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Concept map Every Grades 1–7 standard, arranged by what it builds on. Foundational skills sit on the
left; each arrow points from a prerequisite to the skill that depends on it. Hover a node to
trace its connections, or click a node to see its skills and resources.
Operations & Algebraic Thinking
Number & Operations in Base Ten
Number & Operations — Fractions
Ratios & Proportional Relationships
The Number System
Expressions & Equations
Measurement & Data
Geometry
Statistics & Probability
1.OA.A.1 — Addition & subtraction word problems within 20 1.OA.A.1 Addition & subtraction word problems within 20 1.OA.A.2 — Add three whole numbers 1.OA.A.2 Add three whole numbers 1.OA.B.3 — Properties of addition & subtraction 1.OA.B.3 Properties of addition & subtraction 1.OA.B.4 — Subtraction as an unknown addend 1.OA.B.4 Subtraction as an unknown addend 1.OA.C.5 — Count on to add & subtract 1.OA.C.5 Count on to add & subtract 1.OA.C.6 — Add & subtract within 20 1.OA.C.6 Add & subtract within 20 1.OA.D.7 — Meaning of the equal sign 1.OA.D.7 Meaning of the equal sign 1.OA.D.8 — Find the unknown in an equation 1.OA.D.8 Find the unknown in an equation 1.NBT.A.1 — Count to 120 1.NBT.A.1 Count to 120 1.NBT.B.2 — Tens and ones in two-digit numbers 1.NBT.B.2 Tens and ones in two-digit numbers 1.NBT.B.3 — Compare two-digit numbers 1.NBT.B.3 Compare two-digit numbers 1.NBT.C.4 — Add within 100 1.NBT.C.4 Add within 100 1.NBT.C.5 — Find 10 more or 10 less 1.NBT.C.5 Find 10 more or 10 less 1.NBT.C.6 — Subtract multiples of 10 1.NBT.C.6 Subtract multiples of 10 1.MD.A.1 — Order and compare lengths 1.MD.A.1 Order and compare lengths 1.MD.A.2 — Measure length with units 1.MD.A.2 Measure length with units 1.MD.B.3 — Tell time to the half-hour 1.MD.B.3 Tell time to the half-hour 1.MD.C.4 — Organize and interpret data 1.MD.C.4 Organize and interpret data 1.G.A.1 — Defining attributes of shapes 1.G.A.1 Defining attributes of shapes 1.G.A.2 — Compose 2D and 3D shapes 1.G.A.2 Compose 2D and 3D shapes 1.G.A.3 — Partition shapes into halves & fourths 1.G.A.3 Partition shapes into halves & fourths 2.OA.A.1 — One- and two-step word problems within 100 2.OA.A.1 One- and two-step word problems within 100 2.OA.B.2 — Add & subtract within 20 fluently 2.OA.B.2 Add & subtract within 20 fluently 2.OA.C.3 — Odd and even numbers 2.OA.C.3 Odd and even numbers 2.OA.C.4 — Rectangular arrays as equal addends 2.OA.C.4 Rectangular arrays as equal addends 2.NBT.A.1 — Understand three-digit place value 2.NBT.A.1 Understand three-digit place value 2.NBT.A.2 — Count and skip-count within 1000 2.NBT.A.2 Count and skip-count within 1000 2.NBT.A.3 — Read and write numbers to 1000 2.NBT.A.3 Read and write numbers to 1000 2.NBT.A.4 — Compare three-digit numbers 2.NBT.A.4 Compare three-digit numbers 2.NBT.B.5 — Add & subtract within 100 fluently 2.NBT.B.5 Add & subtract within 100 fluently 2.NBT.B.6 — Add up to four two-digit numbers 2.NBT.B.6 Add up to four two-digit numbers 2.NBT.B.7 — Add and subtract within 1000 2.NBT.B.7 Add and subtract within 1000 2.NBT.B.8 — Mentally add or subtract 10 or 100 2.NBT.B.8 Mentally add or subtract 10 or 100 