# High school: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 19 concepts ready. In the app: https://ai.page/roadmap/ne-high-school Part of: [Nebraska: Mathematics](https://ai.page/roadmap/ne.md) Goal: Nebraska academic standards: Mathematics, High school ## 1. High School Advanced Topics · Probability: Students will interpret and apply concepts of probability. - [The Probability Scale](https://ai.page/c/the-probability-scale/index.md): Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible ## 2. High School Advanced Topics · Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results. - [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. High School Advanced Topics · Logic and Proof: Students will use geometric definitions and theorems to reason abstractly and quantitatively. - [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 ## 4. High School Advanced Topics · Coordinate Geometry and Transformations: Students will demonstrate and represent location, orientation, and relationships on the coordinate plane. - [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 ## 5. High School Advanced Topics · Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create three-dimensional shapes. - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections ## 6. High School Advanced Topics · Algebraic Processes: Students will apply the operational properties when evaluating nonlinear expressions and solving nonlinear equations and inequalities. - [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 ## 7. High School Advanced Topics · Algebraic Relationships: Students will demonstrate and represent relationships with functions. - [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 - [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 ## 8. High School Advanced Topics · Interpretation and Sense Making: Students will reason abstractly and quantitatively using units to solve problems and interpret results in context. - [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 ## 9. High School Advanced Topics · Sets and Operations: Students will compare and contrast subsets and perform operations with subsets of the complex number system to reason and to solve problems. - [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 ## 10. High School · Analyze Data and Interpret Results: Students will represent and analyze the data and interpret the results. - [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type - [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 - [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. High School · Logic and Proof: Students will use geometric definitions and theorems to reason abstractly and quantitatively. - [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 ## 12. High School · Attributes: Students will identify and describe geometric attributes, apply properties and theorems, and create two- dimensional shapes. - [Angles in triangles (age 12+)](https://ai.page/c/angles-in-triangles-age-12/index.md): Know and use the criteria for triangle congruence (SSS, SAS, ASA, RHS), use standard labelling conventions for sides and angles of triangle ABC, and determine whether two triangles are congruent - [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 ## 13. High School · Algebraic Processes: Students will apply the operational properties when evaluating rational expressions and solving linear and quadratic equations, and inequalities. - [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 ## 14. High School · Algebraic Relationships: Students will demonstrate and represent relationships with 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 ## 15. High School · Interpretation and Sense Making: Students will reason abstractly and quantitatively using units to solve problems and interpret results in context. - [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 ## Health: 0 of 100 Of its 19 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): - The Probability Scale has no explanation yet - Estimating answers (age 13+) has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Coordinate Transformations has no explanation yet - 3-D shapes (age 11+) 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 - Algebraic Transformations comes before Solving Linear Equations, which it needs - Algebraic Transformations has no explanation yet - Linear Function Graphs 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 - Number Sets & Infinity has no explanation yet - Pictograms and tally charts (age 11+) has no explanation yet - Comparing measurements has no explanation yet - Scatter Graphs & Correlation has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Angles in triangles (age 12+) has no explanation yet - Coordinates (age 12+) has no explanation yet - Solving Linear Equations has no explanation yet - Proportion has no explanation yet - Estimating by rounding has no explanation yet Credit: The structure of Nebraska academic standards: Mathematics (https://www.education.ne.gov/wp-content/uploads/2022/10/Nebraskas-College-and-Career-Ready-Standards-for-Mathematics-Final-10.20.22.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.