Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe examples of increasing and decreasing patterns in the environment and other contexts
• Name numerals
• Read and write number words including multiples of 10s, and multiples of 100s
• Represent numbers and place value to 1 000
• Represent numbers as number expressions
• Place benchmarks of zero, five, 10, 20, 50, 100 … 1 000
• Skip count by twos, fives, 10, 100s starting anywhere in the number sequence
• Skip count by threes, fours, 25s starting at multiples
• Order sets of numbers in ascending and descending order
• Explain skip counting patterns
• Explain the place value of each digit of given numbers
• Extend given increasing and decreasing patterns
• Create increasing and decreasing patterns for given pattern rules

Skill Descriptor: Justify choices to determine “how many” using personal strategies.

Global Competencies: CTPS

Achievement Indicators:

• Identify quantities using groups, skip counting, and place value concretely, pictorially, and symbolically
• Explain the process used to determine “how many”
• Justify whether sides of number sentences are equal (=) or not equal (≠)

Skill Descriptor: Estimate quantities using benchmarks or referents

Global Competencies: CM, CTPS

Achievement Indicators:

• Select an estimation from multiple possible estimates
• Estimate quantities up to 1,000 using benchmarks or referents
• Estimate the number of groups of 10s and 100s in quantities
• Justify referents or benchmarks
• Estimate solutions for addition and subtraction problems

Skill Descriptor: Demonstrate fluency in addition and subtraction with flexibility, efficiency and accuracy to solve problems

Global Competencies: CTPS

Achievement Indicators:

• Recall addition and subtraction facts to solve problems
• Represent addition and subtraction in numbers to 100 concretely and pictorially
• Record addition and subtraction symbolically
• Create addition or subtraction number sentences and story problems
• Solve addition and subtraction problems

Skill Descriptor: Apply adding and subtracting strategies in-context

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Apply personal or foundational strategies for addition and subtraction to solve problems
• Explain strategies used to add and subtract two two-digit numerals
• Explain rules for adding and subtracting zero
• Justify choice of adding and subtracting strategies for efficiency
• Apply efficient strategies to demonstrate mathematical flexibility

Skill Descriptor: Apply foundational multiplication and division facts with flexibility, efficiency and accuracy to solve problems.

Global Competencies: CTPS, ICE

Achievement Indicators:

• Identify experiences that can be described as multiplication
• Identify experiences that can be described as equal sharing, and experiences that can be described as equal groupings
• Represent multiplication and division for foundational facts of zero, one, two, five, 10 concretely and pictorially
• Record multiplication and division symbolically
• Create multiplication and division number sentences
• Relate multiplication to division, multiplication to repeated addition, and division to repeated subtraction
• Create arrays
• Apply the commutative property
• Solve multiplication and division problems

Skill Descriptor: Explore multiplication and division strategies in-context.

Global Competencies: CTPS, SASM

Achievement Indicators:

• Apply personal strategies for multiplication and division to solve problems
• Explain personal or foundational strategies used to solve problems
• Justify choice of multiplication and division strategies for efficiency
• Apply efficient strategies to demonstrate mathematical flexibility

Skill Descriptor: Collect first-hand and second-hand data.

Global Competencies: CL, CM, CTPS, ICE, SASM

Achievement Indicators:

• Record number of 2D shapes or concrete 3D objects in sets using tally marks
• Compare line plots of displayed data to determine common attributes
• Sort data as first-hand or second-hand data
• Create questions that can be answered by gathering information about self and others, first-hand, and second-hand data
• Organize collected data
• Explain the difference between first-hand and second-hand data
• Answer questions using collected data, line plots, charts, and lists

Skill Descriptor: Explore graphs to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Compare graphs of displayed data to determine common attributes
• Display sets of data using concrete graphs
• Label title and axes of graphs
• Create pictographs using one-to-one correspondence
• Answer questions using concrete graphs and pictographs

Skill Descriptor: Solve one-step addition and subtraction equations.

