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What Brilliant covers for college-level coding and early software careers

Brilliant covers many of the programming and computer science foundations needed for introductory college coursework and early software work, with particular strength in Python, algorithms, data structures, debugging, decomposition, and verifying AI-written code. An August 2026 curriculum audit found coverage of about 88% of the audited MIT introductory Python topic set, 50% of Harvard CS50x, and 28% of a durable-skills framework with 30 learning objectives. Learners should supplement Brilliant with projects and targeted work in areas such as C, SQL, web development, version control, security, and production engineering. Coverage at a glance Benchmark or question Finding MIT introductory Python topic set 88% of the audited topics covered Harvard CS50x 50% of the audited topics covered Durable coding skills for the age of AI 28% overall coverage across 84 substandards; full coverage expected by March 2027 Brilliant’s strongest areas Verification, debugging, specification, decomposition, and abstraction Important areas to supplement Projects, C, SQL, web development, version control, security, and production engineering See how Brilliant’s coding coverage was audited for the scoring method, evidence, and limitations. What should you prepare for? Goal Main emphasis Where it is assessed Preparation priorities An intro-college CS course (e.g. Harvard CS50x, MIT 6.0001) Programming fundamentals, algorithms, data structures, and complexity Problem sets, projects, and exams Fluency in a language (often Python), code tracing, recursion, debugging, and algorithmic thinking A first software job and technical interviews System design, code reading and review, debugging, and working effectively with AI Take-home tasks, pair-programming, and system-design interviews Explaining an approach, reviewing and debugging real code, decomposition, and communication Building real software with AI Specifying, verifying, and integrating AI-written code On the job, continuously Verification, debugging, decomposition, directing AI agents, and security What do modern coding assessments and interviews look like? Setting Format What to practice University courses Problem sets, timed exams, and end-of-term projects Fundamentals, code tracing, recursion, and debugging Technical interviews (shifting in 2025–26) System design, real-codebase debugging, code review, and take-home tasks — and less pure speed-leetcode Designing systems, reviewing and debugging code, and explaining trade-offs On the job Shipping features with AI assistance, reviewing pull requests, and verifying AI output Verifying AI-written code, debugging, decomposition, and security Formats change quickly. Use the linked course and employer materials as the source of truth when planning final review. A practical preparation path Stage What to do Start Build fluency with variables, conditionals, loops, functions, collections, recursion, code tracing, and debugging. Build Make small projects end to end. Practice reading and verifying code — including AI-generated code — and keep an error log by topic. Deepen Work on system design, decomposition, complexity, writing tests, and reasoning about correctness and efficiency. For interviews Practice system design, code review, and debugging under time pressure, and rehearse explaining your approach. Ongoing Learn to direct AI agents, write evaluations, and apply security fundamentals as you build. How can Brilliant help? Brilliant builds the conceptual and programming foundations that underpin both college coursework and durable, AI-era coding skill. Its Python and computer science path develops code reading, conditional logic, loops, functions, debugging, data structures, algorithms, complexity analysis, and — critically — verifying and repairing code, the skills that matter most as AI writes more of it. An August 2026 curriculum audit mapped Brilliant's CS sequence — 4 Foundations courses, the 6-course Python track (165 lessons), and 6 adjacent technology courses — onto both a framework of the durable coding skills that matter in the age of AI and the intro-college courses the field benchmarks against. Overall, Brilliant covers 28% of the durable-skills framework today — concentrated in exactly the skills that endure — and a large share of the standard intro-college courses.