# High school: 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/ma-high-school Part of: [Massachusetts: Mathematics](https://ai.page/roadmap/ma.md) Goal: Massachusetts academic standards: Mathematics, High school ## 1. Model Advanced Quantitative Reasoning · (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. - [Estimating by rounding](https://ai.page/c/estimating-by-rounding-maths/index.md): Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values ## 2. Model Advanced Quantitative Reasoning · (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. - [Estimating answers (age 13+)](https://ai.page/c/estimating-answers-age-13/index.md): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts ## 3. Model Precalculus · Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. - [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 ## 4. Model Precalculus · (+) Multiply a vector by a scalar. - [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 ## 5. Model Mathematics III · Find inverse functions algebraically and graphically. - [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 ## 6. Model Mathematics III · Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. - [Quadratic Graphs](https://ai.page/c/quadratic-graphs/index.md): Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions ## 7. Model Mathematics III · Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations. - [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 ## 8. Model Mathematics II · Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conve - [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 ## 9. Model Mathematics II · Solve quadratic equations in one variable. - [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 ## 10. Model Mathematics I · Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. - [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 ## 11. Model Algebra II · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. - [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 ## 12. High School · Distinguish between situations that can be modeled with linear functions and with exponential functions. - [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 ## 13. High School · Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) that describes a relationship between two quantities. - [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 ## 14. High School · Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. - [Factorising Expressions](https://ai.page/c/factorising-expressions/index.md): Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3) ## 15. High School · Interpret expressions that represent a quantity in terms of its context. - [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% ## 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): - Estimating by rounding has no explanation yet - Estimating answers (age 13+) comes before Plotting Linear Graphs, which it needs - Estimating answers (age 13+) has no explanation yet - Linear Function Graphs comes before Algebraic Transformations, which it needs - Linear Function Graphs has no explanation yet - Plotting Linear Graphs has no explanation yet - Simple formulae comes before Solving Linear Equations, which it needs - Simple formulae has no explanation yet - Quadratic Graphs 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 - Properties of triangles and quadrilaterals has no explanation yet - Solving Linear Equations has no explanation yet - Scatter Graphs & Correlation has no explanation yet - Algebraic Transformations has no explanation yet - Proportion comes before Ratio Notation and Relationships, which it needs - Proportion has no explanation yet - Ratio Notation and Relationships has no explanation yet - Factorising Expressions has no explanation yet - Percentages as Fractions has no explanation yet Credit: The structure of Massachusetts academic standards: Mathematics (http://www.doe.mass.edu/frameworks/math/2017-06.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.