Global Competencies: CM, CTPS

Achievement Indicators:

• Explain the purpose of the symbol in addition and subtraction equations with one unknown
• Create addition and subtraction equations with one unknown
• Solve addition and subtraction equations with one unknown using personal strategies

Skill Descriptor: Relate life to measurements of time.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe duration with standard units of time
• Describe relationships between seconds, minutes, and hours using an analog clock
• Relate minutes past the hour to minutes until the next hour
• Express time orally and numerically from a 12-hour analog and digital clock
• Express time using formats as appropriate to contexts (e.g., 14 h 00; 14:00)
• Describe time of day as a.m. or p.m. relative to 12-hour cycles
• Solve problems involving number of days in a week and the number of months in a year
• Solve problems involving the number of seconds in a minute, the number of minutes in an hour, and the number of days in a month

Skill Descriptor: No skill descriptor for this grade

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CTPS

Achievement Indicators:

• Name numerals
• Read and write number words and expanded notation from zero to 10 000
• Represent numbers and place value to 10 000
• Represent numbers in expanded notation concretely and pictorially
• Identify patterns found in tables and charts
• Place benchmark numbers of zero, five, 10, 20, 50, 100, 1 000 … 10 000
• Explain the place value of each digit of given numbers
• Apply patterns to count with unit fractions
• Extend patterns found in tables and charts

Skill Descriptor: Justify choices to determine “how many” using personal strategies.

Global Competencies: CTPS

Achievement Indicators:

• Identify quantities using groups, place value and multiplication concretely, pictorially, and symbolically
• Identify “how many” given diagrams, sets or concrete 3D objects
• Identify the number of parts (proper/improper fractions) and the number of wholes (proper/mixed fractions) of diagrams or concrete 3D objects
• Identify fractions of a set given diagrams or concrete 3D objects
• Explain the process used to determine “how many”

Skill Descriptor: Describe fractions.

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide examples when fractions are used
• Provide examples when two identical fractions may not represent the same quantity
• Name fractions represented by the shaded and non-shaded parts of regions, sets, and wholes
• Name fractions greater than one using total number of equal parts (improper fractions) or total number of wholes (mixed numbers)
• Sort diagrams by those with equal regions or parts
• Record fractions represented by the shaded and non-shaded parts of regions, sets, and wholes
• Compare unit fractions
• Identify closest benchmarks to given fractions
• Order sets of fractions using patterns, benchmarks, numerators, and denominators
• Represent equivalent fractions concretely and pictorially
• Represent fractions less than one concretely and pictorially
• Represent fractions of a set or whole
• Represent fractions greater than one concretely or pictorially
• Explain the meaning of numerators and denominators

Skill Descriptor: Estimate quantities using benchmarks or referents.

Global Competencies: CTPS

Achievement Indicators:

• Describe situations in which estimates are sufficient
• Estimate quantities up to 10,000 using benchmarks or referents
• Estimate sums and differences using front-end estimation and compensation strategies
• Justify estimation benchmarks or referents

Skill Descriptor: Demonstrate fluency in addition and subtraction with flexibility, efficiency and accuracy to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Represent addition and subtraction with efficiency
• Record addition and subtraction symbolically
• Explain how to keep track of digits that have the same place value when adding and subtracting numbers
• Explain solutions to addition and subtraction problems
• Create addition or subtraction problems for number sentences
• Solve addition and subtraction problems that involve multiple steps

Skill Descriptor: Apply adding and subtracting strategies in-context.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Apply efficient strategies to solve problems
• Justify choice of strategies for efficiency
• Justify the reasonableness of results
• Solve problems using personal and/or foundational strategies

Skill Descriptor: Apply derived multiplication and division facts with flexibility, efficiency and accuracy to solve problems.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Represent multiplication and division concretely or pictorially
• Represent multiplication and division for foundational and derived facts
• Apply the distributive property
• Apply personal strategies to estimate products and quotients
• Create arrays
• Create multiplication and division problems
• Explain the property when multiplying numbers by one
• Explain the property when multiplying or dividing numbers by zero
• Solve multiplication and division problems including word problems, with and without remainders

Skill Descriptor: Explore multiplication and division strategies in-context.

