This page maps Common Core math standards from grade 4 through high school to the Brilliant courses and lessons that address them. Search by standard code or skill to find the closest match. When Brilliant does not currently have a direct lesson for a standard, the mapping says No direct lesson.
GRADE 4
4.OA — Operations & Algebraic Thinking
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 4.OA.1 | Interpret multiplicative comparisons | Multiplication facts | No direct lesson |
| 4.OA.2 | Multiply/divide comparison word problems | Multiplicative comparison | No direct lesson |
| 4.OA.3 | Multi-step word problems with whole numbers | Four operations | No direct lesson |
| 4.OA.4 | Find factor pairs; determine prime/composite | Multiplication/division | exponents-and-radicals > Level 13: Prime Factors, Repeated Prime Factors |
| 4.OA.5 | Generate and analyze number patterns | Arithmetic fluency | systems-of-equations > Level 1-2: Building Patterns, Pattern Rules, Describing Patterns, Building Expressions |
4.NF — Number & Operations—Fractions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 4.NF.1 | Explain fraction equivalence using visual models | 3.NF.3 fraction basics | math-fundamentals > Level 2: Sixths and Twelfths, Eighths and Sixteenths, Making Equivalent Fractions, Simplifying Fractions, Identifying Equivalents |
| 4.NF.2 | Compare fractions with different numerators/denominators | Equivalent fractions | math-fundamentals > Level 3: Comparing Numerators, Comparing Denominators, Comparing Equivalents, Comparing More Equivalents, Identifying the Greatest |
| 4.NF.3 | Add/subtract fractions with like denominators; decompose fractions | Fraction equivalence | math-fundamentals > Level 4: Adding Fractions, Adding Same-Sized Fractions |
| 4.NF.4 | Multiply fraction by whole number | Fraction concept, multiplication | math-fundamentals > Level 5: Multiples of Fractions, Expressing Multiples |
| 4.NF.5 | Express fractions with denominator 10 as equivalent with denominator 100 | Equivalent fractions | percentages > Level 3: Percentages as Tenths, Percentages as Hundredths |
| 4.NF.6 | Decimal notation for fractions with denominator 10 or 100 | Fraction/decimal connection | percentages > Level 3: Percentages as Decimals |
| 4.NF.7 | Compare two decimals to hundredths | Decimal notation | No direct lesson |
4.MD — Measurement & Data
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 4.MD.1 | Unit conversion within a measurement system | Multiplication, fractions | No direct lesson |
| 4.MD.3 | Apply area and perimeter formulas for rectangles | Area/perimeter concepts | geometry-fundamentals > Level 3: Perimeters; Level 5: Polygon Areas |
| 4.MD.5-6 | Understand angle concepts; measure angles with a protractor | Geometry basics | geometry-fundamentals > Level 2: Angles Made by Lines |
| 4.MD.7 | Solve addition/subtraction problems for angle measures | Angle measurement | basic-2d-geometry > Level 3: Angle Hunting Axioms, Advanced Angle Hunts |
4.G — Geometry
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 4.G.1 | Draw/identify lines, angles, rays, parallel/perpendicular lines | Shape attributes | geometry-fundamentals > Level 2: Angles Made by Lines, Parallel Lines |
| 4.G.2 | Classify 2D figures by properties (parallel sides, angle measures) | Lines and angles | geometry-fundamentals > Level 1: Angles in Polygons, Exterior and Interior Angles |
| 4.G.3 | Recognize lines of symmetry | Shape attributes | transformations > Level 10: Reflectional Symmetry, Identifying Symmetry |
GRADE 5
5.OA — Operations & Algebraic Thinking
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 5.OA.1 | Use parentheses/brackets/braces; evaluate expressions | Four operations | exponents-and-radicals > Level 6: Order and Evaluation, Parentheses and Exponents |
| 5.OA.2 | Write and interpret numerical expressions | Arithmetic fluency | linear-expressions-and-equations > Level 1: Variables, Writing Expressions |
| 5.OA.3 | Generate two numerical patterns; form ordered pairs | Pattern recognition | systems-of-equations > Level 2: Describing Patterns, Building Expressions, Linear Expressions |
5.NBT — Number & Operations in Base Ten
