NUM. Number

• Students interpret place value to 100 000.

  Number outcome 1Mastery Cove ref

  Students interpret place value to 100 000.

  Guiding question

  • How can place value support organization of number?

  Knowledge

  • For numbers in base-10, each place has 10 times the value of the place to its right.
  • The digits 0 to 9 indicate the number of groups in each place in a number.
  • The value of each place in a number is the product of the digit and its place value.
  • Numbers can be composed in various ways by using place value.
  • Numbers can be rounded in contexts where an exact count is not needed.
  • The less than sign, < , and the greater than sign, > , are used to show the relationship between two unequal numbers.
  • A zero in the leftmost place of a natural number does not change the value of the number.
  • The dollar sign, $, is placed to the left of the dollar value in English and to the right of the dollar value in French.
  • The cent sign, ¢, is placed to the right of the cent value in English and in French.

  Understanding

  • Place value is the basis for the base-10 system.
  • Place value determines the value of a digit based on its place in a number relative to the ones place.
  • Place value is used to read, write, and compare numbers.

  Skills & procedures

  • Identify the place value of each digit in a natural number.
  • Relate the values of adjacent places.
  • Determine the value of each digit in a natural number.
  • Express natural numbers, using words and numerals.
  • Express various compositions of a natural number, using place value.
  • Round natural numbers to various places.
  • Compare and order natural numbers.
  • Express the relationship between two numbers, using < , > , or = .
  • Count and represent the value of a collection of nickels, dimes, and quarters as cents.
  • Count and represent the value of a collection of loonies, toonies, and bills as dollars.
  • Recognize French and English symbolic representations of monetary values.

  Source

• Students apply strategies for addition and subtraction within 1000.

  Number outcome 2Mastery Cove ref

  Students apply strategies for addition and subtraction within 1000.

  Guiding question

  • How can processes be established for addition and subtraction?

  Knowledge

  • Recall of addition and subtraction number facts facilitates addition and subtraction strategies.
  • Standard algorithms for addition and subtraction are conventional procedures based on place value.
  • Estimation can be used to support addition and subtraction in everyday situations, including
  • when an exact sum or difference is not needed
  • to check if an answer is reasonable

  Understanding

  • Addition and subtraction strategies can be chosen based on the nature of the numbers.
  • Standard algorithms for addition and subtraction may be used for any natural numbers.

  Skills & procedures

  • Relate strategies for the addition and subtraction of two-digit numbers to strategies for the addition and subtraction of three-digit numbers.
  • Model regrouping by place value for addition and subtraction.
  • Explain the standard algorithms for addition and subtraction of natural numbers.
  • Add and subtract natural numbers, using standard algorithms.
  • Estimate sums and differences.
  • Solve problems, using addition and subtraction.

  Source

• Students analyze and apply strategies for multiplication and division within 100.

  Number outcome 3Mastery Cove ref

  Students analyze and apply strategies for multiplication and division within 100.

  Guiding question

  • How can multiplication and division provide new perspectives of number?

  Knowledge

  • Multiplication and division are inverse mathematical operations.
  • Multiplication can represent repeated addition.
  • Multiplication can be interpreted in various ways according to context, such as
  • equal groups
  • an array
  • an area
  • Division can be interpreted in various ways according to context, such as
  • equal sharing
  • equal grouping
  • repeated subtraction
  • The order in which two quantities are multiplied does not affect the product (commutative property).
  • The order in which two numbers are divided affects the quotient.
  • Multiplication or division by 1 results in the same number (identity property).
  • Numbers can be multiplied or divided in parts (distributive property).
  • Multiplication strategies include
  • repeated addition
  • multiplying in parts
  • compensation
  • Division strategies include
  • repeated subtraction
  • partitioning the dividend
  • Products can be expressed symbolically by using the multiplication sign, \times , factors, and the equal sign.
  • Quotients can be expressed symbolically by using the division sign, \div , dividend, divisor, and the equal sign.
  • A missing quantity in a product or quotient can be represented in different ways, including
  • a \times b = \Box
  • a \times \Box = c
  • \Box \times b = c
  • e \div f = \Box
  • e \div \Box = g
  • \Box \div f = g
  • A remainder is the quantity left over after division.
  • A multiplication table shows both multiplication and division facts.
  • Fact families are groups of related multiplication and division number facts.