2.NBT.B.9 — Explain why strategies work 2.NBT.B.9 Explain why strategies work 2.MD.A.1 — Measure length with appropriate tools 2.MD.A.1 Measure length with appropriate tools 2.MD.A.2 — Measure with different length units 2.MD.A.2 Measure with different length units 2.MD.A.3 — Estimate lengths in standard units 2.MD.A.3 Estimate lengths in standard units 2.MD.A.4 — Compare lengths of two objects 2.MD.A.4 Compare lengths of two objects 2.MD.B.5 — Word problems involving lengths 2.MD.B.5 Word problems involving lengths 2.MD.B.6 — Represent numbers on a number line 2.MD.B.6 Represent numbers on a number line 2.MD.C.7 — Tell time to the nearest five minutes 2.MD.C.7 Tell time to the nearest five minutes 2.MD.C.8 — Word problems involving money 2.MD.C.8 Word problems involving money 2.MD.D.9 — Line plots from measurement data 2.MD.D.9 Line plots from measurement data 2.MD.D.10 — Picture graphs and bar graphs 2.MD.D.10 Picture graphs and bar graphs 2.G.A.1 — Recognize and draw shapes by attributes 2.G.A.1 Recognize and draw shapes by attributes 2.G.A.2 — Partition rectangles into rows and columns 2.G.A.2 Partition rectangles into rows and columns 2.G.A.3 — Partition shapes into equal shares 2.G.A.3 Partition shapes into equal shares 3.OA.A.1 — Interpret products of whole numbers 3.OA.A.1 Interpret products of whole numbers 3.OA.A.2 — Interpret whole-number quotients 3.OA.A.2 Interpret whole-number quotients 3.OA.A.3 — Multiplication & division word problems within 100 3.OA.A.3 Multiplication & division word problems within 100 3.OA.A.4 — Find the unknown in an equation 3.OA.A.4 Find the unknown in an equation 3.OA.B.5 — Apply properties of operations 3.OA.B.5 Apply properties of operations 3.OA.B.6 — Division as an unknown-factor problem 3.OA.B.6 Division as an unknown-factor problem 3.OA.C.7 — Fluently multiply & divide within 100 3.OA.C.7 Fluently multiply & divide within 100 3.OA.D.8 — Two-step word problems 3.OA.D.8 Two-step word problems 3.OA.D.9 — Identify arithmetic patterns 3.OA.D.9 Identify arithmetic patterns 3.NBT.A.1 — Round to the nearest 10 or 100 3.NBT.A.1 Round to the nearest 10 or 100 3.NBT.A.2 — Fluently add & subtract within 1000 3.NBT.A.2 Fluently add & subtract within 1000 3.NBT.A.3 — Multiply by multiples of 10 3.NBT.A.3 Multiply by multiples of 10 3.NF.A.1 — Understand a fraction 1/b and a/b 3.NF.A.1 Understand a fraction 1/b and a/b 3.NF.A.2 — Fractions on a number line 3.NF.A.2 Fractions on a number line 3.NF.A.3 — Equivalent fractions & comparing 3.NF.A.3 Equivalent fractions & comparing 3.MD.A.1 — Tell time & measure time intervals 3.MD.A.1 Tell time & measure time intervals 3.MD.A.2 — Measure liquid volume & mass 3.MD.A.2 Measure liquid volume & mass 3.MD.B.3 — Picture graphs & bar graphs 3.MD.B.3 Picture graphs & bar graphs 3.MD.B.4 — Line plots with halves & fourths 3.MD.B.4 Line plots with halves & fourths 3.MD.C.5 — Understand area & unit squares 3.MD.C.5 Understand area & unit squares 3.MD.C.6 — Measure area by counting unit squares 3.MD.C.6 Measure area by counting unit squares 3.MD.C.7 — Relate area to multiplication & addition 3.MD.C.7 Relate area to multiplication & addition 3.MD.D.8 — Perimeter of polygons 