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 5.NBT.1 | Place value system (powers of 10) | Whole number place value | exponents-and-radicals > Level 1: Base 10; Level 3: Powers of 10 on Number Lines, Estimating with Powers of 10 |
| 5.NBT.2 | Explain patterns when multiplying/dividing by powers of 10 | Place value | exponents-and-radicals > Level 15: Powers of 10, Shifting the Decimal Point |
| 5.NBT.5 | Fluently multiply multi-digit whole numbers | Multiplication algorithm | No direct lesson |
| 5.NBT.6 | Divide up to 4-digit by 2-digit divisors | Division algorithm | No direct lesson |
| 5.NBT.7 | Add/subtract/multiply/divide decimals to hundredths | Decimal concepts | linear-expressions-and-equations > Level 12: Adding Percentages, Subtracting Percentages |
5.NF — Number & Operations—Fractions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 5.NF.1 | Add/subtract fractions with unlike denominators | Equivalent fractions | math-fundamentals > Level 4: Adding Unlike Parts, Adding Unit Fractions, Adding Any Fractions |
| 5.NF.2 | Word problems with fraction addition/subtraction | Fraction addition | No direct lesson |
| 5.NF.3 | Interpret a fraction as division | Fraction concept | No direct lesson |
| 5.NF.4 | Multiply fractions and whole numbers | Fraction concept, multiplication | math-fundamentals > Level 5: Fractions of Unit Fractions, Products of Unit Fractions, Fraction of Any Fraction, Multiplying Fractions |
| 5.NF.5 | Interpret multiplication as scaling | Fraction multiplication | geometry-fundamentals > Level 4: Scaling Shapes, Scaling Lengths |
| 5.NF.7 | Divide unit fractions by whole numbers and vice versa | Fraction multiplication | No direct lesson |
5.MD — Measurement & Data
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 5.MD.1 | Convert measurement units within a system | Multiplication, division | No direct lesson |
| 5.MD.3-5 | Understand volume; measure volume by counting unit cubes; relate to multiplication | Multiplication, area | geometry-fundamentals > Level 8: Volume |
5.G — Geometry
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 5.G.1 | Graph points on coordinate plane for real-world problems | Number line | coordinate-plane > Level 1: Coordinates, Coordinate Pairs, Plotting Points, Applied Coordinates |
| 5.G.2 | Graph points to solve real-world and mathematical problems | Coordinate graphing | coordinate-plane > Level 1: Identifying Points, Applied Coordinates |
| 5.G.3 | Classify 2D figures by properties (hierarchy of quadrilaterals) | Shape attributes | geometry-fundamentals > Level 1: Angles in Polygons, Polygon Angle Relationships |
GRADE 6
6.RP — Ratios & Proportional Relationships
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 6.RP.1 | Understand ratio concepts; describe ratio relationships | Fraction/multiplication fluency | proportional-relationships > Level 1: Setting Up Ratios, Scaling Up, Scaling Down, Making a New Mixture |
| 6.RP.2 | Understand unit rate concepts | Ratio understanding | proportional-relationships > Level 4: How Much for One, Computing Unit Rates, Two Unit Rates, Using Unit Rates |
| 6.RP.3a | Make tables of equivalent ratios | Ratio equivalence | proportional-relationships > Level 2: Scaling Up Recipes, Making Batches, Finding Batches, Scale Factor |
| 6.RP.3b | Solve unit rate problems | Unit rate | proportional-relationships > Level 5: Using Unit Rates to Find Cost, Comparing Rates; using-variables > Level 2: Unit Prices |
| 6.RP.3c | Find percent of a quantity; solve percent problems | Ratio, fraction equivalence | percentages > Level 1: Intro to Percentages, Working out Percentages, Percentages as Fractions; Level 3: Finding the Percentage, Calculating the Percentage |
| 6.RP.3d | Use ratios for converting measurement units | Unit rates | using-variables > Level 2: Comparing Offers, Using Unit Prices |
6.NS — The Number System
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 6.NS.1 | Divide fractions by fractions | Fraction multiplication | linear-expressions-and-equations > Level 11: Reciprocals |
| 6.NS.2 | Fluently divide multi-digit numbers | Division algorithm | No direct lesson |
| 6.NS.3 | Fluently add/subtract/multiply/divide multi-digit decimals | Decimal operations | No direct lesson |
