Math Scope & Sequence Grades 3-8 Common Core State Standards

Math Scope & Sequence Grades 3-8 Common Core State Standards Number and Operations in Base Ten Place Value Understand foundations 3.NBT.A.1 4.NBT.A.1, 5.NBT.A.1, of and generalize about 3.NBT.A.2 4.NF.C.6, 5.NBT.A.3 place value 3.NBT.A.3 4.NF7 Extend counting 4.NBT.A.1, 5.NBT.A.1 sequence and read and 4.NBT.A.2, write whole numbers 4.NF.C.6 Compare/order numbers 4.NBT.A.2 5.NBT.A.3 Round numbers 3.NBT.A.1 4.NBT.A.3 5.NBT.A.4 Compose and decompose numbers Addition and Subtraction 4.NBT.B.5 5.NBT.A.1 Fluently add and subtract multi-digit numbers Compose and decompose numbers Use mental arithmetic Use estimation 3.NBT.A.2 4.NBT.B.4 4.NBT.A.2 4.NBT.B.4 4.NBT.A.3 Use algorithms to add and subtract Use and explain strategies based on therelationship between addition and subtraction 3.NBT.A.2 3.NBT.A.2 4.NBT.B.4 4.NBT.B.4 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 1

LF.1009718 Use and explain strategies based on place value and properties of operations 3.NBT.A.2 4.NBT.B.4 5.NBT.B.7 Multiplication and Division Compose and 3.OA.A.1 4.NBT.B.5, 5.NBT.B.5 decompose numbers 3.OA.A.2 4.NBT.B.6, Use and explain 3.OA.B.6 4.NBT.B.5, 5.NBT.B.6, strategies based on the 3.OA.A.4 4.NBT.B.6 5.NBT.B.7 relationship between multiplication and division Use and explain 3.OA.B.5 4.NBT.B.5, 5.NBT.B.6, strategies based on 4.NBT.B.6 5.NBT.B.7 place value and properties of operations Interpret multiplication 4.OA.A.1, equations as 4.OA.A.2 comparisons Interpret remainders 4.NBT.B.6, 5.NBT.B.6 4.OA.A.3 Estimation 4.NBT.A.3, 5.NBT.B.5, 4.NBT.B.6 5.NBT.B.6 Divide and fluently 3.OA.C.7 4.NBT.B.5, 5.NBT.B.5, 6.NS.B.2 multiply multi-digit 3.OA.A.3 4.NBT.B.6 5.NBT.B.6 numbers using standard algorithm Prime factorization 5.NBT.A.2 Whole Numbers Factors and Common 4.NF.A.1 5.NF.A.2 Factors Greatest Common Factor 6.NS.B.4 (GCF) Multiple and Common 4.NF.A.1 5.NF.A.2 Multiples 2 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Least Common Multiple (LCM) Apply Distributive Property Powers and exponents 6.NS.B.4 4.NBT.B.5 5.NBT.B.5 6.NS.B.4 5.NBT.A.2 Square roots of perfect squares 8.EE.A.2 Integers Positive and negative numbers Opposite signs of numbers Graph integers on a number line Order integers Absolute value Additive inverses 6.NS.C.5 6.NS.C.6a 6.NS.C.6, 6.NS.C.6a, 6.NS.C.6c 6.NS.C.7, 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7d 6.NS.C.7, 6.NS.C.7c, 6.NS.C. 7.NS.A.1c 7.NS.A.1a, 7.NS.A.1b Multiplication of integers 7.NS.A.2a Division of integers 7.NS.A.2b Properties of integer exponents 8.EE.A.1 Rational Numbers Graph rational numbers on a number line Order rational numbers on a number line 6.NS.C.6, 6.NS.C.6, 6.NS.C.6c 6.NS.C.7, 6.NS.C.7a MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 3

