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  • Math Kindergarten

    Learning numbers and solving problems with patterns. Your child will represent and describe quantities of things up to 10. They will understand and create repeating patterns and compare objects based on their attributes. They will solve problems involving numbers, patterns and objects, and connect numbers to their everyday life.

  • Math Kindergarten >

    Number

    Develop number sense.

  • Math Kindergarten > Number > Specific Outcome 1

    1. Say the number sequence 1 to 10 by 1s, starting anywhere from 1 to 10 and from 10 to 1.
    • Counting in Order
      Created by Khan Academy.
      assignment
      YouTube

  • Math Kindergarten > Number > Specific Outcome 2

    2. Subitize (recognize at a glance) and name familiar arrangements of 1 to 5 objects or dots.

  • Math Kindergarten > Number > Specific Outcome 3

    3. Relate a numeral, 1 to 10, to its respective quantity.

  • Math Kindergarten > Number > Specific Outcome 4

    4. Represent and describe numbers 2 to 10, concretely and pictorially.

  • Math Kindergarten > Number > Specific Outcome 5

    5. Compare quantities 1 to 10, using one-to-one correspondence.

  • Math Kindergarten >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math Kindergarten > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Demonstrate an understanding of repeating patterns (two or three elements) by:
    • identifying
    • reproducing
    • extending
    • creating
    patterns using manipulatives, sounds and actions.

  • Math Kindergarten > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Sort a set of objects based on a single attribute, and explain the sorting rule.

  • Math Kindergarten >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math Kindergarten > Shape and Space (Measurement) > Specific Outcome 1

    1. Use direct comparison to compare two objects based on a single attribute, such as length (height), mass (weight) and volume (capacity).

  • Math Kindergarten >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them

  • Math Kindergarten > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 1

    1. Sort 3-D objects, using a single attribute.

  • Math Kindergarten > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 2

    2. Build and describe 3-D objects.

  • Math 1

    Building the basics through addition and subtraction facts. Your child will count to 100 in different ways, and describe and estimate quantities to 20. They will understand and apply strategies for addition facts up to and including 9 + 9 and related subtraction facts, and recall addition facts to a sum of 5 and related subtraction facts. They will connect numbers to their everyday life, and find geometric shapes in their surroundings. Your child will solve problems involving numbers, patterns and measurement.

  • Math 1 >

    Number

    Develop number sense.

  • Math 1 > Number > Specific Outcome 1

    1. Say the number sequence 0 to 100 by:
    • 1s forward between any two given numbers
    • 1s backward from 20 to 0
    • 2s forward from 0 to 20
    • 5s and 10s forward from 0 to 100.

  • Math 1 > Number > Specific Outcome 2

    2. Subitize (recognize at a glance) and name familiar arrangements of 1 to 10 objects or dots.

  • Math 1 > Number > Specific Outcome 3

    3. Demonstrate an understanding of counting by:
    • indicating that the last number said identifies “how many”
    • showing that any set has only one count
    • using counting-on
    • using parts or equal groups to count sets.
    • Counting in Order
      Created by Khan Academy.
      assignment
      YouTube

  • Math 1 > Number > Specific Outcome 4

    4. Represent and describe numbers to 20, concretely, pictorially and symbolically.

  • Math 1 > Number > Specific Outcome 5

    5. Compare sets containing up to 20 elements, using:
    • referents
    • one-to-one correspondence to solve problems.

  • Math 1 > Number > Specific Outcome 6

    6. Estimate quantities to 20 by using referents.

  • Math 1 > Number > Specific Outcome 7

    7. Demonstrate an understanding of conservation of number.

  • Math 1 > Number > Specific Outcome 8

    8. Identify the number, up to 20, that is:
    • one more
    • two more
    • one less
    • two less
    than a given number.

  • Math 1 > Number > Specific Outcome 9

    9. Demonstrate an understanding of addition of numbers with answers to 20 and their corresponding subtraction facts, concretely, pictorially and symbolically, by:
    • using familiar mathematical language to describe additive and subtractive actions
    • creating and solving problems in context that involve addition and subtraction
    • modelling addition and subtraction, using a variety of concrete and visual representations, and recording the process symbolically.
    • Adding to 10
      Created by Khan Academy.
      assignment
      YouTube
    • Introduction To Addition
      Created by Khan Academy.
      assignment
      YouTube

  • Math 1 > Number > Specific Outcome 10

    10. Describe and use mental mathematics strategies for basic addition facts and related subtraction facts to 18.
    • Adding to 10
      Created by Khan Academy.
      assignment
      YouTube
    • Introduction To Addition
      Created by Khan Academy.
      assignment
      YouTube

  • Math 1 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 1 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Demonstrate an understanding of repeating patterns (two to four elements) by:
    • describing
    • reproducing
    • extending
    • creating patterns using manipulatives, diagrams, sounds and actions.