  Understanding

  • Quantities can be composed and decomposed through multiplication and division.
  • Sharing and grouping situations can be interpreted as multiplication or division.
  • Multiplication and division strategies can be supported by addition and subtraction.
  • Multiplication number facts have related division facts.

  Skills & procedures

  • Compose a product, using equal groups of objects.
  • Relate multiplication to repeated addition.
  • Relate multiplication to skip counting.
  • Investigate multiplication by 0.
  • Model a quotient by partitioning a quantity into equal groups or groups of a certain size, with or without remainders.
  • Visualize and model products and quotients as arrays.
  • Recognize interpretations of multiplication and division in various contexts.
  • Investigate multiplication and division strategies.
  • Multiply numbers up to a product of 100 and divide numbers with a maximum dividend of 100.
  • Verify a product or quotient, using inverse operations.
  • Determine a missing quantity in a product or quotient in a variety of ways.
  • Express multiplication and division symbolically.
  • Explain the meaning of the remainder in various situations.
  • Solve problems, using multiplication and division in sharing or grouping situations.
  • Examine patterns in multiplication and division, including patterns in multiplication tables and skip counting.
  • Recognize families of related multiplication and division number facts.
  • Recall multiplication number facts, with factors to 10, and related division facts.

  Source

• Students interpret fractions in relation to one whole.

  Number outcome 4Mastery Cove ref

  Students interpret fractions in relation to one whole.

  Guiding question

  • How can fractions contribute to a sense of number?

  Knowledge

  • The same fraction can represent
  • equal parts of one whole length, shape, or object
  • equal groups of one whole quantity
  • equal parts of each equal group in one whole quantity
  • The name of a fraction describes its composition as a number of unit fractions.
  • Fraction notation, (\frac{a}{b}) , relates the numerator, a , a number of equal parts, to the denominator, b , the total number of equal parts in the whole.
  • Equal numerators or equal denominators can facilitate the comparison of fractions.
  • A fraction with a numerator that is equal to its denominator is one whole.
  • Each fraction is associated with a point on the number line.

  Understanding

  • Fractions are numbers between natural numbers.
  • Fractions can represent part-to-whole relationships.
  • A unit fraction describes the size of the equal parts of a fraction.
  • The size of the parts and the total number of equal parts in the whole are inversely related.

  Skills & procedures

  • Model fractions of a whole quantity, length, shape, or object, in various ways, limited to denominators of 12 or less.
  • Visualize fractions as compositions of a unit fraction.
  • Identify the numerator and denominator of a fraction in various representations.
  • Name a given fraction.
  • Express fractions, including one whole, symbolically, limited to denominators of 12 or less.
  • Relate various representations of the same fraction, limited to denominators of 12 or less.
  • Compare the same fraction of different-sized wholes.
  • Compare different fractions of the same whole that have the same denominator.
  • Compare different fractions of the same whole that have the same numerator and different denominators.
  • Express the relationship between two fractions of the same whole, using < , > , or = .
  • Relate a fraction less than one to its position on the number line, limited to denominators of 12 or less.
  • Compare fractions to benchmarks of 0, \frac{1}{2} , and 1.

  Source

GEO. Geometry

• Students relate geometric properties to shape.

  Geometry outcome 1Mastery Cove ref

  Students relate geometric properties to shape.

  Guiding question

  • In what ways might geometric properties refine interpretation of shape?

  Knowledge

  • Geometric properties can describe relationships, including perpendicular, parallel, and equal.
  • Parallel lines or planes are always the same distance apart.
  • Perpendicular lines or planes intersect at a 90° (right) angle.
  • Right angles can be identified by using various referents, such as
  • the corner of a piece of paper
  • the angle between the hands on an analog clock at 3:00
  • a capital letter L
  • Polygons include
  • triangles
  • quadrilaterals
  • pentagons
  • hexagons
  • octagons
  • Regular polygons have sides of equal length and interior angles of equal measure.
  • Transformations include
  • translations
  • rotations
  • reflections
  • The distance between any two vertices of a shape is maintained in the image created by a transformation.