¹ Coverage is increasing every month and we expect to cover all topics by March 2027. Intro-college university-course coverage Course Brilliant coverage Relevant Brilliant courses What learners should supplement MIT 6.0001 — Intro to CS & Programming in Python 88% Thinking in Python, Functions in Python, OOP in Python, Recursion in Python, Algorithms in Python A few library-specific topics (e.g. plotting) Harvard CS50x 50% Thinking in Python, Functions in Python, Algorithms in Python, Data Structures in Python, Digital Circuits, How Technology Works C, SQL, web development (HTML/CSS/JavaScript/Flask), and the final project Durable AI-era skills coverage Skill area Brilliant coverage Relevant Brilliant courses or lessons What learners should supplement Verify — testing, reviewing, and debugging code 45% Functions in Python (Testing Functions, Verifying AI Code, Debugging Dependencies), Recursion in Python, Programming with Functions (Tracing Errors), Algorithms in Python (Reasoning about Correctness) Building evaluations for AI systems; production observability Spec & Design — specifying and structuring a solution 44% Functions in Python (Decompose Problems, Helper Functions, Planning Tasks, Function Contracts), OOP in Python (Planning a Class) Judging what information is relevant; full spec-first discipline Reasoning across levels of abstraction 38% Functions in Python (Decompose Problems, Helper Functions), Programming with Functions (Composing Functions), Thinking in Code (Designing Programs) Transferring reasoning to higher abstractions, such as agent workflows Build — directing AI to implement a spec 14% Functions in Python (Verifying AI Code, Cracking the Code) Orchestrating and integrating multiple AI agents Taste — deciding what is worth building 13% Functions in Python (Function Contracts) Product judgment and defining what "good" means Building incrementally 17% Thinking in Code (Designing Programs) Version control and incremental delivery workflows Security & adversarial thinking 0% — (not yet taught) Secure coding, threat modeling, AI-specific risks (prompt injection, insecure generated code, supply chain) Brilliant's strength lines up with what endures: verification, debugging, decomposition, and abstraction. The lower-coverage areas — directing multiple AI agents, evaluation, security, version control, and product taste — are skills to build elsewhere for now, and are the scope of Brilliant's planned Python-with-AI course. How much relevant practice is available on Brilliant? Practice type Number in Brilliant's current curriculum Lessons where learners run executable code 274 lessons + 618 practice sets (2,081 run-and-edit code problems) Problems requiring learners to trace code and predict its output 161 explicit "What's the output?" problems (in practice, nearly all problems require this) Problems requiring learners to diagnose or repair code 689 (361 repair, 328 diagnose) Problems requiring learners to design or revise an algorithm 561 Problems involving data structures or collections 329 These counts span Brilliant's 10 code-writing CS courses (the 6 Python-track and 4 Foundations courses) — 274 lessons plus 618 practice sets, 3,282 problems total — counted directly from each problem's interactive.² Notably, diagnose-and-repair problems (689) are the most AI-relevant practice of all: reading and fixing code you did not write is the single most durable skill as AI generates more code, and it lives overwhelmingly in the practice sets (649 of 689). What should a learner be able to do? A well-prepared learner should be able to do the following, across two overarching areas. Intro-college computer science foundations Trace a program and predict its output. Write and revise algorithms using selection, iteration, and recursion. Break a problem into modular parts and design clear abstractions. Reason about correctness and efficiency, including complexity. Work with collections of data and common algorithms. Coding with AI Read and understand code they did not write, including AI-generated code. Find, explain, and repair errors systematically. Specify what code should do — and how success will be verified — before building. Verify AI-written code and demonstrate it is correct with evidence. Direct an AI agent toward a specification and recognize when to take over. Resources Coding Skills That Matter in the Age of AI — the durable-skills curriculum Audit methodology and coverage evidence Harvard CS50x · MIT 6.0001 on OCW Best use of Brilliant: build durable programming and computer-science foundations — especially reading, verifying, and debugging code — before or alongside a college course or first job, then combine that work with projects, interview practice, and, where relevant, official course materials. For learners moving from block-based coding into text-based programming, see the next step after Scratch or block-based coding. Notes ¹ Curriculum audit: The mapping used Brilliant’s durable coding skills framework (7 Big Ideas, 30 learning objectives, and 84 substandards) and the current syllabi for Harvard CS50x and MIT 6.0001 (6.100A). Each substandard is weighted equally; partial coverage counts as half. “Covered” means conceptual teaching and practice are available. Coverage judgments are Brilliant’s own; topic coverage does not establish course equivalence. Brilliant is not affiliated with MIT or Harvard. See the audit methodology and coverage evidence. ² Practice counts: counted directly from each problem's interactive across Brilliant's 10 code-writing CS courses (6 Python-track + 4 Foundations), 274 lessons and 618 practice sets, 3,282 problems total.