LF.1009718 Write, interpret, and explain order of rational numbers Graph rational numbers on a coordinate plane Solve real-world problems by graphing points in all 4 quadrants 6.NS.C.7b 6.NS.C.6, 6.NS.C.6c, 6.NS.C 6.NS.C.8 Add and subtract rational numbers Represent addition and subtraction on a number line Interpret sums of rational numbers in real-world contexts Understand subtraction as adding the additive inverse Interpret products and quotients of rational numbers in real-world contexts Distance between two rational numbers on number line Multiply and divide rational numbers Concept of rational numbers Convert rational numbers to decimals 7.NS.A.1, 7.NS.A.1b, 7.NS.A.1c, 7.NS.A. 7.NS.A.1, 7.NS.A.1b 7.NS.A.1b 7.NS.A.1c 7.NS.A.2a, 7.NS.A.2b 7.NS.A.1c 7.NS.A.2, 7.NS.A.2a, 7.NS.A.2b, 7.NS.A.2c 7.NS.A.2b 7.NS.A.2d 4 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Terminating and repeating decimals Solve real-world problems using operations with rational numbers Complex fractions Solve multi-step problems involving rational numbers Convert a decimal expansion which repeats eventually into a rational number Real Numbers Concept of irrational numbers Estimate square roots Know 2 is irrational Compare the size of irrational numbers Approximate location of irrational numbers on number line Number and Operations Fractions, Decimals, and Percents Fractions 7.NS.A.2d 7.NS.A.3 7.RP.A.1, 7.NS.A.3 7EE.3 8.NS.A.1 8.NS.A.1 8.NS.A.1 8.NS.A.2 8.EE.A.2 8.NS.A.2 8.NS.A.2 Represent fractions on a number line 3.NF.A.2.A 3.NF.A.2.B 4.NF.C.6 5.NF.A.2 6.NS.C.6c Equivalent fractions 3.NF.A.3.A 4.NF.A.1, 5.NF.A.1 3.NF.A.3.B 4.NF.C.5 3.NF.A.3.C Unit fractions 3.NF.A.1 4.NF.B.3b, 5.NF.B.7 3.G.A.2 4.NF.B.4a, 4.NF.B.4b MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 5

LF.1009718 Compare and order fractions 3.NF.A.3.D 4.NF.A.2 5.NF.B.5a Find factor pairs and multiples Prime and composite numbers Represent mixed numbers and write as improper fractions Add, subtract, and multiply fractions and mixed numbers Solve word problems involving addition and subtraction of fractions Solve word problems involving multiplication of fractions Round fractions 4.OA.B.4 4.OA.B.4 4.NF.B.3b 4.NF.B.3c, 4.NF.B.3d, 4.NF.B.4 4.NF.B.3d 4.NF.B.4c 5.NBT.A.2 5.NBT.A.2 5.NF.A.1 5.NF.A.1, 5.NF.A.2, 5.NF.B.4, 5.NF.B.5, 5.NF.B.6 5.NF.A.2 5.NF.B.6 5.NF.A.2 Estimate sums and differences of fractions Estimate products of fractions Interpret multiplication with fractions as scaling Interpret fractions as division of numerator by denominator 5.NF.A.2 5.NF.B.4a, 5.NF.B.6 5.NF.B.5 5.NF.B.3 Divide fractions and mixed numbers Solve word problems involving division of fractions 5.NF.B.7 5.NF.B.7c 6.NS.A.1 6.NS.A.1 6 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Decimals Understand decimal 4.NF.C.6 5.NBT.A.3a notation Write fractions as 4.NF.C.6 5.NF.B.5b, decimals 5.NBT.A.3a Compare and order 4.NF.C.6, 5.NF.B.5b, decimals 4.NF.C.7 5.NBT.A.3b Add decimals 4.NF.C.6, 5.NBT.B.7 6.NS.B.3 Subtract/ Multiply/ 5.NBT.B.7 Divide decimals to hundredths Estimate sums and 5.NBT.A.4 differences of decimals by rounding Represent decimals on a number line Subtract/ Multiply/ Divide multi-digit decimals 4.NF.C.6 5.NBT.A.3 6.NS.C.6c 6.NS.B.2, 6.NS.B.3 Convert rational numbers to decimals Terminating and repeating decimals Convert a decimal expansion which repeats eventually into a rational number Non-repeating decimals/ irrational numbers Percent 7.NS.A.2d 7.NS.A.2d 8.NS.1 8.NS.A.1 8.NS.A.1 Percent as rate per 100 Find a percent of a quantity 6.RP.A.3c 6.RP.A.3c MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 7

