# High school: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 28 concepts ready. In the app: https://ai.page/roadmap/ca-on-high-school Part of: [Ontario: Mathematics](https://ai.page/roadmap/ca-on.md) Goal: Ontario curriculum: Mathematics, High school ## 1. Geometry and Measurement · Geometric and Measurement Relationships: demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to - [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 - [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 - [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 - [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 ## 2. Data · Mathematical Modelling: apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into r - [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 - [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. Data · Collection, Representation, and Analysis of Data: describe the collection and use of data, and represent and analyse data involving one and two variables - [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. Algebra · Application of Relations: represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions - [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 ## 5. Algebra · Coding: apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands - [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 ## 6. Number · Number Sense and Operations: apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems - [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 - [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 - [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% ## 7. Number · Powers: represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents - [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 ## 8. Trigonometric Functions · Connecting Graphs and Equations of Sinusoidal Functions: demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the num - [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 ## 9. Trigonometric Functions · Determining and Applying Trigonometric Ratios: determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve pr - [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 ## 10. Discrete Function · Investigating Arithmetic and Geometric Sequences and Series: demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve - [Generating Sequences](https://ai.page/c/generating-sequences/index.md): Generate terms of a sequence from a term-to-term rule (e.g., 'add 3 each time') or a position-to-term rule (e.g., '2n + 1'), and identify whether a sequence is arithmetic, geometric, or neither ## 11. Discrete Function · Representing Sequences: demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal's triangle; - [Nth-Term Rules](https://ai.page/c/nth-term-rules/index.md): Find the nth-term expression for an arithmetic sequence by identifying the common difference and the zero-term, and use it to determine any term in the sequence or test whether a given number belongs to the sequence - [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 ## 12. Exponential Functions · Connecting Graphs and Equations of Exponential Functions: make connections between the numeric, graphical, and algebraic representations of exponential functions; - [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 ## 13. Exponential Functions · Representing Exponential Functions: evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represe - [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 ## 14. Data Management · Working With One-Variable Data: solve problems involving one-variable data by collecting, organizing, analysing, and evaluating data; - [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 ## 15. Trigonometric Functions · Understanding and Applying Radian Measure: demonstrate an understanding of the meaning and application of radian measure; - [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 ## 16. Probability Distributions: · Understanding Probability Distributions for Continuous Random Variables: demonstrate an understanding of continuous probability distributions, make connections to discrete - [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 ## 17. Probability Distributions: · Understanding Probability Distributions for Discrete Random Variables: demonstrate an understanding of discrete probability distributions, represent them numerically, grap - [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 ## 18. Applications of Geometry · Solving Problems Involving Circle Properties: determine circle properties and solve related problems, including those arising from real-world applications - [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 ## 19. Trigonometry · Investigating Similarity and Solving Problems Involving Similar Triangles - [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 ## 20. Analytic Geometry · Solving Problems Involving Properties of Line Segments - [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 - [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 ## Health: 0 of 100 Of its 28 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): - Proportion comes before Proportional Reasoning Vocabulary, which it needs - Proportion comes before Proportion Graphs, which it needs - Proportion comes before Ratio Notation and Relationships, which it needs - Proportion has no explanation yet - Coordinate Transformations has no explanation yet - Compound Units comes before Proportional Reasoning Vocabulary, which it needs - Compound Units has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Algebraic Transformations comes before Solving Linear Equations, which it needs - Algebraic Transformations has no explanation yet - Estimating answers (age 13+) comes before Plotting Linear Graphs, which it needs - Estimating answers (age 13+) has no explanation yet - Scatter Graphs & Correlation comes before Comparing measurements, which it needs - Scatter Graphs & Correlation has no explanation yet - Linear Function Graphs has no explanation yet - Solving Linear Equations has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Number Sets & Infinity comes before Square and cube numbers, which it needs - Number Sets & Infinity 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 - Proportion Graphs has no explanation yet - Trigonometry basics has no explanation yet - Generating Sequences has no explanation yet - Nth-Term Rules has no explanation yet - Numbers on a number line has no explanation yet - Quadratic Graphs comes before Plotting Linear Graphs, which it needs - Quadratic Graphs has no explanation yet - Square and cube numbers has no explanation yet - Comparing measurements has no explanation yet - Ratio Notation and Relationships has no explanation yet - The Probability Scale has no explanation yet - Tree diagrams has no explanation yet - Circles: Circumference & Area has no explanation yet - Simultaneous Equations comes before Plotting Linear Graphs, which it needs - Simultaneous Equations has no explanation yet - Plotting Linear Graphs has no explanation yet - Angles with parallel lines has no explanation yet Credit: The structure of Ontario curriculum: Mathematics (https://www.dcp.edu.gov.on.ca/en/curriculum/secondary-mathematics/courses/mth1w); 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.