# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 21 concepts ready. In the app: https://ai.page/roadmap/ga-grade-6 Part of: [Georgia: Mathematics](https://ai.page/roadmap/ga.md) Goal: Georgia academic standards: Mathematics, Grade 6 ## 1. Patterning & Algebraic Reasoning · Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vert - [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 ## 2. Patterning & Algebraic Reasoning · Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations. - [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 - [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 ## 3. Patterning & Algebraic Reasoning · Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant situations. - [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 - [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 ## 4. Geometric & Spatial Reasoning · Solve relevant problems involving area, surface area, and volume. - [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) - [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 - [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 ## 5. Numerical Reasoning · Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning. - [Proportional Reasoning Vocabulary](https://ai.page/c/proportional-reasoning-vocabulary/index.md): Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts - [Real-World Mathematical Modelling](https://ai.page/c/real-world-mathematical-modelling/index.md): Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations - [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% - [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 ## 6. Numerical Reasoning · Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situatio - [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 ## 7. Numerical Reasoning · Apply operations with whole numbers, fractions and decimals within relevant applications. - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-3/index.md): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line - [Rounding Answers](https://ai.page/c/rounding-answers/index.md): Solve problems which require answers to be rounded to specified degrees of accuracy ## 8. Numerical Reasoning · Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers. - [Dividing unit fractions and whole numbers](https://ai.page/c/dividing-unit-fractions-and-whole-numbers/index.md): Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations - [Mixed & Improper Fractions](https://ai.page/c/mixed-and-improper-fractions/index.md): Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative - [Multi-step problems: choosing operations](https://ai.page/c/multi-step-problems-choosing-operations/index.md): Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts ## 9. Mathematical Practices · Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective - [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 ## Health: 0 of 100 Of its 21 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): - Plotting points in the first quadrant has no explanation yet - Solving Linear Equations has no explanation yet - Numbers on a number line has no explanation yet - Algebraic Notation has no explanation yet - Algebraic Transformations has no explanation yet - Estimating answers (age 10+) has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Volume as additive has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Real-World Mathematical Modelling has no explanation yet - Percentages as Fractions has no explanation yet - Ratio Notation 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 - Fractions on a number line has no explanation yet - Rounding Answers has no explanation yet - Dividing unit fractions and whole numbers has no explanation yet - Mixed & Improper Fractions has no explanation yet - Multi-step problems: choosing operations has no explanation yet - Constructing mathematical arguments has no explanation yet Credit: The structure of Georgia academic standards: Mathematics (https://www.gadoe.org/Curriculum-Instruction-and-Assessment/Curriculum-and-Instruction/Documents/Mathematics/Georgia-K12-Mathematics-Standards/Georgia-Mathematics-Curriculum-Maps/HS-Algebra-Mathematics-Curriculum-Map-NEW-2023.pdf); 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.