  • Math 1 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Translate repeating patterns from one representation to another.

  • Math 1 > Patterns and Relations (Patterns) > Specific Outcome 3

    3. Sort objects, using one attribute, and explain the sorting rule.

  • Math 1 >

    Patterns and Relations (Varaibles and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 1 > Patterns and Relations (Varaibles and Equations) > Specific Outcome 4

    4. Describe equality as a balance and inequality as an imbalance, concretely and pictorially (0 to 20).

  • Math 1 > Patterns and Relations (Varaibles and Equations) > Specific Outcome 5

    5. Record equalities, using the equal symbol.

  • Math 1 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 1 > Shape and Space (Measurement) > Specific Outcome 1

    1. Demonstrate an understanding of measurement as a process of comparing by:
    • identifying attributes that can be compared
    • ordering objects
    • making statements of comparison
    • filling, covering or matching.

  • Math 1 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 1 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 2

    2. Sort 3-D objects and 2-D shapes, using one attribute, and explain the sorting rule.

  • Math 1 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 3

    3. Replicate composite 2-D shapes and 3-D objects.

  • Math 1 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 4

    3. Compare 2-D shapes to parts of 3-D objects in the environment.

  • Math 2

    Using mathematics to solve problems. Your child will count, describe and estimate quantities to 100 in a variety of ways. They will understand and apply strategies for addition facts up to and including 9 + 9 and related subtraction facts, recall addition facts up to and including 5 + 5 and related subtraction facts, and add and subtract numbers to 100. Your child will solve problems using numbers, patterns, measurement and data collection, and use graphs and charts to communicate information.

  • Math 2 >

    Number

    Develop number sense.

  • Math 2 > Number > Specific Outcome 1

    1. Say the number sequence 0 to 100 by:
    • 2s, 5s and 10s, forward and backward, using starting points that are multiples of 2, 5 and 10 respectively
    • 10s, using starting points from 1 to 9
    • 2s, starting from 1.

  • Math 2 > Number > Specific Outcome 2

    2. Demonstrate if a number (up to 100) is even or odd.

  • Math 2 > Number > Specific Outcome 3

    3. Describe order or relative position, using ordinal numbers (up to tenth).

  • Math 2 > Number > Specific Outcome 4

    4. Represent and describe numbers to 100, concretely, pictorially and symbolically.

  • Math 2 > Number > Specific Outcome 5

    5. Compare and order numbers up to 100.

  • Math 2 > Number > Specific Outcome 6

    6. Estimate quantities to 100, using referents.

  • Math 2 > Number > Specific Outcome 7

    7. Illustrate, concretely and pictorially, the meaning of place value for numerals to 100.

  • Math 2 > Number > Specific Outcome 8

    8. Demonstrate and explain the effect of adding zero to, or subtracting zero from, any number.

  • Math 2 > Number > Specific Outcome 9

    9. Demonstrate an understanding of addition (limited to 1- and 2-digit numerals) with answers to 100 and the corresponding subtraction by:
    • using personal strategies for adding and subtracting with and without the support of manipulatives
    • creating and solving problems that involve addition and subtraction
    • using the commutative property of addition (the order in which numbers are added does not affect the sum)
    • using the associative property of addition (grouping a set of numbers in different ways does not affect the sum)
    • explaining that the order in which numbers are subtracted may affect the difference.
    • Adding to 10
      Created by Khan Academy.
      assignment
      YouTube
    • Introduction To Addition
      Created by Khan Academy.
      assignment
      YouTube

  • Math 2 > Number > Specific Outcome 10

    10. Apply mental mathematics strategies for basic addition facts and related subtraction facts to 18.
    • Adding to 10
      Created by Khan Academy.
      assignment
      YouTube
    • Introduction To Addition
      Created by Khan Academy.
      assignment
      YouTube

  • Math 2 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 2 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Demonstrate an understanding of repeating patterns (three to five elements) by:
    • describing
    • extending
    • comparing
    • creating
    patterns using manipulatives, diagrams, sounds and actions.

