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Mathematics

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Mathematics is a subject in which students study patterns and relationships to understand various aspects of the world. Mathematical understanding is connected to many branches of mathematics, including arithmetic, algebra, geometry, data, statistics, and probability. The procedures associated with mathematics range from counting, calculating, and measuring to analyzing, modelling, and generalizing. Communication is also fundamental to mathematics. The language of mathematics has its own system of symbolic notation and a specific vocabulary with which to communicate mathematical thinking concisely.

Mathematical skills and knowledge support the interpretation of diverse quantitative and spatial information and can be applied to solving both theoretical and practical problems. With mathematics, abstract ideas can be visualized, represented, and explained. Mathematics is a powerful tool that can be used to simplify and solve complicated real-life problems.
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Organizing Idea
Number: Quantity is measured with numbers that enable counting, labelling, comparing, and operating.
Guiding Question
How can we communicate quantity?
Guiding Question
How can quantity contribute to our sense of number?
Guiding Question
How can place value support our organization of number?
Learning Outcome
Students interpret and explain quantity to 100.
Learning Outcome
Students analyze quantity to 1000.
Learning Outcome
Students interpret place value.
Knowledge
The absence of quantity is represented by 0.

Canadian money includes
  • nickels
  • dimes
  • quarters
  • loonies
  • toonies
  • five-dollar bills
  • ten-dollar bills
  • twenty-dollar bills
  • fifty-dollar bills
  • hundred-dollar bills
Understanding
Quantity is expressed in words and numerals based on patterns.

Quantity in the world is represented in multiple ways, including with money.
Skills & Procedures
Express quantities using words, objects, or pictures.

Represent quantities using numerals.

Identify a quantity of 0 in familiar situations.

Express the value of each coin and bill within 100 dollars using words and numerals.

Knowledge
The number of objects in a set can be represented by a natural number.

The number line is a spatial interpretation of quantity.

Understanding
There are infinitely many natural numbers.

Each natural number is associated with exactly one point on the number line.


Skills & Procedures
Express quantities using words.

Represent quantities using natural numbers.

Relate a natural number to its position on the number line.
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 using place value.

Numbers can be rounded in context when an exact count is not needed.

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 and write 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.

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.

Compare French and English symbolic representations of monetary values.

Knowledge
Counting can begin at any number.

Counting more than one object at a time is called skip counting.
Understanding
Each number counted includes all previous numbers (counting principle: hierarchical inclusion).

A quantity can be determined by counting more than one object in a set at a time.
Skills & Procedures
Count within 100, forward by 1, starting at any number, according to the counting principles.

Count backward from 20 to 0 by 1.

Skip count to 100, forward by 5 and 10, starting at 0.

Skip count to 20, forward by 2, starting at 0.
Knowledge
A quantity can be skip counted in various ways according to context, including by denominations of coins and bills.
Understanding
A quantity can be interpreted as a composition of groups.
Skills & Procedures
Decompose quantities into groups of 100s, 10s, and ones.

Count within 1000, forward and backward by 1, starting at any number.

Skip count by 20, 25, or 50, starting at 0.

Determine the value of a collection of coins or bills of the same denomination by skip counting.

Knowledge
Familiar arrangements of small quantities facilitate subitizing.
Understanding
A quantity can be perceived as the composition of smaller quantities.
Skills & Procedures
Recognize quantities to 10.
Knowledge
A benchmark is a known quantity to which another quantity can be compared.
Understanding
A quantity can be estimated when an exact count is not needed.
Skills & Procedures
Estimate quantities using benchmarks.

Knowledge
Words that describe a comparison between two quantities include
  • equal
  • not equal
  • greater than
  • less than
The equal sign is =.

The unequal sign is ≠.
Understanding
Two quantities are equal when there is the same number of objects in both sets.
Skills & Procedures
Compare quantities in two sets of objects.

Describe a quantity relative to another quantity.

