Grade 6 - Mathematics (2022)

Mathematics 

Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating.

Algebra: Equations express relationships between quantities.

Geometry: Shapes are defined and related by geometric attributes.

Coordinate Geometry: Location and movement of objects in space can be communicated using a coordinate grid.

Measurement: Attributes such as length, area, volume, and angle are quantified by measurement.

Patterns: Awareness of patterns supports problem solving in various situations.

Statistics: The science of collecting, analyzing, visualizing, and interpreting data can inform understanding and decision making.

Students investigate magnitude with positive and negative numbers.

Students solve problems using standard algorithms for addition and subtraction.

Students analyze numbers using prime factorization and exponentiation.

Students apply standard algorithms to multiplication and division of decimal and natural numbers.

Students relate fractions to quotients.

Students add and subtract fractions with denominators within 100.

Students interpret the multiplication of natural numbers by fractions.

Students apply equivalence to the interpretation of ratios and rates.

Students analyze expressions and solve algebraic equations.

Students analyze shapes through symmetry and congruence.

Students explain location and movement in relation to position in the Cartesian plane.

Students analyze areas of parallelograms and triangles.

Students interpret and express volume.

Students investigate functions to enhance understanding of change.

Students investigate relative frequency using experimental data.

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A quotient with a remainder can be expressed as a decimal number.

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Negative numbers are to the left of zero on the number line visualized horizontally, and below zero on the number line visualized vertically.

Positive numbers can be represented symbolically with or without a positive sign (+).

Negative numbers are represented symbolically with a negative sign (?).

Zero is neither positive nor negative.

Negative numbers communicate meaning in context, including temperature, debt and elevation.

Magnitude is a number of units counted or measured from zero on the number line.

Every positive number has an opposite negative number with the same magnitude.

A number and its opposite are called additive inverses.

The set of integers includes all natural numbers, their additive inverses, and zero.

The sum of any number and its additive inverse is zero.

The sum of two positive numbers is a positive number.

The sum of two negative numbers is a negative number.

The sum of a positive number and a negative number can be interpreted as the sum of zero and another number.

Subtracting a number is the same as adding its additive inverse.

Symmetry of the number line extends infinitely to the left and right of zero or above and below zero.

Direction relative to zero is indicated symbolically with a positive or negative sign.

Magnitude with direction distinguishes between positive and negative numbers.

Any number can be expressed as a sum in infinitely many ways.

The difference of any two numbers can be interpreted as a sum.

Identify negative numbers in familiar contexts, including contexts that use vertical or horizontal models of the number line.

Express positive and negative numbers symbolically, in context.

Relate magnitude to the distance from zero on the number line.

Relate positive and negative numbers, including additive inverses, to their positions on horizontal and vertical models of the number line.

Compare and order positive and negative numbers.

Express the relationship between two numbers, including positive and negative numbers, using <, >, or =.

Investigate addition of an integer and its additive inverse.

Express zero as the sum of integers in multiple ways.

Model the sum of two positive integers.

Model the sum of two negative integers.

Model the sum of a positive and negative integer as the sum of zero and another integer.

Add any two integers.

Express a difference as a sum.

Standard algorithms are reliable procedures for addition and subtraction.

Contexts for problems involving addition and subtraction include money and metric measurement.

Addition and subtraction of numbers in problem-solving contexts is facilitated by standard algorithms.

Solve problems in various contexts using standard algorithms for addition and subtraction.

The order in which three or more numbers are multiplied does not affect the product (associative property).

Any composite number can be expressed as a product of smaller numbers (factorization).

Prime factorization represents a number as a product of prime numbers.

Any composite factor of a number can be determined from its prime factors.

Repeated multiplication of identical factors can be represented symbolically as a power (exponentiation).

A power, A^n, includes a base, A, representing the repeated factor, and an exponent, nn, indicating the number of repeated factors.

Any repeated prime factor within a prime factorization can be expressed as a power.

A product can be composed in multiple ways.

The prime factors of a number provide a picture of its divisibility.

Different representations of a product can provide new perspectives of its divisibility.

A power is divisible by its base.

Compose a product in multiple ways, including with more than two factors.

Express the prime factorization of a composite number.

Determine common factors for two natural numbers, using prime factorization.

