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Number and Ratios: Understanding and OperationsLevel A(K-1) Number Base TenAcademic SkillCCRSMWOTLPriority TopicResourcesManipulativesTwo digit numbers represent an amount of tens and an amount of pare two digit numbersAdd and subtract two digit pare two two-digit numbers with the symbols >, =, and <.1.NBT.2, 1.NBT.3, 1.NBT.4, 1.NBT.5, 1.NBT.6, Number: Developing understanding of whole number place value for tens and onesNumber: Developing understanding of addition and subtraction and the properties of these operations.Number Power 1 - P 8-11, 24S.V. Building Strategies Mathematicsp-30-45, Common Core Basic Lesson(s) 1.2S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.1, EMPower Plus Everyday Math L 1, 6EdReady GED Unit 1.1Color TilesBase 10 BlocksRekenreks Bead RackLevel B (2-3) Number Base TenThree digit numbers represent the amount of hundreds, tens, and pare two three-digit numbers using >, =, and < .Add and subtract within 10002.NBT.1, 2.NBT.2, 2.NBT.3, 2.NBT.4, 2.NBT.7, 2.NBT.8, 2.NBT.9, 3.NBT.2, 3.NBT.3Number: Extending understanding of base-10 notation Number: Adding and subtracting to 1,000; fluency and application to 100 Number: Understanding multiplication and division of whole numbers to 100 Number: Understanding division as inverse of multiplication; single-digit divisors Number Power 1 p 13,25S.V. Building Strategies MathematicsP 47-53,Common Core Basic Lesson(s) 1.1S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.2,EMPower Plus Everyday Math L 1, 4, 5, 9EdReady GED Unit 1.1, 1.2, 1.3Rekenreks Bead RackBase 10 BlocksLevel C (4-5, +6) – Number Base TenAdd and subtract multi-digit whole numbers.Multiply whole numbers up to 4 digits by one digit.Divide 4 digit dividends and 1 digit divisors.Read, write, and compare decimals to thousandths.4.NBT.4, 4.NBT.5, 4.NBT.6, 5.NBT.3, 5.NBT.3a, 5.NBT.3b, 5.NBT.5, 5.NBT.6, 5.NBT.7, 6.NS.2, 6.NS.3Number: Extending the number system to positive rational numbers Number: Extending place value understanding for decimals to thousandths Number: Attaining fluency with operations, using multi-digit whole numbers and decimals Number Power 1P 26-29,43-59, 71-88,S.V. Building Strategies Mathematicsp. 62-75,90-98Common Core Basic Lesson(s) 1.3, 2.1S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.6EMPower Plus split it up L 1,2, 6, 7,8, 11EMPower Plus split it up L 10EMPower Plus Everyday Math L 2, 13EdReady GED Unit 1.3, 3.1, 3.2, 9.2CCRPW Number Concepts Lesson 9Decimal TowerRekenreks Bead RackBase 10 BlocksLevel B (2-3) – FractionsUnderstand a fraction as 1 part when the whole is partitioned into equal parts.Represent fractions on a number line.3.NF.1, 3.NF.2, 3.NF.2a, 3.NF.2b, Number: Developing understanding of fractions, especially unit fractionsS.V. Building Strategies MathematicsP118- 120Common Core Basic Lesson(s) 3.1Common Core Achieve Lesson(s) 1.1Empower Plus: Benchmarks Fractions L 1, 2, 3, 5EdReady GED Unit 2.1F.U.N. Number LineFraction TilesCuisenaire RodsLevel C (4-5, +6) – FractionsCompare 2 fractions with different numerators and different denominators using the symbols >,<, or =..Add and subtract mixed numbers with like denominators.Add and subtract fractions with unlike denominators.Solve word problems involving addition and subtraction of fractions, multiplication of a fraction by a whole number.Multiply a fraction by a whole number.Divide unit fractions by whole numbers and whole numbers by unit fractions.4.NF.1, 4.NF.2, 4.NF.3c, 4.NF.3d, 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c, 5.NF.1, 5.NF.3, 5.NF.4, 5.NF.7, 5.NF.7a, 5.NF.7b, 6.RP.1, 6.RP.2Number: Understanding fraction equivalence and comparison Number: Developing fluency with sums and differences of fractions Number: Connecting ratio and rate to whole number multiplication and divisionNumber Power 1P 15-17, S.V. Building Strategies MathematicsP 121-143Common Core Basic Lesson(s) 3.2,3.3,3.