# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 27 concepts ready. In the app: https://ai.page/roadmap/sc-grade-6 Part of: [South Carolina: Mathematics](https://ai.page/roadmap/sc.md) Goal: South Carolina academic standards: Mathematics, Grade 6 ## 1. Patterns, Algebra, and Functional Reasoning · Apply mathematical patterns, properties, and algorithms to the set of rational numbers to find sums, differences, products, and quotients and to write equ - [Constructing mathematical arguments](https://ai.page/c/constructing-mathematical-arguments/index.md): Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches - [Real-world fraction multiplication](https://ai.page/c/real-world-fraction-multiplication/index.md): Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations - [Algebraic Transformations](https://ai.page/c/algebraic-transformations/index.md): Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations - [Simple formulae](https://ai.page/c/simple-formulae/index.md): Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-maths/index.md): Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations ## 2. Patterns, Algebra, and Functional Reasoning · . Write, simplify, and evaluate algebraic expressions; write and solve algebraic equations and inequalities. - [Algebraic Notation](https://ai.page/c/algebraic-notation/index.md): Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently - [Ratio Notation](https://ai.page/c/ratio-notation/index.md): Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations - [Substituting into Formulae](https://ai.page/c/substituting-into-formulae/index.md): Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations - [Solving Linear Equations](https://ai.page/c/solving-linear-equations/index.md): Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients - [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign) ## 3. Numerical Reasoning · Utilize rational numbers in mathematical and real-world situations. - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-5/index.md): Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements - [Number Sets & Infinity](https://ai.page/c/number-sets-and-infinity/index.md): Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers - [Sign Rules for Multiplication](https://ai.page/c/sign-rules-for-multiplication/index.md): Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient ## 4. Numerical Reasoning · Translate among multiple representations of rational numbers. - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100% ## 5. Measurement, Geometry, and Spatial Reasoning · Graph on the coordinate plane. - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context ## 6. Measurement, Geometry, and Spatial Reasoning · Determine angle and/or side relationships. - [Measuring angles](https://ai.page/c/measuring-angles/index.md): Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure - [Angles with parallel lines](https://ai.page/c/angles-with-parallel-lines/index.md): Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles ## 7. Measurement, Geometry, and Spatial Reasoning · Determine the measurements of geometric figures. - [Estimating answers (age 10+)](https://ai.page/c/estimating-answers-age-10/index.md): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³) - [Volume as additive](https://ai.page/c/volume-as-additive/index.md): Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms - [Area of Triangles & Parallelograms](https://ai.page/c/area-of-triangles-and-parallelograms/index.md): Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles) - [Angles in triangles (age 11+)](https://ai.page/c/angles-in-triangles-age-11/index.md): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning - [Nets of 3-D Shapes](https://ai.page/c/nets-of-3-d-shapes/index.md): Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net ## 8. Data, Probability, and Statistical Reasoning · Calculate and interpret probability. - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages - [Calculating Simple Probability](https://ai.page/c/calculating-simple-probability/index.md): Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations ## 9. Data, Probability, and Statistical Reasoning · Analyze data sets to identify their statistical elements. - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers ## Health: 0 of 100 Of its 27 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Constructing mathematical arguments has no explanation yet - Real-world fraction multiplication has no explanation yet - Algebraic Transformations comes before Algebraic Notation, which it needs - Algebraic Transformations comes before Solving Linear Equations, which it needs - Algebraic Transformations has no explanation yet - Simple formulae comes before Solving Linear Equations, which it needs - Simple formulae comes before Substituting into Formulae, which it needs - Simple formulae has no explanation yet - Numbers on a number line comes before Solving Linear Equations, which it needs - Numbers on a number line has no explanation yet - Algebraic Notation has no explanation yet - Ratio Notation has no explanation yet - Substituting into Formulae has no explanation yet - Solving Linear Equations has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Positive and Negative Numbers has no explanation yet - Numbers on a number line has no explanation yet - Number Sets & Infinity has no explanation yet - Sign Rules for Multiplication has no explanation yet - Percentages as Fractions has no explanation yet - Plotting points in the first quadrant has no explanation yet - Measuring angles has no explanation yet - Angles with parallel lines has no explanation yet - Estimating answers (age 10+) has no explanation yet - Volume as additive has no explanation yet - Area of Triangles & Parallelograms has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Nets of 3-D Shapes has no explanation yet - The 0-to-1 Probability Scale has no explanation yet - Calculating Simple Probability has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Comparing measurements has no explanation yet Credit: The structure of South Carolina academic standards: Mathematics (https://ed.sc.gov/instruction/standards/mathematics/standards/2025-south-carolina-college-and-career-ready-mathematics-standards/); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.