Mathematics 9

What a power means

I can read and write powers, name the base and exponent, and switch between a power and repeated multiplication.

Powers with negative bases

I can evaluate powers with negative bases and explain why (−2)⁴ and −2⁴ are different numbers.

The zero exponent

I can use a pattern to explain why any non-zero base raised to the exponent 0 equals 1.

Solving problems with powers

I can use powers to solve problems about area, volume and repeated growth.

Product law

I can multiply powers with the same base by adding the exponents.

Quotient law

I can divide powers with the same base by subtracting the exponents.

Power of a power

I can raise a power to a power by multiplying the exponents.

Powers of products and quotients

I can apply an exponent across a product or a quotient.

Combining the laws

I can choose and combine the right exponent laws to simplify multi-step expressions.

What rational numbers are

I can identify rational numbers in any form and place them on a number line.

Comparing and ordering

I can compare and order rational numbers written in different forms.

Rationals between rationals

I can find a rational number between any two given rationals.

Adding and subtracting decimals

I can add and subtract positive and negative decimals.

Adding and subtracting fractions

I can add and subtract fractions and mixed numbers with any signs.

Multiplying and dividing decimals

I can multiply and divide positive and negative decimals.

Multiplying and dividing fractions

I can multiply and divide fractions and mixed numbers with any signs.

Problem solving with rationals

I can solve multi-step, real-context problems using rational numbers.

Order of operations with exponents

I can apply the order of operations, including exponents.

Order of operations with rationals

I can evaluate expressions that mix rational numbers, brackets and exponents.

Perfect squares and their roots

I can determine the square root of rational perfect squares.

Fraction and decimal perfect squares

I can recognize when a fraction or decimal is a perfect square.

Approximating square roots

I can estimate the square root of a non-perfect square using perfect-square benchmarks.

Roots between two values

I can find a number whose square root lies between two given values.

Spotting linear patterns

I can spot a linear pattern in a table, picture or story and describe how it grows.

From pattern to equation

I can write a linear equation that generalizes a pattern from a problem context.

Verify and predict

I can verify a pattern equation by substitution and use it to predict far-off terms.

Graphing a linear relation

I can build a table of values from a linear relation and graph it as a straight line.

Reading linear graphs

I can read a linear graph and describe what its features mean in the real context.

Interpolate and extrapolate

I can use a linear graph to estimate values between points (interpolate) and beyond them (extrapolate) to solve problems.

One-step equations

I can solve one-step equations like ax = b and x/a = b with rational numbers, and verify the solution.

Two-step equations

I can solve two-step equations like ax + b = c and x/a + b = c, undoing operations in the right order.

Equations with fractions and decimals

I can solve equations whose coefficients and constants are fractions or decimals.

Variables on both sides

I can solve equations with the variable on both sides, like ax = b + cx and ax + b = cx + d.

Equations with brackets

I can expand brackets and solve equations like a(x + b) = c and a(bx + c) = d(ex + f).

Modelling problems with equations

I can translate a real problem into a linear equation (including a/x = b), solve it, and check the answer against the story.

What inequalities mean

I can represent an inequality and its solution set in words, symbols and on a number line.

Solving inequalities

I can solve linear inequalities with rational coefficients, flipping the sign when multiplying or dividing by a negative.

Inequalities in context

I can model limit-situations with inequalities, solve them, and verify the solution set makes sense.

Polynomial vocabulary

I can identify the terms, coefficients, constant and degree of a polynomial (degree ≤ 2).

Modelling polynomials

I can represent polynomials with tile models and connect the picture to the symbols.

Like terms and equivalent expressions

I can identify like terms and recognize equivalent polynomial expressions.

Adding polynomials

I can add polynomial expressions (degree ≤ 2) symbolically and with models.

Subtracting polynomials

I can subtract polynomial expressions (degree ≤ 2) and explain the strategy.

Multiplying by a monomial

I can multiply a polynomial (degree ≤ 2 result) by a monomial, symbolically and with area models.

Dividing by a monomial

I can divide a polynomial by a monomial and explain each step.

Central and inscribed angles

I can use the fact that a central angle is twice the inscribed angle on the same arc to find missing angles.

Inscribed angles on the same arc

I can use the fact that inscribed angles on the same arc are congruent, and justify my reasoning.

The perpendicular-to-a-chord property

I can use the fact that the perpendicular from the centre to a chord bisects the chord.

Solving chord problems

I can combine chord properties with the Pythagorean theorem to find lengths in circles.

Tangents and radii

I can use the fact that a tangent is perpendicular to the radius at the point of tangency.

Combining circle properties

I can solve multi-step circle problems that combine tangent, chord and angle properties, justifying each step.

Surface area foundations

I can compute the surface area of right prisms and cylinders — the building blocks of composite objects.

Composite objects and overlap

I can find the surface area of composite objects, subtracting the hidden faces where solids join.

Surface-area problem solving

I can solve real-context surface-area problems — painting, wrapping, coating composite objects.

What makes polygons similar

I can decide whether polygons are similar using equal angles and proportional sides.

Solving with similarity

I can use proportions in similar polygons to find missing side lengths in real problems.

Reading scale diagrams

I can interpret scale diagrams and determine the scale factor from them.

Drawing to scale

I can draw enlargements and reductions of 2-D shapes for a given scale factor.

Line symmetry

I can identify and draw all lines of symmetry in 2-D shapes and designs.

Rotation symmetry

I can determine the order and angle of rotation symmetry of shapes and designs.

Bias, language and ethics

I can explain how bias, question language, and ethics affect what data gets collected and what it can honestly claim.

Cost, timing, privacy and culture

I can explain how cost, timing, privacy and cultural sensitivity shape real data collection, using real cases.

Population vs. sample

I can distinguish a population from a sample and recognize when each is the right way to answer a question.

Defending your choice

I can choose population or sample for a question and defend the choice with accuracy, cost and practicality.

Planning the investigation

I can formulate an investigation question and design a collection plan with social considerations and a population-or-sample choice.

Collecting and displaying

I can collect data by my plan and display it in an appropriate, honest format.

Analyzing and concluding

I can analyze displayed data and draw conclusions that actually answer the investigation question.

Probability in everyday decisions

I can explain how probability is used in society and interpret what stated probabilities actually mean.

Assumptions behind the numbers

I can identify the assumptions behind a stated probability and how probabilities get misused or misread.