LF.1009718 Solve percent problems for whole 6.RP.A.3c Percent proportion Percent equation Simple interest Sales tax and gratuities Markups and markdowns Commissions and fees Percent error 7.RP.A.3 7.RP.A.3 7.RP.A.3 7.RP.A.3 7.RP.A.3 7.RP.A.3 7.RP.A.3 Ratio and Proportional Relationships Ratios and Rates Understand the concept of a ratio Use ratio and rate language Understand the concept of a unit rate Solve real-world problems using ratios and rates Tables of equivalent ratios Graph ratio tables 6.RP.A.1 6.RP.A.1, 6.RP.A.2 6.RP.A.2 6.RP.A.3 6.RP.A.3a 6. RP.3a 7.RP.A.3 7.RP.A.2a Unit Pricing 6.RP.A.3b Constant speed 6.RP.A.3b Use ratios to convert measurements Unit rates involving fractions (complex fractions) 6.RP.A.3d 7.RP.A.3 7.RP.A.1 8 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Ratio and probability 7.SP.C.8a Interpret unit rate as the slope Rate of change of a linear function 8.EE.B.5 8.F.B.4 Proportional Relationships Recognize and represent proportional relationships Identify proportional relationships using tables or graphs Constant of proportionality (unit rate) Represent proportional relationships by equations Explain what a point on the graph of a proportional relationship means Solve proportions 7.RP.A.2 7.RP.A.2a 7.RP.A.2b, 7.RP.A.2d 7.RP.A.2c 7.RP.A.2d 7.RP.A.3 Use proportional relationships to solve multistep ratio problems Graph proportional relationships Scale drawings 7.RP.A.3 7.RP.A.2a 7.G.A.1 8.EE.B.5 Compare two different proportional relationships 8.EE.B.5 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 9

LF.1009718 Algebra and Functions Algebraic Representation Identify/ generate/ 3.OA.D.9 4.NBT.A.1, 5.OA.B.3, explain patterns 4.NBT.B.4, 5.NBT.A.1, 4.OA.C 5.NBT Solve addition and 3.OA.D.8 4.OA.A.3 subtraction word problems Assess the 3.OA.D.8 4.OA.A.3, 5.NBT.B.5, reasonableness of 4.NBT.A.3, 5.NBT.B.6 answers by rounding and 4.NBT.B.6 estimating Determine the unknown/ 3.OA.D.8 4.OA.A.2, 5.NBT.B.6 variable 4.OA.A.3 Write and solve number 3.OA.D.8 4.OA.A.1, 5.NBT.B.6 sentences/equations 4.OA.A.2, 4.OA.A.3, 4.NBT.B.5, 4.NBT.B.6 Order of operations 4.OA.A.3 5.OA.A.1 6.EE.A.2c Write and solve 3.OA.D.8 4.OA.A.2, 5.NBT.B.5 multiplication and 4.OA.A.3 division word problems Write and evaluate numerical expressions Write and evaluate expressions involving variables 3.OA.D.8 4.OA.A.3 5.OA.A.1, 5.OA.A.2 3.OA.D.8 4.OA.A.3 5.OA.A.1, 5.OA.A.2 6.EE.A.1 6.EE.A.2, 6.EE.A.2a, 6.EE.A.2c, 6.EE.B.6 Identify and generate 3.OA.D.8 4.OA.C.5 nonnumeric patterns Apply properties of 3.OA.D.8 4.OA.C.5, 5.NBT.B.5 6.EE.A.1, 7.EE.A.1, operations 4.NBT.B.5 6.EE.A.3 7.EE.A.2 Parts of an expression 6.EE.A.2b 10 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Identify equivalent expressions 6.EE.A.4 Properties of integer exponents Use scientific notation to estimate quantities Perform operations using scientific notation Choose units of appropriate size for very large or very small quantities Scientific notation and technology 8.EE.A.1 8.EE.A.3 8.EE.A.4 8.EE.A.4 8.EE.A.4 Equations and Inequalities Identify values that make an equation or inequality true Use variables and expressions to solve real-world problems Write and solve equations of the form x + p = q and px = q Inequalities of the form x > c or x < c Graph inequalities on a number line Solve equations of the formpx + q = r and p(x + q) = r Compare an algebraic solution to an arithmetic solution 6.EE.B.5 6.EE.B.6 6.EE.B.7 6.EE.C.8 6.EE.C.8 7.EE.B.4 7.EE.B.4b 7.EE.B.4, 7.EE.B.4a 7.EE.B.4a MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 11

