Mathematics, Secondary 2

Meanings of a fraction: part of a whole, division, ratio, operator, measure

I can identify the different meanings of a fraction: part of a whole, a division, a ratio, an operator and a measurement.

Recognizing ratios and rates

I can recognize a ratio and a rate and tell the two apart.

The concept of absolute value

I can define and use absolute value as a distance, for example the difference between two numbers or the distance between two points.

Squares and square roots

I can compute squares and square roots within a sequence of operations.

Powers with integral exponents

I can compute numbers in exponential notation with integral exponents.

Sequences of operations in the correct order

I can compute, in writing, sequences of operations on decimals following the order of operations, with up to two levels of parentheses.

Order of magnitude with scientific notation

I can estimate the order of magnitude of a real number using scientific notation.

Comparing numbers across notations

I can compare numbers expressed in different ways: fractional, decimal, exponential, percentage, square root and scientific notation.

Approximating the result of a calculation

I can approximate the result of an operation or a sequence of operations to check reasonableness.

Comparing ratios and rates qualitatively

I can compare ratios and rates qualitatively (equivalent rates and ratios, unit rate).

Comparing ratios and rates quantitatively

I can compare ratios and rates quantitatively using equivalent rates, ratios and unit rates.

Representing numbers in fractional or decimal notation

I can represent, read and write a number in fractional or decimal notation and choose the clearer form for a situation.

Translating a situation with a ratio or a rate

I can translate a situation into a ratio or a rate and write it correctly.

Operating on positive fractions

I can carry out operations on positive numbers written in fractional notation, with or without objects or diagrams.

Recognizing a proportional situation

I can recognize a proportional situation from its context, a table of values or a graph.

Finding the whole from a percentage

I can find the value corresponding to 100 per cent when given a part and its percentage.

Interpreting ratios and rates

I can interpret a ratio or a rate in context and explain what it tells us.

Effect of changing a term in a ratio or rate

I can describe the effect of changing a term in a ratio or a rate.

Representing a proportional situation

I can represent or interpret a proportional situation using a graph, a table of values or a proportion.

Solving proportional situations with strategies

I can solve proportional situations (direct or inverse variation) using strategies such as the unit-rate method, factor of change, or a proportion.

The idea of an unknown

I can identify and use an unknown — a specific value a letter stands for that we solve to find.

Variables and constants

I can identify variables and constants in an expression or situation.

The idea of a parameter

I can identify a parameter — a constant in a rule that sets its shape but can be changed between situations.

Vocabulary of algebraic expressions

I can use the terms coefficient, degree, term, constant term and like terms correctly.

Distinguishing an unknown from a variable

I can distinguish an unknown (a value to find) from a variable (a quantity that varies).

Building an algebraic expression

I can construct an algebraic expression from a situation using an appropriate representation.

Representing an equation another way

I can represent an equation using another type of representation when it helps.

Interpreting an algebraic expression in context

I can interpret an algebraic expression in light of the context it models.

Equivalent algebraic expressions

I can recognize or construct equivalent algebraic expressions.

Transforming equalities to keep them balanced

I can transform equalities and equations to maintain equivalence, and justify each step.

Transforming equalities and equations

I can transform equalities and equations to maintain equivalence and justify the steps.

Evaluating an algebraic expression

I can calculate the numeric value of an algebraic expression for given values.

Describing a pattern with an equation

I can describe, in words and in mathematical language, a numerical pattern using an equation.

Operating on algebraic expressions

I can add, subtract, multiply and divide algebraic expressions by a constant, and multiply first-degree monomials.

Describing relations or formulas

I can describe, in words and mathematical language, a series of numbers using relations or formulas.

Analyzing a situation across representations

I can analyze a situation using different types of representation and move between them.

Factoring out a common factor

I can factor out the common factor in numerical or algebraic expressions using distributivity.

Manipulating and rearranging formulas

I can manipulate relations or formulas, for example isolating one element.

Representing a situation with a graph

I can represent a situation generally using a graph.

Solving first-degree equations ax + b = cx + d

I can use different methods to solve first-degree equations of the form ax + b = cx + d.

Validating a solution by substitution

I can validate a solution, with or without technological tools, by substituting it back.

Interpreting solutions and making decisions

I can interpret solutions or make decisions, if necessary, depending on the context.

Decomposing plane figures

I can decompose plane figures into circles (sectors), triangles or quadrilaterals to measure them.

Right prisms, cylinders and pyramids

I can identify right prisms, right cylinders and right pyramids and their parts.

Constructing the image under a dilatation

I can construct the image of a figure under a dilatation with a positive scale factor.

Justifying statements about lengths

I can justify statements concerning measures of length.