Represent equal quantities symbolically.

Represent unequal quantities symbolically.
Knowledge
The less than sign is <.

The greater than sign is >.
Understanding
Each natural number is one greater than the natural number to its left on the number line, visualized horizontally.
Skills & Procedures
Compare and order natural numbers.

Describe a natural number as greater than, less than, or equal to another natural number using words or symbols.
Guiding Question
How can addition and subtraction provide perspectives of number?
Guiding Question
How can we interpret addition and subtraction?
Guiding Question
How can we establish processes for addition and subtraction?
Learning Outcome
Students acquire an understanding of addition and subtraction within 20.
Learning Outcome
Students explain addition and subtraction within 100.
Learning Outcome
Students apply addition and subtraction within 1000.
Knowledge
Addition and subtraction are opposite (inverse) mathematical operations.

Addition is a process of combining quantities to find a sum.

Subtraction is a process of finding the difference between quantities.

The order in which two quantities are added does not affect the sum (commutative property).

The order in which two quantities are subtracted affects the difference.

Addition of 0 to any number, or subtraction of 0 from any number, results in the same number (zero property).
Understanding
Quantities can be composed or decomposed through addition and subtraction.
Skills & Procedures
Compose quantities within 20 in various ways.


Knowledge
The order in which more than two numbers are added does not affect the sum (associative property).
Understanding
A sum can be composed in multiple ways.
Skills & Procedures
Compose a sum in multiple ways, including with more than two addends.


Knowledge
Recall of addition and subtraction number facts facilitates addition and subtraction strategies.

Estimation can be used when an exact sum or difference is not needed and to check if an answer is reasonable.

Standard algorithms for addition and subtraction are conventional procedures based on place value.
Understanding
Addition and subtraction strategies can be chosen based on the nature of the numbers.

Standard algorithms are universal tools for addition and subtraction and may be used for any natural numbers independently of their nature.
Skills & Procedures
Add and subtract natural numbers.

Estimate sums and differences.

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.

Solve problems using addition and subtraction.
Knowledge
Strategies are meaningful steps taken to solve problems.

Addition and subtraction strategies include
  • counting on
  • counting back
  • decomposition
  • compensation
The addition sign is +.

The subtraction sign is -.

The equal sign is =.

Understanding
Addition and subtraction can show a change in quantity through joining, separating, or comparing.
Skills & Procedures
Investigate addition and subtraction strategies.

Add and subtract within 20.

Express addition and subtraction symbolically.

Solve problems using addition and subtraction in joining, separating, or comparing situations.

Model transactions with money, limited to dollar values within 20 dollars.

Knowledge
Familiar addition and subtraction number facts facilitate addition and subtraction strategies.
Understanding
Addition and subtraction can represent the sum or difference of countable quantities (e.g., marbles or blocks) or measurable lengths (e.g., string length or student height).

Skills & Procedures
Recall and apply addition number facts, with addends to 10, and related subtraction number facts.

Add and subtract numbers within 100.

Solve problems using addition and subtraction of countable quantities or measurable lengths.

Model transactions with money, limited to dollar values within 100 dollars or cent values within 100 cents.
Knowledge
Addition and subtraction number facts represent part-part-whole relationships.

In a part-part-whole relationship, the sum represents the whole and the difference represents a missing part.

Fact families are groups of related addition and subtraction number facts.
Understanding
Addition number facts have related subtraction number facts.
Skills & Procedures
Identify patterns in addition and subtraction, including patterns in addition tables.

Recognize families of related addition and subtraction number facts.

Recall addition number facts, with addends to 10, and related subtraction number facts.
Guiding Question
In what ways can we interpret the composition of number?
Guiding Question
In what ways can composition characterize number?
Guiding Question
How can multiplication and division provide new perspectives of number?
Learning Outcome
Students represent equal sharing and grouping of quantities within 20.

Learning Outcome
Students interpret even and odd quantities within 100.

