The canonical, EzSteps-owned K–12 topic catalogue. Every row is a single checkable mastery target with an age range, a depth ladder, prerequisite edges, named visual models, and a crosswalk to ten instructional systems.
Showing 280 of 280 topics.
| Topic | Strand | Cluster | Grade | Ages | Depths | Signals | CCSS |
|---|---|---|---|---|---|---|---|
| Make sense of a problem and persevere | Practices | Reasoning habits | K | 5–18 | 1level | — | MP1 |
| Count, read, write, and order whole numbers | Number | Counting and cardinality | K | 4–9 | 3levels | — | K.CC.A.1K.CC.A.2K.CC.A.3+3 |
| Connect quantity, counting, and cardinality | Number | Counting and cardinality | K | 3–6 | 1level | — | K.CC.B.4K.CC.B.5 |
| Recognise small quantities at a glance | Number | Counting and cardinality | K | 3–7 | 1level | — | K.CC.B.4K.OA.A.3 |
| Compare quantities and numerical values | Number | Counting and cardinality | K | 4–10 | 3levels | — | K.CC.C.6K.CC.C.71.NBT.B.3+2 |
| Compose and decompose numbers | Number | Place value and base ten | K | 4–9 | 1level | — | K.OA.A.3K.NBT.A.11.NBT.B.2 |
| Addition and subtraction as actions and relationships | Number | Addition and subtraction | K | 4–9 | 1level | — | K.OA.A.1K.OA.A.21.OA.A.1+2 |
| Recognise and name shapes | Geometry | Shapes and attributes | K | 3–7 | 1level | — | K.G.A.1K.G.A.21.G.A.1 |
| Sort, classify, and count categories | Data & chance | Data questions and collection | K | 4–8 | 1level | — | K.MD.B.31.MD.C.4 |
| Reason abstractly and quantitatively | Practices | Reasoning habits | G1 | 6–18 | 1level | — | MP2 |
| Construct arguments and critique reasoning | Practices | Reasoning habits | G1 | 6–18 | 1level | — | MP3 |
| Place value and base-ten structure | Number | Place value and base ten | G1 | 5–12 | 3levels | — | 1.NBT.B.22.NBT.A.12.NBT.A.3+3 |
| Addition and subtraction facts within 20 | Number | Addition and subtraction | G1 | 5–9 | 1level | Fluency | 1.OA.C.51.OA.C.62.OA.B.2 |
| Skip counting and multiples | Number | Multiplication and division | G1 | 5–9 | 1level | — | 2.NBT.A.23.OA.A.14.OA.B.4 |
| Even and odd numbers | Number | Factors, primes, and number structure | G1 | 6–9 | 1level | — | 2.OA.C.3 |
| Equivalence as a relation, not an answer cue | Number | Patterns and properties | G1 | 6–13 | 3levels | — | 1.OA.D.71.OA.D.86.EE.A.4 |
| Partition wholes into equal shares | Rational numbers | Fraction meaning | G1 | 5–9 | 1level | — | 1.G.A.32.G.A.33.NF.A.1 |
| Missing numbers in equations | Expressions | Pre-algebraic thinking | G1 | 6–11 | 1level | — | 1.OA.D.83.OA.A.4 |
| Describe and sort shapes by attributes | Geometry | Shapes and attributes | G1 | 5–10 | 1level | — | 1.G.A.12.G.A.13.G.A.1 |
| Compose and decompose shapes | Geometry | Shapes and attributes | G1 | 4–10 | 1level | — | K.G.B.61.G.A.22.G.A.1 |
| Measure length | Geometry | Measurement | G1 | 5–10 | 1level | — | 1.MD.A.11.MD.A.22.MD.A.1+1 |
| Tell time and find elapsed time | Geometry | Measurement | G1 | 5–10 | 1level | — | 1.MD.B.32.MD.C.73.MD.A.1 |
| Money: counting and making change | Geometry | Measurement | G1 | 5–10 | 1level | — | 2.MD.C.84.MD.A.2 |
| Picture graphs and bar charts | Data & chance | Data displays | G1 | 5–12 | 1level | — | 1.MD.C.42.MD.D.103.MD.B.3 |
| Model with mathematics | Practices | Reasoning habits | G2 | 7–18 | 1level | — | MP4 |
| Use tools strategically | Practices | Reasoning habits | G2 | 7–18 | 1level | — | MP5 |
| Attend to precision | Practices | Reasoning habits | G2 | 7–18 | 1level | — | MP6 |
| Look for and use structure | Practices | Reasoning habits | G2 | 7–18 | 1level | — | MP7 |
| Estimate, bound, and check reasonableness | Practices | Reasoning habits | G2 | 7–18 | 1level | — | MP1MP6 |
| Mental strategies for addition and subtraction | Number | Addition and subtraction | G2 | 6–11 | 1level | — | 1.NBT.C.42.NBT.B.52.NBT.B.8+1 |
| Multi-digit addition and subtraction | Number | Addition and subtraction | G2 | 7–11 | 3levels | Fluency | 2.NBT.B.52.NBT.B.62.NBT.B.7+2 |
| Equal groups, arrays, and the meaning of multiplication | Number | Multiplication and division | G2 | 7–11 | 1level | — | 2.OA.C.43.OA.A.13.OA.A.3+1 |
| Sharing, grouping, and the meaning of division | Number | Multiplication and division | G2 | 7–11 | 1level | — | 3.OA.A.23.OA.A.33.OA.B.6 |
| Properties of operations | Number | Patterns and properties | G2 | 7–14 | 3levels | — | 1.OA.B.33.OA.B.56.EE.A.3+1 |