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.4KET NSG 1.5, 2.1Empower Plus: Benchmarks Fractions L 4,8, 10EdReady GED Unit 2.1, 2.2, 2.3, 4.1, 4.2CCRPW Number Concepts Lesson 2, 7, 8CCRPW Ratios, Prop, and Percent Lesson 1, 3Fraction TilesLevel D (+6, 7-8) – Number SystemsUnderstanding and ordering absolute value.Represent addition and subtraction on a horizontal or vertical number line.Extend understandings of multiplication, division, addition, and subtraction to rational numbers.Understand that integers can be divided, as long as the divisor is not zero.Convert a rational number to a decimal using long division.6.NS.7, 7.NS.1, 7.NS.1b, 7.NS.1c, 7.NS.1d, 7.NS.2, 7.NS.2a, 7.NS.2b, 7.NS.2c, 7.NS.2d, 7.NS.3Number: Extending number sense and fluency with operations to all rational numbers 1.1 M.I.1.1-H.I.S.V. Building Strategies MathematicsP 126-128Common Core Basic Lesson(s) 4.1Common Core Achieve Lesson(s) 1.1S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.3, 1.5KET NSG 1.1, 1.2KET AR 1.1EdReady GED Unit 1.4CCRPW Number Concepts Lesson 1, 3CCRPW Basic Algebra Lesson 3F.U.N. Number LineLevel D (+6, 7-8) – Ratio and Proportional ReasoningMake tables of equivalent ratios to compare ratiosFind a percent of a quantity as a rate per 100Recognize and represent proportional relationshipIdentify the constant of proportionality in table, graphs, equations, and diagrams.Explain what a point (x,y) on the graph of a proportional relationship means.Use proportional relationship[s t solve multistep ration and percent problems, (simple interest, tax, etc)6.RP.3, 6.RP.3a, 6.RP.3b, 6.RP.3c, 6.RP.3d, 7.RP.1, 7.RP.2, 7.RP.2a, 7.RP.2b, 7.RP.2c, 7.RP.2d, 7.RP.3Number: Understanding ratio and rate and using them to solve problems2.1-M.I.2.2- M.I.S.V. Building Strategies MathematicsP 150-162Common Core Basic Lesson(s) 7.1, 7.4, 7.5,7.6, 9.2Common Core Achieve Lesson(s) 2.1, 2.2S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 1.7KET NSG 2.2, 2.3EdReady GED Unit 5.2, 13.1CCRPW Ratios, Prop, and Percent Lesson 4, 5, 6,7, 8, 9, 10, 11 , 12Cuisenaire RodsLevel E (H.S.) – Number and QuantityRewrite radicals and rational exponents.Choose and interpret units consistently in formulas.N.RN.2, N.Q.1, N.Q.3Number: Extending understanding of number systems to the set of real numbers Number: Writing equivalent expressions involving radicals and rational exponents Number: Reasoning quantitatively and the use of units and appropriate levels of precision1.1-A.S.1.2 A.S.Number Power 3P24-37Common Core Basic Lesson(s)8.1, 8.2Common Core Achieve Lesson(s) 1.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.3KET NSG 1.6EdReady GED Unit 11.1CCRPW Number Concepts Lesson 5Algebra and FunctionsLevel A (K-1)– Operations and Algebraic ThinkingAcademic SkillCCRSMWOTLPriority TopicResourcesManipulativesCommutative Property of addition, 8+3=11 then 3+8=11Associative property of addition, 2+6+4=2+10=12Relate Counting to addition and subtractionAdd and subtract within 20Determine the unknown whole number in addition or subtraction equation, 8+?=111.OA.3, 1.OA.4, 1.OA.5, 1.OA.6, 1.OA.8Common Core Basic Lesson(s) 1.4, 1.6, EMPower Plus Everyday Math L 2, 7F.U.N. Number LineMath BalanceLevel B (2-3) – Operations and Algebraic ThinkingAdd and subtract within 100 to solve 1 and 2 step word problems, using equations with a symbol for the unknown.Interpret products and quotients of whole numbers.Use multiplication and division within 100 to solve word problems.Determine the whole number in a multiplication or division equation relating 3 whole numbers (6x6=?2.OA.1, 2.OA.2, 3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.6, Common Core Basic Lesson(s) 4.2,4.3S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.2EMPower Plus Everyday Math L 6, 10Level C (4-5, +6) – Operations and Algebraic ThinkingUse parentheses, brackets, or braces to evaluate expressions,Write and evaluate expressions involving whole number exponents.Write, read, and evaluate expressions with letters.Express the calculation “Subtract y from 5” as 5-yIdentify parts of an expression using terms -sum, term product, factor, quotient, coefficient.Perform arithmetic operations in the conventional order when there are no parentheses (order of operations).Use variables to represent numbers.in a real-world problem4.OA.1, 4.OA.5, 5.OA.1, 5.OA.2, 6.EE.1, 6.EE.2, 6.EE.2a, 6.EE.2b, 6.EE.2c, 6.EE.6, 6.EE.9Algebra: Writing, evaluating, and interpreting