Foundations of Mathematics, Grade 10 (Applied)
Ontario · Grade 10 · Mathematics — the complete curriculum-aligned outline, taught skill by skill by MapleMind's AI tutor.
3Units
9Lessons
34Skills
Unit 1: Measurement and Trigonometry
Similar triangles and right-triangle trigonometry, using the imperial and metric systems for everyday measurement, and finding surface area and volume of common 3-D figures, including the sphere.
Similar Triangles
- Verifying properties of similar triangles
- Finding side lengths in similar triangles
- Solving real problems with similar triangles
Right-Triangle Trigonometry
- Defining the sine, cosine, and tangent ratios
- Finding sides and angles in right triangles
- Solving real-life right-triangle problems
- Exploring how an occupation uses trigonometry
Surface Area and Volume, Imperial and Metric
- Using the imperial system to solve measurement problems
- Converting between imperial and metric measurements
- Finding the surface area of a pyramid
- Solving surface area and volume problems
- Developing the volume formula for a sphere
Unit 2: Modelling Linear Relations
Solving first-degree equations and formulas, graphing and writing equations of lines, and solving and interpreting systems of two linear equations.
Solving First-Degree Equations
- Solving first-degree equations, including fractional coefficients
- Finding the value of a variable using a formula
- Rewriting a line's equation in y = mx + b form
Graphing and Writing Equations of Lines
- Connecting rate of change to slope
- Recognizing y = mx + b and the special cases x = a, y = b
- The geometric meaning of m and b
- Exploring properties of slope
- Graphing lines by hand
- Determining a line's equation from a graph, slope-intercept, slope-point, or two points
Solving and Interpreting Systems of Linear Equations
- Finding the point of intersection graphically
- Solving linear systems algebraically
- Solving realistic problems with linear systems
Unit 3: Quadratic Relations
Expanding, factoring, and graphing quadratic relations, and solving problems by interpreting quadratic graphs — a graphical-first approach without completing the square or the quadratic formula.
Identifying Characteristics of Quadratic Relations
- Expanding and simplifying products and squares of binomials
- Factoring binomials and trinomials using a common factor
- Factoring simple trinomials x² + bx + c
- Factoring the difference of squares
Graphing Quadratic Relations
- Collecting and graphing quadratic data
- Recognizing a parabola from a table of second differences
- Identifying the key features of a parabola
- Comparing standard-form and factored-form graphs
Solving Problems by Interpreting Graphs of Quadratic Relations
- Solving quadratic problems by interpreting a graph
- Interpreting key features from an experimental quadratic graph
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