Global Competencies: CTPS, SASM

Achievement Indicators:

• Apply personal or foundational strategies for multiplication and division to solve problems
• Explain strategies used to multiply and divide
• Justify choice of multiplication and division strategies for efficiency
• Apply efficient strategies to demonstrate mathematical flexibility

Skill Descriptor: Create graphs to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify mathematical relationships using charts and diagrams
• Compare graphs where different intervals or correspondences are used
• Explain why many-to-one correspondence or one-to-one correspondence are used in graphs
• Describe relationships in Venn diagrams: when the circles intersect; when one circle is contained in the other; when the circles are separate
• Complete Carroll diagrams by inserting data into squares
• Create and label pictographs and bar graphs to display sets of data
• Justify choice of interval and correspondence for displayed sets of data in graphs
• Apply the use of Carroll diagrams, Venn diagrams, pictographs, and bar graphs to solve problems

Skill Descriptor: Solve one-step equations.

Global Competencies: CM, CTPS

Achievement Indicators:

• Represent one-step equations and addition and subtraction problems involving part-part-whole
• Represent multiplication and division problems involving equal grouping or partitioning (equal sharing) using symbols to represent the unknown
• Record equations from concrete and pictorial representations
• Apply “guess and test” to solve one-step equations
• Interpret one-step equations with one unknown
• Solve story problems by identifying unknowns
• Solve equations with the unknown on the left or right side of the equation

Skill Descriptor: Estimate and measure using personal referents and measurement tools.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Identify personal referents for one centimetre, one metre, one square centimeter, one square metre
• Estimate length using personal referents
• Estimate perimeters of 2D shapes and concrete 3D objects
• Estimate area of 2D shapes using personal referents
• Measure and record length and width of 2D shapes
• Measure and record length, width, and height of concrete 3D objects
• Measure and record the perimeter of regular and irregular 2D shapes and concrete 3D objects
• Measure and record area of regular and irregular 2D shapes
• Create line segments using rulers
• Explain strategies used to measure regular and irregular 2D shapes (length, perimeter, area)
• Explain why squares are efficient units for measuring area

Skill Descriptor: Describe 2D shapes.

Global Competencies: CTPS

Achievement Indicators:

• Describe 2D shapes using language such as parallel, intersecting, perpendicular, vertical, or horizontal
• Describe 2D shapes found in the environment and other contexts
• Identify properties of symmetrical and non-symmetrical 2D shapes
• Identify properties of triangles according to their sides and/or their interior angles
• Identify properties of congruent 2D shapes
• Measure congruence of 2D shapes using superimposition
• Reproduce 2D shapes in different orientations with and without technology
• Explain sorting rules for 2D shapes (e.g. polygons/non-polygons, regular/irregular polygons, number of sides, length of sides, interior angles, symmetrical/non-symmetrical)

Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CTPS

Achievement Indicators:

• Name numerals
• Read and write number words and expanded notation from zero to 1 000 000
• Represent numbers and place value to 1 000 000
• Explain the place value of each digit of given numbers
• Place benchmark numbers of zero, five, 10, 20, 50, 100, 1 000, 10 000, … 1 000 000
• Order numbers, decimals, and mixed sets of fractions

Skill Descriptor: Justify choices to determine “how many” using personal strategies.

Global Competencies: CTPS

Achievement Indicators:

• Identify “how many” given diagrams, sets or concrete 3D objects
• Identify fractions and equivalent decimals by the number of parts (proper/improper fractions) and the number of wholes (proper/mixed fractions) of diagrams or concrete 3D objects
• Identify fractions and equivalent decimals within sets of diagrams or concrete 3D objects

Skill Descriptor: Describe decimals (tenths, hundredths, thousandths).

Global Competencies: CM, CTPS

Achievement Indicators:

• Provide examples when decimals are used
• Represent equivalent tenths, hundredths, and thousandths for decimals
• Represent equivalent fractions and decimals
• Represent money values using decimals
• Record decimals for parts of a set, parts of a region, and parts of units of measure
• Record fractions as decimals and vice-versa
• Explain the place value of each digit of given decimals

Skill Descriptor: Estimate quantities to solve problems.