| 6.NS.5 | Understand positive/negative numbers in context | Whole number concepts | negative-numbers > Level 1: Positives and Negatives, Negative Numbers, Making Integers |
| 6.NS.6 | Understand rational numbers on number line; ordered pairs in all 4 quadrants | Integer concepts | negative-numbers > Level 5: The Number Line, Addition on the Number Line; coordinate-plane > Level 2: Negative Coordinates, Points in Quadrants |
| 6.NS.7 | Understand ordering and absolute value of rational numbers | Number line, integers | negative-numbers > Level 6: Ordering Integers, Ordering Negatives, Absolute Value, Absolute Value Inequalities, Reasoning with Absolute Value |
| 6.NS.8 | Solve problems by graphing in all 4 quadrants | Coordinate plane | coordinate-plane > Level 2: Plotting Negative Coordinates, Identifying More Points, City Temperatures |
6.EE — Expressions & Equations
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 6.EE.1 | Write/evaluate numerical expressions with exponents | Arithmetic operations | exponents-and-radicals > Level 1: Multiplication Patterns, Exponents, Bases, Special Bases and Exponents |
| 6.EE.2 | Write/read/evaluate algebraic expressions | Variable concept | linear-expressions-and-equations > Level 1: Variables, Finding Unknown Values, Combining and Coefficients, Writing Expressions |
| 6.EE.3 | Apply properties of operations to generate equivalent expressions | Expression writing | linear-expressions-and-equations > Level 4: Combining Terms; pre-algebra > Level 5: Combining Like Terms |
| 6.EE.4 | Identify equivalent expressions | Equivalent expression generation | pre-algebra > Level 5: Combining in Equations, Rearranging Terms |
| 6.EE.5 | Understand solving an equation as finding values that make it true | Variable concept | pre-algebra > Level 1: Finding Unknowns, Equations with Unknowns; Level 2: Finding Solutions |
| 6.EE.6 | Use variables to represent numbers; write expressions | Equation concept | using-variables > Level 1: Using Variables, Adjusting Formulas, More Than One Variable |
| 6.EE.7 | Solve real-world equations of the form x + p = q, px = q | Equation understanding | linear-expressions-and-equations > Level 2: Dividing to Solve, Solving in Two Steps |
| 6.EE.8 | Write an inequality; recognize infinitely many solutions | Equation solving | linear-expressions-and-equations > Level 3: Solutions to Inequalities, Graphing Solutions, Reading Inequalities |
| 6.EE.9 | Represent and analyze quantitative relationships between dependent/independent variables | Variable concept | proportional-relationships > Level 7: Writing Equations, Equation from a Point |
6.G — Geometry
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 6.G.1 | Find area of triangles, quadrilaterals, polygons by composing/decomposing | Area concept | geometry-fundamentals > Level 5: Polygon Areas; basic-2d-geometry > Level 5: Composite Figure Warm-ups, Complementary Areas, Inclusion and Exclusion |
| 6.G.2 | Find volume of right rectangular prisms with fractional edges | Volume concept | geometry-fundamentals > Level 8: Volume |
| 6.G.3 | Draw polygons on coordinate plane; find side lengths | Coordinate plane | coordinate-plane > Level 5: Distance Between Points; Level 3: Horizontal Lines, Vertical Lines |
| 6.G.4 | Represent 3D figures using nets; find surface area | Area of polygons | geometry-fundamentals > Level 7: Surface Area, Surface Area Shortcut, Pyramids and Cones |
6.SP — Statistics & Probability
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 6.SP.1-2 | Recognize statistical questions; understand distribution | Data awareness | basic-math > Level 1: Means, Distributions; visual-exploration > Level 1: Histograms |
| 6.SP.3 | Recognize measures of center and variability | Distribution understanding | basic-math > Levels 1-5: Means, Medians, Modes; Level 6: Quartiles, Interquartile Range |
| 6.SP.4 | Display data in plots (dot plots, histograms, box plots) | Data representation | basic-math > Level 6: Boxplots; Level 7: Adding Whiskers, Matching the Boxplot; visual-exploration > Level 1: Histograms, Bar Charts |
| 6.SP.5 | Summarize data sets (mean, median, IQR, mean absolute deviation) | Measures of center | basic-math > Level 8: Outliers, Skewing the Mean, Defining Outliers; Level 6: Interquartile Range |
GRADE 7
7.RP — Ratios & Proportional Relationships