Learning Outcome
Students acquire an understanding of multiplication and division within 100.
Knowledge
Sharing involves partitioning a quantity into a certain number of groups.

Grouping involves partitioning a quantity into groups of a certain size.
Understanding
Quantity can be partitioned by sharing or grouping.
Skills & Procedures
Partition a set of objects by sharing and grouping.

Demonstrate conservation of number when sharing or grouping.
Knowledge
An even quantity will have no remainder when partitioned into two equal groups or groups of two.

An odd quantity will have a remainder of one when partitioned into two equal groups or groups of two.
Understanding
All natural numbers are either even or odd.
Skills & Procedures
Model even and odd quantities by sharing and grouping.

Describe a quantity as even or odd.

Partition a set of objects by sharing or grouping, with or without remainders.
Knowledge
Multiplication and division are inverse mathematical operations.

Multiplication is repeated addition.

Multiplication by two is doubling and multiplication by three is tripling.

Division is a process of sharing or grouping to find a quotient.

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).
Understanding
Quantities can be composed and decomposed through multiplication and division.
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 with or without remainders.

Visualize and model products and quotients as arrays.


Knowledge
Multiplication strategies include
  • repeated addition
  • multiplying in parts
  • compensation
Division strategies include
  • repeated subtraction
  • partitioning the dividend
The multiplication symbol is ×.

The division symbol is ÷.

The equal sign is =.

A remainder is the quantity left over after division.

Understanding
Sharing and grouping situations can be interpreted as multiplication or division.

Multiplication and division strategies can be supported by addition and subtraction.
Skills & Procedures
Investigate multiplication and division strategies.

Multiply and divide within 100.

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.

Knowledge
A multiplication table shows both multiplication and division facts.

Fact families are groups of related multiplication and division number facts.
Understanding
Multiplication number facts have related division facts.
Skills & Procedures
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.
Guiding Question
In what ways can parts and wholes be related?
Guiding Question
In what ways can parts compose a whole?
Guiding Question
How can fractions contribute to our sense of number?
Learning Outcome
Students recognize one-half as a part-whole relationship.
Learning Outcome
Students interpret one whole using halves and quarters.
Learning Outcome
Students interpret fractions as part-whole relationships.
Knowledge
One-half can be one of two equal groups.
Understanding
In a quantity partitioned into two equal groups, each group represents one-half of the quantity.
Skills & Procedures
Identify one-half in familiar situations.

Partition an even set of objects into two equal groups.


Knowledge
One-half is one of two equal parts.

One-quarter is one of four equal parts.
Understanding
When a quantity is partitioned into equal groups, each group represents an equal part of the whole quantity.
Skills & Procedures
Partition an even set of objects into two equal groups and four equal groups.

Describe one of two equal groups as one-half and one of four equal groups as one-quarter.

Describe a whole set of objects as a composition of halves and as a composition of quarters.
Knowledge
Fraction notation, , relates the the numerator, a, as a number of equal parts, to the denominator, b, as the total number of equal parts in the whole.

A whole quantity can be a whole set of objects or a whole object that can be partitioned.

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.

Skills & Procedures
Partition a whole into 12 or fewer equal parts.

Describe a whole as a fraction, limited to denominators of 12 or less.

Model fractions of a whole, limited to denominators of 12 or less.

Express fractions symbolically.

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, , and 1.
Knowledge
The whole can be any size and is designated by context.

Fractions can be compared by considering the number of parts or the size of parts.

Understanding
Fractions are interpreted relative to the whole.

The size of the parts and the number of partitions in the whole are inversely related.
Skills & Procedures
Recognize the whole to which a fraction refers in various situations.

Compare the same fraction of different-sized wholes.

Compare different fractions with the same denominator.

Compare different fractions with the same numerator.
Guiding Question
How can the composition of fractions facilitate agility in operating with fractions?
Learning Outcome
Students acquire an understanding of addition and subtraction of fractions with like denominators.
Knowledge
A unit fraction is any one part of a whole divided into equal parts.

