About this Resource
This resource outlines the latest Mathematics Grades 7-9 KUSPs.
Draft Mathematics (7–9) Curriculum
August 30, 2026
Mathematics is a universal language relying on a shared understanding of symbols and procedures to communicate ideas efficiently. It is a powerful tool used every day to solve real-world problems. The beauty of mathematics inspires curiosity about our world and the universe. Mathematics involves learning across various disciplines, including arithmetic, algebra, geometry, statistics, and probability. In all disciplines, procedures may range from counting, calculating, and measuring to analyzing, modelling, and generalizing. Engaging with mathematics allows students to develop logical thinking skills, which contribute to effective decision making and problem solving. Students are able to extend their thinking beyond personal experiences through flexible and collaborative learning opportunities. Mathematics experiences provide students with opportunities to build foundational numeracy skills through engagement with various types of quantitative and spatial information.
Numeracy is a foundational building block of learning and is developed in all subjects in various ways. Central to the development of numeracy, the mathematics curriculum helps students acquire and apply the knowledge and skills necessary to engage with quantitative and spatial information in a variety of situations. Numeracy focuses on counting, comparing, and calculating with numbers; describing, representing, and measuring shapes and objects; collecting, organizing, and interpreting data; and creating and interpreting diagrams, graphs, and tables. Numeracy skills support real-world pursuits, including managing time, using and managing finances, following instructions, understanding statistics, navigating with maps, and reading schedules and statements. With a focus on numeracy, the mathematics curriculum provides all students with a solid foundation of mathematical knowledge, understanding, and skills to set them up for future success.
Mathematics education is an ongoing process of connecting students’ concrete experiences to their comprehension of abstract concepts. A recognition of numbers and their application to counting and comparing form foundational knowledge and skills for students as they encounter a variety of quantitative information in their lives. The development of these skills supports students as they participate in family, community, and cultural activities. As their experiences broaden, students also learn that operations with numbers provide reliable and efficient options to counting and comparing. Students acquire knowledge of basic number facts that can be applied to operations with various types of numbers, including natural, integer, and rational numbers, when using commonly recognized algorithms. Students also communicate by using conventional mathematical symbols, notation, and vocabulary. As students are exposed to more and varied quantitative information, they learn about different types of numbers and their applications to various situations, such as decimals for money, integers for temperature, and fractions for baking and construction. In developing algebraic thinking skills, students transfer their understandings of properties of numbers to new contexts.
Although mathematics is often considered the study of numbers, it also provides the tools to interpret spatial information in the world. The earliest mathematical experiences of children involve exploration of the space and objects around them. Mathematics provides the foundations for precisely describing, defining, and measuring spatial information. Students learn geometric properties that define shapes and angles, and can communicate the relationships by using symbols and symbolic notation. They also develop an understanding of measurement, progressing from direct comparison, to accurately measuring with various standard units and tools, to applying formulas for area, surface area, and volume. Students extend their application of spatial knowledge and skills from concrete to abstract situations, precisely describing location and movement of shapes in a plane. Building an understanding of geometric properties, theorems, and formulas enables students to appreciate complex patterns within traditional cultural designs, solve real-world problems, and propose innovative solutions.
Through their educational experiences, students develop competencies that work together with learning outcomes to support successful learning and application of mathematics in their lives. Students apply their foundational knowledge, understandings, skills, and procedures to solve problems. They visualize and reason to move from what is known to what is sought. Thinking logically about a problem, choosing a strategy, reaching a conclusion, and justifying the solution help students develop confidence in their mathematical thinking and decision making. As students collaborate with others and explain their processes and thinking, they develop the ability to communicate thoughtfully and clearly. These competencies reinforce both literacy and numeracy skills and continue to develop throughout students’ lives to support a wide variety of needs, such as financial literacy.
Competencies, along with the foundational knowledge and skills of mathematics, are important contributions to the future success of students. Students will apply abilities in computation, managing information, reasoning, and problem solving in daily life and in future educational pursuits and careers. Mathematics will help students interact in society with confidence and intellectual curiosity. Students will rely on their mathematical knowledge and skills as they continue into adulthood in our interconnected and ever-changing world.