LF.1009718 Solve multi-step problems involving rational numbers Solve inequalities of the form px + q < r or px + q < r 7.EE.B.3 7.EE.B.4, 7.EE.B.4b Solve linear equations with one, infinitely many, or no solutions Solve linear equations with rational coefficients Solve equations of the form x 2 = p and x 3 = p Equations in Two Variables 7.EE.B.4a 8.EE.C.7, 8.EE.C.7a 8.EE.C.7, 8.EE.C.7b 8.EE.A.2 Dependent and independent variables Write equations using two variables 6.EE.C.9 6.EE.C.9 Form ordered pairs Tables of ordered pairs Graphs of ordered pairs Analyze patterns and relationships 5.OA.B.3, 5.G.A.1, 5.G.A 5.OA.B.3, 5.G.A.1, 5.G.A 5.OA.B.3, 5.G.A.1, 5.G.A 5.OA.B.3 6.EE.C.9 6.EE.C.9 Represent proportional relationships by equations 7.RP.A.2c Use similar triangles to explain slope of a line 8.EE.B.6 12 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Derive the equations y = mx and y = mx + b Solve systems of linear equations by graphing Solve systems of linear equations algebraically Solve problems leading to two linear equations in two variables 8.EE.B.6 8.EE.C.8, 8.EE.C.8a 8.EE.C.8, 8.EE.C.8b 8.EE.C.8, 8.EE.C.8c Functions Relations and functions Understand functions Graph of a function Compare properties of functions Identify nonlinear functions Linear functions in y = mx + b form Construct a function Rate of change and initial value of a function Qualitative graphs 8.F.A.1 8.F.A.1 8.F.A.1 8.F.A.2 8.F.A.3 8.F.A.3 8.F.A.4 8.F.A.4 8.F.A.5 Measurement Linear Measurement Measure to half and quarter of an inch Measure to eight of an inch Choose appropriate customary or metric unit of length Measure metric units of length 4.MD.A.1, 5.MD.B.2 5.MD.B.2 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 13

LF.1009718 Know measurement equivalencies within a measurement system Convert customary and metric units of length Solve linear measurement word problems using the four operations Perimeter and Area 4.MD.A.1 4.MD.A.1,, 4.MD.A.3 Apply the formula for perimeter Use concepts of area to measure area Decompose rectangles to find area Use unit squares to measure area Apply the formula for area Relate area and perimeter Volume Choose appropriate metric unit of capacity 3.MD.D.8 3.MD.C.5.A 3.MD.C.5.B 3.MD.C.7.D 3.MD.C.7.C 3.MD.C.6 3.MD.C.5.A 3.MD.C.5.B 3.MD.C.7.A 3.MD.C.7.B 3.MD.D.8 3.MD.A.2 4.MD.A.3 4.MD.A.3 4.MD.A.3 4.MD.A.3 4.MD.A.1 Convert metric units of capacity Choose appropriate customary unit of capacity Measure customary units of capacity Convert customary units of capacity 4.MD.A.1, 4.MD.A.1, 4.MD.A.1, 14 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Measure in unit cubes by 5.MD.C.3, counting 5.MD.C.4 Relate volume to 5.MD. 5 multiplication and addition Solve word problems 3.MD.A.2, involving volume using 4.MD.A.3 the four operations Weight and Mass Choose appropriate metric unit of mass 3.MD.A.2 4.MD.A.1 Measure metric units of mass Solve word problems involving mass 3.MD.A.2 3.MD.A.2 Choose appropriate 4.MD.A.1, customary unit of weight Measure customary units of weight Convert customary units 4.MD.A.1, of weight Convert metric units of 4.MD.A.1, mass Solve word problems 3.MD.A.2, involving weight and 4.MD.A.3 mass using the four operations Time Convert units of time 4.MD.A.1, Solve word problems 3.MD.A.1, involving time using the 4.MD.A.3 four operations MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 15