Fractions with common denominators are multiples of the same unit fraction.
Understanding
Any fraction can be interpreted as a composition of unit fractions.
Skills & Procedures
Decompose a fraction into unit fractions.

Express a fraction as repeated addition of a unit fraction.

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

Add and subtract fractions within one whole, limited to common denominators of 12 or less.

Solve problems involving fractions, limited to common denominators of 12 or less.
Organizing Idea
Algebra: Equations express relationships between quantities.
Guiding Question
How can equality facilitate agility with number?
Learning Outcome
Students interpret equality with equations.
Knowledge
The equal sign is not a signal to perform a given computation.

The left and right sides of an equation are interchangeable.
Understanding
An equation uses the equal sign to indicate equality between two expressions.

Two expressions are equal if they represent the same number.
Skills & Procedures
Write equations that represent equality between a number and an expression or between two different expressions of the same number.
Knowledge
A symbol may represent an unknown value in an equation.
Understanding
Equations can include unknown values.
Skills & Procedures
Model equations that include an unknown value.

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.

Organizing Idea
Geometry: Shapes are defined and related by geometric attributes.
Guiding Question
In what ways can we characterize shape?
Guiding Question
How can shape influence our perception of space?
Guiding Question
In what ways might geometric properties refine our interpretation of shape?
Learning Outcome
Students interpret shape in two and three dimensions.

Learning Outcome
Students analyze and explain geometric attributes of shape.
Learning Outcome
Students relate geometric properties to shape.
Knowledge
Two-dimensional
shapes include
  • squares
  • circles
  • rectangles
  • triangles
Three-dimensional shapes include
  • cubes
  • prisms
  • cylinders
  • spheres
  • pyramids
  • cones
A line of symmetry indicates the division between the matching halves of a symmetrical shape.

Understanding
A shape can be modelled in various sizes and orientations.

A shape can be composed of two or more shapes.

A shape is symmetrical if it can be decomposed into matching halves.
Skills & Procedures
Identify shapes in various sizes and orientations.

Model two-dimensional shapes.

Sort shapes according to one attribute and describe the sorting rule.

Compose and decompose two- or three-dimensional shapes.

Identify shapes within two- or three-dimensional composite shapes.

Investigate symmetry of two-dimensional shapes by folding and matching.

Knowledge
Common geometric attributes include
  • sides
  • vertices
  • faces or surfaces
Two-dimensional shapes may have sides that are line segments.

Three-dimensional shapes may have faces that are two-dimensional shapes.
Understanding
Shapes are defined according to geometric attributes.

A shape can be visualized as a composition of other shapes.
Skills & Procedures
Sort shapes according to two geometric attributes and describe the sorting rule.

Relate the faces of three-dimensional shapes to two-dimensional shapes.

Create a picture or design with shapes from verbal instructions, visualization, or memory.

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 right angle.

Familiar representations of a right angle may include
  • 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.

Understanding
Geometric properties are relationships between geometric attributes.

Geometric properties define a class of polygon.
Skills & Procedures
Investigate geometric properties within polygons.

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.
Knowledge
A shape can change orientation or position through slides (translations), turns (rotations), or flips (reflections).


Understanding
Geometric attributes do not change when a shape is translated, rotated, or reflected.

First Nations, Métis, and Inuit translate, rotate, and reflect shapes in the creation of cultural art.
Skills & Procedures
Investigate translation, rotation, and reflection of two- and three-dimensional shapes.

Describe geometric attributes of two- and three-dimensional shapes in various orientations.

Recognize translation, rotation, or reflection of shapes represented in First Nations, Métis, or Inuit art inspired by the natural world.

