# 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/pa-grade-6 Part of: [Pennsylvania: Mathematics](https://ai.page/roadmap/pa.md) Goal: Pennsylvania academic standards: Mathematics, Grade 6 ## 1. Statistics and Probability · Display, analyze, and summarize numerical data sets in relation to their context. - [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 - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability ## 2. Geometry · Find area, surface area, and volume by applying formulas and using various strategies. - [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 - [Using Simple Formulae](https://ai.page/c/using-simple-formulae/index.md): Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width)) - [Area of compound shapes](https://ai.page/c/area-of-compound-shapes/index.md): Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas - [Properties of triangles and quadrilaterals](https://ai.page/c/properties-of-triangles-and-quadrilaterals/index.md): Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths ## 3. Expressions and Equations · Use variables to represent two quantities in a real-world problem that change in relationship to one another. - [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 - [Compound Units](https://ai.page/c/compound-units/index.md): Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units ## 4. Expressions and Equations · Create, solve, and interpret one variable equations or inequalities in real-world and mathematical problems. - [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 - [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) ## 5. Expressions and Equations · Identify, write, and evaluate numerical and algebraic expressions. - [Writing Algebraic Equations](https://ai.page/c/writing-algebraic-equations/index.md): Express missing number problems algebraically using letters for unknowns; translate word problems into equations - [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 - [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 ## 6. Ratios and Proportional Relationships · Represent and/or solve real world and mathematical problems using rates, ratios, and/or percents. - [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% - [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 - [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 - [Dividing Quantities by Ratio](https://ai.page/c/dividing-quantities-by-ratio/index.md): Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole - [Ratio Notation and Relationships](https://ai.page/c/ratio-notation-and-relationships/index.md): Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios - [Proportion](https://ai.page/c/proportion/index.md): Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations ## 7. The Number System · Understand ordering and absolute value of rational numbers. - [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 ## 8. The Number System · Understand that positive and negative numbers are used together to describe quantities having opposite directions or values and locations on the number line and coordinate plane. - [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 ## 9. The Number System · Apply number theory concepts (specifically, factors and multiples). - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems ## 10. The Number System · Compute with multi-digit numbers using the four arithmetic operations with or without a calculator. - [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 ## 11. The Number System · Solve real-world and mathematical problems involving division of fractions. - [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result - [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 ## 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): - Statistical Analysis Vocabulary has no explanation yet - Comparing measurements has no explanation yet - Experimental probability has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Using Simple Formulae has no explanation yet - Area of compound shapes has no explanation yet - Properties of triangles and quadrilaterals 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 - Compound Units comes before Proportion, which it needs - Compound Units comes before Proportional Reasoning Vocabulary, which it needs - Compound Units has no explanation yet - Solving Linear Equations comes before Writing Algebraic Equations, which it needs - Solving Linear Equations comes before Substituting into Formulae, which it needs - Solving Linear Equations has no explanation yet - Numbers on a number line has no explanation yet - Expressions & Equations Vocabulary comes before Algebraic Notation, which it needs - Expressions & Equations Vocabulary has no explanation yet - Writing Algebraic Equations has no explanation yet - Algebraic Notation has no explanation yet - Substituting into Formulae has no explanation yet - Percentages as Fractions has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Ratio Notation comes before Factors, multiples, and primes, which it needs - Ratio Notation has no explanation yet - Dividing Quantities by Ratio has no explanation yet - Ratio Notation and Relationships has no explanation yet - Proportion has no explanation yet - Numbers on a number line comes before Positive and Negative Numbers, which it needs - Numbers on a number line has no explanation yet - Positive and Negative Numbers has no explanation yet - Factors, multiples, and primes has no explanation yet - Mixed & Improper Fractions comes before Dividing fractions (unit fractions), which it needs - Mixed & Improper Fractions has no explanation yet - Dividing fractions (unit fractions) has no explanation yet - Real-world fraction multiplication has no explanation yet Credit: The structure of Pennsylvania academic standards: Mathematics (https://www.pdesas.org/Page/Viewer/ViewPage/12/); 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.