Global Competencies: CTPS, SASM

Achievement Indicators:

• Describe estimation contexts used to: make predictions; check the reasonableness of answers; determine approximate answers; overestimate
• Estimate sums, differences, products, quotients, using estimation strategies
• Estimate sums and differences of positive fractions and mixed numbers
• Estimate sums and differences of decimals

Skill Descriptor: Demonstrate fluency in multiplication and division facts with flexibility, efficiency and accuracy to solve problems

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Describe division contexts where it is appropriate to: round up the quotient; ignore the remainder
• Represent multiplication and division concretely, pictorially, or symbolically
• Apply foundational and derived multiplication and division facts
• Apply the distributive property to represent two-digit factors in expanded form
• Solve multiplication and division problems

Skill Descriptor: Apply multiplication and division strategies in-context.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Apply personal or foundational strategies for multiplication and division to solve problems
• Explain strategies used to multiply and divide
• Explain why multiplying by zero produces a product of zero
• Explain why division by zero is undefined
• Justify choice of multiplication and division strategies for efficiency
• Apply efficient strategies to demonstrate mathematical flexibility

Skill Descriptor: Add and subtract decimals to solve problems (limited to thousandths).

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Apply compatible numbers strategy
• Apply front-end estimation to place the decimal point in a sum or difference
• Add and subtract decimals using mental mathematics strategies
• Add and subtract decimals (limited to thousandths)
• Solve problems including money and measurement

Skill Descriptor: Add and subtract fractions and mixed numbers to solve problems (limited to positive sums and differences).

Global Competencies: CTPS

Achievement Indicators:

• Represent fractions and mixed numbers concretely and pictorially
• Represent fractions greater than one concretely and pictorially
• Express improper fractions as mixed numbers and vice-versa
• Estimate sums and differences
• Determine common denominators for sets of positive fractions and mixed numbers
• Add and subtract positive fractions and mixed numbers
• Simplify fractions and mixed numbers
• Justify the reasonableness of solutions

Skill Descriptor: Interpret graphs to solve problems.

Global Competencies: CTPS

Achievement Indicators:

• Describe graphs and patterns using mathematics language like one more, one less, five more, five less, etc.
• Compare graphs to determine their attributes
• Extrapolate data in graphs using patterns
• Record mathematical expressions representing patterns and relationships in graphs
• Create graphs representing sets of data that include title, axes, intervals, and legend
• Create graphs with and without the use of technology
• Apply conclusions from graphs to answer questions

Skill Descriptor: Determine the probability of outcomes occurring in probability experiments to solve problems.

Global Competencies: CM, CTPS, ICE

Achievement Indicators:

• Classify likelihood of single outcomes occurring or provide examples of events that are impossible, possible, or certain
• Classify outcomes from given probability experiments that are less likely, equally likely, or more likely to occur than other outcomes
• Plot likelihood of single outcomes occurring along a continuum of possibilities
• Conduct probability experiments multiple times to collect data
• Design, conduct probability experiment, and record the likelihood of single outcomes occurring that are impossible, possible, or certain
• Conduct probability experiments in which one outcome is less likely, equally likely, or more likely to occur than the other outcome

Skill Descriptor: Solve one-step equations.

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify unknowns in problems
• Represent problems as equations
• Record equations where the unknown is represented by a letter variable
• Create problems representing equations with one unknown
• Solve single-variable equations with the unknown in any of the terms

Skill Descriptor: Estimate and measure using personal referents and measurement tools.

Global Competencies: CM, CTPS, SASM

Achievement Indicators:

• Identify personal referents for one centimetre, one metre, one square centimetre, one square metre, one gram, one kilogram, one millimetre, one kilometre, one millilitre, one litre
• Match standard units to referents
• Estimate mass, length, and capacity using personal referents
• Explain the relationship between place value and standard units of measure
• Measure and record length and width of 2D shapes
• Measure and record length, width, and height of concrete 3D objects
• Measure and record mass of concrete 3D objects
• Measure and record volume of liquid

Skill Descriptor: No skill descriptor for this grade