Knowledge
Rigid transformations include
  • translations
  • rotations
  • reflections
Understanding
Geometric properties do not change when a polygon undergoes rigid transformation.
Skills & Procedures
Examine geometric properties of polygons by translating, rotating, or reflecting using hands-on materials or digital applications.
Organizing Idea
Measurement: Attributes such as length, area, volume, and angle are quantified by measurement.
Guiding Question
In what ways can length provide perspectives of size?
Guiding Question
How can length contribute to our interpretation of space?
Guiding Question
In what ways can we communicate length?
Learning Outcome
Students apply an understanding of size to the interpretation of length.
Learning Outcome
Students communicate length using units.
Learning Outcome
Students explain length using standard units.
Knowledge
Length may refer to the size of any one-dimensional measurable attribute of an object, including:
  • height
  • width
  • depth
  • diameter
A length does not need to be a straight line.

The length of empty space between two points is called distance.

Familiar contexts of distance include
  • distance between objects or people
  • distance between home and school
  • distance between towns or cities
Understanding
Length is a measurable attribute that describes the amount of fixed space between the end points of an object.

Length remains the same if an object is repositioned but may be named differently.
Skills & Procedures
Recognize the height, width, or depth of an object as lengths in various orientations.

Recognize the diameter of a circle as a length.

Compare and order objects according to length.

Describe distance in familiar contexts.
Knowledge
Tiling is the process of measuring a length with many copies of a unit without gaps or overlaps.

Iterating is the process of measuring a length by repeating one copy of a unit without gaps or overlaps.

Length can be measured more efficiently using a measuring tool that shows iterations of a unit.

The unit can be chosen based on the length to be measured.

Length can be measured with non-standard units or standard units (e.g., centimetres).

Standard units enable a common language around measurement.
Understanding
Length is quantified by measurement.

Length is measured with equal-sized units that themselves have length.

The size of the unit and the number of units in the length are inversely related.

Skills & Procedures
Measure length with non-standard units by tiling, iterating, or using a self-created measuring tool.

Compare and order measurements of different lengths measured with the same non-standard units, and explain the choice of unit.

Compare measurements of the same length measured with different non-standard units.

Measure length with standard units by tiling or iterating with a centimetre.

Compare and order measurements of different lengths measured with centimetres.
Knowledge
The metric system, or système international d’unités (SI), is a base-10 system first adopted in France.

The basic unit of length in the metric system is the metre.

Metric units are named using prefixes that indicate the relationship to the basic unit (e.g., for length, the prefix centi- indicates there are 100 centimetres in a metre).

Metric units are abbreviated for convenience (e.g., metre is abbreviated with m and centimetre is abbreviated with cm).

Standard measuring tools show iterations of a standard unit from an origin.

The other, older, system of measurement that is also commonly used in the United States and Canada is sometimes called the imperial system and uses “Canadian units.”

“Canadian or imperial” units that are still commonly used include miles, yards, feet, inches, acres, pounds, quarts, pints, and ounces. You may encounter these in hospitals (birth announcements), housing and property (square footage/acreage), cooking and drink (pounds,ounces, quarts, pints), some roads and cars (miles, mileage, miles per hour, gallons), railways, and other contexts where integration with the United States is important.

The perimeter of a polygon is the sum of the lengths of its sides.
Understanding
Length is measured in standard units according to the metric system.

An alternative system, the imperial system, still partly in use, uses “Canadian units” (sometimes called “imperial units”). This system is important to know about because it provides core numeracy for current everyday life, understanding works of the past, and literacy concerning culture and trade with our biggest trading partner, the United States.

Length can be expressed in various units according to context and desired precision.

Length remains the same when decomposed or rearranged.
Skills & Procedures
Relate the metric system to the place value system.

Relate centimetres to metres.

Justify the choice of centimetres or metres to measure various lengths.

Measure lengths of straight lines and curves, with centimetres or metres, using a standard measuring tool.

Express length in centimetres or metres.

Convert commonly used units of measure between metric and Canadian (imperial) units within 100.

Determine perimeter of polygons.

Determine the length of an unknown side given the perimeter of a polygon.

