Grade 9 Math: Alberta Curriculum & PAT Prep

Grade 9 Math curriculum: 9 units, 45 lessons (Alberta Mathematics (Grade 9))

Unit 1: Square Roots & Surface Area

• Perfect Squares Review, Warm up for the PAT year by recalling why numbers like 16, 49, and 144 are perfect squares — each is the area of a square with whole-number sides.
• Square Roots of Perfect Squares, Undo squaring to evaluate square roots exactly: the root of 81 is 9 because 9 times 9 gives 81 — no estimating required.
• Square Roots of Non-Perfect Squares, Estimate square roots of non-perfect squares by trapping them between perfect squares — root 20 sits between 4 and 5, just under 4.5.
• Surface Area of Right Rectangular Prisms, Calculate the surface area of a right rectangular prism by finding all six face areas and adding them up — nets make every face easy to see.
• Surface Area of Composite Objects, Break a composite object into simpler solids, total the exposed faces, and subtract the overlapping areas hidden where the pieces join.

Unit 2: Powers & Exponent Laws

• What are Powers?, Powers turn repeated multiplication into shorthand — write 2 x 2 x 2 x 2 x 2 as 2^5, then name the base, the exponent, and the value.
• Powers of Ten & Zero Exponents, See why any nonzero base raised to the exponent zero equals 1, and use powers of ten like 10^3 = 1000 to write large numbers compactly.
• Order of Operations with Powers, Apply BEDMAS when powers appear mid-expression — evaluate exponents before multiplying, and see how (-3)^2 differs from -3^2.
• Exponent Laws 1: Multiply and Divide Powers, Multiply powers with the same base by adding exponents, and divide by subtracting — turn 3^4 x 3^2 into 3^6 without expanding anything.
• Exponent Laws Part II: Power, Product, and Quotient Rules, Raise a power to a power by multiplying exponents, then extend the laws to products and quotients like (2 x 5)^3.

Unit 3: Rational Numbers

• Introduction to Rational Numbers, Rational numbers cover every fraction, terminating or repeating decimal, and integer in Grade 9 — compare them and place them on a number line.
• Adding Rational Numbers, Add positive and negative fractions, decimals, and mixed numbers by building common denominators and keeping careful track of signs.
• Subtracting Rational Numbers, Subtract rational numbers by adding the opposite, handling negatives like 3/4 - (-1/2) and mixed numbers without sign slips.
• Multiplying Rational Numbers, Multiply fractions, decimals, and mixed numbers, using sign rules to decide whether each product lands positive or negative.
• Dividing Rational Numbers, Divide fractions by multiplying by the reciprocal, then carry the same sign rules through decimals and mixed numbers.
• Order of Operations with Rational Numbers, BEDMAS still rules when fractions and decimals mix — clear brackets and exponents first, then multiply, divide, add, and subtract in order.

Unit 4: Linear Equations

• Writing Equations from Patterns, From number patterns to algebra — find the constant difference in a table of values and write the linear equation that predicts any term.
• Understanding and Graphing Linear Relations, Graph linear relations from a table or an equation, and see why a constant rate of change lines the points up perfectly straight.
• Slope and the Equation of a Line, Measure steepness as rise over run, then connect slope and y-intercept to write the equation of a line in y = mx + b form.
• Matching Equations and Graphs, Match each linear equation to its graph by checking slope direction, steepness, and where the line crosses the y-axis.

Unit 5: Polynomials

• Introduction to Polynomials, Name the parts of a polynomial — terms, coefficients, constants, and degree — and classify monomials, binomials, and trinomials.
• Like Terms and Simplifying Polynomials, Combine like terms to simplify polynomials: 3x + 5x collapses to 8x, while 3x and 3x^2 must stay separate.
• Adding Polynomials, Add polynomials by grouping like terms across brackets — line up the x^2 terms, x terms, and constants before combining.
• Subtracting Polynomials, Subtract one polynomial from another by flipping every sign in the second bracket, the classic spot where dropped negatives cost marks.
• Multiplying Polynomials by a Constant and Monomial, Distribute a constant or a monomial across every term: 3x(2x + 4) expands to 6x^2 + 12x, one product at a time.
• Dividing Polynomials by a Constant and Monomial, Divide a polynomial by a constant or monomial one term at a time — 6x^2 + 9x divided by 3x becomes 2x + 3. Check by multiplying back.