| Mass, capacity, and temperature | Geometry | Measurement | G2 | 6–12 | 1level | — | 2.MD.A.33.MD.A.24.MD.A.1 |
| Dot plots and line plots | Data & chance | Data displays | G2 | 7–18 | 1level | — | 2.MD.D.94.MD.B.46.SP.B.4 |
| Money sense and spending decisions | Modeling | Money and finance | G2 | 6–12 | 1level | — | 2.MD.C.84.MD.A.2 |
| Look for repeated reasoning and generalise | Practices | Reasoning habits | G3 | 8–18 | 1level | — | MP8 |
| Translate among representations | Practices | Reasoning habits | G3 | 8–18 | 1level | — | MP2MP4MP5 |
| Diagnose, explain, and repair an error | Practices | Reasoning habits | G3 | 8–18 | 1level | — | MP3MP6 |
| Rounding and estimation | Number | Place value and base ten | G3 | 8–14 | 3levels | — | 3.NBT.A.14.NBT.A.35.NBT.A.4 |
| Multiplication and division fact fluency | Number | Multiplication and division | G3 | 8–12 | 1level | Fluency | 3.OA.C.73.OA.B.5 |
| Inverse operations and checking | Number | Patterns and properties | G3 | 7–14 | 1level | — | 3.OA.B.66.EE.B.7 |
| Unit fractions and fractions as numbers | Rational numbers | Fraction meaning | G3 | 7–11 | 1level | — | 3.NF.A.13.NF.A.2 |
| Equivalent fractions | Rational numbers | Fraction meaning | G3 | 8–12 | 3levels | — | 3.NF.A.34.NF.A.1 |
| Compare and order fractions | Rational numbers | Fraction meaning | G3 | 8–12 | 1level | — | 3.NF.A.3d4.NF.A.2 |
| Classify quadrilaterals and the shape hierarchy | Geometry | Shapes and attributes | G3 | 8–15 | 1level | — | 3.G.A.15.G.B.35.G.B.4+1 |
| Perimeter | Geometry | Perimeter, area, and volume | G3 | 7–13 | 1level | — | 3.MD.D.84.MD.A.3 |
| Area of rectangles | Geometry | Perimeter, area, and volume | G3 | 7–13 | 1level | — | 3.MD.C.53.MD.C.63.MD.C.7+1 |
| Language of chance | Data & chance | Probability | G3 | 7–12 | 1level | — | 7.SP.C.5 |
| Multi-digit multiplication | Number | Multiplication and division | G4 | 9–13 | 3levels | — | 4.NBT.B.55.NBT.B.5 |
| Multi-digit division and interpreting the quotient | Number | Multiplication and division | G4 | 9–13 | 3levels | — | 4.NBT.B.65.NBT.B.64.OA.A.3 |
| Factors, multiples, and divisibility | Number | Factors, primes, and number structure | G4 | 9–13 | 3levels | — | 4.OA.B.46.NS.B.4 |
| Prime and composite numbers | Number | Factors, primes, and number structure | G4 | 9–13 | 1level | — | 4.OA.B.4 |
| Generate, describe, and extend numerical patterns | Number | Patterns and properties | G4 | 8–13 | 1level | — | 4.OA.C.55.OA.B.3 |
| Structural mental arithmetic | Number | Patterns and properties | G4 | 9–15 | 1level | — | 6.EE.A.37.EE.A.1 |
| Mixed numbers and improper fractions | Rational numbers | Fraction meaning | G4 | 9–12 | 1level | — | 4.NF.B.3b4.NF.B.3c5.NF.A.1 |
| Add and subtract fractions and mixed numbers | Rational numbers | Fraction operations | G4 | 9–13 | 3levels | — | 4.NF.B.35.NF.A.15.NF.A.2 |
| Multiply a fraction by a whole number | Rational numbers | Fraction operations | G4 | 9–12 | 1level | — | 4.NF.B.4 |
| Decimal place value and equivalence | Rational numbers | Decimals | G4 | 9–13 | 1level | — | 4.NF.C.54.NF.C.64.NF.C.7+3 |
| Multiplicative comparison | Ratio & proportion | Ratio and rate | G4 | 8–12 | 1level | — | 4.OA.A.14.OA.A.2 |
| Describing a pattern with a rule | Expressions | Pre-algebraic thinking | G4 | 8–13 | 1level | — | 4.OA.C.55.OA.B.36.EE.A.2 |
| Classify triangles | Geometry | Shapes and attributes | G4 | 9–15 | 1level | — | 4.G.A.25.G.B.3HSG-CO.B.3 |
| Unit systems and conversion | Geometry | Measurement | G4 | 9–15 | 1level | — | 4.MD.A.15.MD.A.16.RP.A.3d |
| Measure and classify angles | Geometry | Measurement | G4 | 9–15 | 1level | — | 4.MD.C.54.MD.C.64.MD.C.7 |
| Points, lines, planes, segments, and rays | Geometry | Lines and angles | G4 | 9–16 | 1level | — | 4.G.A.1HSG-CO.A.1 |
| Line and rotational symmetry | Geometry | Transformations and congruence | G4 | 8–15 | 1level | — | 4.G.A.3HSG-CO.A.3 |
| Prime factorisation | Number | Factors, primes, and number structure | G5 | 10–14 | 1level | — | 6.NS.B.46.EE.A.1 |
| Order of operations | Number | Patterns and properties | G5 | 10–14 | 1level | — | 5.OA.A.15.OA.A.26.EE.A.1+1 |
| Multiply fractions and interpret scaling | Rational numbers | Fraction operations | G5 | 10–13 | 1level | — | 5.NF.B.45.NF.B.55.NF.B.6 |