Note: Formulas are expressed symbolically in the curriculum to indicate conventional notation. Students are not required to memorize formulas to achieve the learning outcomes.
From Kindergarten to Grade 6, students are actively building foundational skills related to computation; for this reason, the learning outcomes in K–6 mathematics are intended to be achieved without the support of calculators. However, classroom activities are not always focused on learning and practising computational skills. Teachers may choose to allow students to use a calculator to reduce cognitive load while they engage in an activity, such as solving a puzzle or a problem, where computational skills are not the focus. The K–6 learning outcomes, however, must be assessed without students’ use of a calculator.
At all levels, students should develop the ability to choose tools suited to the mathematical task. As students advance to grades 7–9, technology can enhance their ability to explore and understand new mathematical concepts. The use of calculators in the Number organizing idea should be introduced progressively to allow time for students to develop a strong foundation of number sense. Students should see the value in a variety of tools and be confident to make choices that support learning.
| Grade 7 | |||
| Organizing Idea | Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations. | ||
| Guiding Question | How can the symmetry of the number line contribute to a sense of number? | ||
| Learning Question | Students analyze positive and negative numbers. | ||
| Knowledge | Understanding | Skills & Procedures | |
Absolute value represents the magnitude of any number from zero. A negative fraction can be expressed equivalently as Negative decimal numbers can be found in real-world situations, such as
| Every fraction and decimal number has an additive inverse with the same absolute value and opposite sign. | Relate the absolute value of positive and negative numbers, including decimal numbers and fractions, to their positions on the number line. Convert between fractions and decimal numbers, including negative numbers. Compare and order positive and negative numbers, including decimal numbers and fractions. Discuss real-world situations involving negative decimal numbers. | |
| Grade 7 | |||
| Organizing Idea | Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations. | ||
| Guiding Question | How can operations on positive and negative numbers be understood? | ||
| Learning Question | Students apply operations to positive and negative numbers. | ||
| Knowledge | Understanding | Skills & Procedures | |
The symbol, −, can indicate a negative number or the subtraction operation. Addition does not always result in a greater number, and subtraction does not always result in a smaller number. Subtraction can be expressed as addition, i.e., a − b = a + (−b). Addition and subtraction of positive and negative numbers can be supported by various processes for adding and subtracting decimal numbers and fractions, such as
| Addition and subtraction of integers can be represented as numerical expressions. | Distinguish the meaning of the symbol, −, represented in a numerical expression. Add and subtract any two integers. Assess the reasonableness of a sum or difference of two integers. Solve problems involving addition and subtraction of integers. | |
The product or quotient of
Multiplication can be represented symbolically in various ways, i.e., a × b, a ⋅ b, a(b), and (a)(b). Any negative number can be expressed as the product of its inverse and −1, i.e., −a = −1(a). | Products and quotients can be represented as numerical expressions in infinitely many ways. | Multiply and divide any two integers. Investigate whether a product or quotient of three or more integers will be positive or negative. Create various expressions of the same product, using positive and negative factors. Assess the reasonableness of a product or quotient of integers. Solve problems involving multiplication and division of integers. | |
| Grade 7 | |||
| Organizing Idea | Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations. | ||
| Guiding Question | How can different representations provide new perspectives of squares and cubes? | ||
| Learning Question | Students interpret perfect squares and perfect cubes. | ||
| Knowledge | Understanding | Skills & Procedures | |
The product of two identical factors is a perfect square. A perfect square can be expressed symbolically as repeated multiplication or as a power with the exponent two, i.e., a × a = a2. The square root of a perfect square is one of the two identical factors and can be expressed symbolically by using a radical sign, √□. A perfect square can be represented by the area of a square, while the side length can be expressed as a square root. | A square can be interpreted as a number and as a shape. | Identify the base and exponent in a perfect square. Model a given perfect square as a square region. Express perfect squares and square roots symbolically. Recall perfect squares within 144 and their square roots, limited to natural numbers. Solve problems involving perimeter and area of squares, limited to side lengths that are natural numbers. | |