Knowledge
Indirect comparison is useful when objects are fixed in place or difficult to move.
Understanding
The size of two objects can be compared indirectly with a third object.
Skills & Procedures
Compare the length, area, mass, or capacity of two objects directly, or indirectly using a third object.

Order objects according to length, area, mass, or capacity.

Describe the size of an object in relation to another object, using comparative language.

Knowledge
A referent is a personal or familiar representation of a known length.

A common referent for a centimetre is the width of the tip of the little finger.
Understanding
Length can be estimated when a measuring tool is not available.
Skills & Procedures
Identify referents for a centimetre.

Estimate length by visualizing the iteration of a referent for a centimetre.

Investigate First Nations, Métis, or Inuit use of the land in estimations of length.
Knowledge
A benchmark is a known length to which another length can be compared.

A referent is a personal or familiar representation of a known length.

A common referent for a metre is the distance from a doorknob to the floor.
Understanding
Length can be estimated when less accuracy is required.
Skills & Procedures
Identify referents for a centimetre and a metre.

Estimate length by comparing to a benchmark of a centimetre or metre.

Estimate length by visualizing the iteration of a referent for a centimetre or metre.

Organizing Idea
Patterns: Awareness of patterns supports problem solving in various situations.
Guiding Question
What can pattern communicate?
Guiding Question
How can pattern characterize change?
Guiding Question
How can diverse representations of pattern contribute to our interpretation of change?
Learning Outcome
Students examine pattern in cycles.
Learning Outcome
Students explain and generalize pattern.
Learning Outcome
Students analyze pattern in numerical sequences.
Knowledge
A cycle can express repetition of events or experiences.

Cycles include
  • seasons
  • day/night
  • life cycles
  • calendars
A pattern remains the same when elements are represented in different forms, including
  • sounds
  • objects
  • pictures
  • symbols
  • actions
Patterns can be extended by reasoning about existing elements.

Understanding
A pattern that appears to repeat may not repeat in the same way forever.

A cycle is a repeating pattern that repeats in the same way forever.

Skills & Procedures
Recognize cycles encountered in daily routines and nature.

Investigate cycles found in nature that inform First Nations, Métis, or Inuit practices.

Identify the pattern core, up to four elements, in a cycle.

Identify a missing element in a repeating pattern or cycle.

Describe change and constancy in repeating patterns and cycles.

Create different representations of the same repeating pattern or cycle, limited to a pattern core of up to four elements.

Extend a sequence of elements in various ways to create repeating patterns.


Knowledge
Change can be an increase or a decrease in the number and size of elements.

Pascal’s triangle is a triangular arrangement of numbers that illustrates multiple repeating, growing, and symmetrical patterns.

Understanding
A pattern can show increasing or decreasing change.

A pattern is more evident when the elements are represented, organized, aligned, or oriented in familiar ways.
Skills & Procedures
Describe non-repeating patterns encountered in surroundings, including in art, architecture, and nature.

Examine the representation, organization, alignment, or orientation of patterns in First Nations, Métis, or Inuit design.

Investigate pattern in Pascal’s triangle.

Create and express growing patterns using sounds, objects, pictures, or actions.

Explain the change and constancy in a given non-numerical growing pattern.

Extend a non-numerical growing pattern.

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.


Understanding
A sequence is a list of terms arranged in a certain order.

Sequences may be finite or infinite.
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.
Knowledge
A pattern core becomes more complex as more attributes change between elements.
Understanding
A pattern core can vary in complexity.
Skills & Procedures
Create and express a repeating pattern with a pattern core of up to four elements that change by more than one attribute.
Knowledge
Numerical sequences can be constructed using addition, subtraction, multiplication, or division.
Understanding
A sequence can progress according to a pattern.
Skills & Procedures
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.

Guess the next term in a sequence by inferring the pattern from the previous terms.