| Divide fractions and interpret the quotient | Rational numbers | Fraction operations | G5 | 10–14 | 3levels | — | 5.NF.B.76.NS.A.1 |
| Add, subtract, multiply, and divide decimals | Rational numbers | Decimals | G5 | 10–14 | 3levels | Fluency | 5.NBT.B.76.NS.B.3 |
| The coordinate plane | Linear | Lines and slope | G5 | 9–14 | 1level | — | 5.G.A.15.G.A.26.NS.C.8 |
| Volume of prisms and cylinders | Geometry | Perimeter, area, and volume | G5 | 10–16 | 1level | — | 5.MD.C.35.MD.C.56.G.A.2+2 |
| Choose, convert, and interpret units | Modeling | Units and precision | G5 | 9–18 | 1level | — | 5.MD.A.16.RP.A.3dHSN-Q.A.1 |
| Greatest common factor and least common multiple | Number | Factors, primes, and number structure | G6 | 10–14 | 3levels | — | 6.NS.B.4 |
| Convert between fractions and decimals | Rational numbers | Decimals | G6 | 10–15 | 1level | — | 7.NS.A.2d8.NS.A.1 |
| Percent as a rate per hundred | Rational numbers | Percent | G6 | 10–14 | 1level | — | 6.RP.A.3c |
| Convert among fractions, decimals, and percents | Rational numbers | Percent | G6 | 10–15 | 1level | Fluency | 6.RP.A.3c7.NS.A.2d |
| Positive and negative numbers | Rational numbers | Integers and rational numbers | G6 | 10–14 | 1level | — | 6.NS.C.56.NS.C.66.NS.C.7 |
| Absolute value as magnitude and distance | Rational numbers | Integers and rational numbers | G6 | 11–16 | 1level | — | 6.NS.C.7c7.NS.A.1HSA-REI.B.3 |
| Ordering and density of rational numbers | Rational numbers | Integers and rational numbers | G6 | 11–16 | 1level | — | 6.NS.C.66.NS.C.78.NS.A.1 |
| Ratio language and notation | Ratio & proportion | Ratio and rate | G6 | 10–14 | 1level | — | 6.RP.A.1 |
| Equivalent ratios and scaling | Ratio & proportion | Ratio and rate | G6 | 10–14 | 1level | — | 6.RP.A.3a |
| Unit rates and rate reasoning | Ratio & proportion | Ratio and rate | G6 | 10–15 | 3levels | — | 6.RP.A.26.RP.A.3b7.RP.A.1 |
| Unit conversion and dimensional reasoning | Ratio & proportion | Percent and scaling applications | G6 | 11–18 | 1level | — | 6.RP.A.3dHSN-Q.A.1 |
| Variables, constants, coefficients, and terms | Expressions | Expressions and equivalence | G6 | 10–15 | 1level | — | 6.EE.A.2b |
| Translate words and contexts into expressions | Expressions | Expressions and equivalence | G6 | 10–16 | 1level | — | 6.EE.A.2a7.EE.A.2HSA-SSE.A.1 |
| Evaluate expressions for given values | Expressions | Expressions and equivalence | G6 | 10–16 | 1level | Fluency | 6.EE.A.2cHSA-SSE.A.1 |
| Algebraic properties and justification | Expressions | Expressions and equivalence | G6 | 11–17 | 1level | — | 6.EE.A.37.EE.A.1HSA-SSE.A.2 |
| Combine like terms | Expressions | Expressions and equivalence | G6 | 11–16 | 1level | Fluency | 6.EE.A.37.EE.A.1 |
| Distributive property and factoring out | Expressions | Expressions and equivalence | G6 | 11–17 | 1level | — | 6.EE.A.37.EE.A.1HSA-SSE.A.2 |
| Recognise and generate equivalent expressions | Expressions | Expressions and equivalence | G6 | 11–17 | 1level | — | 6.EE.A.4HSA-SSE.B.3 |
| Equality as a preserved relationship | Equations | Equality and balance | G6 | 10–16 | 1level | — | 6.EE.B.56.EE.B.6 |
| One-step addition and subtraction equations | Equations | Solving linear equations | G6 | 10–15 | 1level | Fluency | 6.EE.B.7 |
| One-step multiplication and division equations | Equations | Solving linear equations | G6 | 10–15 | 1level | Fluency | 6.EE.B.7 |
| Verify solutions and reasonableness | Equations | Solving linear equations | G6 | 10–18 | 1level | — | 6.EE.B.5HSA-REI.A.1 |
| Inequalities and solution sets | Equations | Inequalities | G6 | 10–16 | 1level | — | 6.EE.B.8 |
| Area of triangles, parallelograms, and trapezoids | Geometry | Perimeter, area, and volume | G6 | 10–16 | 1level | — | 6.G.A.17.G.B.6 |
| Area of composite figures | Geometry | Perimeter, area, and volume | G6 | 10–16 | 1level | — | 6.G.A.17.G.B.6 |
| Surface area and nets | Geometry | Perimeter, area, and volume | G6 | 11–17 | 1level | — | 6.G.A.47.G.B.6HSG-GMD.A.3 |
| Statistical questions and variability | Data & chance | Data questions and collection | G6 | 10–16 | 1level | — | 6.SP.A.16.SP.A.2 |
| Types of data | Data & chance | Data questions and collection | G6 | 10–18 | 1level | — | 6.SP.A.1HSS-ID.A.1 |
| Histograms and binning | Data & chance | Data displays | G6 | 11–18 | 1level | — | 6.SP.B.4HSS-ID.A.1 |