expressions and equationsCommon Core Basic Lesson(s) 5.1Common Core Achieve Lesson(s)1.2S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s)3.1KET NSG 1.3KET AR 1.2, 2.1, 2.2, 3.2, 5.1, 6.3EMPower Plus Everyday Math L 8, 11EdReady GED Unit 9.1, 9.4, 10.1, 14.2CCRPW Basic Algebra Lesson 1, 2, 9Level D (+6, 7-8) – Expressions and EquationsApply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.Solve problems with positive and negative rational numbers. Convert between forms as appropriate.A function is a rule that assigns each input exactly one output.The equation y=mx+b defines a linear function whose graph is a straight line.Use variables to construct simple equations and inequalities.Solve problems leading to equations of the form px+q=r, and p(x+q)=rSolve word problems leading to inequalities of the form px+q>r or px+q<rGraph proportional relationships, interpreting the unit rate as the slope of the graph.Solve linear equations in one variable.Solve linear equations with rational number coefficients.Analyze and solve pairs of simultaneous linear equations.7.EE.1, 7.EE.3, 7.EE.4, 7.EE.4a, 7.EE.4b, 8.EE.5, 8.EE.7, 8.EE.7a, 8.EE.7b, 8.EE.8, 8.EE.8a, 8.EE.8b, 8.EE.8cAlgebra: Applying proportional relationships Algebra: Working with expressions and linear equations Algebra: Solving linear equations and systems of linear equations2.3- M.I.2.1-H.mon Core Basic Lesson(s) 8.3, 5.2, 5.3Common Core Achieve Lesson(s) 3.1, 3.2, 3.3S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.4, 3.6, 3.8, 3.13KET AR 2.3, 3.1EdReady GED Unit 3.1, 10.1, 10.2, 10.3, 13.2, 14.1, 16.1, 16.2CCRPW Basic Algebra Lesson 8Level D (+6, 7-8) – FunctionsSolve systems of two linear equations in two variables algebraically.Solve real-world and mathematical problems leading to two linear equations in two variables. 8.F.1, 8.F.3, Algebra: Developing the concept of function Algebra: Graphing functions in the coordinate plane and analyzing their graphs2.2-H.mon Core Basic Lesson(s) 6.1Common Core Achieve Lesson(s) 5.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.7KET AR 5.2EdReady GED Unit 14.1, 17.1, 17.2CCRPW Basic Algebra Lesson 11, 13Level E (H.S.)– AlgebraInterpret factors and coefficientsUse the structure of an expression to identify ways to rewrite it.Factor a quadratic expression to reveal the zeros of the function it defines.Rewrite simple rational expressions in different forms.Create equations and inequalities in one variable and use them to solve problems.Create equations in two or more variables to represent relationships between quantities.Graph equations on coordinate axes with labels and scales.Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.Solve quadratic equations in one variable.A.SSE.1, A.SSE.1a, A.SSE.2 A.SSE.3, A.SSE.3a, A.APR.1 A.APR.6, A.CED.1 A.CED.2, A.CED.3, A.REI.3, A.REI.4Algebra: Interpreting and using the structure of expressions to solve problems Algebra: Operating with algebraic expressions, including polynomials and rational expressions2.1 -A.mon Core Basic Lesson(s) 6.2, 6.3Common Core Achieve Lesson(s) 3.4, 4.1, 4.2, 4.3, 4.4, 5.3, 6.2S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.10, 3.11KET AR 3.2, 3.3, 3.4, 4.1, 4.2, 6.1, 7.2EdReady GED Unit 11.2, 11.3, 12.2, 12.3, 14.3, 15.1, 16.5CCRPW Basic Algebra Lesson 14Level E (H.S.)– FunctionsRelate the domain of a function to its graph.Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.Graph functions expressed symbolically. Use the properties of exponents to interpret expressions for exponential pare two functions represented in different ways.Write a function that describes a relationship between two quantities.Distinguish between situations that can be modeled with a linear functions and exponential functions.Recognize when one quantity changes at a constant rate.Interpret the parameters in a linear or exponential function.F.IF.4, F.IF.5, F.IF.7, F.IF.8b F.IF.9, F.BF.1, F.LE.1, F.LE.1b, F.LE.1c, F.LE.5Algebra: Defining, evaluating, comparing, and modeling with linear, quadratic, and exponential functions and equations Algebra: Building, interpreting, and analyzing functions using different representations Algebra: Reasoning with and solving linear, quadratic, and exponential equations and linear inequalities2.2 -A.S.2.3 -A.mon Core Basic Lesson(s) 6.5Common Core Achieve Lesson(s)1.3, 6.1, 6.