  • Math 2 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Demonstrate an understanding of increasing patterns by:
    • describing
    • extending
    • comparing
    • creating
    numerical (numbers to 100) and non-numerical patterns using manipulatives, diagrams, sounds and actions.

  • Math 2 > Patterns and Relations (Patterns) > Specific Outcome 3

    3. Sort a set of objects, using two attributes, and explain the sorting rule.

  • Math 2 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 2 > Patterns and Relations (Variables and Equations) > Specific Outcome 4

    4. Demonstrate and explain the meaning of equality and inequality, concretely and pictorially.

  • Math 2 > Patterns and Relations (Variables and Equations) > Specific Outcome 5

    5. Record equalities and inequalities symbolically, using the equal symbol or the not equal symbol.

  • Math 2 >

    Shapes and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 2 > Shapes and Space (Measurement) > Specific Outcome 1

    1. Relate the number of days to a week and the number of months to a year in a problem-solving context.

  • Math 2 > Shapes and Space (Measurement) > Specific Outcome 2

    2. Relate the size of a unit of measure to the number of units (limited to nonstandard units) used to measure length and mass (weight).

  • Math 2 > Shapes and Space (Measurement) > Specific Outcome 3

    3. Compare and order objects by length, height, distance around and mass (weight), using nonstandard units, and make statements of comparison.

  • Math 2 > Shapes and Space (Measurement) > Specific Outcome 4

    4. Measure length to the nearest nonstandard unit by:
    • using multiple copies of a unit
    • using a single copy of a unit (iteration process).

  • Math 2 > Shapes and Space (Measurement) > Specific Outcome 5

    5. Demonstrate that changing the orientation of an object does not alter the measurements of its attributes.

  • Math 2 >

    Shapes and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 2 > Shapes and Space (3-D Objects and 2-D Shapes) > Specific Outcome 6

    6. Sort 2-D shapes and 3-D objects, using two attributes, and explain the sorting rule.

  • Math 2 > Shapes and Space (3-D Objects and 2-D Shapes) > Specific Outcome 7

    7. Describe, compare and construct 3-D objects, including:
    • cubes
    • spheres
    • cones
    • cylinders
    • pyramids.

  • Math 2 > Shapes and Space (3-D Objects and 2-D Shapes) > Specific Outcome 8

    8. Describe, compare and construct 2-D shapes, including:
    • triangles
    • squares
    • rectangles
    • circles.

  • Math 2 > Shapes and Space (3-D Objects and 2-D Shapes) > Specific Outcome 9

    9. Identify 2-D shapes as parts of 3-D objects in the environment.

  • Math 2 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 2 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Gather and record data about self and others to answer questions.

  • Math 2 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Construct and interpret concrete graphs and pictographs to solve problems.

  • Math 3

    Introduction to multiplication and division. Your child will learn about numbers to 1000, using place value. They will understand, apply and recall addition facts up to and including 9 + 9 and related subtraction facts, and add and subtract 2- and 3-digit numbers, including the use of mental mathematics strategies. Your child will understand and recall multiplication to 5 x 5 and related division facts. They will solve problems involving number, patterns, measurement and data, and use symbols to solve one-step addition and subtraction equations.

  • Math 3 >

    Number

    Develop number sense.

  • Math 3 > Number > Specific Outcome 1

    1. Say the number sequence 0 to 1000 forward and backward by:
    • 5s, 10s or 100s, using any starting point
    • 3s, using starting points that are multiples of 3
    • 4s, using starting points that are multiples of 4
    • 25s, using starting points that are multiples of 25.

  • Math 3 > Number > Specific Outcome 2

    2. Represent and describe numbers to 1000, concretely, pictorially and symbolically.

  • Math 3 > Number > Specific Outcome 3

    3. Compare and order numbers to 1000.

  • Math 3 > Number > Specific Outcome 4

    4. Estimate quantities less than 1000, using referents.

  • Math 3 > Number > Specific Outcome 5

    5. Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.

  • Math 3 > Number > Specific Outcome 6

    6. Describe and apply mental mathematics strategies for adding two 2-digit numerals.

  • Math 3 > Number > Specific Outcome 7

    7. Describe and apply mental mathematics strategies for subtracting two 2-digit numerals.

  • Math 3 > Number > Specific Outcome 8

    8. Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context.