How Brilliant's coding coverage was audited

Brilliant’s coding coverage percentages come from an August 2026 curriculum audit conducted at the substandard level. Each essential-knowledge point in Brilliant’s durable coding skills framework was labeled Covered, Partial, or Gap, then scored with the formula (Covered + ½ × Partial) ÷ all substandards in the group. This page explains the evidence and calculation behind the coverage claims in What Brilliant covers for college-level coding and early software careers. The skills being measured are defined in Coding skills that matter in the age of AI. How coverage was scored Every substandard was assigned one of three labels: Covered: A Brilliant lesson teaches the idea directly. Partial: The idea is present, but is not the lesson’s focus or is covered indirectly. Gap: The idea is not currently taught. For each skill area, coverage was calculated as: (Covered + 0.5 × Partial) ÷ Total substandards The overall score uses the same formula across all 84 substandards. This means every substandard has equal weight. Coverage measures whether teaching and practice exist, not how much time a learner spends on the topic or whether Brilliant is equivalent to a university course. Results by skill area Skill area Coverage Covered Partial Gap Substandards Taste: what’s worth building 13% 0 1 3 4 Spec and design 44% 4 7 6 17 Build 14% 0 4 10 14 Verify 45% 7 5 9 21 Reasoning across levels of abstraction 38% 1 4 3 8 Building incrementally 17% 0 2 4 6 Security and adversarial thinking 0% 0 0 14 14 Overall 28% 12 23 49 84 Brilliant’s strongest coverage is in verification, debugging, decomposition, and abstraction. The largest gaps are in security, multi-agent orchestration, evaluation and measurement, version control, product judgment, and relevance judgment. Evidence used The audit reviewed Brilliant’s current Python and computer science curriculum and linked each Covered or Partial judgment to one or more live lessons. Examples include: Functions in Python: Function Contracts Functions in Python: Decompose Problems Functions in Python: Verifying AI Code Functions in Python: Debugging Dependencies Algorithms in Python: Reasoning about Correctness Thinking in Code: Designing Programs Introductory college course benchmarks The audit also compared Brilliant’s Python and Foundations tracks with the published topic sets for two widely used introductory courses. Course Audited coverage Interpretation MIT 6.0001 / 6.100A: Introduction to Computer Science and Programming in Python 88% Brilliant covers most audited topics from variables through object-oriented programming, recursion, testing, debugging, and complexity. Harvard CS50x 50% Brilliant covers many programming, algorithm, data-structure, and memory topics. C, SQL, web development, and the final project remain outside the mapped coverage. These percentages describe topic coverage only. They do not establish course equivalence, academic credit, learning outcomes, or guaranteed readiness. Brilliant is not affiliated with MIT or Harvard. Limits and update policy Coverage judgments are Brilliant’s own and involve expert interpretation. Partial coverage counts as half regardless of how broad or deep that partial coverage is. The audit reflects the curriculum available in August 2026. Results should be updated when courses or benchmark syllabi change. A topic being present does not prove that every learner has mastered it. Practice counts and learner assessment results use separate methodologies and should not be interpreted as coverage scores.

What subjects does Brilliant teach?

