# Grade 8: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 15 concepts ready. In the app: https://ai.page/roadmap/pa-grade-8 Part of: [Pennsylvania: Mathematics](https://ai.page/roadmap/pa.md) Goal: Pennsylvania academic standards: Mathematics, Grade 8 ## 1. Statistics and Probability · Understand that patterns of association can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. - [Scatter Graphs & Correlation](https://ai.page/c/scatter-graphs-and-correlation/index.md): Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions ## 2. Statistics and Probability · Analyze and interpret bivariate data displayed in multiple representations. - [Simultaneous Equations](https://ai.page/c/simultaneous-equations/index.md): Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations - [Scatter Graphs](https://ai.page/c/scatter-graphs/index.md): Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate ## 3. Geometry · Apply volume formulas of cones, cylinders, and spheres - [Circles: Circumference & Area](https://ai.page/c/circles-circumference-and-area/index.md): Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts ## 4. Geometry · Solve problems involving right triangles by applying the Pythagorean theorem. - [Types of angles (age 13+)](https://ai.page/c/types-of-angles-age-13/index.md): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts ## 5. Geometry · Apply properties of geometric transformations to verify congruence or similarity. - [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original ## 6. Functions · Represent or interpret functional relationships between quantities using tables, graphs, and descriptions. - [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 - [Linear Function Graphs](https://ai.page/c/linear-function-graphs/index.md): Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context ## 7. Functions · Define, evaluate, and compare functions displayed algebraically, graphically, or numerically in tables or by verbal descriptions. - [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 ## 8. Expressions and Equations · Write, solve, graph, and interpret linear equations in one or two variables, using various methods. - [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 - [Plotting Linear Graphs](https://ai.page/c/plotting-linear-graphs/index.md): Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line ## 9. Expressions and Equations · Represent and use expressions and equations to solve problems involving radicals and integer exponents. - [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 - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers-maths/index.md): Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations - [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) ## 10. The Number System · Apply concepts of rational and irrational numbers. - [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 ## Health: 0 of 100 Of its 15 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): - Scatter Graphs & Correlation has no explanation yet - Simultaneous Equations comes before Plotting Linear Graphs, which it needs - Simultaneous Equations comes before Solving Linear Equations, which it needs - Simultaneous Equations has no explanation yet - Scatter Graphs has no explanation yet - Circles: Circumference & Area has no explanation yet - Types of angles (age 13+) has no explanation yet - Coordinate Transformations has no explanation yet - Ratio Notation and Relationships has no explanation yet - Linear Function Graphs comes before Substituting into Formulae, which it needs - Linear Function Graphs comes before Algebraic Transformations, which it needs - Linear Function Graphs has no explanation yet - Algebraic Transformations comes before Solving Linear Equations, which it needs - Algebraic Transformations has no explanation yet - Solving Linear Equations comes before Substituting into Formulae, which it needs - Solving Linear Equations has no explanation yet - Plotting Linear Graphs has no explanation yet - Substituting into Formulae has no explanation yet - Square and cube numbers has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Number Sets & Infinity 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.