The product of three identical positive factors is a perfect cube. A perfect cube can be expressed symbolically as repeated multiplication or as a power with the exponent three, i.e., a × a × a = a3. The cube root of a perfect cube is one of the three identical natural number factors and can be expressed symbolically by using a radical sign, ∛□. The volume of a cube can be represented by a perfect cube, while the length of an edge can be expressed as a cube root. | A cube can be interpreted as a number and as a shape. | Identify the base and exponent in a perfect cube. Model a given perfect cube as a cubic region. Express perfect cubes and cube roots symbolically. Recall perfect cubes within 125 and their cube roots, limited to natural numbers. Solve problems involving volume of cubes, limited to edge lengths that are natural numbers. | |
| Grade 7 | |||
| Organizing Idea | Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations. | ||
| Guiding Question | How can multiplication and division be generalized? | ||
| Learning Question | Students interpret multiplication and division of positive fractions and of positive decimal numbers. | ||
| Knowledge | Understanding | Skills & Procedures | |
The product of two fractions is the fraction resulting from multiplication of the numerators and multiplication of the denominators, i.e., Multiplication of two fractions can be represented by a model, e.g., an area model. The product of two proper fractions is less than its factors. A proper fraction is a fraction in which the numerator is less than them denominator. The product of two fractions is equivalent to the product of any equivalent forms of those fractions. | The product of two fractions can be interpreted as part of a part. | Model multiplication of fractions. Relate the product of a fraction by a fraction to part of a part. Multiply two fractions. Compare products of fractions in various equivalent forms, including simplest form. Solve problems involving multiplication of two fractions. | |
Division by a fraction is equivalent to multiplication by its reciprocal, i.e., A reciprocal is the multiplicative inverse of a fraction. The product of a fraction and its reciprocal is 1. The quotient of a number and a proper fraction is greater than the number. Division of two fractions can be facilitated by representing the fractions with common denominators. The quotient of two fractions with common denominators is the quotient of the two numerators, i.e., | The quotient of any quantity and a fraction can be interpreted as the number of fraction-sized groups that compose the quantity. | Relate a number to its reciprocal. Prove that multiplication of a fraction and its reciprocal is 1. Divide a natural number by a fraction and vice versa. Divide a fraction by a fraction. Investigate the composition of a quantity by fraction-sized groups. Solve problems involving division of two fractions. | |
Multiplication and division of a decimal number by a decimal number can be supported by processes, such as
Equivalent division expressions can be created when dividing decimal numbers by multiplying the divisor and dividend by the same factor. | Equivalent expressions can facilitate multiplication and division of decimal numbers. | Multiply and divide decimal numbers, including dividing a natural number by a decimal number. Solve problems involving decimal numbers, including in real-world situations | |
The conventional order of operations applies to integers, fractions, and decimal numbers. | Equivalent forms of mathematical expressions can facilitate evaluation. | Evaluate numerical expressions according to the order of operations. | |
| Grade 7 | |||
| Organizing Idea | Number: Numbers are organized into systems with unique notation to communicate quantities and to facilitate calculations. | ||
| Guiding Question | In what ways can proportional relationships be characterized? | ||
| Learning Question | Students analyze multiplicative relationships between equivalent ratios. | ||
| Knowledge | Understanding | Skills & Procedures | |
The terms of a ratio can be any numbers, including integers, decimal numbers, or fractions. The first term of a ratio can be less than or greater than the second term. A ratio can be iterated by multiplying both terms by the same factor, e.g., A ratio can be partitioned by dividing both terms by the same factor, e.g., Equivalent ratios are related by a factor. The factor relating equivalent ratios can be a natural number, decimal number, or fraction. A proportional relationship expressed as a/b = c/d is equivalent to ad = bc. The first terms and the second terms of two equivalent ratios can be added or subtracted, respectively, to generate another equivalent ratio. Equal first terms or equal second terms can facilitate the comparison of ratios. A percentage can be represented as a ratio, i.e., A ratio can be converted into a percentage by multiplying by 100. A percentage can be interpreted as a sum of benchmark percentages, including 1%, 5%, 10%, 25%, 50%. A percentage can be less than 1% or greater than 100%. Proportional reasoning can be applied in real-world situations, including