3.MD.D.8 Perimeter of polygons 3.G.A.1 — Categories of shapes & attributes 3.G.A.1 Categories of shapes & attributes 3.G.A.2 — Partition shapes into equal areas 3.G.A.2 Partition shapes into equal areas 4.OA.A.1 — Multiplication as comparison 4.OA.A.1 Multiplication as comparison 4.OA.A.2 — Multiplicative comparison word problems 4.OA.A.2 Multiplicative comparison word problems 4.OA.A.3 — Multistep word problems & remainders 4.OA.A.3 Multistep word problems & remainders 4.OA.B.4 — Factors, multiples, prime & composite 4.OA.B.4 Factors, multiples, prime & composite 4.OA.C.5 — Generate & analyze patterns 4.OA.C.5 Generate & analyze patterns 4.NBT.A.1 — Place value: ten times as much 4.NBT.A.1 Place value: ten times as much 4.NBT.A.2 — Read, write & compare multi-digit numbers 4.NBT.A.2 Read, write & compare multi-digit numbers 4.NBT.A.3 — Round multi-digit whole numbers 4.NBT.A.3 Round multi-digit whole numbers 4.NBT.B.4 — Add & subtract with the standard algorithm 4.NBT.B.4 Add & subtract with the standard algorithm 4.NBT.B.5 — Multiply multi-digit numbers 4.NBT.B.5 Multiply multi-digit numbers 4.NBT.B.6 — Divide with up to four-digit dividends 4.NBT.B.6 Divide with up to four-digit dividends 4.NF.A.1 — Equivalent fractions 4.NF.A.1 Equivalent fractions 4.NF.A.2 — Compare fractions 4.NF.A.2 Compare fractions 4.NF.B.3 — Add & subtract fractions 4.NF.B.3 Add & subtract fractions 4.NF.B.4 — Multiply a fraction by a whole number 4.NF.B.4 Multiply a fraction by a whole number 4.NF.C.5 — Tenths & hundredths 4.NF.C.5 Tenths & hundredths 4.NF.C.6 — Decimal notation for fractions 4.NF.C.6 Decimal notation for fractions 4.NF.C.7 — Compare decimals to hundredths 4.NF.C.7 Compare decimals to hundredths 4.MD.A.1 — Relative sizes of units & conversions 4.MD.A.1 Relative sizes of units & conversions 4.MD.A.2 — Measurement word problems 4.MD.A.2 Measurement word problems 4.MD.A.3 — Area & perimeter formulas 4.MD.A.3 Area & perimeter formulas 4.MD.B.4 — Line plots with fractions 4.MD.B.4 Line plots with fractions 4.MD.C.5 — Angles & angle measurement concepts 4.MD.C.5 Angles & angle measurement concepts 4.MD.C.6 — Measure & sketch angles 4.MD.C.6 Measure & sketch angles 4.MD.C.7 — Angle measure is additive 4.MD.C.7 Angle measure is additive 4.G.A.1 — Points, lines, rays & angles 4.G.A.1 Points, lines, rays & angles 4.G.A.2 — Classify two-dimensional figures 4.G.A.2 Classify two-dimensional figures 4.G.A.3 — Lines of symmetry 4.G.A.3 Lines of symmetry 5.OA.A.1 — Grouping symbols in expressions 5.OA.A.1 Grouping symbols in expressions 5.OA.A.2 — Write and interpret numerical expressions 5.OA.A.2 Write and interpret numerical expressions 5.OA.B.3 — Number patterns and ordered pairs 5.OA.B.3 Number patterns and ordered pairs 5.NBT.A.1 — Place value: 10 times and one-tenth 5.NBT.A.1 Place value: 10 times and one-tenth 5.NBT.A.2 — Powers of 10 and decimals 5.NBT.A.2 Powers of 10 and decimals 5.NBT.A.3 — Read and compare decimals to thousandths 5.NBT.A.3 Read and compare decimals to thousandths 5.NBT.A.4 — Round decimals to any place 5.NBT.A.4 Round decimals to any place 5.NBT.B.5 — Multiply multi-digit whole numbers 5.NBT.B.5 Multiply multi-digit whole numbers 