  Understanding

  • Geometric properties are relationships between geometric attributes.
  • Geometric properties define a class of polygon.
  • Geometric properties do not change when a polygon undergoes a transformation.

  Skills & procedures

  • Investigate the relationships between the sides of a polygon, including perpendicular, parallel, and equal, using referents for 90° or by measuring.
  • Investigate the relationships between vertices of a polygon, including equal or right angles, using direct comparison or referents for 90°.
  • Describe geometric properties of regular and irregular polygons.
  • Sort polygons according to geometric properties and describe the sorting rule.
  • Classify polygons as regular or irregular, using geometric properties.
  • Examine geometric properties of polygons by translating, rotating, or reflecting, using hands-on materials or digital applications.

  Source

  Practice coming soon

MEA. Measurement

• Students determine length, using standard units.

  Measurement outcome 1Mastery Cove ref

  Students determine length, using standard units.

  Guiding question

  • In what ways can length be communicated?

  Knowledge

  • The basic unit of length in the metric system is the metre.
  • Metric units are named by using prefixes that indicate the relationship to the basic unit, including
  • milli: one thousand millimetres in one metre
  • centi: one hundred centimetres in one metre
  • deci: ten decimetres in one metre
  • Metric units are abbreviated for convenience, including
  • m: metre
  • dm: decimetre
  • cm: centimetre
  • mm: millimetre
  • Standard measuring tools show iterations of a standard unit from an origin.
  • Units of length in the imperial system include inch, foot, and yard, related in these ways:
  • 12 inches in one foot
  • 36 inches in one yard
  • 3 feet in one yard
  • Approximate conversions between metric and imperial are useful in real-world situations, including
  • 2 \frac{1}{2} centimetres are approximately 1 inch
  • 1 metre is approximately 3 feet
  • 30 centimetres are approximately 1 foot
  • 1 metre is approximately 1 yard
  • The perimeter of a polygon is the sum of the lengths of its sides.
  • A benchmark is a known length to which another length can be compared.
  • Length can be estimated by using a personal or familiar referent.

  Understanding

  • Length is measured in standard units according to the metric system and the imperial system.
  • Length can be expressed in various units according to context and desired precision.
  • Length remains the same when decomposed or rearranged.
  • Length can be estimated when less accuracy is required.

  Skills & procedures

  • Relate millimetres, centimetres, and metres.
  • Relate inches to feet and yards.
  • Justify the choice of millimetres, centimetres, or metres to measure various lengths.
  • Measure lengths of straight lines and curves, with millimetres, centimetres, or metres.
  • Recognize length expressed in metric or imperial units.
  • Approximate a measurement in inches, feet, or yards, using centimetres or metres.
  • Determine the perimeter of polygons.
  • Determine the length of an unknown side, given the perimeter of a polygon.
  • Identify referents for a centimetre and a metre.
  • Estimate length by comparing to a benchmark.
  • Estimate length by visualizing the iteration of a referent for a centimetre or metre.

  Source

• Students interpret angles.

  Measurement outcome 2Mastery Cove ref

  Students interpret angles.

  Guiding question

  • How can angles broaden an understanding of space?

  Knowledge

  • Angle defines the space in
  • corners
  • bends
  • turns or rotations
  • intersections
  • slopes
  • The arms of an angle can be line segments or rays.
  • A vertex is the common end point of two arms.
  • Superimposing is the process of placing one angle over another to compare angles.
  • A referent is a personal or familiar representation of a known angle.

  Understanding

  • An angle is formed when two arms meet at a vertex.
  • An angle can be interpreted as the motion of a length rotated about a vertex.
  • Two angles can be compared directly or indirectly.

  Skills & procedures

  • Recognize various angles in surroundings.
  • Recognize situations in which an angle can be perceived as motion.
  • Compare two angles directly by superimposing.
  • Compare two angles indirectly by superimposing a third angle.
  • Estimate which of two angles is greater.
  • Identify referents for 90°.
  • Identify 90° angles in the environment, using a referent.

