# High school: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 31 concepts ready. In the app: https://ai.page/roadmap/ca-mb-high-school

Part of: [Manitoba: Mathematics](https://ai.page/roadmap/ca-mb.md)

Goal: Manitoba curriculum: Mathematics, High school

## 1. Statistics and Probability

- [Tree diagrams](https://ai.page/c/tree-diagrams/index.md): Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

## 2. Shape and Space

- [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
- [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

## 3. Patterns and Relations (Patterns)

- [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
- [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
- [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

## 4. Number

- [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

## 5. Angle Construction

- [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
- [Understanding angles (age 12+)](https://ai.page/c/understanding-angles-age-12/index.md): Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

## 6. Consumer Decisions

- [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

## 7. 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
- [Types of angles (age 13+)](https://ai.page/c/types-of-angles-age-13/index.md): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
- [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
- [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

## 8. 2-D Geometry

- [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

## 9. Relations and Functions

- [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
- [Proportion Graphs](https://ai.page/c/proportion-graphs/index.md): Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed
- [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

## 10. 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)
- [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
- [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-5/index.md): Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

## 11. Measurement

- [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
- [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
- [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

## 12. Statistics

- [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

## 13. 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))

## 14. 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

## Health: 0 of 100

Of its 31 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):

- Tree diagrams has no explanation yet
- Coordinate Transformations has no explanation yet
- Properties of triangles and quadrilaterals has no explanation yet
- Ratio Notation and Relationships comes before Proportional Reasoning Vocabulary, which it needs
- Ratio Notation and Relationships comes before Proportion Graphs, which it needs
- Ratio Notation and Relationships has no explanation yet
- Solving Linear Equations has no explanation yet
- Scatter Graphs & Correlation comes before Comparing measurements, which it needs
- Scatter Graphs & Correlation has no explanation yet
- Square and cube numbers has no explanation yet
- Number Sets & Infinity has no explanation yet
- Angles with parallel lines has no explanation yet
- Understanding angles (age 12+) 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
- Angle sums in triangles and polygons has no explanation yet
- Types of angles (age 13+) has no explanation yet
- Trigonometry basics comes before Simple formulae, which it needs
- Trigonometry basics has no explanation yet
- Plotting Linear Graphs comes before Linear Function Graphs, which it needs
- Plotting Linear Graphs has no explanation yet
- Circles: Circumference & Area has no explanation yet
- Simultaneous Equations has no explanation yet
- Linear Function Graphs has no explanation yet
- Proportion Graphs has no explanation yet
- Quadratic Graphs has no explanation yet
- Factorising Expressions comes before Expanding Single Brackets, which it needs
- Factorising Expressions has no explanation yet
- Simple formulae has no explanation yet
- Numbers on a number line has no explanation yet
- Proportional Reasoning Vocabulary has no explanation yet
- Coordinates (age 12+) has no explanation yet
- Proportion has no explanation yet
- Pictograms and tally charts (age 11+) has no explanation yet
- Comparing measurements has no explanation yet
- The Probability Scale has no explanation yet
- Complementary events has no explanation yet
- Expanding Single Brackets has no explanation yet

Credit: The structure of Manitoba curriculum: Mathematics (https://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/gr9.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.