| Box plots and the five-number summary | Data & chance | Data displays | G6 | 11–18 | 1level | — | 6.SP.B.4HSS-ID.A.1 |
| Mean, median, and mode | Data & chance | Centre, spread, and shape | G6 | 10–18 | 1level | — | 6.SP.B.5HSS-ID.A.2HSS-ID.A.3 |
| Range, IQR, and deviation | Data & chance | Centre, spread, and shape | G6 | 11–18 | 3levels | — | 6.SP.B.5HSS-ID.A.2 |
| Shape, skew, and outliers | Data & chance | Centre, spread, and shape | G6 | 11–18 | 1level | — | 6.SP.B.5HSS-ID.A.3 |
| Distance, rate, and time | Modeling | Classic model families | G6 | 10–18 | 3levels | — | 6.RP.A.3b7.RP.A.1HSA-CED.A.1 |
| Use data to compare and decide | Modeling | Modelling and decisions | G6 | 11–18 | 1level | — | 6.SP.B.5HSS-ID.A.2HSS-IC.B.6 |
| Describe a repeatable procedure | Modeling | Algorithms and tools | G6 | 10–18 | 1level | — | HSA-REI.A.1 |
| Add and subtract integers | Rational numbers | Integers and rational numbers | G7 | 11–15 | 1level | Fluency | 7.NS.A.1 |
| Multiply and divide rational numbers | Rational numbers | Integers and rational numbers | G7 | 11–16 | 1level | Fluency | 7.NS.A.27.NS.A.3 |
| Constant of proportionality | Ratio & proportion | Proportional relationships | G7 | 11–16 | 1level | — | 7.RP.A.2a7.RP.A.2b7.RP.A.2c+1 |
| Tables, graphs, and equations for proportional relationships | Ratio & proportion | Proportional relationships | G7 | 11–16 | 1level | — | 7.RP.A.28.EE.B.5 |
| Solving proportions | Ratio & proportion | Proportional relationships | G7 | 11–16 | 1level | — | 7.RP.A.27.RP.A.3 |
| Percent increase, decrease, markup, and discount | Ratio & proportion | Percent and scaling applications | G7 | 11–17 | 3levels | — | 7.RP.A.3 |
| Scale drawings and scale factors | Ratio & proportion | Percent and scaling applications | G7 | 11–16 | 1level | — | 7.G.A.1 |
| Two-step equations | Equations | Solving linear equations | G7 | 11–16 | 1level | Fluency | 7.EE.B.4a |
| Build equations from word problems | Equations | Solving linear equations | G7 | 11–18 | 3levels | — | 7.EE.B.4aHSA-CED.A.1HSA-CED.A.3 |
| Solve one- and multi-step inequalities | Equations | Inequalities | G7 | 11–17 | 1level | Fluency | 7.EE.B.4bHSA-REI.B.3 |
| Circumference and area of circles | Geometry | Perimeter, area, and volume | G7 | 11–17 | 1level | — | 7.G.B.4 |
| Cross-sections of solids | Geometry | Perimeter, area, and volume | G7 | 12–18 | 1level | — | 7.G.A.3HSG-GMD.B.4 |
| Angle pair relationships | Geometry | Lines and angles | G7 | 11–17 | 1level | — | 7.G.B.5HSG-CO.C.9 |
| Parts of a circle | Geometry | Circles | G7 | 11–18 | 1level | — | HSG-C.A.27.G.B.4 |
| Collecting data: surveys, observations, experiments | Data & chance | Data questions and collection | G7 | 11–18 | 1level | — | 6.SP.B.5HSS-IC.A.1HSS-IC.B.3 |
| Misleading data displays | Data & chance | Data displays | G7 | 11–18 | 1level | — | HSS-ID.A.1HSS-IC.B.6 |
| Compare two distributions | Data & chance | Centre, spread, and shape | G7 | 12–18 | 1level | — | 7.SP.B.37.SP.B.4HSS-ID.A.2 |
| Population, sample, and generalisation | Data & chance | Sampling and inference | G7 | 11–18 | 1level | — | 7.SP.A.17.SP.A.2HSS-IC.A.1 |
| Random sampling and bias | Data & chance | Sampling and inference | G7 | 12–18 | 1level | — | 7.SP.A.2HSS-IC.B.3 |
| Sampling variability and margin of error | Data & chance | Sampling and inference | G7 | 12–18 | 1level | — | 7.SP.A.2HSS-IC.B.4 |
| Simulation for probability and inference | Data & chance | Sampling and inference | G7 | 12–18 | 1level | — | 7.SP.C.8cHSS-IC.B.5 |
| Outcomes, events, and sample spaces | Data & chance | Probability | G7 | 11–18 | 1level | — | 7.SP.C.77.SP.C.8aHSS-CP.A.1 |
| Theoretical versus experimental probability | Data & chance | Probability | G7 | 11–18 | 1level | — | 7.SP.C.67.SP.C.7 |
| Compound events and counting outcomes | Data & chance | Probability | G7 | 12–18 | 1level | — | 7.SP.C.8HSS-CP.B.9 |
| Tax, tip, discount, markup, and commission | Modeling | Classic model families | G7 | 11–18 | 1level | — | 7.RP.A.3 |
| Simple interest | Modeling | Money and finance | G7 | 12–18 | 1level | — | 7.RP.A.3HSN-Q.A.1 |
| State assumptions and constraints | Modeling | Modelling and decisions | G7 | 11–18 | 1level | — | HSA-CED.A.3HSN-Q.A.2 |
| Estimation and order-of-magnitude reasoning | Modeling | Algorithms and tools | G7 | 11–18 | 1level | Enrichment | HSN-Q.A.2HSN-Q.A.3 |