Brilliant's core strengths are math and coding. If you're comfortable with the four basic operations — adding, subtracting, multiplying, and dividing — you're ready to start. Subject areas Math Brilliant has an extensive math library, starting with advanced arithmetic and building up through the most challenging topics. This is our deepest and most comprehensive subject area. Topics include: Fractions, decimals, and advanced arithmetic Pre-algebra and algebra Geometry and trigonometry Probability and statistics Calculus and differential equations Linear algebra and number theory Coding Learn to code and think computationally, from first principles to advanced topics. Topics include: Python programming Thinking in Code (programming fundamentals) Algorithms and data structures How AI works Computer memory and architecture Software engineering fundamentals Data Science Build data analysis skills to work with real-world datasets. Topics include: Data analysis fundamentals Statistics and probability Data visualization Applied data analysis Science & Technology Explore scientific concepts and how modern technology works. Topics include: Classical mechanics and physics Neural networks and machine learning Large language models (LLMs) Digital circuits and computing Cryptocurrency and blockchain How courses are organized Courses on Brilliant are structured as interactive lessons that combine: Clear explanations of concepts Hands-on problems to solve Instant feedback on your work Visual simulations and animations You can explore individual courses or follow Learning Paths — curated sequences that guide you from fundamentals to advanced topics in a specific subject area. Accessing course content Both free and Premium users can access all subjects on Brilliant. The difference is in how much you can learn per day and how much Koji access you have — free users get a limited preview, while Premium subscribers have full, unlimited access to Koji. Learn more about free vs. Premium. Ready to start learning? Get started on Brilliant or browse all courses at brilliant.org/courses.

What math does Brilliant cover?