Determine divisibility of a natural number from its prime factorization.

Identify the base and exponent in a power.

Express the product of identical factors as a power, including within a prime factorization.

Describe the divisibility of numbers represented in various forms.

Standard algorithms are reliable procedures for multiplication and division of numbers, including decimal numbers.

Multiplication and division of decimal numbers is facilitated by standard algorithms.

Explain the standard algorithms for multiplication and division of decimal numbers.

Multiply and divide up to 3-digit natural or decimal numbers by 2-digit natural numbers, using standard algorithms.

Assess the reasonableness of a product or quotient using estimation.

Solve problems using multiplication and division, including problems involving money.

An equal-sharing situation can be represented by a fraction in which the numerator represents the quantity to be shared and the denominator represents the number of shares.

Division can be used to determine an equal share.

Division of the numerator by the denominator of a fraction provides the equivalent decimal number.

Fractions represent quotients in equal-sharing situations.

All equivalent fractions represent the same quotient.

Model an equal-sharing situation in more than one way.

Describe an equal-sharing situation using a fraction.

Express a fraction as a division statement and vice versa.

Convert a quotient from fraction to decimal form using division.

Addition and subtraction of fractions is facilitated by representing the fractions with common denominators.

Denominators are related if one is a multiple of the other.

Multiplication of one denominator by the factor that relates it to another denominator achieves common denominators.

The product of the denominators of two fractions provides a common denominator.

Fractions with common denominators have the same units.

Any numbers with the same unit can be compared, added, or subtracted.

Recognize two fractions with related denominators.

Determine the factor that relates one denominator to another.

Express two fractions with common denominators.

Add and subtract fractions.

Solve problems involving addition and subtraction of fractions.

Multiplication of a natural number by a fraction is equivalent to multiplication by the fraction's numerator and division by its denominator. a* b/c = ab/c. ?

Multiplication by a unit fraction is equivalent to division by its denominator. a*1/b = a/b. ?

The product of a fraction and a natural number is the fraction with a numerator that is the product of the numerator of the given fraction and the natural number a denominator that is the denominator of the given fraction a/b*c= ac/b. ?

Multiplication does not always result in a larger number.

Multiplication of a natural number by a fraction can be interpreted as repeated addition of the fraction.

Multiplication of a fraction by a natural number can be interpreted as taking part of a quantity.

Relate multiplication of a natural number by a fraction to repeated addition of the fraction.

Multiply a natural number by a fraction.

Relate multiplication by a unit fraction to division.

Multiply a natural number by a unit fraction.

Model a fraction of a natural number.

Multiply a fraction by a natural number.

Solve problems using multiplication of a fraction and a natural number.

A proportional relationship exists when one quantity is a multiple of the other.

Equivalent ratios can be created by multiplying or dividing both terms of a given ratio by the same number.

A proportion is an expression of equivalence between two ratios.

A rate describes the proportional relationship represented by a set of equivalent ratios.

A unit rate expresses a proportional relationship as a rate with a second term of 1.

A percentage describes a proportional relationship between a quantity and 100.

Percent of a number can be determined by multiplying the number by the percent and dividing by 100.

All equivalent ratios express the same proportional relationship.

A rate can be used to extend a given proportional relationship to different quantities.

Determine whether two ratios are equivalent.

Determine an equivalent ratio using a proportion.

Express a unit rate to represent a given rate, including unit price and speed.

Relate percentage of a number to a proportion.

Determine a percent of a number, limited to percentages within 100%.

Solve problems involving ratios, rates, and proportions.

Powers can appear in numerical expressions.

The conventional order of operations includes performing operations in parentheses, followed by evaluating powers before other operations.

Algebraic terms with exactly the same variable are like terms.

Constant terms are like terms.

Like terms can be combined through addition or subtraction.

The terms of an algebraic expression can be rearranged according to algebraic properties.

Algebraic properties include commutative property of addition: a + b = b + a, for any two numbers a and b commutative property of multiplication: ab = ba for any two numbers a and b, associative property of addition: (a + b) + c = a + (b + c), associative property of multiplication: a(bc) = b(ac) and distributive property: a(b + c) = ab + ac.

All simplified forms of an equation have the same solution.

The conventional order of operations can be applied to simplify or evaluate expressions.