| Integer exponents and exponent laws | Rational numbers | Real and complex numbers | G8 | 12–16 | 3levels | — | 8.EE.A.18.EE.A.2HSN-RN.A.1 |
| Scientific notation and magnitude | Rational numbers | Real and complex numbers | G8 | 12–17 | 1level | — | 8.EE.A.38.EE.A.4HSN-Q.A.1 |
| Irrational numbers and rational approximation | Rational numbers | Real and complex numbers | G8 | 12–17 | 1level | — | 8.NS.A.18.NS.A.2HSN-RN.B.3 |
| Square roots and cube roots | Rational numbers | Real and complex numbers | G8 | 12–17 | 1level | — | 8.EE.A.2HSN-RN.A.2 |
| Similar figures and proportional sides | Ratio & proportion | Percent and scaling applications | G8 | 12–17 | 1level | — | 8.G.A.4HSG-SRT.A.2HSG-SRT.B.5 |
| How scaling changes length, area, and volume | Ratio & proportion | Percent and scaling applications | G8 | 12–18 | 1level | — | 7.G.A.1HSG-GMD.A.3HSG-MG.A.2 |
| Multi-step linear equations | Equations | Solving linear equations | G8 | 12–17 | 3levels | — | 8.EE.C.7bHSA-REI.B.3 |
| Equations with variables on both sides | Equations | Solving linear equations | G8 | 12–17 | 1level | — | 8.EE.C.7a8.EE.C.7bHSA-REI.B.3 |
| Rearrange formulas for a chosen variable | Equations | Solving linear equations | G8 | 12–18 | 1level | — | HSA-CED.A.46.EE.C.9 |
| Relations, functions, and the one-output rule | Functions | Function concept | G8 | 12–17 | 1level | — | 8.F.A.1HSF-IF.A.1 |
| Translate among words, tables, graphs, and rules | Functions | Function concept | G8 | 12–18 | 1level | — | 8.F.A.28.F.B.4HSF-IF.C.9 |
| Rate of change and slope | Linear | Lines and slope | G8 | 12–18 | 1level | — | 8.EE.B.58.EE.B.68.F.B.4+1 |
| Intercepts and initial value | Linear | Lines and slope | G8 | 12–18 | 1level | — | 8.F.B.4HSF-IF.B.4HSA-REI.D.10 |
| Forms of a linear equation | Linear | Lines and slope | G8 | 13–18 | 3levels | Fluency | 8.EE.B.6HSA-CED.A.2HSF-BF.A.1a |
| Graph lines from equations, tables, and contexts | Linear | Lines and slope | G8 | 12–18 | 1level | — | 8.EE.B.5HSF-IF.C.7aHSA-REI.D.10 |
| Build and interpret linear models | Linear | Lines and slope | G8 | 12–18 | 1level | — | 8.F.B.4HSF-LE.A.2HSF-LE.B.5+1 |
| Solve systems by graphing | Linear | Systems | G8 | 12–18 | 1level | — | 8.EE.C.8aHSA-REI.C.6HSA-REI.D.11 |
| One, none, or infinitely many solutions | Linear | Systems | G8 | 12–18 | 1level | — | 8.EE.C.8bHSA-REI.C.6 |
| Fit a line to data | Linear | Linear fitting | G8 | 12–18 | 1level | — | 8.SP.A.28.SP.A.3HSS-ID.B.6a+1 |
| Polygons and their angle sums | Geometry | Shapes and attributes | G8 | 12–17 | 1level | — | HSG-CO.C.118.G.A.5 |
| Volume of cones, pyramids, and spheres | Geometry | Perimeter, area, and volume | G8 | 13–18 | 1level | — | 8.G.C.9HSG-GMD.A.1HSG-GMD.A.3 |
| Parallel lines and transversals | Geometry | Lines and angles | G8 | 12–18 | 1level | — | 8.G.A.5HSG-CO.C.9 |
| Triangle angle sum and exterior angles | Geometry | Lines and angles | G8 | 11–18 | 1level | — | 8.G.A.5HSG-CO.C.10 |
| Rigid motions: translations, rotations, reflections | Geometry | Transformations and congruence | G8 | 12–18 | 3levels | — | 8.G.A.18.G.A.28.G.A.3+2 |
| Congruence and congruence criteria | Geometry | Transformations and congruence | G8 | 13–18 | 1level | — | 8.G.A.2HSG-CO.B.6HSG-CO.B.7+2 |
| Dilations and similarity transformations | Geometry | Transformations and congruence | G8 | 13–18 | 1level | — | 8.G.A.38.G.A.4HSG-SRT.A.1+1 |
| Pythagorean theorem and its converse | Geometry | Right triangles and trigonometry | G8 | 12–18 | 3levels | — | 8.G.B.68.G.B.78.G.B.8+1 |
| Distance and midpoint | Geometry | Coordinate geometry | G8 | 13–18 | 1level | — | 8.G.B.8HSG-GPE.B.7 |
| Two-way frequency tables | Data & chance | Association and fit | G8 | 12–18 | 1level | — | 8.SP.A.4HSS-ID.B.5 |
| Scatter plots and association | Data & chance | Association and fit | G8 | 12–18 | 1level | — | 8.SP.A.18.SP.A.2HSS-ID.B.6 |
| Precision, accuracy, and significant figures | Modeling | Units and precision | G8 | 12–18 | 1level | — | HSN-Q.A.3 |
| Bounds, error, and reasonableness | Modeling | Units and precision | G8 | 12–18 | 1level | — | HSN-Q.A.37.EE.B.3 |
| Question claims, scales, and sources | Modeling | Modelling and decisions | G8 | 12–18 | 1level | — | HSS-IC.B.6HSS-ID.C.9 |
| Read a graph as a claim about a situation | Modeling | Algorithms and tools | G8 | 11–18 | 1level | — | 8.F.B.5HSF-IF.B.4 |