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 7.RP.1 | Compute unit rates with complex fractions | 6.RP unit rates | proportional-relationships > Level 4: Computing Unit Rates; Level 3: Scaling Down to Scale Up, Scaling in One Move |
| 7.RP.2 | Recognize/represent proportional relationships | Unit rates, ratios | proportional-relationships > Level 5-6: Using Unit Rates to Find Cost, Comparing Rates, Plotting Equivalent Ratios, Graphing Relationships, Constant of Proportionality |
| 7.RP.2a | Decide if two quantities are proportional (tables, graphs) | Proportional relationship concept | proportional-relationships > Level 6: Plotting Equivalent Ratios, Using Graphs, Constant of Proportionality |
| 7.RP.2b | Identify constant of proportionality | Proportional graphs | proportional-relationships > Level 6: Constant of Proportionality; linear-functions > Level 4: Proportional Relationships |
| 7.RP.2c | Represent proportional relationships by equations | Constant of proportionality | proportional-relationships > Level 7: Writing Equations, Equation from a Point, Graphing from an Equation |
| 7.RP.3 | Use proportional relationships to solve percent problems | Percentages, ratios | percentages > Level 2: Percent Increase, Calculating Percent Increase; Level 4: Percent Decrease, Calculating Percent Decrease, Finding the Original Price |
7.NS — The Number System
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 7.NS.1 | Add and subtract rational numbers | 6.NS integer understanding | negative-numbers > Level 2: Adding Negatives, Adding Negatives and Positives; Level 3: Missing Values, Subtracting Positives, Subtracting Negatives; Level 4: Adding The Opposite, Subtracting Using Addition; Level 5: Addition on the Number Line, Adding Large Integers |
| 7.NS.2 | Multiply and divide rational numbers | Integer addition/subtraction | exponents-and-radicals > Level 2: Powers of -1, Negative Bases |
| 7.NS.3 | Solve real-world problems with rational number operations | Rational number operations | negative-numbers > Level 8: Order in Expressions, Strategic Rearrangement, Longer Expressions; using-variables > Level 3: Calculating Percentages |
7.EE — Expressions & Equations
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 7.EE.1 | Apply properties to add, subtract, factor, expand linear expressions | 6.EE equivalent expressions | linear-expressions-and-equations > Level 4: Combining Terms, Combining to Solve; Level 8: Distributing, Distributing with Negatives; Level 9: Factoring Constants, Greatest Common Factor |
| 7.EE.2 | Rewrite expressions in different forms to illuminate quantities | Expression manipulation | pre-algebra > Level 5: Combining Like Terms, Combining in Equations, Rearranging Terms |
| 7.EE.3 | Solve multi-step real-world problems with rational numbers | Rational number operations | linear-expressions-and-equations > Level 12: Adding Percentages, Comparing Deals; using-variables > Level 3: Working with Percentages |
| 7.EE.4a | Solve word problems leading to equations of the form px + q = r, p(x + q) = r | Expression/equation solving | linear-expressions-and-equations > Level 2: Solving in Two Steps, Multiple Steps; Level 8: Distributing to Solve |
| 7.EE.4b | Solve word problems leading to inequalities of the form px + q > r | Inequality concepts | linear-expressions-and-equations > Level 3: Finding the Boundary, Solving Inequalities; Level 7: Solving Inequalities |
7.G — Geometry
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 7.G.1 | Scale drawings of geometric figures | Ratios, proportional relationships | geometry-fundamentals > Level 4: Scaling Shapes, Scaling Lengths; transformations > Level 11-13: Dilating Points, Dilating Shapes, Similarity |
| 7.G.2 | Draw geometric shapes with given conditions | Geometry basics | basic-2d-geometry > Level 4: Triangle Inequality, Congruent and Similar Triangles |
| 7.G.3 | Describe 2D figures from slicing 3D figures | 3D shape understanding | No direct lesson |
| 7.G.4 | Know formulas for area/circumference of circle | Area, pi concept | geometry-fundamentals > Level 3: Circumference, Arc Length; Level 5: Circle Areas |
