The complete AERO Mathematics standards catalogue for grades 6–10, each mapped to the MYP Mathematics Criteria A–D it best assesses.
Select and apply mathematics to solve problems in familiar and unfamiliar situations, and communicate solutions correctly.
36 lessons · 105 AERO Math standards
Apply mathematical problem-solving techniques to recognise patterns, describe them as relationships or general rules, and justify or prove findings.
28 lessons · 48 AERO Math standards
Use appropriate mathematical language, forms of representation and logical, complete lines of reasoning.
34 lessons · 85 AERO Math standards
Identify relevant elements of authentic situations, model them mathematically and evaluate the accuracy of the model.
32 lessons · 54 AERO Math standards
Prove and apply theorems about circles, including relationships among inscribed angles, central angles, radii, chords and tangents.
Derive and use formulas for arc length and sector area, including the use of radian-style proportional reasoning.
Use permutations and combinations, together with the fundamental counting principle, to compute probabilities of compound events.
Derive and use the equation of a circle, and solve problems involving intersections of lines and circles algebraically.
Use mean and standard deviation to describe data, and use the normal distribution to estimate proportions of populations where appropriate.
Graph exponential functions, describe growth and decay, and use logarithms to solve simple exponential equations.
Solve problems involving simple and compound interest, appreciation, depreciation and inflation using exponential models.
Find inverse functions for simple functions, understand composition of functions and interpret both in context.
Work fluently with surds, rational exponents and exact values, choosing exact or approximate forms appropriately.
Add, subtract and multiply polynomials, and understand that polynomials form a system closed under these operations.
Identify zeros of polynomials when suitable factorisations are available and use the zeros to construct a rough graph of the function.
Apply the addition and multiplication rules of probability, including mutually exclusive, independent and dependent events, using Venn diagrams and tree diagrams.
Build quadratic models from data or descriptions, convert between standard, factored and vertex forms, and interpret parameters in context.
Simplify rational expressions, perform operations with them, and solve simple rational equations, identifying restrictions and extraneous solutions.
Distinguish between surveys, experiments and observational studies, evaluate sampling methods and bias, and communicate findings from a complete statistical investigation.
Solve problems involving the surface area and volume of prisms, pyramids, cylinders, cones, spheres and composite solids, including right-triangle work in three dimensions.
Identify the effect on the graph of a function of replacing f(x) by f(x) + k, k·f(x), f(kx) and f(x + k), and describe transformations of linear, quadratic and exponential graphs.
Apply the sine rule, the cosine rule and the formula Area = ½ab·sin C to find unknown measurements in any triangle.
Find the area of triangles, special quadrilaterals and polygons by composing and decomposing shapes.
Draw polygons in the coordinate plane given vertices, and use coordinates to find side lengths.
Display numerical data in plots on a number line, including dot plots, histograms and box plots.
Understand that a set of data collected to answer a statistical question has a distribution described by its centre, spread and overall shape.
Solve real-world and mathematical problems by writing and solving one-step equations of the form x + p = q and px = q.
Write inequalities of the form x > c or x < c to represent constraints, and graph their solution sets on a number line.
Use variables to represent two quantities that change in relation to one another, and analyse the relationship using tables, graphs and equations.
Write and evaluate numerical expressions involving whole-number exponents.
Write, read and evaluate expressions in which letters stand for numbers, using correct terms such as sum, term, product, factor, quotient and coefficient.
Apply the properties of operations to generate and identify equivalent expressions.
Recognise that measures of centre summarise data with a single number, while measures of variation describe how values differ.
Understand the concept of a ratio and use ratio language to describe a relationship between two quantities.
Understand the concept of a unit rate a/b associated with a ratio a:b (b ≠ 0) and use rate language in context.
Use ratio and rate reasoning to solve real-world and mathematical problems using tables, tape diagrams, double number lines and equations.
Find a percent of a quantity as a rate per 100, and solve problems involving finding the whole given a part and the percent.
Use ratio reasoning to convert measurement units and to transform units appropriately when multiplying or dividing quantities.
Recognise a statistical question as one that anticipates variability in the data related to the question.
Represent three-dimensional figures using nets and use the nets to find surface area.
Understand opposites, and interpret absolute value as distance from zero on a number line.
Order and compare rational numbers, and interpret statements of inequality on a number line.
Plot points in all four quadrants, identify reflections across the axes, and find distances between points with the same first or second coordinate.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithms.
Find greatest common factors and least common multiples, and use the distributive property to rewrite sums.
Understand that positive and negative numbers describe quantities with opposite directions or values, and use them in real-world contexts.
Summarise numerical data sets by describing measures of centre and variability, including interquartile range and mean absolute deviation.
Find the volume of right rectangular prisms with fractional edge lengths using V = lwh and V = Bh.
Use facts about supplementary, complementary, vertical and adjacent angles in multi-step problems to write and solve simple equations for an unknown angle.
Know and use the formulas for the area and circumference of a circle and explain the relationship between them.
Informally assess the degree of visual overlap of two numerical data distributions, measuring the difference between centres as a multiple of a measure of variability.
Draw geometric shapes with given conditions and notice the conditions that determine a unique triangle, more than one triangle or no triangle.
Solve multi-step real-life problems with positive and negative rational numbers in any form, using tools strategically and assessing reasonableness.
Use variables to represent quantities and construct simple equations of the form px + q = r and p(x + q) = r to solve problems, comparing algebraic and arithmetic approaches.
Solve word problems leading to inequalities of the form px + q > r or px + q < r, graph the solution set and interpret it in context.
Apply properties of operations to add, subtract, factor and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms can show how the quantities in a problem are related.
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
Add and subtract rational numbers, representing addition and subtraction on a horizontal or vertical number line, and understand that p − q = p + (−q).