| Spreadsheets and iterative modelling | Modeling | Algorithms and tools | G8 | 12–18 | 1level | — | HSF-BF.A.1aHSF-LE.A.2 |
| Structure of the real number system | Rational numbers | Real and complex numbers | G9 | 13–18 | 1level | — | HSN-RN.B.3 |
| Rational exponents and radicals | Rational numbers | Real and complex numbers | G9 | 13–18 | 1level | — | HSN-RN.A.1HSN-RN.A.2 |
| Direct variation | Ratio & proportion | Variation | G9 | 13–18 | 1level | — | 7.RP.A.2HSF-LE.A.1b |
| Polynomial language and standard form | Expressions | Polynomial expressions | G9 | 13–18 | 1level | — | HSA-SSE.A.1HSA-APR.A.1 |
| Add and subtract polynomials | Expressions | Polynomial expressions | G9 | 13–18 | 1level | — | HSA-APR.A.1 |
| Multiply monomials and apply exponent laws | Expressions | Polynomial expressions | G9 | 13–18 | 1level | Fluency | HSA-APR.A.1HSN-RN.A.1 |
| Multiply binomials and general polynomials | Expressions | Polynomial expressions | G9 | 13–18 | 3levels | — | HSA-APR.A.1 |
| Difference of squares and perfect-square trinomials | Expressions | Polynomial expressions | G9 | 13–18 | 1level | — | HSA-SSE.A.2HSA-APR.A.1 |
| Factor out a greatest common factor | Expressions | Polynomial expressions | G9 | 12–18 | 1level | — | HSA-SSE.A.2HSA-SSE.B.3a |
| Factor quadratic expressions | Expressions | Polynomial expressions | G9 | 13–18 | 3levels | Fluency | HSA-SSE.A.2HSA-SSE.B.3a |
| Rational expressions and domain restrictions | Expressions | Rational and radical expressions | G9 | 13–18 | 1level | — | HSA-APR.D.6HSA-APR.D.7 |
| Operate on rational expressions | Expressions | Rational and radical expressions | G9 | 13–18 | 1level | — | HSA-APR.D.7 |
| Simplify and operate on radical expressions | Expressions | Rational and radical expressions | G9 | 13–18 | 1level | — | HSN-RN.A.2 |
| Compound inequalities and interval notation | Equations | Inequalities | G9 | 13–18 | 1level | — | HSA-REI.B.3HSA-CED.A.1 |
| Absolute-value equations and inequalities | Equations | Inequalities | G9 | 13–18 | 1level | — | HSA-REI.B.3HSA-CED.A.1 |
| Domain, range, and restrictions | Functions | Function concept | G9 | 13–18 | 1level | — | HSF-IF.A.1HSF-IF.B.5 |
| Function notation and evaluation | Functions | Function concept | G9 | 13–18 | 1level | — | HSF-IF.A.2 |
| Key features of a graph | Functions | Function behaviour | G9 | 13–18 | 1level | — | HSF-IF.B.4HSF-IF.C.7 |
| Average rate of change | Functions | Function behaviour | G9 | 13–18 | 1level | — | HSF-IF.B.6 |
| Choose a function family for a situation | Functions | Function behaviour | G9 | 13–18 | 1level | — | HSF-LE.A.1HSF-LE.A.3HSF-IF.C.9 |
| Sequences as functions | Functions | Sequences | G9 | 13–18 | 1level | — | HSF-IF.A.3 |
| Parallel and perpendicular lines | Linear | Lines and slope | G9 | 13–18 | 1level | — | HSG-GPE.B.5HSA-CED.A.2 |
| Solve systems by substitution | Linear | Systems | G9 | 13–18 | 1level | — | HSA-REI.C.6 |
| Solve systems by elimination | Linear | Systems | G9 | 13–18 | 1level | Fluency | HSA-REI.C.5HSA-REI.C.6 |
| Model situations with systems | Linear | Systems | G9 | 13–18 | 1level | — | HSA-CED.A.3HSA-REI.C.6 |
| Linear inequalities in two variables | Linear | Linear inequalities in two variables | G9 | 13–18 | 1level | — | HSA-REI.D.12 |
| Connect products, factors, and zeros | Quadratics | Solving quadratics | G9 | 13–18 | 1level | — | HSA-SSE.A.2HSA-APR.B.3HSF-IF.C.8a |
| The zero-product property | Quadratics | Solving quadratics | G9 | 13–18 | 1level | — | HSA-REI.B.4bHSA-APR.B.3 |
| Solve quadratics by factoring | Quadratics | Solving quadratics | G9 | 13–18 | 1level | Fluency | HSA-REI.B.4b |
| Solve quadratics by square roots | Quadratics | Solving quadratics | G9 | 13–18 | 1level | — | HSA-REI.B.4b |
| The quadratic formula | Quadratics | Solving quadratics | G9 | 13–18 | 1level | Fluency | HSA-REI.B.4b |
| Solve quadratics graphically | Quadratics | Solving quadratics | G9 | 13–18 | 1level | — | HSA-REI.D.11HSF-IF.C.7a |
| Features of the parabola | Quadratics | Parabola structure | G9 | 13–18 | 1level | — | HSF-IF.C.7aHSF-IF.B.4 |
| Exponent laws in algebraic expressions | Exp & log | Exponential change | G9 | 13–18 | 1level | Fluency | HSN-RN.A.1HSN-RN.A.28.EE.A.1 |
| Exponential growth and decay | Exp & log | Exponential change | G9 | 13–18 | 3levels | — | 8.F.A.3HSF-LE.A.1cHSF-LE.A.2+1 |