Area of circles and sectors

I can compute the area of circles and of sectors.

Area of composite figures

I can compute the area of figures that split into circles (sectors), triangles or quadrilaterals.

Lateral and total area of prisms, cylinders, pyramids

I can compute the lateral or total surface area of right prisms, right cylinders and right pyramids.

Surface area of decomposable solids

I can compute the lateral or total area of solids that split into right prisms, cylinders or pyramids.

Area under an isometry

I can find the area of figures resulting from an isometry.

Area under a similarity transformation

I can find the area of a figure resulting from a similarity transformation.

Describing circles and sectors

I can describe circles and sectors and their parts.

Justifying statements about area

I can justify statements concerning measures of area.

Lines and segments in figures

I can identify a diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter and chord.

Justifying with congruence, similarity, equivalence

I can justify statements using definitions or properties of congruent, similar or equivalent figures.

Justifying with angle properties

I can justify statements using definitions or properties associated with angles and their measures.

Properties of plane figures via transformations

I can identify properties of plane figures using geometric transformations and constructions.

Justifying with properties of plane figures and solids

I can justify statements using definitions or properties of plane figures and solids.

Nets of a solid

I can determine the possible nets of a solid.

Properties and invariants of transformations

I can identify properties and invariants resulting from geometric constructions and transformations.

Recognizing congruent or similar figures

I can recognize congruent or similar figures.

Naming the solid from a net

I can name the solid that corresponds to a given net.

Identifying congruence via transformations

I can identify congruence (translation, rotation and reflection) between two figures.

Recognizing the transformation between a figure and its image

I can recognize the geometric transformation(s) linking a figure and its image.

Types of angles formed by lines

I can describe complementary, supplementary, adjacent, vertically opposite, alternate and corresponding angles.

Relationships between SI units of area

I can establish relationships between SI units of area.

Altitude, apothem and lateral face

I can identify the altitude, the apothem and the lateral face of a solid.

Constructing the image under a transformation

I can construct the image of a figure under a translation, rotation or reflection.

Properties and invariants of congruent or similar figures

I can determine the properties and invariants of congruent or similar figures.

Duration versus position in time

I can distinguish between duration and position in time.

Finding angle measures using angle properties

I can determine angle measures using properties of complementary, supplementary, vertically opposite, alternate and corresponding angles.

Perimeter and circumference relations

I can construct and use relations to calculate the perimeter or circumference of figures.

Constructing area relations

I can construct and use relations to calculate the area of quadrilaterals, triangles and circles (sectors).

Recognizing a dilatation

I can recognize a dilatation (enlargement or reduction) with a positive scale factor.

Central angles and arcs

I can find degree measures of central angles and their arcs.

Segments and lengths in a plane figure

I can identify and measure segments in a plane figure: circumference, radius, diameter, arc length, and segments from an isometry or similarity.

Metric relations in plane figures

I can determine, through exploration or deduction, different metric relations in plane figures.

Locating numbers on an axis

I can locate objects or numbers on an axis, based on the types of numbers studied.

Locating points in the Cartesian plane

I can locate points in a Cartesian plane using x- and y-coordinates.

Stratified and cluster sampling

I can choose and describe stratified and cluster sampling methods.

Choosing a representative sample

I can choose a representative sample of a population.

Recognizing sources of bias

I can recognize possible sources of bias in a survey or study.

Types of statistical variables

I can distinguish qualitative, discrete quantitative and continuous quantitative variables.

Frequency tables and circle graphs

I can represent data in a table of variables or frequencies, or using a circle (pie) graph.

Comparing one-variable distributions

I can compare two one-variable distributions.

The concept of the arithmetic mean

I can describe the arithmetic mean as a levelling or balance point.

Calculating and interpreting the mean

I can calculate and interpret an arithmetic mean.

Range and interquartile range

I can find the range of each part of a box-and-whisker plot and the interquartile range.

Percentiles

I can find and interpret a percentile.

Choosing the appropriate statistical measure

I can choose the appropriate statistical measures for a given situation.

Multi-step random experiments

I can conduct or simulate random experiments involving one or more steps (with or without replacement, with or without order).

Networks, tables and Venn diagrams

I can use networks, tables and Venn diagrams to organize outcomes.

Odds versus probability

I can choose and apply the concept of odds (odds for and odds against).

Types of events

I can recognize certain, probable, impossible, simple, complementary and compatible events.

Mutually exclusive and independent events

I can distinguish mutually exclusive from non-mutually-exclusive events, and dependent from independent events.

Theoretical versus experimental probability

I can distinguish theoretical from experimental probability.

Calculating the probability of an event

I can calculate the probability of an event.