| 7.G.5 | Use facts about supplementary, complementary, vertical, adjacent angles | Angle concepts | geometry-fundamentals > Level 2: Angles Made by Lines, Parallel Lines; basic-2d-geometry > Level 3: Angle Hunting Axioms, Advanced Angle Hunts |
| 7.G.6 | Solve problems involving area, volume, surface area of 2D and 3D objects | Area, volume formulas | geometry-fundamentals > Level 5: Polygon Areas, Circle Areas; Level 7: Surface Area; Level 8: Volume, Pyramids and Cones |
7.SP — Statistics & Probability
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 7.SP.1-2 | Understand sampling; use data from random samples for population inference | Data/distribution concepts | visual-exploration > Level 5: Data Tables, Drawing Conclusions |
| 7.SP.3-4 | Compare two data distributions; use measures of center/variability | Mean, median, IQR | basic-math > Level 7: Comparing Distributions; Level 6: Interquartile Range |
| 7.SP.5 | Understand probability between 0 and 1 | Fraction/ratio concepts | probability-fundamentals > Level 1: Estimating Probabilities, Simulating Outcomes |
| 7.SP.6 | Approximate probability from relative frequency | Probability concept | probability-fundamentals > Level 1: The Past And The Future, Changing Fortunes |
| 7.SP.7 | Develop probability models for simple/compound events | Experimental probability | probability-fundamentals > Level 2: Combining Probabilities; Level 3: Building Models, Tuning Models |
| 7.SP.8 | Find probabilities of compound events | Probability models | probability-fundamentals > Level 2: Conditional Probability, Total Probability; Level 3: Dependence and Independence |
GRADE 8
8.NS — The Number System
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 8.NS.1 | Know that irrational numbers exist; rational number decimal expansions | Fraction/decimal conversion | exponents-and-radicals > Level 4: Square Roots of Non-Squares; quadratics > Level 10: Irrational Solutions |
| 8.NS.2 | Approximate irrationals on a number line | Irrational number concept | exponents-and-radicals > Level 3: Powers of 2 on the Number Line, Powers of 3 on the Number Line; Level 4: Squares on the Number Line |
8.EE — Expressions & Equations
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 8.EE.1 | Know/apply properties of integer exponents | 6.EE.1 exponent basics | exponents-and-radicals > Level 9: Product Rule, Power Rule, Powers of a Product; Level 10: Exponent Zero; Level 11: Negative Exponents; Level 12: Quotients |
| 8.EE.2 | Use square/cube root symbols; evaluate square/cube roots of small perfect squares/cubes | Exponent concepts | exponents-and-radicals > Level 4: Squaring, Square Roots, The Inverse of Squaring; Level 5: Cubes, Cube Roots, Higher Order Roots |
| 8.EE.3 | Use numbers in scientific notation; estimate very large/small quantities | Powers of 10 | exponents-and-radicals > Level 15: Powers of 10, Shifting the Decimal Point, Adding/Multiplying/Dividing in Scientific Notation |
| 8.EE.4 | Perform operations with scientific notation | Scientific notation basics | exponents-and-radicals > Level 15: Adding, Multiplying, Dividing, Estimating Products/Quotients in Scientific Notation |
| 8.EE.5 | Graph proportional relationships; interpret unit rate as slope | Proportional relationships | linear-functions > Level 3: Change per One, Identifying Slopes, Computing Slopes; Level 4: Proportional Relationships |
| 8.EE.6 | Use similar triangles to explain slope; derive y = mx + b | Slope, proportionality | linear-functions > Level 4: Base Fees, Graphing Linear Functions, Writing the Whole Expression; Level 5: Slope of a Line, Through a Point |
| 8.EE.7 | Solve linear equations in one variable | Equation basics | linear-expressions-and-equations > Levels 2-6: Full progression from two-step to negatives; Level 10: No Solutions, Many Solutions, Identifying Solutions |
| 8.EE.8 | Analyze/solve systems of two linear equations | Single-variable equation solving | pre-algebra > Level 8: Systems with Scales, Balancing with Substitution, Writing Systems, Substituting Groups; Level 9: Elimination, Multiplying to Eliminate |
8.F — Functions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 8.F.1 | Understand that a function assigns exactly one output to each input | Equation concepts | introduction-to-functions > Level 1: Finding the Rule, Word Functions, Repeating Outputs, Deducing the Rule; Level 4: Function Requirements, Vertical Line Test |