  Source

  Practice coming soon

PAT. Patterns

• Students analyze patterns in numerical sequences.

  Patterns outcome 1Mastery Cove ref

  Students analyze patterns in numerical sequences.

  Guiding question

  • How can diverse representations of patterns contribute to interpretation of change?

  Knowledge

  • Ordinal numbers can indicate position in a sequence.
  • Finite sequences, such as a countdown, have a definite end.
  • Infinite sequences, such as the natural numbers, never end.
  • Numerical sequences can be constructed by using addition, subtraction, multiplication, or division.

  Understanding

  • A sequence is a list of terms arranged in a certain order.
  • Sequences may be finite or infinite.
  • A sequence can progress according to a pattern.

  Skills & procedures

  • Recognize familiar numerical sequences, including the sequence of even or odd numbers.
  • Describe position in a sequence, using ordinal numbers.
  • Differentiate between finite and infinite sequences.
  • Recognize skip-counting sequences in various representations, including rows or columns of a multiplication table.
  • Determine any missing term in a skip-counting sequence, using multiplication.
  • Describe the change from term to term in a numerical sequence, using mathematical operations.

  Source

  Practice coming soon

TIM. Time

• Students tell time, using clocks.

  Time outcome 1Mastery Cove ref

  Students tell time, using clocks.

  Guiding question

  • How can duration be communicated?

  Knowledge

  • Clocks relate seconds to minutes and hours according to a base-60 system.
  • The basic unit of time is the second.
  • One second is \frac{1}{60} of a minute.
  • One minute is \frac{1}{60} of an hour.
  • Analog and digital clocks represent time of day.
  • Time of day can be expressed as a duration relative to 12:00 in two 12-hour cycles.
  • Time of day can be expressed as a duration relative to 0:00 in one 24-hour cycle in some contexts, including French-language contexts.

  Understanding

  • Clocks are standard measuring tools used to communicate time.

  Skills & procedures

  • Investigate relationships between seconds, minutes, and hours, using an analog clock.
  • Relate minutes past the hour to minutes until the next hour.
  • Describe time of day as a.m. or p.m. relative to 12-hour cycles of day and night.
  • Tell time, using analog and digital clocks.
  • Express time of day in relation to one 24-hour cycle.

  Source

STA. Statistics

• Students interpret and explain representations of data.

  Statistics outcome 1Mastery Cove ref

  Students interpret and explain representations of data.

  Guiding question

  • How can representation support communication?

  Knowledge

  • Statistical questions are questions that can be answered by collecting data.
  • First-hand data is collected by the person using the data.
  • Second-hand data is data collected by others from sources such as websites and social media.

  Understanding

  • Representation connects data to a statistical question.
  • Representation expresses data specific to a unique time and place.
  • Representation tells a story about data.

  Skills & procedures

  • Formulate statistical questions for investigation.
  • Predict the answer to a statistical question.
  • Collect data, using digital or non-digital tools and resources.
  • Represent first-hand and second-hand data in a dot plot or bar graph with one-to-one correspondence.
  • Describe the story that a representation tells about a collection of data in relation to a statistical question.
  • Examine First Nations, Métis, or Inuit representations of data.
  • Consider possible answers to a statistical question based on the data collected.

  Source

ALG. Algebra

• Students illustrate equality with equations.

  Algebra outcome 1Mastery Cove ref

  Students illustrate equality with equations.

  Guiding question

  • How can equality facilitate agility with number?

  Knowledge

  • An equation uses the equal sign to indicate equality between two expressions.
  • The left and right sides of an equation are interchangeable.
  • Equations can be modelled by using a balance.
  • A symbol may represent an unknown value in an equation.

  Understanding

  • Two expressions are equal if they represent the same number.
  • Equations can have unknown values.

  Skills & procedures

  • Write equations that represent equality between a number and an expression or between two different expressions of the same number.
  • Model equations that include an unknown value, including with a balance.
  • Determine an unknown value on the left or right side of an equation, limited to equations with one operation.
  • Solve problems, using equations, limited to equations with one operation.

  Source

  Practice coming soon

CG. Coordinate Geometry