with fractional edge lengths in the context of solving real-6.G.2- IQL 10-1, 10-1,Ch.10 PSILAUSD Secondary MathematicsMathematics Assessment ProjectRepresenting Data Using Grouped,Frequency Graphs and Box PlotsFAL (6.SP)6.G.1Illustrative MathematicsSame Base and Height, Variation 1,Same Base and Height, Variation 2,Finding Areas of Polygons, Base andHeight, Polygons in the CoordinatePlane, Sierpinski's Carpet6.G.2Illustrative MathematicsComputing Volume Progression 1,Computing Volume Progression 4,Banana Bread,Computing Volume Progression 2,November 19, 2014 DraftPage 11

California Math Textbook to Curriculum Map Alignment for CC Grade 6world and mathematical problems.Computing Volume Progression 3Inside Mathematicsbuilding blocks6.G.3. Draw polygons in the coordinate plane given coordinates forthe vertices; use coordinates to find the length of a side joining pointswith the same first coordinate or the same second coordinate. Applythese techniques in the context of solving real-world andmathematical problems.6.G.3- 9-56.G.3Illustrative MathematicsPolygons in the Coordinate Plane6.G.4. Represent three-dimensional figures using nets made up ofrectangles and triangles, and use the nets to find the surface area ofthese figures. Apply these techniques in the context of solving realworld and mathematical problems.6.G.4- Ch.10 PSI, IQL 103, 10-3, IQL 10-4, 10-4,IQL 10-5, 10-56.G.4Illustrative MathematicsNets for Pyramids and PrismsMathematics Assessment ProjectOptimizing: Security CamerasLaws of Arithmetic, Optimizing:Packing It In, Using Coordinates toInterpret and Represent Data,Designing: Candy CartonsFAL (6.G.1-4)LAUSD Secondary MathematicsNovember 19, 2014 DraftPage 12

California Math Textbook to Curriculum Map Alignment for CC Grade 6 LAUSD Secondary Mathematics November 19, 2014 Draft Page 2 what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems invo