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 2.5, 2.6, 3.16, 3.17EdReady GED Unit 18.1, 18.4GeometryLevel A (K-1)– Geometry and Geometric MeasurementAcademic SkillCCRSMWOTLPriority TopicResourcesManipulativesAnalyze and compare 2 and 3 dimensional shapes, in different sizes and pose 2 or 3 dimensional shapes to create composites.Express the length of an object as a whole number of units, by laying multiple copies of shorter objects end to end.K.G.4, 1.G.2, 1.MD.2Geometry: Describing and reasoning about shapes and their attributes Geometry: Developing understanding of linear measurementCommon Core Basic Lesson(s) 12.1S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 4.5KET NSG 4.7EdReady GED Unit 6.1, 7.1Pattern BlocksOmnifix cubesLevel B(2-3) – Geometry and Geometric MeasurementPartition shapes into parts with equal areas, express the area as a unit fraction.Estimate lengths using units of inches, feet, cm, and meters. Measure to determine difference in length.Tell and write time to the nearest minute.Measure and estimate liquid volumes and masses of objects using standard units of g, kg, and l.Recognize area as an attribute of plane figures and understand concepts of area measurement. Measure areas by counting unit squares.Relate area to the operations of multiplication and addition.Multiply side lengths to find areas of rectangles with whole-number side lengths.3.G.2, 2.MD.3, 2.MD.4, 3.MD.1, 3.MD.2, 3.MD.5, 3.MD.6, 3.MD.7, 3.MD.7a, 3.MD.7b, 3.MD.7c, 3.MD.7dGeometry: Using standard units of measure for length, time, liquid volume, and mass Geometry: Developing understanding of area and its relationship to addition and multiplication Geometry: Analyzing and partitioning 2-dimensional shapesCommon Core Basic Lesson(s) 11.1, 11.2, 12.2, 12.7 S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 2.1Empower Plus: Benchmarks Fractions L 6, 7, 9EdReady GED Unit 6.2Level C (4-5, +6) – Geometry and Geometric MeasurementDraw points, lines, line segments, rays, angles, and perpendicular and parallel lines.Use a pair of perpendicular number lines, axes, to define a coordinate system, with the origin at the intersection.Find a given point in the plane using an ordered pair of numbers.Graph points in the first quadrant of the coordinate plane.Find area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles. Draw polygons in the coordinate plane.Understand concepts of volume measurement. Apply the formulas V=l x w x h and V=b x h for rectangular prisms.4.G.1, 5.G.1, 5.G.2, 5.G.3, 6.G.1, 6.G.3, 5.MD.3 5.MD.4, 5.MD.5, 5.MD.5a, 5.MD.5b, 5.MD.5cGeometry: Developing understanding of the coordinate plane Geometry: Classifying geometric 2-dimensional figures based on properties Geometry: Developing an understanding and solving problems involving volume and surface areaCommon Core Basic Lesson(s) 12.3, 12.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 3.15, 4.1, 4.3KET NSG 4.1,4.5EdReady GED Unit 7.1, 7.2, 7.3, 8.1, 9.3CCRPW Number Concepts Lesson 4Level D (+6, 7-8) – GeometrySolve problems involving scale drawings of geometric figures.Know and use the formula for the area and circumference of a circle.Solve problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.Understand when a two-dimensional figure is congruent or similar to another figure.Use the Pythagorean Theorem to determine the unknown side lengths in a right triangle.Use the Pythagorean Theorem to find the distance between two points in a coordinate system,7.G.1, 7.G.4, 7.G.6, 8.G.2, 8.G.4, 8.G.7, 8.G.8Geometry: Solving problems involving scale drawings Geometry: Solving problems involving 2- and 3-dimensional figures: area, surface area, and volume Geometry: Analyzing 2- and 3-dimensional shapes using side length and angle measurements, similarity, and congruence Geometry: Applying the Pythagorean theorem3.1- M.I.3.2- M.I.3.1-H.I.3.2-H.mon Core Basic Lesson(s) 12.5Common Core Achieve Lesson(s)7.1, 7.2S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 2.2, 4.2, 4.4, 4.6KET NSG 4.2,4.3, 4.4EdReady GED Unit 7.1, 7.2Level E (H.S.) – GeometryUse congruence and similarity for triangles to solve problems and to prove relationships.Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.G.SRT.5, G.GMD.3Geometry: Applying similarity and congruence concepts to geometric figures, including triangles Geometry: Using geometric models and volume formulas to solve measurement problems3.1- A.mon Core Basic Lesson(s)12.6Common Core Achieve Lesson(s) 7.3, 7.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s)4.7, 4.8KET NSG 4.6Data, Probability, and Statistical MeasurementLevel C (4-5, +6) – Measurement and DataAcademic SkillCCRSMWOTLPriority TopicResourcesManipulativesRecognize a statistical question.A set of data has a distribution which can be described by its center, spread, and overall shape.A measure of center and a measure of variation describes its value with a single number.6.SP.1, 6.SP.2, 6.SP.3Statistics and Probability: Developing understanding of statistical variabilityCommon Core Basic Lesson(s) 9.1Level D (+6, 7-8) – Statistics and ProbabilitySummarize numerical data sets in relation to their context by reporting number of observations, mean, median, range, and variation.Understand that a sample population can be used to gain information about a population.Use data from a random sample to draw inferences about a population.Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences.Probability of a chance event is a number between 0 and 1.Construct and interpret scatter plots.Straight lines are widely used to model relationships between two variables.Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.Construct and interpret a two-way table summarizing data on to categorical variables collected from the same subjects.6.SP.5, 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 8.SP.1 8.SP.2, 8.SP.3, 8.SP.4, Statistics and Probability: Understanding patterns of association for bivariate data and describing them with a linear equation, when appropriate Statistics and Probability: Summarizing and interpreting data and data distributions Statistics and Probability: Understanding and applying probability concepts Statistics and Probability: Drawing inferences about populations based on random samples (probability distributions)4.1- M.I.4.2- M.I.4.1-H.I.4.2-H.mon Core Basic Lesson(s) 6.4, 9.3Common Core Achieve Lesson(s) 2.4, 8.1S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 2.3, 2.4KET NSG 3.1, 3.3EdReady GED Unit 8.2, 8.4Level E (H.S.) – Interpreting DataRepresent data with plots on the real number line (dot plots, histograms and box plots).Interpret differences in shape, center, and spread in the context of the data sets.Summarize categorical data for two categories in two-way frequency tables.Interpret relative frequencies in the context of the data.Interpret the slope and the intercept of a linear model.S.ID.1, S.ID.3, S.ID.5, S.ID.7, Statistics and Probability: Summarizing, representing, and interpreting one- and two-variable data, including using frequency tables4.1- A.mon Core Basic Lesson(s) 10.2, 10.3Common Core Achieve Lesson(s) 5.1, 5.2, 8.3, 8.4S.V. Mathematical Reasoning Workbook/ Student Book Lesson(s) 2.7KET NSG 3.2EdReady GED Unit 8.3CCRPW Basic Algebra Lesson 12F.U.N. Number LineThe outline combines multiple CCRS resources onto one source. The six columns are:Academic Skill- a summary of the academic skills that the level of standards RS- the focus standards which can be found in their entirety in the CCRS Progressions document.MWOTL- the corresponding Major Work of the LevelPriority Topic - topics as assigned by StandardsWork in Guide to Effectively Managing Higher-level Content Standards in Mathematics. M.I.Middle Intermediate LevelH.I.High Intermediate Level A.S.Adult Secondary Level Resources- units and sections primarily from resources that have been determined to be aligned with the CCRSS.V.- Stech VaughnCCRPW- College and Career Readiness Practice Workbook (McGraw Hill)KET NSG- KET FastForward Reasoning with Numbers, Statistics, and GeometryKET AR- KET FastForward Algebraic ReasoningManipulatives- items that have been suggested by the resources. ................
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