| Multiplicative relationships are foundational to proportional reasoning. | Generate equivalent ratios by iterating or partitioning a ratio. Determine the factor that relates equivalent ratios. Determine an unknown value in given equivalent ratios. Generate an equivalent ratio, using two existing equivalent ratios. Compare two ratios that have common first or second terms. Determine a percentage of a natural number by iterating or partitioning benchmark percentages. Determine percentages of natural numbers less than 1% and greater than 100%. Solve problems involving proportional reasoning in real-world situations. | |
| Grade 7 | |||
| Organizing Idea | Algebra: Generalizing arithmetic with expressions, equations, and inequalities supports problem solving in real-world situations. | ||
| Guiding Question | How can equivalence provide new perspectives of equations? | ||
| Learning Question | Students apply equivalence to solving linear equations, limited to integers. | ||
| Knowledge | Understanding | Skills & Procedures | |
Simplifying algebraic expressions on one or both sides of an equation results in an equivalent equation. Algebraic expressions can be simplified by applying algebraic properties and by combining like terms. Adding or subtracting the same algebraic or constant term on both sides of an equation results in an equivalent equation. A solution is a value that, when substituted into the equation, satisfies the equation. | Equations can be expressed in infinitely many equivalent ways. | Simplify algebraic expressions on one or both sides of an equation, using algebraic properties, including the distributive property. Solve linear equations with algebraic terms on both sides of the equation. Verify the solution to a linear equation by substituting the solution into any equivalent equation. Solve problems involving real-world situations, using linear equations. | |
| Grade 7 | |||
| Organizing Idea | Geometry: The properties of geometric objects are explained through justification and proof. | ||
| Guiding Question | In what ways can geometric objects be interpreted? | ||
| Learning Question | Students analyze the structure and relationships of geometric objects. | ||
| Knowledge | Understanding | Skills & Procedures | |
Geometric objects are abstract mathematical concepts and include
A straight line can be interpreted as a series of adjacent points that extends infinitely in two opposite directions. A ray is the portion of a straight line that extends infinitely in one direction from a given point on the line. A line segment is the portion of a straight line between two given points. An angle is formed by two straight lines, line segments, or rays that share a vertex. A polygon is a closed figure made of three or more line segments that only intersect at the vertices. Symbolic notation can be used to communicate geometric objects, including
Relationships between geometric objects can be communicated by using
| Symbols and symbolic notation can be used to represent relationships between geometric objects. | Differentiate between straight lines, rays, line segments, angles, and polygons. Model geometric objects, using hands-on materials or a digital geometry environment. Identify straight lines, rays, line segments, angles, and triangles, using symbols and symbolic notation. Represent relationships between geometric objects, using symbols and symbolic notation | |
A point common to two or more geometric objects is called an intersection. Angle relationships at the intersection of straight lines, line segments, or rays include
A transversal is a straight line, line segment, or ray that intersects two or more parallel lines Angle relationships at the intersections of a transversal and two or more parallel lines include congruent corresponding angles, which are in the same relative position at each point of intersection. | Relationships between geometric objects can be found at intersections. | Investigate angle relationships at the intersection of two straight lines. Identify corresponding angles at intersections of parallel lines and a transversal. Verify that two lines are parallel, using angles at intersections of a transversal. Model angle relationships, using hands-on materials or a digital geometry environment. Solve problems involving angle relationships at intersections. | |
In congruent polygons, corresponding
Congruence of geometric objects can be represented with symbols, including
Symbolic notation can be used to communicate congruence of geometric objects, including
| Congruence of geometric objects can be verified through symbols and symbolic notation. | Identify corresponding sides and corresponding angles of congruent polygons. Identify congruent angles and congruent line segments indicated with symbols in congruent polygons. Verify that geometric objects are congruent, using symbolic notation. Solve problems involving congruent polygons. | |
| Grade 7 | |||
| Organizing Idea | Measurement: Attributes such as length, area, volume, and angle are quantified by measurement. | ||
| Guiding Question | In what ways can measurable attributes of circles influence perspectives of size? | ||
| Learning Question | Students interpret and explain area and circumference of circles. | ||
| Knowledge | Understanding | Skills & Procedures | |
