# High school: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 32 concepts ready. In the app: https://ai.page/roadmap/ca-ab-high-school Part of: [Alberta: Mathematics](https://ai.page/roadmap/ca-ab.md) Goal: Alberta curriculum: Mathematics, High school ## 1. Relations and Functions - [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 - [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 - [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 - [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 - [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 (Collecting and Analyzing Information) - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability ## 3. Shape and Space (Transformations) - [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 ## 4. Shape and Space (3-D Objects and 2-D 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 ## 5. Shape and Space (Measurement) - [Unit Conversions](https://ai.page/c/unit-conversions/index.md): Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate - [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 - [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 - [Measuring angles (age 11+)](https://ai.page/c/measuring-angles-age-11/index.md): Draw and measure line segments and angles accurately using ruler and protractor, and interpret scale drawings to extract real measurements - [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 ## 6. Patterns and Relations (Variables and Equations) - [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 - [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 - [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 ## 7. Number (Number Concepts and Number Operations) - [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% - [Powers of Ten Notation](https://ai.page/c/powers-of-ten-notation/index.md): Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances ## 8. Algebra and Number - [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) - [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 - [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 ## 9. Measurement - [Trigonometry basics](https://ai.page/c/trigonometry-basics/index.md): Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem - [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 ## 10. Number - [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 ## 11. Geometry - [Angles with parallel lines](https://ai.page/c/angles-with-parallel-lines/index.md): Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles ## 12. Algebra - [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 ## 13. Permutations, Combinations and Binomial Theorem - [Expanding Single Brackets](https://ai.page/c/expanding-single-brackets/index.md): Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers - [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 ## 14. Trigonometry - [Angle sums in triangles and polygons](https://ai.page/c/angle-sums-in-triangles-and-polygons/index.md): Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons ## 15. 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 - [Complementary events](https://ai.page/c/complementary-events/index.md): Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A)) ## Health: 0 of 100 Of its 32 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 answers (age 13+) has no explanation yet - Simultaneous Equations comes before Solving Linear Equations, which it needs - Simultaneous Equations 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 - Ratio Notation and Relationships comes before Proportional Reasoning Vocabulary, which it needs - Ratio Notation and Relationships has no explanation yet - Scatter Graphs & Correlation has no explanation yet - Experimental probability comes before The Probability Scale, which it needs - Experimental probability has no explanation yet - Coordinate Transformations has no explanation yet - 3-D shapes (age 11+) has no explanation yet - Unit Conversions 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 - Circles: Circumference & Area has no explanation yet - Measuring angles (age 11+) has no explanation yet - Estimating by rounding 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 - Substituting into Formulae has no explanation yet - Simple formulae comes before Solving Linear Equations, which it needs - Simple formulae has no explanation yet - Percentages as Fractions has no explanation yet - Powers of Ten Notation comes before Square and cube numbers, which it needs - Powers of Ten Notation has no explanation yet - Positive and Negative Numbers has no explanation yet - Factorising Expressions comes before Expanding Single Brackets, which it needs - Factorising Expressions has no explanation yet - Square and cube numbers has no explanation yet - Number Sets & Infinity has no explanation yet - Trigonometry basics has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Proportion has no explanation yet - Angles with parallel lines has no explanation yet - Solving Linear Equations has no explanation yet - Expanding Single Brackets has no explanation yet - Algebraic Transformations has no explanation yet - Angle sums in triangles and polygons has no explanation yet - The Probability Scale has no explanation yet - Complementary events has no explanation yet Credit: The structure of Alberta curriculum: Mathematics (https://curriculum.learnalberta.ca/curriculum/en/c/mat6); 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.