  • Math 3 > Number > Specific Outcome 9

    9. Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2- and 3-digit numerals), concretely, pictorially and symbolically, by:
    • using personal strategies for adding and subtracting with and without the support of manipulatives
    • creating and solving problems in context that involve addition and subtraction of numbers.

  • Math 3 > Number > Specific Outcome 10

    10. Apply mental mathematics strategies and number properties in order to understand and recall basic addition facts and related subtraction facts to 18.

  • Math 3 > Number > Specific Outcome 11

    11. Demonstrate an understanding of multiplication to 5 × 5 by:
    • representing and explaining multiplication using equal grouping and arrays
    • creating and solving problems in context that involve multiplication
    • modelling multiplication using concrete and visual representations, and recording the process symbolically
    • relating multiplication to repeated addition
    • relating multiplication to division.
    • Introduction to Multiplication
      Created by Khan Academy.
      assignment
      YouTube

  • Math 3 > Number > Specific Outcome 12

    12. Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 × 5) by:
    • representing and explaining division using equal sharing and equal grouping
    • creating and solving problems in context that involve equal sharing and equal grouping
    • modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically
    • relating division to repeated subtraction
    • relating division to multiplication.
    • Introduction to Division
      Created by Khan Academy.
      assignment
      YouTube

  • Math 3 > Number > Specific Outcome 13

    13. Demonstrate an understanding of fractions by:
    • explaining that a fraction represents a part of a whole
    • describing situations in which fractions are used
    • comparing fractions of the same whole that have like denominators.

  • Math 3 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 3 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Demonstrate an understanding of increasing patterns by:
    • describing
    • extending
    • comparing
    • creating
    numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.

  • Math 3 > Patterns and Relations (Patterns) > Specific Outcome 2

    1. Demonstrate an understanding of decreasing patterns by:
    • describing
    • extending
    • comparing
    • creating
    numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.

  • Math 3 > Patterns and Relations (Patterns) > Specific Outcome 3

    3. Sort objects or numbers, using one or more than one attribute.

  • Math 3 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 3 > Patterns and Relations (Variables and Equations) > Specific Outcome 4

    4. Solve one-step addition and subtraction equations involving a symbol to represent an unknown number.

  • Math 3 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 3 > Shape and Space (Measurement) > Specific Outcome 1

    1. Relate the passage of time to common activities, using nonstandard and standard units (minutes, hours, days, weeks, months, years).

  • Math 3 > Shape and Space (Measurement) > Specific Outcome 2

    2. Relate the number of seconds to a minute, the number of minutes to an hour and the number of days to a month in a problem-solving context.

  • Math 3 > Shape and Space (Measurement) > Specific Outcome 3

    3. Demonstrate an understanding of measuring length (cm, m) by:
    • selecting and justifying referents for the units cm and m
    • modelling and describing the relationship between the units cm and m
    • estimating length, using referents
    • measuring and recording length, width and height.

  • Math 3 > Shape and Space (Measurement) > Specific Outcome 4

    4. Demonstrate an understanding of measuring mass (g, kg) by:
    • selecting and justifying referents for the units g and kg
    • modelling and describing the relationship between the units g and kg
    • estimating mass, using referents
    • measuring and recording mass.

  • Math 3 > Shape and Space (Measurement) > Specific Outcome 5

    5. Demonstrate an understanding of perimeter of regular and irregular shapes by:
    • estimating perimeter, using referents for cm or m
    • measuring and recording perimeter (cm, m)
    • constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter.

  • Math 3 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 3 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 6

    6. Describe 3-D objects according to the shape of the faces and the number of edges and vertices.

  • Math 3 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 7

    7. Sort regular and irregular polygons, including:
    • triangles
    • quadrilaterals
    • pentagons
    • hexagons
    • octagons
    according to the number of sides.

  • Math 3 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 3 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Collect first-hand data and organize it using:
    • tally marks
    • line plots
    • charts
    • lists
    to answer questions.

  • Math 3 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Construct, label and interpret bar graphs to solve problems.

  • Math 4

    Learning about fractions and decimals. Your child will learn about and compare numbers to 10 000, and add and subtract decimal numbers to hundredths. They will understand and recall multiplication and division facts to 7 x 7, and multiply and divide by 1-digit numbers, including the use of mental mathematics strategies. Your child will compare and order fractions, solve one-step equations, and find the area of 2-D shapes.