A circle is a 2-D shape structured by a set of points that are all the same distance from one point, known as the centre. The perimeter of a circle is called circumference. The radius of a circle is the distance from the centre to any point on the circle. The diameter is the distance across a circle, through the centre, and is twice the length of the radius. Area and circumference are different interpretations of the size of a circle. There is a constant ratio π (pi) that relates the circumference of any circle and its diameter. The circumference of a circle can be expressed as the product of its diameter and π, represented symbolically as The area of a circle can be divided into equal sized pie-shaped slices (sectors) and rearranged to form an approximation of a parallelogram. The area of a circle can be expressed as the product of the square of its radius and π, represented symbolically as | The size of a circle is determined by its radius. | Create circles, given the radius, using a compass or a digital geometry environment. Investigate the relationship between the circumference of a circle and its diameter. Determine the diameter of a circle, given its circumference and using 3.14 as an approximation for π. Derive the symbolic notation to calculate the area of a circle from the area of a parallelogram. Calculate the area and circumference of a circle, given its radius or diameter and using 3.14 as an approximation for π. Solve problems involving circumference and area of circles. | |
| Grade 7 | |||
| Organizing Idea | Measurement: Attributes such as length, area, volume, and angle are quantified by measurement. | ||
| Guiding Question | In what ways can area provide perspectives of volume? | ||
| Learning Question | Students analyze volume of right prisms and right cylinders. | ||
| Knowledge | Understanding | Skills & Procedures | |
A prism is a solid 3-D shape with rectangular lateral faces and two parallel congruent polygonal bases. The base of a prism can be any polygon, including rectangles and triangles. A prism is named according to the shape of its base. Any face of a rectangular prism can be interpreted as the base. A cylinder is a solid 3-D shape with one curved lateral surface and parallel congruent circular bases. Dimensions of a rectangular prism are its length, width, and height. Dimensions of a cylinder are its radius and height. Dimensions can be used for calculating the volume of a 3-D shape. The dimensions of a 3-D shape must be measured in the same units to calculate volume. The volume of a prism can be represented as the volume of a single layer of 1 × 1 × 1 cubes multiplied by the total number of layers. The volume of any prism or cylinder can be generalized as the product of the area of the base and the perpendicular height of the prism or cylinder, represented symbolically as | The volume of a prism or cylinder can be explained as a product of dimensions. | Relate the name of a prism to the shape of its base. Differentiate the lateral faces and lateral surfaces from the bases of prisms and cylinders oriented in various ways. Model volume of rectangular prisms by iterating the volume of a single layer, using hands-on materials or a digital geometry environment. Calculate the volume of rectangular prisms, triangular prisms, and cylinders. Determine the area of the base of rectangular prisms, triangular prisms, and cylinders, given volume and height. Determine the height of rectangular prisms, triangular prisms, and cylinders, given volume and area of the base. Solve problems involving volume of prisms and cylinders. | |
| Grade 7 | |||
| Organizing Idea | Functions: Functions model relationships between changing quantities in real-world situations. | ||
| Guiding Question | In what ways can functions be characterized? | ||
| Learning Question | Students interpret functions through domain and range. | ||
| Knowledge | Understanding | Skills & Procedures | |
The independent and dependent variables, respectively, represent the input and output values of a function. A relation is any correspondence between two changing quantities represented by input values and output values. A function is a relation where each input value corresponds to exactly one output value. The domain of a function is the set of all possible input values and can be communicated in words. The range of a function is the set of all possible output values and can be communicated in words. A function can be discrete or continuous. Domain and range can be discrete or continuous, and the maximum and minimum values can be restricted to model a real-world situation. Domain and range can be interpreted from various representations of a function, including
The graph of a discrete function is the set of points described by ordered pairs. The graph of a continuous function is a line that connects all points described by ordered pairs. The graph of a function will be intersected at no more than one point by a vertical line drawn on the Cartesian plane, known as the vertical line test. | Domain and range are attributes of a function. | Distinguish between discrete and continuous functions. Describe the domain and range of a function. Describe restrictions on the domain and range of a function that models a real-world situation. Graph a function that models a real-world situation, given a table of values. Determine whether a relation is a function. | |
| Grade 7 | |||