LF.1009718 Data Sets and Populations Organize, represent, and 3.MD.B.3 4.MD.B.4 5.MD.B.2 interpret data 3.MD.B.4 Generate data in whole units of linear measurement Generate data in 4.MD.B.4 5.MD.B.2 fractions of an inch Recognize statistical questions Distribution of a set of data 6.SP.A.1 6.SP.A.2 Statistics and population samples Random sampling of populations Draw inferences from random samples Multiple samples of data Visual overlap of data distributions Comparative inferences between two populations 3.MD.B.3 7.SP.A.1 7.SP.A.1 7.SP.A.2 7.SP.A.2 7.SP.B.3 7.SP.B.4 Measures of Center and Variability Measures of center 6.SP.A.3 7.SP.B.3, 7.SP.B.4 Median 6.SP.B.5c Mean 6.SP.B.5c Measures of variation 6.SP.A.3 7.SP.B.3, 7.SP.B.4 Range Outliers 6.SP.A.2, 6.SP.A.3 6.SP.B.5c 16 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Interquartile range Mean absolute deviation Shape of the data distribution Summarize and describe numerical data sets 6.SP.B.5c 6.SP.B.5c 6.SP.B.5d 6.SP.B.5, 6.SP.B.5a, 6.SP.B.5b, 6.SP.B.5c Comparative inferences between two populations 7.SP.B.3, 7.SP.B.4 Represent Data, Statistical Displays Make line plots using generated linear measurement data Solve addition and subtraction of fractions problems involving line plot analysis Solve multiplication and division of fractions problems involving line plot analysis 4.MD.B.4 4.MD.B.4 5.MD.B.2 5.MD.B.2 5.MD.B.2 Dot plots 6.SP.B.4 7.SP.B.3 Histograms 6.SP.B.4 7.SP.B.3 Box plots 6.SP.B.4 7.SP.B.3 Scatter plots Clustering and outliers Positive and negative association Linear and nonlinear association 8.SP.A.1 8.SP.A.1 8.SP.A.1 8.SP.A.1 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 17

LF.1009718 Line of best fit Use the equation of a linear model to solve problems Two-way tables 8.SP.A.2 8.SP.A.3 8.SP.A.4 Probability Probability and chance events Likely and unlikely events Relative frequency Develop a probability model Compare theoretical and experimental probability 7.SP.C.5 7.SP.C.5 7.SP.C.6 7.SP.C.7, 7.SP.C.7a, 7.SP.C.7b 7.SP.C.7 Compound events Sample spaces Number of outcomes Permutations Simulations Fair and unfair games 7.SP.C.8, 7.SP.C.8a 7.SP.C.8, 7.SP.C.8b 7.SP.C.8a 7.SP.C.8a 7.SP.C.6, 7.SP.C.7, 7.SP.C.8, 7.SP.C.8c 7.SP.C.7b Geometry Two- and Three-Dimensional Shapes and Figures Classify two-dimensional figures by their properties 3.G.A.1 5.G.B.4 18 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Describe properties of 3.G.A.1 5.MD.C.3 three-dimensional figures Identify, describe, and 3.G.A.1 4.G.A.1, 5.G.B.3, classify triangles and 4.G.A.2 5.G.B.4 quadrilaterals by their attributes Measure sides and 5.G.B.3, angles of triangles and 5.G.B.4 quadrilaterals Draw and identify points, 4.G.A.1 lines, segments, rays, and angles in two- dimensional figures Identify lines of 4.G.A.3 symmetry/ symmetric figures Draw polygons on the coordinate plane Use coordinates to find the length of sides of polygons 6.G.A.3 6.G.A.3 Draw geometric shapes Construct triangles from 3 measures of angles or sides Circles and circumference 7.G.A.2 7.G.A.2 7.G.B.4 Angle Measure and Relationships Explore angles of twodimensional shapes Classify angles by their attributes Measure and draw angles 4.G.A.1, 4.MD.C.5 4.G.A.1, 4.MD.C.5, 4.G.A.1, 4.MD.C.5, 4.MD.C.6 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 19