  • Math 4 >

    Number

    Develop number sense.

  • Math 4 > Number > Specific Outcome 1

    1. Represent and describe whole numbers to 10 000, pictorially and symbolically.

  • Math 4 > Number > Specific Outcome 2

    2. Compare and order numbers to 10 000.

  • Math 4 > Number > Specific Outcome 3

    3. Demonstrate an understanding of addition of numbers with answers to 10 000 and their corresponding subtractions (limited to 3- and 4-digit numerals) by:
    • using personal strategies for adding and subtracting
    • estimating sums and differences
    • solving problems involving addition and subtraction.

  • Math 4 > Number > Specific Outcome 4

    4. Apply the properties of 0 and 1 for multiplication and the property of 1 for division.

  • Math 4 > Number > Specific Outcome 5

    5. Describe and apply mental mathematics strategies to determine basic multiplication facts to 9 × 9 and related division facts.

  • Math 4 > Number > Specific Outcome 6

    6. Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) to solve problems by:
    • using personal strategies for multiplication with and without concrete materials
    • using arrays to represent multiplication
    • connecting concrete representations to symbolic representations
    • estimating products
    • applying the distributive property.

  • Math 4 > Number > Specific Outcome 7

    7. Demonstrate an understanding of division (1-digit divisor and up to 2-digit dividend) to solve problems by:
    • using personal strategies for dividing with and without concrete materials
    • estimating quotients
    • relating division to multiplication.

  • Math 4 > Number > Specific Outcome 8

    8. Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to:
    • name and record fractions for the parts of a whole or a set
    • compare and order fractions
    • model and explain that for different wholes, two identical fractions may not represent the same quantity
    • provide examples of where fractions are used.

  • Math 4 > Number > Specific Outcome 9

    9. Represent and describe decimals (tenths and hundredths), concretely, pictorially and symbolically.

  • Math 4 > Number > Specific Outcome 10

    10. Relate decimals to fractions and fractions to decimals (to hundredths).

  • Math 4 > Number > Specific Outcome 11

    11. Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by:
    • using personal strategies to determine sums and differences
    • estimating sums and differences
    • using mental mathematics strategies
    to solve problems.

  • Math 4 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 4 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Identify and describe patterns found in tables and charts.

  • Math 4 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Translate among different representations of a pattern, such as a table, a chart or concrete materials.

  • Math 4 > Patterns and Relations (Patterns) > Specific Outcome 3

    3. Represent, describe and extend patterns and relationships, using charts and tables, to solve problems.

  • Math 4 > Patterns and Relations (Patterns) > Specific Outcome 4

    4. Identify and explain mathematical relationships, using charts and diagrams, to solve problems.

  • Math 4 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 4 > Patterns and Relations (Variables and Equations) > Specific Outcome 5

    5. Express a given problem as an equation in which a symbol is used to represent an unknown number.

  • Math 4 > Patterns and Relations (Variables and Equations) > Specific Outcome 6

    6. Solve one-step equations involving a symbol to represent an unknown number.

  • Math 4 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 4 > Shape and Space (Measurement) > Specific Outcome 1

    1. Read and record time, using digital and analog clocks, including 24-hour clocks.

  • Math 4 > Shape and Space (Measurement) > Specific Outcome 2

    2. Read and record calendar dates in a variety of formats.

  • Math 4 > Shape and Space (Measurement) > Specific Outcome 3

    3. Demonstrate an understanding of area of regular and irregular 2-D shapes by:
    • recognizing that area is measured in square units
    • selecting and justifying referents for the units cm2 or m2
    • estimating area, using referents for cm2 or m2
    • determining and recording area (cm2 or m2)
    • constructing different rectangles for a given area (cm2 or m2) in order to demonstrate that many different rectangles may have the same area.

  • Math 4 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 4 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 4

    4. Describe and construct right rectangular and right triangular prisms.

  • Math 4 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.

  • Math 4 > Shape and Space (Transformations) > Specific Outcome 5

    5. Demonstrate an understanding of congruency, concretely and pictorially.

  • Math 4 > Shape and Space (Transformations) > Specific Outcome 6

    6. Demonstrate an understanding of line symmetry by:
    • identifying symmetrical 2-D shapes
    • creating symmetrical 2-D shapes
    • drawing one or more lines of symmetry in a 2-D shape.