| Linear versus exponential change | Exp & log | Exponential change | G9 | 13–18 | 1level | — | HSF-LE.A.1HSF-LE.A.3 |
| Similar triangles and proportional reasoning | Geometry | Transformations and congruence | G9 | 13–18 | 1level | — | HSG-SRT.A.3HSG-SRT.B.4HSG-SRT.B.5 |
| Work and combined-rate problems | Modeling | Classic model families | G9 | 13–18 | 1level | — | HSA-CED.A.1HSA-REI.A.2 |
| Mixture, concentration, and weighted average | Modeling | Classic model families | G9 | 13–18 | 1level | — | HSA-CED.A.1HSA-REI.A.3 |
| Budgets, constraints, and trade-offs | Modeling | Money and finance | G9 | 11–18 | 1level | — | HSA-CED.A.1HSA-CED.A.3HSN-Q.A.1 |
| Cost, revenue, profit, and break-even | Modeling | Money and finance | G9 | 13–18 | 1level | — | HSA-CED.A.2HSA-REI.C.6HSF-IF.B.4 |
| Inverse and joint variation | Ratio & proportion | Variation | G10 | 14–18 | 1level | — | HSF-IF.C.7dHSA-CED.A.1 |
| Divide polynomials | Expressions | Polynomial expressions | G10 | 14–18 | 1level | — | HSA-APR.B.2HSA-APR.D.6 |
| Radical equations and extraneous solutions | Equations | Non-linear equations | G10 | 14–18 | 1level | — | HSA-REI.A.2 |
| Transformations of functions | Functions | Function behaviour | G10 | 14–18 | 3levels | — | HSF-BF.B.3HSF-IF.C.7 |
| Piecewise-defined functions | Functions | Function behaviour | G10 | 14–18 | 1level | — | HSF-IF.C.7b |
| Arithmetic sequences and series | Functions | Sequences | G10 | 14–18 | 1level | — | HSF-BF.A.2HSF-LE.A.2 |
| Geometric sequences and series | Functions | Sequences | G10 | 14–18 | 1level | — | HSF-BF.A.2HSF-LE.A.2HSA-SSE.B.4 |
| Recursive and explicit definitions | Functions | Sequences | G10 | 14–18 | 1level | — | HSF-BF.A.1aHSF-BF.A.2 |
| Systems of inequalities and feasible regions | Linear | Linear inequalities in two variables | G10 | 14–18 | 1level | — | HSA-CED.A.3HSA-REI.D.12 |
| Residuals and goodness of fit | Linear | Linear fitting | G10 | 14–18 | 1level | — | HSS-ID.B.6b |
| Complete the square | Quadratics | Solving quadratics | G10 | 14–18 | 3levels | — | HSA-REI.B.4aHSF-IF.C.8a |
| The discriminant and the nature of roots | Quadratics | Parabola structure | G10 | 14–18 | 1level | — | HSA-REI.B.4bHSN-CN.C.7 |
| Vertex form and the meaning of completing the square | Quadratics | Parabola structure | G10 | 14–18 | 1level | — | HSF-IF.C.8aHSA-SSE.B.3b |
| Build and interpret quadratic models | Quadratics | Parabola structure | G10 | 14–18 | 1level | — | HSF-IF.B.4HSA-CED.A.1HSF-IF.C.8a |
| Compound interest and repeated percentage change | Exp & log | Exponential change | G10 | 14–18 | 1level | — | HSF-LE.A.1cHSA-SSE.B.3cHSN-Q.A.1 |
| Graphs of exponential functions | Exp & log | Exponential change | G10 | 14–18 | 1level | — | HSF-IF.C.7eHSF-BF.B.3 |
| Square-root and cube-root functions | Exp & log | Radical and rational functions | G10 | 14–18 | 1level | — | HSF-IF.C.7bHSF-BF.B.3 |
| Inverse-proportion models | Exp & log | Radical and rational functions | G10 | 14–18 | 1level | — | HSF-IF.C.7dHSA-CED.A.1 |
| Side-splitter and proportionality theorems | Geometry | Transformations and congruence | G10 | 14–18 | 1level | — | HSG-SRT.B.4HSG-CO.C.10 |
| Special right triangles | Geometry | Right triangles and trigonometry | G10 | 14–18 | 1level | — | HSG-SRT.C.6HSG-SRT.B.4 |
| Right-triangle trigonometry | Geometry | Right triangles and trigonometry | G10 | 14–18 | 1level | — | HSG-SRT.C.6HSG-SRT.C.7HSG-SRT.C.8 |
| Arc length and sector area | Geometry | Circles | G10 | 14–18 | 1level | — | HSG-C.B.5HSG-C.A.2 |
| Circle angle and chord theorems | Geometry | Circles | G10 | 14–18 | 1level | — | HSG-C.A.2HSG-C.A.3HSG-C.A.4 |
| The equation of a circle | Geometry | Circles | G10 | 14–18 | 1level | — | HSG-GPE.A.1 |
| Using slope to establish geometric properties | Geometry | Coordinate geometry | G10 | 14–18 | 1level | — | HSG-GPE.B.4HSG-GPE.B.5 |
| Coordinate (analytic) proof | Geometry | Coordinate geometry | G10 | 14–18 | 1level | — | HSG-GPE.B.4 |
| Partition a segment in a given ratio | Geometry | Coordinate geometry | G10 | 14–18 | 1level | — | HSG-GPE.B.6 |
| Compass-and-straightedge constructions | Geometry | Constructions and proof | G10 | 12–18 | 1level | — | HSG-CO.D.12HSG-CO.D.13 |
| Definitions, postulates, theorems, and proof | Geometry | Constructions and proof | G10 | 13–18 | 3levels | — | HSG-CO.C.9HSG-CO.C.10HSG-CO.C.11+1 |
