# High school: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 12 concepts ready. In the app: https://ai.page/roadmap/nj-high-school Part of: [New Jersey: Mathematics](https://ai.page/roadmap/nj.md) Goal: New Jersey academic standards: Mathematics, High school ## 1. Vector and Matrix Quantities · 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 ## 2. Seeing Structure in Expressions · 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) ## 3. Seeing Structure in Expressions · 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% ## 4. Reasoning with Equations and Inequalities · 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 ## 5. Linear and Exponential Models · Distinguish between situations that can be modeled with linear functions and with exponential functions. - [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 ## 6. Interpreting Functions · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. - [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. Building Functions · Find inverse functions. - [Using inverse operations](https://ai.page/c/using-inverse-operations/index.md): Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations - [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 ## 8. Building Functions · Write a function 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 ## 9. Similarity, Right Triangles, and Trigonometry · Verify experimentally the properties of dilations given by a center and a scale factor: - [Coordinates (age 12+)](https://ai.page/c/coordinates-age-12/index.md): Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids ## 10. Using Probability to Make Decisions · Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. For example, find the forecasted value of an in - [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 ## 11. Interpreting Categorical and Quantitative Data · 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 ## Health: 0 of 100 Of its 12 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 Linear Graphs comes before Linear Function Graphs, which it needs - Plotting Linear Graphs has no explanation yet - Factorising Expressions has no explanation yet - Percentages as Fractions has no explanation yet - Solving Linear Equations comes before Using inverse operations, which it needs - Solving Linear Equations has no explanation yet - Linear Function Graphs has no explanation yet - Quadratic Graphs has no explanation yet - Using inverse operations has no explanation yet - Simple formulae has no explanation yet - Ratio Notation and Relationships has no explanation yet - Coordinates (age 12+) has no explanation yet - Estimating by rounding has no explanation yet - Scatter Graphs & Correlation has no explanation yet Credit: The structure of New Jersey academic standards: Mathematics (https://airtable.com/appAqCJWFHZMaNUh2/tblGy4kx6tGuscLHj/viwE5G0UuqG8WME5q/recLphlO9Cy9AXXDA/fldIxltCXshIi374r/attQThKD0HEWuLGJA?blocks=hide); 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.