# High school: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 14 concepts ready. In the app: https://ai.page/roadmap/sd-high-school Part of: [South Dakota: Mathematics](https://ai.page/roadmap/sd.md) Goal: South Dakota academic standards: Mathematics, High school ## 1. High School - 4th Year Mathematics · (+)Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding calculating the 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. High School - 4th Year Mathematics · (+)Analyze conic sections using equations and graphs. - [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 - [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 ## 3. High School - 4th Year Mathematics · (+)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. High School - Algebra II · 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 ## 5. High School - Algebra II · Interpret expressions that represent a quantity in terms of its context. - [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) ## 6. High School - Geometry · Derive using similarity the length of the arc intercepted by an angle is proportional to the radius. - [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 - [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 ## 7. High School - Geometry · Use geometric descriptions of rigid motions to transform figures. - [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 ## 8. High School - Algebra 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 ## 9. High School - Algebra I · Write a function (linear, quadratic, and exponential) that describes a relationship between two quantities. - [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 ## 10. High School - Algebra I · 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 ## 11. High School - Algebra I · 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) ## 12. High School - Algebra I · Interpret expressions that represent a quantity in terms of its context. - [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 ## Health: 0 of 100 Of its 14 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+) has no explanation yet - Quadratic Graphs has no explanation yet - Linear Function Graphs comes before Algebraic Transformations, which it needs - Linear Function Graphs has no explanation yet - Ratio Notation and Relationships has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Coordinates (age 12+) comes before Coordinate Transformations, which it needs - Coordinates (age 12+) has no explanation yet - Coordinate Transformations has no explanation yet - Scatter Graphs & Correlation 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 - Solving Linear Equations has no explanation yet - Factorising Expressions has no explanation yet - Algebraic Transformations has no explanation yet Credit: The structure of South Dakota academic standards: Mathematics (http://doe.sd.gov/contentstandards/documents/SD-Math-Standard.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.