Brilliant covers math from grade 4 foundations through college-level topics. Its school-math paths include fractions, pre-algebra, Algebra I, geometry, Algebra II, precalculus, and calculus; other courses cover probability, statistics, logic, number theory, contest math, vectors, and matrices. Four grade-banded paths run from grades 4–12, while Advanced Math and enrichment courses extend beyond high school. Brilliant’s math curriculum is comprehensive in scope, but it is organized by concept rather than as a one-to-one copy of every school or exam syllabus. Course names and grade bands verified August 10, 2026. Brilliant math coverage at a glance Math area Current Brilliant courses Approximate level Foundational math and pre-algebra Fractions, Solving Equations, Negative Numbers, Coordinate Plane, Percents, and Proportional Reasoning Grades 4–7 Algebra I and integrated math Linear Equations, Coordinate Geometry, Linear Relationships, Exponents and Radicals, Visual Algebra, Introduction to Functions, Linear Systems, and Quadratics Grades 7–11 Geometry Geometry and Measurement, Coordinate Geometry, Coordinate Transformations, and Geometric Thinking Middle school through advanced enrichment Algebra II and precalculus Quadratics, Exponentials and Logarithms, Trigonometric Functions, Polar Coordinate Plane, Complex Numbers, Polynomials, Equations and Curves, and Vectors and Matrices Grades 9–12 Calculus and advanced math Calculus and Vectors and Matrices Advanced high school, college, and adult learners Probability, statistics, and data Everyday Statistics, Probability and Chance, Exploring Data Visually, Probability in Data, Clustering and Classification, Regression, and Predicting with Probability Foundational through advanced Logic, discrete math, and enrichment Logic, Number Theory, Contest Math, Math Puzzles, Strategy Puzzles, Infinity, and Bayesian Probability Varies by course and prerequisite What grade levels does Brilliant math cover? Brilliant’s structured school-math progression begins with grade 4–5 fractions and extends through grade 12 algebra and precalculus topics. It’s most commonly used in grades 5–12, while advanced courses also serve college students and adults. Learning path Published grade band Courses in the path Math Foundations Grades 4–7 Fractions; Solving Equations; Negative Numbers; Coordinate Plane; Percents; Proportional Reasoning Algebra Fundamentals Grades 7–9 Linear Equations; Coordinate Geometry; Linear Relationships; Exponents and Radicals; Visual Algebra Intermediate Algebra Grades 8–11 Introduction to Functions; Linear Systems; Quadratics; Coordinate Transformations; Exponentials and Logarithms Advanced Algebra Grades 11–12 Trigonometric Functions; Polar Coordinate Plane; Complex Numbers; Polynomials; Equations and Curves; Vectors and Matrices Advanced Math Advanced Calculus; Vectors and Matrices The bands overlap because readiness can differ by topic. They describe the intended level of the material, not a formal placement decision or a promise that each path reproduces a local grade-level curriculum. How learners use Brilliant at different levels Learner stage Common uses Upper elementary Build foundations in fractions, equations, geometry, and problem solving; provide enrichment for learners ready for additional challenge. Middle and secondary school Support current coursework, strengthen prerequisites, develop conceptual understanding, or explore more advanced mathematics. College and adult learning Refresh foundational skills, prepare for more advanced study, or explore topics not previously studied. Looking for a starting course rather than a coverage list? Use the course placement guide. For a description of what children typically learn in each school grade, see What math should my child know at each grade?. Does Brilliant cover Algebra I? Yes. Brilliant covers central Algebra I concepts across the Algebra Fundamentals and Intermediate Algebra paths, including linear equations and inequalities, graphs, functions, systems, exponents, radicals, and quadratics. Brilliant does not package this material as one universal Algebra I syllabus because schools sequence topics differently. Compare the named courses with the learner’s syllabus when exact alignment matters. Does Brilliant cover geometry? Yes. Brilliant covers measurement, angles, area, circles, similarity, the Pythagorean theorem, surface area, volume, coordinate geometry, transformations, symmetry, and more advanced geometric reasoning across four courses. Brilliant is especially useful for visual and interactive exploration. A school Geometry course may also require a specific sequence of constructions, formal proofs, vocabulary, and assessments, so check local requirements before using Brilliant as the only course resource. Does Brilliant cover Algebra II and precalculus? Yes. Brilliant’s Intermediate Algebra and Advanced Algebra paths cover many topics found in Algebra II, Integrated Math II and III, and Precalculus. These include quadratics, exponential and logarithmic functions, trigonometric functions, polar coordinates, complex numbers, polynomials, advanced graphs, vectors, and matrices. The material is distributed across focused courses rather than one course labeled “Algebra II” or “Precalculus.” Does Brilliant cover calculus? Yes. Brilliant’s Calculus course teaches key ideas in limits, derivatives, integrals, rates of change, accumulation, and infinite series through interactive problems and visual models. For AP Calculus or another formal exam, pair Brilliant with the current official framework, calculator requirements, free-response practice, and full-length exams. Does Brilliant teach probability and statistics? Yes. Brilliant covers descriptive statistics, data visualization, probability, conditional probability, expected value, regression, probabilistic prediction, and Bayesian reasoning across the Everyday Math, Data Analysis, and Mind-Bending Math paths. This range lets a learner begin with intuitive chance and data questions, then move into modeling, inference, and decision-making under uncertainty. Does Brilliant cover elementary math? Partly. The grade-banded math sequence begins with a fractions course labeled for grades 4–5, followed by equations for grades 5–6 and several grades 6–7 foundation courses. Brilliant also offers geometry, statistics, probability, and problem-solving material accessible to some elementary learners. Brilliant does not present a complete K–3 arithmetic sequence. Parents seeking a full elementary curriculum should compare the catalog with the child’s school standards and use another source for uncovered topics and routine fluency practice. Is Brilliant a complete math curriculum? Brilliant has a broad, structured math curriculum from foundational through advanced topics. It can teach concepts, provide interactive practice, strengthen prerequisites, and extend learning beyond a standard syllabus. “Complete,” however, depends on the requirement being measured. No single Brilliant path promises to reproduce every local course sequence, assignment type, proof requirement, state standard, or exam format. If the learner needs… Use Brilliant for… Also check… Conceptual instruction and problem solving Interactive lessons, models, feedback, and unfamiliar problems Whether additional routine practice is needed An exact school-course match The closest courses and prerequisite topics The teacher’s syllabus and required assessments Common Core alignment Lessons mapped to many grade 4 through high-school standards The standard-by-standard mapping and any marked gaps AP or other exam preparation Understanding the underlying mathematics The official framework, question formats, timing, and practice exams School credit or formal placement Evidence of completed work The school’s own credit and placement policies Is Brilliant aligned with Common Core math standards? Brilliant has a lesson-level mapping from Common Core grade 4 standards through high-school Algebra, Functions, Geometry, Number and Quantity, and Statistics and Probability. The map names the closest Brilliant lesson for each covered standard and explicitly marks standards with no direct lesson. For the standards-level answer, use Common Core math coverage: grade-by-grade Brilliant lesson mapping. Keeping the detailed mapping on that page avoids duplicating hundreds of standards here. What this page covers, and where to go next This page is the source of truth for which math subjects, courses, and grade bands Brilliant covers. Use the focused guides below for adjacent questions: Grade expectations: What math should my child know at each grade? Course selection: Course placement guide Acceleration: How to help your child get ahead in math Enrichment: Is Brilliant good for enrichment? Standards alignment: Common Core math coverage Sources [1] Brilliant, “Courses”, current learning paths, course titles, and grade bands accessed August 10, 2026. [2] Brilliant, “What grade levels does Brilliant cover?”, updated March 12, 2026. [3] Brilliant, “What subjects does Brilliant teach?”, updated February 5, 2026. [4] Brilliant, “Math”, accessed August 10, 2026. [5] Common Core State Standards Initiative, “Mathematics Standards”.