| 8.F.2 | Compare properties of two functions (algebraically, graphically, in tables, verbally) | Function concept | introduction-to-functions > Level 3: Graphing Linear Functions, Interpreting Graphed Functions, Intercepts and Intervals |
| 8.F.3 | Interpret y = mx + b as linear; give examples of nonlinear functions | Linear functions | linear-functions > Level 1: Points on a Line, Nonlinear Relationships; Level 4: Graphing Linear Functions; introduction-to-functions > Level 3: Graphing Squared Functions |
| 8.F.4 | Construct a function to model a linear relationship; determine rate of change/initial value | Linear function concepts | linear-functions > Level 2: Finding Rates of Change, Rates from Points, Initial Conditions, Using Two Points; Level 4: Finding the Constant Term, Finding the Linear Term, Writing the Whole Expression |
| 8.F.5 | Describe qualitatively the functional relationship between quantities from a graph | Graph interpretation | introduction-to-functions > Level 3: Interpreting Graphed Functions, Increasing and Decreasing; Level 5: Real-World Functions |
8.G — Geometry
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 8.G.1 | Verify properties of rotations, reflections, translations | Geometry basics | transformations > Level 1: Translating Points, Translating Shapes; Level 3: Rotating Shapes; Level 7: Reflecting Across Axes, Reflecting Shapes |
| 8.G.2 | Understand congruence through sequences of transformations | Transformation concepts | transformations > Level 10: Congruence, Proving Congruence |
| 8.G.3 | Describe effect of dilations, translations, rotations, reflections on 2D figures using coordinates | Coordinate plane, transformations | transformations > Level 2: Coordinate-wise Translation; Level 4: Rotating by 180/90/270 degrees; Level 8: Reflecting Coordinates, Reflecting Across y=x |
| 8.G.4 | Understand similarity through sequences of transformations | Congruence, dilation | transformations > Level 11-13: Dilating Points, Dilating Shapes, Similarity, Identifying Similarity |
| 8.G.5 | Use informal arguments to establish angle relationships (parallel lines cut by transversal, triangle angle sum, exterior angles) | Angle concepts | geometry-fundamentals > Level 2: Angles Made by Lines, Parallel Lines, Triangle Sides and Angles; basic-2d-geometry > Level 3: Internal Angles in a Polygon |
| 8.G.6 | Explain proof of Pythagorean Theorem and its converse | Geometry, area concepts | basic-2d-geometry > Level 1: Pythagoras' Theorem; geometry-fundamentals > Level 6: The Pythagorean Theorem |
| 8.G.7 | Apply Pythagorean Theorem to find unknown side lengths in real-world problems | Pythagorean Theorem | geometry-fundamentals > Level 6: Pythagorean Triples, Applications; basic-2d-geometry > Level 11: Applying the Pythagorean Theorem |
| 8.G.8 | Apply Pythagorean Theorem to find distance between two points on coordinate plane | Pythagorean Theorem, coordinate plane | coordinate-plane > Level 5: Distance Between Points; basic-2d-geometry > Level 9: Right Triangles, Thales + Pythagoras |
| 8.G.9 | Know/apply formulas for volumes of cones, cylinders, spheres | Volume concept | geometry-fundamentals > Level 8: Volume, Pyramids and Cones |
8.SP — Statistics & Probability
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| 8.SP.1 | Construct/interpret scatter plots for bivariate data | Coordinate plane, data concepts | visual-exploration > Level 4: Observing Relationships, Reading Scatter Plots |
| 8.SP.2 | Know that lines are widely used to model relationships; fit a line informally | Scatter plots | visual-exploration > Level 3: Trends, Comparing Trends |
| 8.SP.3 | Use equation of linear model to solve problems; interpret slope and intercept | Linear equations, scatter plots | linear-functions > Level 4: Interpreting a Function |
| 8.SP.4 | Construct/interpret two-way tables for bivariate categorical data | Data organization | visual-exploration > Level 5: Data Tables, Filtering with Logic |
HIGH SCHOOL — ALGEBRA (HSA)
HSA-SSE — Seeing Structure in Expressions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSA-SSE.1 | Interpret expressions in terms of context | 8.EE expression concepts | using-variables > Level 1: Using Formulas, Using Variables, Adjusting Formulas |