Unit 6: Linear Equations & Inequalities

• Solving One-Step and Two-Step Equations, Solve one- and two-step equations like 2x + 3 = 11 by undoing operations in reverse order — subtract 3 first, then divide by 2.
• Balancing Equations: Variables on Both Sides, Collect variables on one side and constants on the other to solve equations like 5x - 2 = 3x + 8, keeping both sides balanced at every step.
• Introduction to Linear Inequalities, Translate phrases like at most and at least into inequality symbols, then graph solution sets on a number line using open or closed dots.
• Solving Inequalities with Addition and Subtraction, Keep the inequality sign pointing the same way while you add or subtract the same amount from both sides to isolate the variable.
• Solving Inequalities with Multiplication and Division, Multiply or divide both sides of an inequality, and learn why the sign flips the moment the multiplier or divisor is negative.

Unit 7: Similarity & Transformations

• Scale Diagrams, Enlargements & Reductions, Use scale factors to enlarge or reduce a diagram — a factor of 2 doubles every length, while a factor of 1/2 shrinks it to half size.
• Similar Polygons, Test whether two polygons are similar by matching equal angles and checking that all pairs of corresponding sides share one ratio.
• Similar Triangles, Similar triangles share their angle measures, so a proportion of corresponding sides lets you solve for missing heights and distances.
• Reflections & Line of Symmetry, Reflect shapes across a mirror line and count lines of symmetry — one in an isosceles triangle, four in a square.
• Rotations & Rotational Symmetry, Rotate figures by 90, 180, or 270 degrees and describe rotational symmetry by its order — a square matches itself four times in one full turn.
• Identifying Symmetry on the Cartesian Plane, Locate line and rotational symmetry on the Cartesian plane, using coordinates to confirm mirror images and centres of rotation.

Unit 8: Circle Geometry

• Properties of Tangents to a Circle, A tangent touches a circle at exactly one point and meets the radius there at 90 degrees — use that fact to find missing angles and side lengths.
• Properties of Chords in a Circle, Chords follow a reliable rule — the perpendicular from the centre of a circle bisects the chord — and it unlocks missing lengths fast.
• Properties of Angles in a Circle, Compare inscribed and central angles standing on the same arc: the central angle is always double the inscribed one.

Unit 9: Probability & Statistics

• Probability in Society, Probability shows up in forecasts, games, and opinion polls — weigh the chances, then question the assumptions behind each claim.
• Potential Problems with Collecting Data, Spot bias, leading questions, timing, and privacy issues that can skew survey results before any data even gets collected.
• Using Samples and Populations to Collect Data, Decide when to survey an entire population and when a sample has to do, and weigh what each choice means for your conclusions.
• Selecting a Sample, Choose among random, stratified, and convenience samples, then defend which method best represents the population being studied.
• Designing a Project Plan, Plan a complete statistics project — pose a question, choose a data collection method, and map out how results will be analyzed and shared.

Frequently asked questions

What's on the Grade 9 math PAT?

The Grade 9 PAT covers the whole Alberta Grade 9 math curriculum: Square Roots & Surface Area, Powers & Exponent Laws, Rational Numbers, Linear Equations, Polynomials, Linear Equations & Inequalities, Similarity & Transformations, Circle Geometry, Probability & Statistics. It has a calculator-free Part A and a longer Part B with a calculator, written near the end of the school year.

How many units are in Alberta Grade 9 math?

Grade 9 Math on Studyio has 9 units: Square Roots & Surface Area, Powers & Exponent Laws, Rational Numbers, Linear Equations, Polynomials, Linear Equations & Inequalities, Similarity & Transformations, Circle Geometry, Probability & Statistics. That's 45 lessons in total, matching the Alberta curriculum from the first unit through exam review.

How do I prepare for the Grade 9 PAT?

Start early and work unit by unit instead of cramming the week before. Redo quizzes until you can solve each question without hints, then write timed PAT-style practice tests to build exam stamina. Studyio includes PAT practice with instant feedback and step-by-step solutions for every question.

Is Studyio aligned to the Alberta curriculum?

Yes. Every Grade 9 Math lesson on Studyio follows the Alberta Program of Studies: the same units, in the same order, they're taught in class. The course has 9 units and 45 lessons, each with a voice-over walkthrough, worked examples, and a practice quiz with step-by-step solutions.

Is Studyio free?

Yes. Studyio is free to start, with no credit card required. The free plan includes lesson access, unlimited quizzes, and step-by-step solutions. Pro, $7.99 a month or $73.99 a year after a 7-day free trial, unlocks unlimited Provincial Achievement Test (PAT) practice and unlimited help from Ms. Emma, Studyio's AI tutor.