5.NBT.B.6 — Divide by two-digit divisors 5.NBT.B.6 Divide by two-digit divisors 5.NBT.B.7 — Add, subtract, multiply, divide decimals 5.NBT.B.7 Add, subtract, multiply, divide decimals 5.NF.A.1 — Add and subtract unlike fractions 5.NF.A.1 Add and subtract unlike fractions 5.NF.A.2 — Fraction word problems and estimation 5.NF.A.2 Fraction word problems and estimation 5.NF.B.3 — Fractions as division 5.NF.B.3 Fractions as division 5.NF.B.4 — Multiply fractions 5.NF.B.4 Multiply fractions 5.NF.B.5 — Multiplication as scaling 5.NF.B.5 Multiplication as scaling 5.NF.B.6 — Multiply fractions and mixed numbers 5.NF.B.6 Multiply fractions and mixed numbers 5.NF.B.7 — Divide with unit fractions 5.NF.B.7 Divide with unit fractions 5.MD.A.1 — Convert measurement units 5.MD.A.1 Convert measurement units 5.MD.B.2 — Line plots with fractions 5.MD.B.2 Line plots with fractions 5.MD.C.3 — Understand volume 5.MD.C.3 Understand volume 5.MD.C.4 — Measure volume with unit cubes 5.MD.C.4 Measure volume with unit cubes 5.MD.C.5 — Relate volume to multiplication 5.MD.C.5 Relate volume to multiplication 5.G.A.1 — Understand the coordinate plane 5.G.A.1 Understand the coordinate plane 5.G.A.2 — Graph points in the first quadrant 5.G.A.2 Graph points in the first quadrant 5.G.B.3 — Attributes of 2-D figure categories 5.G.B.3 Attributes of 2-D figure categories 5.G.B.4 — Classify 2-D figures in a hierarchy 5.G.B.4 Classify 2-D figures in a hierarchy 6.RP.A.1 — Understand ratio concepts and language 6.RP.A.1 Understand ratio concepts and language 6.RP.A.2 — Understand unit rates 6.RP.A.2 Understand unit rates 6.RP.A.3 — Solve ratio and rate problems 6.RP.A.3 Solve ratio and rate problems 6.NS.A.1 — Divide fractions by fractions 6.NS.A.1 Divide fractions by fractions 6.NS.B.2 — Divide multi-digit numbers 6.NS.B.2 Divide multi-digit numbers 6.NS.B.3 — Add, subtract, multiply, and divide decimals 6.NS.B.3 Add, subtract, multiply, and divide decimals 6.NS.B.4 — Greatest common factor and least common multiple 6.NS.B.4 Greatest common factor and least common multiple 6.NS.C.5 — Positive and negative numbers in context 6.NS.C.5 Positive and negative numbers in context 6.NS.C.6 — Rational numbers on the number line 6.NS.C.6 Rational numbers on the number line 6.NS.C.7 — Order and absolute value of rational numbers 6.NS.C.7 Order and absolute value of rational numbers 6.NS.C.8 — Graph points in four quadrants 6.NS.C.8 Graph points in four quadrants 6.EE.A.1 — Evaluate expressions with exponents 6.EE.A.1 Evaluate expressions with exponents 6.EE.A.2 — Write and evaluate expressions with variables 6.EE.A.2 Write and evaluate expressions with variables 6.EE.A.3 — Generate equivalent expressions 6.EE.A.3 Generate equivalent expressions 6.EE.A.4 — Identify equivalent expressions 6.EE.A.4 Identify equivalent expressions 6.EE.B.5 — Solve equations and inequalities by substitution 6.EE.B.5 Solve equations and inequalities by substitution 6.EE.B.6 — Use variables to write expressions 6.EE.B.6 Use variables to write expressions 6.EE.B.7 — Solve one-step equations 6.EE.B.7 Solve one-step equations 6.EE.B.8 — Write and graph inequalities 6.EE.B.8 Write and graph inequalities 6.EE.C.9 — Relate dependent and independent variables 6.EE.C.9 Relate dependent and independent variables 6.G.A.1 — Area of triangles and polygons 6.G.A.1 Area of triangles and polygons 6.G.A.2 — Volume with fractional edge lengths 6.G.A.2 Volume with fractional edge lengths 6.G.A.3 — Draw polygons in the coordinate plane 6.G.A.3 Draw polygons in the coordinate plane 6.G.A.4 — Surface area using nets 6.G.A.4 Surface area using nets 6.SP.A.1 — Recognize statistical questions 6.SP.A.1 Recognize statistical questions 6.SP.A.2 — Describe data distributions 6.SP.A.2 Describe data distributions 6.SP.A.3 — Measures of center and variability 6.SP.A.3 Measures of center and variability 6.SP.B.4 — Display data with plots 6.SP.B.4 Display data with plots 6.SP.B.5 — Summarize numerical data sets 6.SP.B.5 Summarize numerical data sets 7.RP.A.1 — Unit rates with fractions 7.RP.A.1 Unit rates with fractions 7.RP.A.2 — Recognize proportional relationships 7.RP.A.2 Recognize proportional relationships 7.RP.A.3 — Ratio and percent problems 7.RP.A.3 Ratio and percent problems 7.NS.A.1 — Add and subtract rational numbers 7.NS.A.1 Add and subtract rational numbers 7.NS.A.2 — Multiply and divide rational numbers 7.NS.A.2 Multiply and divide rational numbers 7.NS.A.3 — Operations with rational numbers 7.NS.A.3 Operations with rational numbers 7.EE.A.1 — Factor and expand linear expressions 7.EE.A.1 Factor and expand linear expressions 7.EE.A.2 — Rewrite expressions to see relationships 7.EE.A.2 Rewrite expressions to see relationships 7.EE.B.3 — Multi-step problems with rational numbers 7.EE.B.3 Multi-step problems with rational numbers 7.EE.B.4 — Write equations and inequalities 7.EE.B.4 Write equations and inequalities 7.G.A.1 — Scale drawings of figures 7.G.A.1 Scale drawings of figures 7.G.A.2 — Draw triangles from given conditions 7.G.A.2 Draw triangles from given conditions 7.G.A.3 — Cross sections of 3D figures 7.G.A.3 Cross sections of 3D figures 7.G.B.4 — Area and circumference of circles 7.G.B.4 Area and circumference of circles 7.G.B.5 — Angle relationships and equations 7.G.B.5 Angle relationships and equations 7.G.B.6 — Area, volume, and surface area 7.G.B.6 Area, volume, and surface area 7.SP.A.1 — Sampling and valid inferences 7.SP.A.1 Sampling and valid inferences 7.SP.A.2 — Draw inferences from samples 7.SP.A.2 Draw inferences from samples 7.SP.B.3 — Compare two data distributions 7.SP.B.3 Compare two data distributions 7.SP.B.4 — Compare populations using center and spread 7.SP.B.4 Compare populations using center and spread 7.SP.C.5 — Probability as a number 0 to 1 7.SP.C.5 Probability as a number 0 to 1 7.SP.C.6 — Estimate probability from frequency 7.SP.C.6 Estimate probability from frequency 7.SP.C.7 — Develop probability models 7.SP.C.7 Develop probability models 7.SP.C.8 — Probabilities of compound events 7.SP.C.8 Probabilities of compound events Columns are prerequisite depth, not grade — so a Grade 4 skill that depends on a Grade 3 one
sits to its right, showing exactly how the two years connect.
Prerequisite progressions and skills from the CZI Learning Commons Knowledge Graph (CC BY-4.0), based on the Student Achievement Partners Coherence Map.