  • Math 4 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 4 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Demonstrate an understanding of many-to-one correspondence.

  • Math 4 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Construct and interpret pictographs and bar graphs involving many-to-one correspondence to draw conclusions.

  • Math 5

    Using mathematics to solve problems. Your child will understand, recall and apply multiplication and related division facts to 9 x 9. They will multiply 2-digit by 2-digit numbers, and divide 3-digit numbers by 1-digit numbers, including the use of mental mathematics strategies. Your child will compare fractions with like and unlike denominators, and describe, compare, add and subtract decimal numbers (to thousandths). They will also write and solve one-step equations to solve problems with whole number solutions, and learn about probability.

  • Math 5 >

    Number

    Develop number sense.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Number > Specific Outcome 1

    1. Represent and describe whole numbers to 1 000 000.

  • Math 5 > Number > Specific Outcome 2

    2. Use estimation strategies in problem-solving contexts.

  • Math 5 > Number > Specific Outcome 3

    3. Apply mental mathematics strategies and number properties in order to understand and recall basic multiplication facts (multiplication tables) to 81 and related division facts.

  • Math 5 > Number > Specific Outcome 4

    4. Apply mental mathematics strategies for multiplication.

  • Math 5 > Number > Specific Outcome 5

    5. Demonstrate, with and without concrete materials, an understanding of multiplication (2-digit by 2-digit) to solve problems.

  • Math 5 > Number > Specific Outcome 6

    6. Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit), and interpret remainders to solve problems.

  • Math 5 > Number > Specific Outcome 7

    7. Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to:
    • create sets of equivalent fractions
    • compare fractions with like and unlike denominators.

  • Math 5 > Number > Specific Outcome 8

    8. Describe and represent decimals (tenths, hundredths, thousandths), concretely, pictorially and symbolically.

  • Math 5 > Number > Specific Outcome 9

    9. Relate decimals to fractions and fractions to decimals (to thousandths).

  • Math 5 > Number > Specific Outcome 10

    10. Compare and order decimals (to thousandths) by using:
    • benchmarks
    • place value
    • equivalent decimals.

  • Math 5 > Number > Specific Outcome 11

    11. Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).

  • Math 5 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 5 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Determine the pattern rule to make predictions about subsequent elements.

  • Math 5 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Patterns and Relations (Variables and Equations) > Specific Outcome 2

    2. Express a given problem as an equation in which a letter variable is used to represent an unknown number (limited to whole numbers).

  • Math 5 > Patterns and Relations (Variables and Equations) > Specific Outcome 3

    3. Solve problems involving single-variable, one-step equations with whole number coefficients and whole number solutions.

  • Math 5 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Shape and Space (Measurement) > Specific Outcome 1

    1. Identify 90º angles.

  • Math 5 > Shape and Space (Measurement) > Specific Outcome 2

    2. Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.

  • Math 5 > Shape and Space (Measurement) > Specific Outcome 3

    3. Demonstrate an understanding of measuring length (mm) by:
    • selecting and justifying referents for the unit mm
    • modelling and describing the relationship between mm and cm units, and between mm and m units.

  • Math 5 > Shape and Space (Measurement) > Specific Outcome 4

    4. Demonstrate an understanding of volume by:
    • selecting and justifying referents for cm3 or m3 units
    • estimating volume, using referents for cm3 or m3
    • measuring and recording volume (cm3 or m3)
    • constructing right rectangular prisms for a given volume.

  • Math 5 > Shape and Space (Measurement) > Specific Outcome 5

    5. Demonstrate an understanding of capacity by:
    • describing the relationship between mL and L
    • selecting and justifying referents for mL or L units
    • estimating capacity, using referents for mL or L
    • measuring and recording capacity (mL or L).

  • Math 5 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 6

    6. Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are:
    • parallel
    • intersecting
    • perpendicular
    • vertical
    • horizontal.

  • Math 5 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 7

    7. Identify and sort quadrilaterals, including:
    • rectangles
    • squares
    • trapezoids
    • parallelograms
    • rhombuses
    according to their attributes.

  • Math 5 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Shape and Space (Transformations) > Specific Outcome 8

    8. Identify and describe a single transformation, including a translation, rotation and reflection of 2-D shapes.

  • Math 5 > Shape and Space (Transformations) > Specific Outcome 9

    9. Perform, concretely, a single transformation (translation, rotation or reflection) of a 2-D shape, and draw the image.

