## elementary Block:

# Mathematics

Learners work individually, in partners, or in groups within the context of critical thinking, reasoning, and problem-solving. They combine, compare, multiply, and share (divide) quantities, and work with increasing

magnitude, fractions and decimals. Learners develop and communicate their understanding through concrete, pictorial, and/or symbolic representations of mathematics. Problem-solving includes the use of mathematical tools (manipulatives), drawings, written work, and technology. Learners create and ask questions while applying understanding to concepts and events in their lives. Formal mathematics learning experiences will present mathematics as a means to quantify and organize their world.

#### CONTEXTS AND CONCEPTS

##### EXPERIMENTATION

**STRATEGIES**

- Determining when to use and developing mental procedures and strategies
- Determining appropriate units of measure
- Determining the reasonableness of an answer and explaining thinking or rules

**PROCESSES**

- Using mathematical rules and algorithms
- Using manipulatives
- Algorithms
- Standard measurement
- Modeling
- Creating graphs

**FLUENCY**

- Computation skills, formats, and representations of numbers
- Automaticity (with foundational facts)
- Working with polyhedrons
- Working with curved surfaces
- Scale

**COMMUNICATION**

- Representing mathematics concretely, pictorially, and symbolically
- Using mathematical vocabulary
- Using mathematical symbols
- Standard notation
- Mathematical expressions

### Strand: Number

#### Big Idea: Number Sense

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

**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 (≠)

#### Big Idea: Operations

**Skill Descriptor:** Estimate quantities using benchmarks or referents

**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

### Strand: Statistics and Probability

#### Big Idea: Data Analysis

**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

### Strand: Patterns and Relations

#### Big Idea: Algebra

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

**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

### Strand: Shape and Space

#### Big Idea: Measurement

**Skill Descriptor:** Relate life to measurements of time.

**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

#### Big Idea: 2D Shapes and 3D Objects

**Skill Descriptor:** *No skill descriptor for this grade*

### Strand: Number

#### Big Idea: Number Sense

**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.

**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

#### Big Idea: Operations

**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.

**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

### Strand: Statistics and Probability

#### Big Idea: Data Analysis

**Skill Descriptor:** Create graphs to solve problems.

**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

### Strand: Patterns and Relations

#### Big Idea: Algebra

**Skill Descriptor:** Solve one-step equations.

**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

### Strand: Shape and Space

#### Big Idea: Measurement

**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

#### Big Idea: 2-D Shapes and 3-D Objects

**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)

### Strand: Number

#### Big Idea: Number Sense

**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).

**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

#### Big Idea: Operations

**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

### Strand: Statistics and Probability

#### Big Idea: Data Analysis

**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

#### Big Idea: Chance and Uncertainty

**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

### Strand: Patterns and Relations

#### Big Idea: Algebra

**Skill Descriptor:** Solve one-step equations.

**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

### Strand: Shape and Space

#### Big Idea: Measurement

**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

#### Big Idea: 2-D Shapes and 3-D Objects

**Skill Descriptor:** *No skill descriptor for this grade*