| HSA-SSE.2 | Use structure of expression to identify ways to rewrite it | Expression manipulation | quadratics > Level 3: Undistributing, Finding One Factor, Factoring Quadratics; linear-expressions-and-equations > Level 9: Factoring Constants, Greatest Common Factor |
| HSA-SSE.3 | Choose/produce equivalent form to reveal properties (factor quadratics, complete the square, properties of exponentials) | Factoring, quadratics | quadratics > Level 11: Completing the Square; Level 12: Rewriting in Vertex Form; Level 14: Reading Different Forms, Choosing the Right Form |
HSA-APR — Arithmetic with Polynomials and Rational Expressions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSA-APR.1 | Add, subtract, multiply polynomials | Expression operations | quadratics > Level 1: Multiplying Expressions, Multiplying Binomials; Level 2: Distributing and Combining; pre-algebra > Level 3-4: Distributing, Factoring |
| HSA-APR.3 | Identify zeros of polynomials to construct rough graph | Factoring | quadratics > Level 6: Solutions to Quadratic Equations, Plotting x-Intercepts, Factored Form |
HSA-CED — Creating Equations
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSA-CED.1 | Create equations/inequalities in one variable | Expression/equation solving | linear-expressions-and-equations > Level 3: Reading Inequalities; Level 13: Writing Compound Inequalities; quadratics > Level 7: Solving by Factoring |
| HSA-CED.2 | Create equations in two or more variables | Single-variable equations | linear-functions > Level 5: Through Two Points, Point-Slope Form, Equations in Point-Slope Form; Level 7: Standard Form of an Equation |
| HSA-CED.3 | Represent constraints with equations/inequalities/systems | Multi-variable equations | linear-functions > Level 8: Writing Inequalities, Cost Inequalities; pre-algebra > Level 8: Writing Systems of Equations |
| HSA-CED.4 | Rearrange formulas to highlight a quantity of interest | Equation solving | pre-algebra > Level 2: Rewriting Equations, Isolating Unknowns; using-variables > Level 1: Equivalent Formulas |
HSA-REI — Reasoning with Equations and Inequalities
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSA-REI.1 | Explain each step in solving a simple equation | Equation solving | pre-algebra > Level 2: Solving an Equation; linear-expressions-and-equations > Level 2: Equation Solving Moves |
| HSA-REI.3 | Solve linear equations/inequalities in one variable | Equation fundamentals | linear-expressions-and-equations > Levels 2-7: Complete progression |
| HSA-REI.4 | Solve quadratic equations (factoring, completing the square, quadratic formula) | Factoring, expression manipulation | quadratics > Level 7: Solving by Factoring; Level 9: Solving by Undoing; Level 11: Completing the Square; Level 13: The Quadratic Formula |
| HSA-REI.5-6 | Solve systems of equations (substitution, elimination) | Single-variable equations | pre-algebra > Level 8: Substituting Groups, Isolating and Substituting; Level 9: Elimination, Multiplying to Eliminate |
| HSA-REI.7 | Solve system of linear and quadratic equations | Systems, quadratics | Partially covered in quadratics |
| HSA-REI.10 | Understand solutions to equation in two variables as a graph | Coordinate plane | linear-functions > Level 4: Graphing Linear Functions; quadratics > Level 6: Plotting Solutions, Plotting x-Intercepts |
| HSA-REI.11 | Explain why intersection points of graphs are solutions | Graphing equations | linear-functions > Level 8: Graphing Inequalities; systems-of-equations > Level 5: Comparing Linear Expressions |
| HSA-REI.12 | Graph solutions to linear inequalities/systems of inequalities | Inequality solving | linear-functions > Level 8: The Boundary Line, Graphing Inequalities; coordinate-plane > Level 4: Identifying Regions, Marking Boundaries |
HIGH SCHOOL — FUNCTIONS (HSF)
HSF-IF — Interpreting Functions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSF-IF.1 | Understand function notation; domain and range | 8.F function concept | introduction-to-functions > Level 1: Finding the Rule; Level 8: Domain, Range, Domain and Range |
| HSF-IF.2 | Use function notation; evaluate functions | Function concept | introduction-to-functions > Level 2: Numeric Rules, Writing Rules, Deducing Numeric Rules |