Is Brilliant aligned with Common Core State Standards?

Yes. Brilliant’s math lessons align with many Common Core State Standards for Mathematics (CCSS-M), and Brilliant provides two complementary alignment tools. Use the standard-first map when you have a Common Core standard and need a relevant Brilliant lesson. Use the lesson-first guide when you have a Brilliant lesson and need to identify the Common Core standards it supports. Choose the right alignment tool If you are starting with… Use this resource Best for A Common Core math standard, standard code, or grade-level requirement Common Core math coverage: grade-by-grade Brilliant lesson mapping Parents, homeschool educators, curriculum planning, and identifying coverage or gaps A Brilliant lesson or course Brilliant lesson alignment to Common Core Teachers choosing or documenting classroom assignments The two resources show the same type of relationship in opposite directions. One begins with the standard; the other begins with the Brilliant lesson. How does Brilliant align with Common Core math standards? Brilliant maps individual math lessons to relevant Common Core standards based on the concepts and skills addressed in each lesson. The mappings cover areas such as number and operations, ratios, equations, functions, geometry, statistics, probability, and advanced high-school mathematics. Brilliant lessons emphasize conceptual understanding, visual reasoning, and problem solving. A mapped lesson can help a learner develop understanding related to a standard, but it may not reproduce every activity, assessment, fluency requirement, or instructional sequence in a local curriculum. Does Brilliant cover every Common Core math standard? Not every standard has a direct Brilliant lesson. The standard-first map lists the closest relevant lesson when one exists and explicitly marks standards for which Brilliant does not currently have a direct lesson. This makes the map useful for planning: Parents and homeschool educators can begin with a grade-level standard and find relevant Brilliant material. Teachers can identify lessons that support the standards they are teaching. Curriculum planners can see both areas of alignment and areas that require another resource. Is Brilliant a complete Common Core curriculum? Brilliant can support learning across many Common Core math standards, but it is not organized as a one-to-one reproduction of a school curriculum. Course sequences, pacing, required assessments, and implementation expectations vary by school and system. Use the alignment tools to identify relevant Brilliant lessons, then compare the results with the curriculum or standards your learner is expected to follow. Frequently asked questions Why are there two alignment resources? They support different workflows. The standard-first map answers “Which Brilliant lesson addresses this standard?” The lesson-first guide answers “Which standards does this Brilliant lesson address?” Can families use these resources without a school account? Yes. The standard-first map can help any parent, homeschool educator, or learner find Brilliant lessons related to a particular Common Core math standard. Access to particular lessons depends on the learner’s Brilliant plan. How current are the mappings? Brilliant’s course and lesson catalog changes over time. Use the last-verified date on each mapping and check the current course catalog when exact lesson availability matters. Related resources What math does Brilliant cover? What subjects does Brilliant teach? Explore Brilliant’s courses Sources [1] Common Core State Standards Initiative, “Mathematics Standards”. [2] Brilliant, “Which Common Core standards does each Brilliant lesson align with?”, accessed August 2026. [3] Brilliant, “Courses”, accessed August 2026.

Common Core math coverage: grade-by-grade Brilliant lesson mapping

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

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