Algebraic properties ensure equivalence of algebraic expressions.

Algebraic expressions on each side of an equation can be simplified into equivalent expressions to facilitate equation solving.

Evaluate numerical expressions involving operations in parentheses and powers according to the order of operations.

Investigate like terms by modelling an algebraic expression.

Simplify algebraic expressions by combining like terms.

Express the terms of an algebraic expression in a different order in accordance with algebraic properties.

Simplify algebraic expressions on both sides of an equation.

Solve equations, limited to equations with one or two operations.

Determine different strategies for solving equations.

Verify the solution to an equation by evaluating expressions on each side of the equation.

Solve problems using equations, limited to equations with one or two operations.

Symmetrical shapes can be mapped by any combination of reflections and rotations.

A tessellation is the tiling of a plane with symmetrical shapes.

Tessellations are evident in First Nations and Mtis star blanket designs that convey a specific purpose.

Shapes related by symmetry are congruent to each other.

Congruent shapes may not be related by symmetry.

Symmetry is a relationship between two shapes that can be mapped exactly onto each other through reflection or rotation.

Congruence is a relationship between two shapes of identical size and shape.

Congruence is not dependent on orientation or location of the shapes.

Verify symmetry of two shapes by reflecting or rotating one shape onto another.

Describe the symmetry between two shapes as reflection symmetry or rotation symmetry.

Visualize and describe a combination of two transformations that relate symmetrical shapes.

Describe the symmetry modelled in a tessellation.

Investigate tessellations found in objects, art, or architecture.

Demonstrate congruence between two shapes in any orientation by superimposing using hands-on materials or digital applications.

Describe symmetrical shapes as congruent.

The Cartesian plane is named after French mathematician René Descartes.

The Cartesian plane uses coordinates, (x, y), to indicate the location of the point where the vertical line passing through (x, 0) and the horizontal line passing through (0, y) intersect.

The x-axis consists of those points whose y-coordinate is zero, and the y-axis consists of those points whose x-coordinate is zero.

The x-axis and the y-axis intersect at the origin, (0, 0).

An ordered pair is represented symbolically as (x, y).

An ordered pair indicates the horizontal distance from the y-axis with the x-coordinate and the vertical distance from the x-axis with the y-coordinate.

A translation describes a combination of horizontal and vertical movements as a single movement.

A reflection describes movement across a line of reflection.

A rotation describes an amount of movement around a turn centre along a circular path in either a clockwise or counter-clockwise direction.

Location can be described using the Cartesian plane.

The Cartesian plane is the two-dimensional equivalent of the number line.

Location can change as a result of movement in space.

Change in location does not imply change in orientation.

Relate the axes of the Cartesian plane to intersecting horizontal and vertical representations of the number line.

Locate a point in the Cartesian plane given the coordinates of the point.

Describe the location of a point in the Cartesian plane using coordinates.

Model a polygon in the Cartesian plane using coordinates to indicate the vertices.

Describe the location of the vertices of a polygon in the Cartesian plane using coordinates.

Create an image of a polygon in the Cartesian plane by translating the polygon.

Describe the horizontal and vertical components of a given translation.

Create an image of a polygon in the Cartesian plane by reflecting the polygon over the x-axis or y-axis.

Describe the line of reflection of a given reflection.

Create an image of a polygon in the Cartesian plane by rotating the polygon 90°, 180°, or 270° about one of its vertices, clockwise or counter-clockwise.

Describe the angle and direction of a given rotation, limited to rotations of 90°, 180°, or 270° about a vertex.

Relate the coordinates of a polygon and its image after translation, reflection, or rotation in the Cartesian plane.

A parallelogram is any quadrilateral with two pairs of parallel and equal sides.

Any side of a parallelogram can be interpreted as the base.

The height of a parallelogram is the perpendicular distance from its base to its opposite side.

The area of a triangle is half of the area of a parallelogram with the same base and height.

Two triangles with the same base and height must have the same area.

Area of composite shapes can be interpreted as the sum of the areas of multiple shapes, such as triangles and parallelograms.

The area of a parallelogram can be generalized as the product of the perpendicular base and height.

The area of a triangle can be interpreted relative to the area of a parallelogram.

An area can be decomposed in infinitely many ways.