| HSF-IF.3 | Recognize sequences as functions with integer domains | Function understanding | systems-of-equations > Level 9-10: Exponential Patterns, Building Exponential Expressions |
| HSF-IF.4 | Interpret key features of graphs/tables (intercepts, intervals, increasing/decreasing, maxima/minima, symmetry, end behavior) | Graphing functions | introduction-to-functions > Level 3: Intercepts and Intervals, Increasing and Decreasing; quadratics > Level 12: Maximum or Minimum Value; Level 14: Axis of Symmetry |
| HSF-IF.5 | Relate domain of function to its graph; in context | Domain concepts | introduction-to-functions > Level 9: Squares and Ranges, Square Roots and Domains, Identifying Domain and Range |
| HSF-IF.6 | Calculate/interpret average rate of change from a function | Slope, rate of change | linear-functions > Level 2: Finding Rates of Change, Rates from Points |
| HSF-IF.7 | Graph functions (linear, quadratic, polynomial, exponential, piecewise) and show key features | Graphing basics | introduction-to-functions > Level 3: Graphing Linear/Squared/Absolute Value; Level 6: Plotting Piecewise Functions; quadratics > Level 8: Graphing Vertex Form; exponential-functions > Level 7: Stepping Along Exponentials |
| HSF-IF.8 | Write a function in equivalent forms to reveal properties (vertex form, factored form, exponential growth/decay) | Multiple function forms | quadratics > Level 14: Reading Different Forms, Choosing the Right Form; exponential-functions > Level 6: Modeling Compound Interest, Modeling Depreciation |
| HSF-IF.9 | Compare properties of two functions represented differently | Multiple representations | systems-of-equations > Level 8: Quadratic Versus Linear, Comparing Kinds of Growth |
HSF-BF — Building Functions
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSF-BF.1 | Write a function that describes a relationship | Function concepts | linear-functions > Level 4: Writing the Whole Expression; exponential-functions > Level 2: Deducing Exponential Functions; Level 5: Building Exponentials |
| HSF-BF.2 | Write arithmetic and geometric sequences recursively/explicitly | Sequence concepts | systems-of-equations > Level 2-3: Building Expressions, Building Linear Expressions; Level 9-10: Exponential Patterns, Building Exponential Expressions |
| HSF-BF.3 | Identify effect of transformations on graphs (f(x) + k, kf(x), f(kx), f(x + k)) | Function graphing | introduction-to-functions > Level 12: Vertical/Horizontal Shifting, Combining Shifts, Vertical/Horizontal Stretching; Level 13: Reflection Across x-Axis, y-Axis |
| HSF-BF.4 | Find inverse functions | Function composition | introduction-to-functions > Level 14: Inverting a Function, Finding the Input, Finding the Inverse Function, Graphing Inverse Functions, Invertibility |
HSF-LE — Linear, Quadratic, and Exponential Models
| CC Standard | Skill | Prerequisite | Brilliant Course / Lessons |
|---|---|---|---|
| HSF-LE.1 | Distinguish between linear and exponential growth | Linear functions, exponents | systems-of-equations > Level 8: A Different Kind of Growth, Linear or Quadratic, Comparing Kinds of Growth, Quadratic Versus Linear; exponential-functions > Level 4: Linear Comparisons, Quadratic Comparisons |
| HSF-LE.2 | Construct linear and exponential functions from description/table/graph | Function building | linear-functions > Level 2: Using Two Points; exponential-functions > Level 2: Finding the Base and Coefficient, Deducing Exponential Functions; Level 5: Building Exponentials, Building Decay Functions |
| HSF-LE.3 | Observe that exponential growth eventually exceeds polynomial growth | Growth comparison | exponential-functions > Level 4: Comparing Growth, Comparing Decay |
| HSF-LE.4 | Express exponential models as logarithms for solving | Exponential functions | exponential-functions > Level 9: Counting Days, Log-Exponent Pairs, Inverse of Exponentiation; Level 13: Taking Logs of Both Sides, Solving Using Logarithms |
| HSF-LE.5 | Interpret parameters in linear/exponential functions in context | Function building | exponential-functions > Level 6: Modeling Compound Interest, Interest Comparisons; linear-functions > Level 4: Interpreting a Function |