Organizing Idea
Time: Duration is described and quantified with time.
Guiding Question
How can time characterize change?
Guiding Question
How can duration support our interpretation of time?
Guiding Question
How can we communicate duration?
Learning Outcome
Students explain time in relation to cycles.
Learning Outcome
Students relate duration to time.
Learning Outcome
Students tell time using clocks.
Knowledge
Time can be perceived through observable change.

First Nations, Métis, and Inuit experience time through sequences and cycles in nature, including cycles of seasons and stars.

Cycles from a calendar include days of the week and months of the year.
Understanding
Time is an experience of change.

Time can be perceived as a cycle.

Skills & Procedures
Describe cycles of time encountered in daily routines and nature.

Describe observable changes that indicate a cycle of time.

Relate cycles of seasons and stars to First Nations, Métis, or Inuit practices.

Identify cycles from a calendar.
Knowledge
Events can be related to calendar dates.

Comparative language for describing duration can include
  • longer
  • shorter
  • sooner
  • later
Duration can be measured in non-standard units, including events, natural cycles, or personal referents.
Understanding
Time can be communicated in various ways.

Duration is the measure of an amount of time from beginning to end.

Duration can be measured in various units according to context.
Skills & Procedures
Express significant events using calendar dates.

Describe the duration between or until significant events using comparative language.

Describe the duration of events using non-standard units.

Relate First Nations’ winter counts to duration.
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 of a minute.

One minute is 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 according to context.
Knowledge
Standard units of time can include
  • years
  • months
  • weeks
  • days
  • hours
  • minutes
  • seconds
Understanding
Duration is quantified by measurement.
Skills & Procedures
Describe the relationship between days, weeks, months, and years.

Describe the duration between or until significant events using standard units of time.
Organizing Idea
Statistics: The science of collecting, analyzing, visualizing, and interpreting data can inform understanding and decision making.
Guiding Question
How can we use data as we wonder about our world?
Guiding Question
How can data inform representation?
Guiding Question
How can representation support communication?
Learning Outcome
Students acquire an understanding of data.
Learning Outcome
Students relate data to representation.
Learning Outcome
Students interpret and explain representation.
Knowledge
Data can be collected information.
Understanding
Data can be answers to questions.
Skills & Procedures
Share wonderings about people, things, events, or experiences.

Pose questions about people, things, events, or experiences in the learning environment.

Gather data by sharing answers to questions.
Knowledge
Data can be collected by conducting a survey.

First-hand data is data collected by the person using the data.
Understanding
Data can be collected to answer questions.
Skills & Procedures
Generate questions for a specific investigation within the learning environment.

Collect first-hand data by questioning people within the learning environment.
Knowledge
Statistical questions are questions that can be answered by collecting data.
Understanding
Representation connects data to a statistical question.
Skills & Procedures
Formulate statistical questions for investigation.

Predict the answer to a statistical question.
Knowledge
A graph is a visual representation of data.

A graph can represent data by using objects, pictures, or numbers.
Understanding
Data can be represented in a graph.
Skills & Procedures
Collaborate to construct a concrete graph using data collected in the learning environment.

Create a pictograph from a concrete graph.
Knowledge
Data can be recorded using tally marks, words, or counts.

Graphs can include
  • pictographs
  • bar graphs
  • dot plots
Data can be expressed through First Nations, Métis, or Inuit stories.

A graph can include features such as
  • a title
  • a legend
  • axes
  • axis labels
Understanding
Data can be represented in various ways.
Skills & Procedures
Record data in a table.

Construct graphs to represent data.

Compare the features of pictographs, dot plots, and bar graphs.
Knowledge
Second-hand data is data collected by others.

Sources of second-hand data include
  • newspapers
  • maps
  • databases
  • websites
  • social media
  • stories
Understanding
Representation expresses data specific to a unique time and place.

Representation tells a story about data.
Skills & Procedures
Collect second-hand data using digital or non-digital tools and resources.

Represent 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.