| Organizing Idea | Statistics: The science of collecting, analyzing, visualizing, and interpreting data can inform understanding and decision making. | ||
| Guiding Question | How can statistics support generalizations? | ||
| Learning Question | Students interpret sample data. | ||
| Knowledge | Understanding | Skills & Procedures | |
A population is a complete set of elements, such as people, animals, objects, or events, that are the focus of a statistical question. A population is defined by one or more shared characteristics, such as age, location, time, or type. A census is the collection of data from an entire population. A sample is a subset of a population. A sample can be used in place of a population when a census would be
A representative sample has the same defining characteristics as the population. A representative sample can be obtained by using random sampling methods, including
| Samples can represent populations. | Identify the population for a statistical question. Justify the use of data from a sample or a census in various situations. Describe a representative sample for a population in relation to a statistical question. Explain the process for obtaining a representative sample by using a chosen random sampling method. | |
Quantitative data are numerical data that can be discrete or continuous. Discrete data are countable, specific values within a range, between which other values cannot exist. Continuous data are measurable values within a range, between which infinitely many other values can exist. Numbers used to describe a sample are called statistics, including
The mean describes the centre of a data set by using the sum of the data values divided by the number of data values, e.g., The median is the middle value, or the mean of the two middle values, in a set of data ordered numerically. The range is the difference between the maximum and minimum values of a data set. | Data collected from a sample can be summarized by using statistics. | Determine mean, median, mode, and range for a set of quantitative data collected from a representative sample. Compare statistics from two different samples of the same population. Draw conclusions about a population, using statistics from a representative sample. | |
| Grade 7 | |||
| Organizing Idea | Probability: Modelling randomness and quantifying the likelihood of events can inform decision making where uncertainty exists. | ||
| Guiding Question | In what ways can likelihood be explained? | ||
| Learning Question | Students interpret theoretical and experimental probability. | ||
| Knowledge | Understanding | Skills & Procedures | |
A set is a collection of objects of any nature. An outcome is any possible result of an experiment. An event is a set of outcomes, and any outcome that matches the event is called a favourable outcome. A simple event is when only one event can occur. The probability of an event numerically represents its likelihood. Events that are certain have a probability of 1. Events that are impossible have a probability of 0. Equally likely outcomes have the same probability. Not all events have an equal likelihood, e.g., a biased coin. | Probability quantifies the likelihood that an event occurs. | Describe favourable outcomes for a given event. Describe one outcome as more or less likely than another outcome. Describe situations where not all events are equally likely. Explain certain and impossible events. | |
Theoretical probability is the likelihood of an event occurring under ideal conditions. If all outcomes are equally likely, the theoretical probability is the ratio of the number of favourable outcomes to the total number of outcomes. Experimental probability is determined by using data collected from repeated trials of an experiment. Experimental probability compares the number of favourable outcomes to the total number of trials of an experiment. Sample space is the list of all possible outcomes for a situation or an experiment and does not include the frequency of each outcome. The sum of the probabilities within a sample space is 1. A situation can be simulated if it has the same number of possible outcomes and each outcome occurs with the same probability, e.g., within a sample space, a coin has two equally likely outcomes and a die has six. Probability can be expressed in various ways, including
In an experiment, the outcome of any trial is unknown before it occurs, except for certain and impossible events. Repeated trials of an experiment have no influence on each other. Probability can inform decision making in various situations, such as games and weather forecasts. | Over a large number of trials, experimental probability models theoretical probability. | Express, in various ways, the theoretical probability for each of the possible outcomes in a situation. Predict the experimental probability of an event, using theoretical probability. Collect data from multiple trials of an experiment with equally likely outcomes. Simulate situations by generating a sample space. Determine the experimental probability of an event. Compare the experimental probability to the theoretical probability for a given event. Relate probability to decision making in various situations. | |
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