Multiply and divide rational numbers, applying sign rules and understanding that quotients are rational when the divisor is not zero.
Convert a rational number to a decimal using long division, and know that the decimal form terminates or eventually repeats.
Solve real-world and mathematical problems involving the four operations with rational numbers.
Understand that the probability of a chance event is a number between 0 and 1 that expresses its likelihood.
Approximate the probability of a chance event by collecting data, and compare experimental results with a theoretical probability model.
Find probabilities of compound events using organised lists, tables, tree diagrams and simulation.
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
Decide whether two quantities are in a proportional relationship by testing equivalent ratios in a table or graphing on a coordinate plane.
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams and verbal descriptions, and represent it as y = kx.
Use proportional relationships to solve multi-step ratio and percent problems, including simple interest, tax, markup, discount, commission, tips and percent error.
Understand that statistics can gain information about a population by examining a sample, and that random sampling tends to produce representative samples.
Use data from a random sample to draw inferences about a population, generating multiple samples to gauge the variation in estimates.
Solve problems involving scale drawings of geometric figures, computing actual lengths and areas and reproducing a drawing at a different scale.
Describe the two-dimensional figures that result from slicing right rectangular prisms and right rectangular pyramids.
Establish facts about the angle sum and exterior angle of triangles, angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity.
Construct and interpret scatter plots for bivariate measurement data, describing patterns such as clustering, outliers, positive or negative association, and linear or non-linear association.
Know that straight lines model many bivariate relationships, informally fit a line of best fit and use the equation to solve problems, interpreting slope and intercept.
Understand that patterns of association in bivariate categorical data can be seen by displaying frequencies and relative frequencies in a two-way table.
Know and apply the properties of integer exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, and evaluate square roots of small perfect squares and cube roots of small perfect cubes.
Understand that a function is a rule that assigns to each input exactly one output, and that the graph of a function is the set of ordered pairs consisting of an input and its output.
Compare properties of two functions represented algebraically, graphically, numerically in tables or by verbal descriptions, and interpret the rate of change and initial value in context.
Construct a function to model a linear relationship between two quantities, determining the rate of change and initial value from a description, a table or a graph, and sketch graphs of qualitative features.
Solve linear equations in one variable, including equations with rational coefficients, expressions requiring expansion and collection of like terms, and equations with one solution, infinitely many solutions or no solution.
Graph proportional relationships, interpret the unit rate as the slope of the graph, and compare two different proportional relationships represented in different ways.
Use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line, and derive the equations y = mx and y = mx + c.
Explain a proof of the Pythagorean theorem and its converse.
Apply the Pythagorean theorem to determine unknown side lengths in right triangles in two and three dimensions, and to find the distance between two points in the coordinate plane.
Know that numbers that are not rational are called irrational, and understand that every number has a decimal expansion that is repeating, terminating or non-repeating.
Use rational approximations of irrational numbers to compare their sizes and locate them approximately on a number line.
Use numbers expressed as a single digit times an integer power of ten to estimate very large or very small quantities and to express how many times as much one is than the other.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used, and choose units of appropriate size.
Analyse and solve pairs of simultaneous linear equations graphically and algebraically, understanding that solutions correspond to points of intersection.
Verify experimentally the properties of rotations, reflections and translations of lines, line segments, angles and parallel lines.
Describe sequences of transformations that map one figure onto another, and understand congruence through rigid motions and similarity through dilations.
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
Know and use the formulas for the volumes of cones, cylinders and spheres to solve real-world and mathematical problems.
Fit a linear function to bivariate data, interpret slope and intercept in context, compute and interpret the correlation coefficient, and distinguish correlation from causation.
Prove theorems about lines, angles, triangles and parallelograms, and use congruence criteria such as SSS, SAS, ASA and RHS.
Use coordinates to compute midpoints, distances, gradients, and to prove properties of figures, including criteria for parallel and perpendicular lines.
Distinguish between situations that can be modelled with linear functions and those modelled with exponential functions, and construct exponential models from tables, graphs or descriptions.
Use function notation, evaluate functions for inputs in their domains, and interpret statements about domain and range in context.
Interpret key features of graphs and tables, including intercepts, intervals of increase and decrease, maxima, minima and symmetry, for a function that models a relationship.
Create equations and inequalities in one or two variables to represent relationships, and use them to solve problems and graph solution sets.
Describe events as subsets of a sample space, and use two-way tables and Venn diagrams to compute conditional probabilities and test independence.
Solve quadratic equations in one variable by inspection, factorising, completing the square, using the quadratic formula and graphing, and recognise when there are no real solutions.
Graph quadratic functions, identifying the vertex, axis of symmetry, intercepts, maximum or minimum and end behaviour, and relate the algebraic form to the graph.
Use units to guide the solution of multi-step problems, choose levels of accuracy appropriate to limitations of measurement, and calculate percent error.
Simplify and perform operations with radical expressions, including rationalising simple denominators.
Rewrite expressions involving radicals using rational exponents and explain the equivalence.
Understand that side ratios in right triangles are properties of the angles, define the sine, cosine and tangent ratios, and use them with the Pythagorean theorem to solve right triangles.
Write arithmetic and geometric sequences recursively and explicitly, and use them to model situations.
Use similarity criteria to establish relationships in geometric figures and solve problems involving lengths, areas and volumes of similar figures.
Interpret the structure of expressions and rewrite them in equivalent forms, including factorising quadratics and using the difference of two squares.
Solve systems of linear equations exactly and approximately, and graph solutions of systems of linear inequalities in two variables.
Represent data with plots on the real number line and compare centre, spread and shape of two or more data sets, accounting for outliers.