Rearrange the area of a parallelogram to form a rectangular area using hands-on materials or digital applications.

Determine the area of a parallelogram using multiplication.

Determine the base or height of a parallelogram using division.

Model the area of a parallelogram as two congruent triangles.

Describe the relationship between the area of a triangle and the area of a parallelogram with the same base and height.

Determine the area of a triangle, including various triangles with the same base and height.

Solve problems involving the areas of parallelograms and triangles.

Visualize the decomposition of composite areas in various ways.

Determine the area of composite shapes using the areas of triangles and parallelograms.

Volume can be measured in non-standard units or standard units.

Volume is expressed in the following standard units, derived from standard units of length: cubic centimetres and cubic metres.

A cubic centimetre (cm3) is a volume equivalent to the volume of a cube measuring 1 centimetre by 1 centimetre by 1 centimetre.

A cubic metre (m3) is a volume equivalent to the volume of a cube measuring 1 metre by 1 metre by 1 metre.

The volume of a right rectangular prism can be interpreted as the product of the two-dimensional base area and the perpendicular height of the prism.

Volume is a measurable attribute that describes the amount of three-dimensional space occupied by a three-dimensional shape.

The volume of a prism can be interpreted as the result of perpendicular motion of an area.

Volume remains the same when decomposed or rearranged.

Volume is quantified by measurement.

Volume is measured with congruent units that themselves have volume and do not need to resemble the shape being measured.

The volume of a right rectangular prism can be perceived as cube-shaped units structured in a three-dimensional array.

Recognize volume in familiar contexts.

Model volume of prisms by dragging or iterating an area using hands-on materials or digital applications.

Create a model of a three-dimensional shape by stacking congruent non-standard units or cubic centimetres without gaps or overlaps.

Express volume in non-standard units or cubic centimetres.

Visualize and model the volume of various right rectangular prisms as three-dimensional arrays of cube-shaped units.

Determine the volume of a right rectangular prism using multiplication.

Solve problems involving volume of right rectangular prisms.

A variable can be interpreted as the values of a changing quantity.

A function can involve quantities that change over time, such as height of a person or plant, temperature and distance travelled.

A table of values lists the values of the independent variable in the first column or row and the values of the dependent variable in the second column or row to represent a function at certain points.

The values of the independent variable are represented by x-coordinates in the Cartesian plane.

The values of the dependent variable are represented by y-coordinates in the Cartesian plane.

A function is a correspondence between two changing quantities represented by independent and dependent variables.

Each value of the independent variable in a function corresponds to exactly one value of the dependent variable.

Identify the dependent and independent variables in a given situation, including situations involving change over time.

Describe the rule that determines the values of the dependent variable from values of the independent variable.

Represent corresponding values of the independent and dependent variables of a function in a table of values and as points in the Cartesian plane.

Write an algebraic expression that represents a function.

Recognize various representations of the same function.

Determine a value of the dependent variable of a function given the corresponding value of the independent variable.

Investigate strategies for determining a value of the independent variable of a function given the corresponding value of the dependent variable.

Solve problems involving a function.

Relative frequency can be used to compare the same category of data across multiple data sets.

Relative frequency can be represented in various forms.

Equally likely outcomes of an experiment have the same chance of occurring.

An event can be described as a combination of potential outcomes of an experiment, including heads or tails from a coin toss, any roll of a die and the result of spinning a spinner.

The law of large numbers states that more independent trials of an experiment result in a better estimate of the expected likelihood of an event.

Relative frequency expresses the frequency of a category of data as a fraction of the total number of data values.

Frequency can be a count of categorized observations or trials in an experiment.

Relative frequency of outcomes can be used to estimate the likelihood of an event.

Relative frequency varies between sets of collected data.

Relative frequency provides a better estimate of the likelihood of an event with larger amounts of data.

Interpret frequency of categorized data as relative frequency.

Express relative frequencies as decimals, fractions, or percentages.

Identify the possible outcomes of an experiment involving equally likely outcomes.

Collect categorized data through experiments.

Predict the likelihood of an event based on the possible outcomes of an experiment.

Determine relative frequency for categories of a sample of data.

Describe the likelihood of an outcome in an experiment using relative frequency.

Analyze relative frequency statistics from experiments with different sample sizes.