LF.1009718 Recognize angle measures as additive Solve addition and subtraction problems to determine measures of unknown angles 4.MD.C.7 4.G.A.1, 4.MD.C.7 Supplementary angles Complementary angles Vertical angles Adjacent angles 7.G.B.5 7.G.B.5 7.G.B.5 7.G.B.5 Sum of angles in a triangle Exterior angle of a triangle Parallel lines cut by a transversal Angle-angle criterion for similar triangles 8.G.A.5 8.G.A.5 8.G.A.5 8.G.A.5 Area and Surface Area Area of triangles 6.G.A.1 Area of parallelograms 6.G.A.1 Area of trapezoids 6.G.A.1 Area of composite figures Area of a circle 6.G.A.1 7.G.B.6 7.G.B.4 Informal derivation of area of circle from circumference Represent threedimensional figures using nets 6.G.A.4 7.G.B.4 20 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Use nets to find surface area Surface area of rectangular prisms Surface area of triangular prisms 6.G.A.4 6.G.A.4 6.G.A.4 7.G.B.6 7.G.B.6 Surface area of pyramids 6.G.A.4 7.G.B.6 Surface area of composite figures Surface area of cylinders 7.G.B.6 7.G.B.4 Volume Understand concepts of volume Measure volume by counting cubes Relate volume to addition and multiplication Apply the formula for volume Build composite figures and find the volume Volume of right rectangular prism Volume of triangular prisms Volume of pyramids Volume of composite figures 5.MD.C.3 5.MD.C.4 5.MD.C.5b, 5.MD.C.5c 5.MD.C.5b 5.MD.C.5c 5.MD.C.5a 6.G.A.2 7.G.B.6 7.G.B.6 7.G.B.6 7.G.B.6 Volume of a cone 8.G.C.9 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 21

LF.1009718 Volume of a cylinder Volume of a sphere Changes in dimensions 8.G.C.9 8.G.C.9 8.G.C.9 Scale Drawings and constructions Compute lengths and areas of figures from scale drawings Reproduce scale drawings with a different scale Draw geometric shapes Construct triangles from 3 measures of angles or sides Plane sections of threedimensional figures 7.G.A.1 7.G.A.1 7.G.A.2 7.G.A.2 7.G.A.3 Transformations, Congruency, and Similarity Properties of rotations Properties of reflections Properties of translations Line segments, angles, and parallel lines in transformations Congruent figures based on transformations Effect of transformations using coordinates Similar figures based on transformations 8.G.A.1 8.G.A.1 8.G.A.1 8.G.A.1a, 8.G.A.1b, 8.G.A.1c 8.G.A.2 8.G.A.3 8.G.A.4 22 Common Core State Standards SCOPE & SEQUENCE MATH Grades 3-8

Pythagorean Theorem Proof of the Pythagorean Theorem Converse of the Pythagorean Theorem Apply the Pythagorean Theorem to solve realworld and mathematical problems Distance between two points in the coordinate plane 8.G.B.6 8.G.B.6 8.G.B.7 8.G.B.8 MATH Grades 3-8 SCOPE & SEQUENCE Common Core State Standards 23