| Model with geometry | Geometry | Constructions and proof | G10 | 13–18 | 1level | — | HSG-MG.A.1HSG-MG.A.2HSG-MG.A.3 |
| Correlation and its limits | Data & chance | Association and fit | G10 | 14–18 | 1level | — | HSS-ID.C.8HSS-ID.C.9 |
| Experimental design | Data & chance | Sampling and inference | G10 | 14–18 | 1level | — | HSS-IC.B.3HSS-IC.B.5 |
| Addition rule and mutually exclusive events | Data & chance | Probability | G10 | 14–18 | 1level | — | HSS-CP.B.7 |
| Conditional probability and independence | Data & chance | Probability | G10 | 14–18 | 1level | — | HSS-CP.A.2HSS-CP.A.3HSS-CP.A.4+3 |
| Geometric probability | Data & chance | Probability | G10 | 13–18 | 1level | — | 7.G.B.4HSS-MD.A.1 |
| Optimise under constraints | Modeling | Modelling and decisions | G10 | 14–18 | 1level | — | HSA-CED.A.3HSA-REI.D.12 |
| Sensitivity: how outputs respond to inputs | Modeling | Modelling and decisions | G10 | 14–18 | 1level | — | HSF-IF.C.9HSA-CED.A.2 |
| Complex numbers and their arithmetic | Rational numbers | Real and complex numbers | G11 | 15–18 | 1level | — | HSN-CN.A.1HSN-CN.A.2HSN-CN.A.3+1 |
| Remainder and factor theorems | Expressions | Polynomial expressions | G11 | 15–18 | 1level | — | HSA-APR.B.2HSA-APR.B.3 |
| Simplify expressions with complex numbers | Expressions | Rational and radical expressions | G11 | 15–18 | 1level | — | HSN-CN.A.1HSN-CN.A.2 |
| Rational equations and excluded values | Equations | Non-linear equations | G11 | 15–18 | 1level | — | HSA-REI.A.2 |
| Exponential equations | Equations | Non-linear equations | G11 | 15–18 | 1level | — | HSF-LE.A.4HSA-REI.A.2 |
| Logarithmic equations and domain checks | Equations | Non-linear equations | G11 | 15–18 | 1level | — | HSF-LE.A.4HSF-BF.B.5 |
| Inverse relations and inverse functions | Functions | Function behaviour | G11 | 15–18 | 1level | — | HSF-BF.B.4 |
| Composition of functions | Functions | Function behaviour | G11 | 15–18 | 1level | — | HSF-BF.A.1c |
| Arithmetic combinations of functions | Functions | Function behaviour | G11 | 15–18 | 1level | — | HSF-BF.A.1b |
| Real and complex roots of polynomials | Quadratics | Higher-degree polynomials | G11 | 15–18 | 1level | — | HSN-CN.C.7HSN-CN.C.9HSA-APR.B.3 |
| Polynomial end behaviour | Quadratics | Higher-degree polynomials | G11 | 15–18 | 1level | — | HSF-IF.C.7c |
| Graph polynomials from factored form | Quadratics | Higher-degree polynomials | G11 | 15–18 | 1level | — | HSF-IF.C.7cHSA-APR.B.3 |
| Select and critique polynomial models | Quadratics | Higher-degree polynomials | G11 | 15–18 | 1level | Enrichment | HSA-CED.A.2HSF-IF.C.9 |
| The number e and continuous growth | Exp & log | Exponential change | G11 | 15–18 | 1level | — | HSF-LE.A.4HSF-IF.C.8b |
| Logarithms as inverses of exponentials | Exp & log | Logarithms | G11 | 15–18 | 1level | — | HSF-BF.B.4HSF-LE.A.4 |
| Laws of logarithms | Exp & log | Logarithms | G11 | 15–18 | 1level | Fluency | HSF-BF.B.5HSF-LE.A.4 |
| Graphs of logarithmic functions | Exp & log | Logarithms | G11 | 15–18 | 1level | — | HSF-IF.C.7eHSF-BF.B.3 |
| Logarithmic scales and models | Exp & log | Logarithms | G11 | 15–18 | 1level | — | HSF-LE.A.4HSF-IF.C.9HSN-Q.A.1 |
| Rational functions and asymptotes | Exp & log | Radical and rational functions | G11 | 15–18 | 1level | — | HSF-IF.C.7dHSA-APR.D.6 |
| Compare function families | Exp & log | Radical and rational functions | G11 | 15–18 | 1level | — | HSF-LE.A.3HSF-IF.C.9 |
| The unit circle and radian measure | Geometry | Right triangles and trigonometry | G11 | 15–18 | 1level | — | HSF-TF.A.1HSF-TF.A.2HSF-TF.A.3 |
| Graphs of sine and cosine | Geometry | Right triangles and trigonometry | G11 | 15–18 | 1level | — | HSF-TF.B.5HSF-IF.C.7e |
| Trigonometric identities | Geometry | Right triangles and trigonometry | G11 | 15–18 | 1level | — | HSF-TF.C.8 |
| Law of sines and law of cosines | Geometry | Right triangles and trigonometry | G11 | 15–18 | 1level | — | HSG-SRT.D.10HSG-SRT.D.11 |
| Permutations and combinations | Data & chance | Probability | G11 | 14–18 | 1level | — | HSS-CP.B.9 |
| Expected value and fair games | Data & chance | Probability | G11 | 15–18 | 1level | — | HSS-MD.A.2HSS-MD.B.5HSS-MD.B.7 |
| The normal distribution | Data & chance | Probability | G11 | 15–18 | 1level | — | HSS-ID.A.4 |
| Loans, credit, and amortisation | Modeling | Money and finance | G11 | 15–18 | 1level | — | HSF-BF.A.1aHSF-LE.A.1cHSN-Q.A.1 |