  • Math 5 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Differentiate between first-hand and second-hand data.

  • Math 5 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Construct and interpret double bar graphs to draw conclusions.

  • Math 5 >

    Statistics and Probability (Chance and Uncertainty)

    Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.
    • Math Website For Elementary
      This website for teachers to print worksheets/templates/flashcards
      assignment
      Website

  • Math 5 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 3

    3. Describe the likelihood of a single outcome occurring, using words such as:
    • impossible
    • possible
    • certain.

  • Math 5 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 4

    4. Compare the likelihood of two possible outcomes occurring, using words such as:
    • less likely
    • equally likely
    • more likely.

  • Math 6

    Operations with numbers. Your child will convert between improper fractions and mixed numbers, learn about and use integers, and understand the meaning of ratio and percent. They will multiply and divide decimal numbers, and perform operations with whole numbers using order of operations. Your child will use variables, graphs and tables to show number patterns.

  • Math 6 >

    Number

    Develop number sense.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Number > Specific Outcome 1

    1. Demonstrate an understanding of place value, including numbers that are:
    • greater than one million
    • less than one thousandth.

  • Math 6 > Number > Specific Outcome 2

    2. Solve problems involving whole numbers and decimal numbers.

  • Math 6 > Number > Specific Outcome 3

    3. Demonstrate an understanding of factors and multiples by:
    • determining multiples and factors of numbers less than 100
    • identifying prime and composite numbers
    • solving problems using multiples and factors.

  • Math 6 > Number > Specific Outcome 4

    4. Relate improper fractions to mixed numbers and mixed numbers to improper fractions.
    • Mixed Numbers and Improper Fractions
      Created by Khan Academy.
      assignment
      YouTube

  • Math 6 > Number > Specific Outcome 5

    5. Demonstrate an understanding of ratio, concretely, pictorially and symbolically.

  • Math 6 > Number > Specific Outcome 6

    6. Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically.
    • Percentage of a Whole Number
      Created by Khan Academy.
      assignment
      YouTube

  • Math 6 > Number > Specific Outcome 7

    7. Demonstrate an understanding of integers, concretely, pictorially and symbolically.

  • Math 6 > Number > Specific Outcome 8

    8. Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural number divisors).
    • Introduction to Multiplying Decimals
      Created by Khan Academy.
      assignment
      YouTube

  • Math 6 > Number > Specific Outcome 9

    9. Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).
    • BEDMAS Solve and Colour
      Students solve problems following order of operations and then colour the section accordingly.
      assignment
      Website
    • Introduction to Order of Operations
      Created by Khan Academy.
      assignment
      YouTube

  • Math 6 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Represent and describe patterns and relationships, using graphs and tables.

  • Math 6 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Demonstrate an understanding of the relationships within tables of values to solve problems.

  • Math 6 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Patterns and Relations (Variables and Equations) > Specific Outcome 3

    3. Represent generalizations arising from number relationships, using equations with letter variables.

  • Math 6 > Patterns and Relations (Variables and Equations) > Specific Outcome 4

    4. Express a given problem as an equation in which a letter variable is used to represent an unknown number.

  • Math 6 > Patterns and Relations (Variables and Equations) > Specific Outcome 5

    5. Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.

  • Math 6 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Shape and Space (Measurement) > Specific Outcome 1

    1. Demonstrate an understanding of angles by:
    • identifying examples of angles in the environment
    • classifying angles according to their measure
    • estimating the measure of angles, using 45°, 90° and 180° as reference angles
    • determining angle measures in degrees
    • drawing and labelling angles when the measure is specified.

  • Math 6 > Shape and Space (Measurement) > Specific Outcome 2

    2. Demonstrate that the sum of interior angles is:
    • 180° in a triangle
    • 360° in a quadrilateral.

  • Math 6 > Shape and Space (Measurement) > Specific Outcome 3

    3. Develop and apply a formula for determining the:
    • perimeter of polygons
    • area of rectangles
    • volume of right rectangular prisms.

  • Math 6 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 4

    4. Construct and compare triangles, including:
    • scalene
    • isosceles
    • equilateral
    • right
    • obtuse
    • acute
    in different orientations.
    • How to Categorize Triangles
      Created by Khan Academy.
      assignment
      YouTube

  • Math 6 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 5

    5. Describe and compare the sides and angles of regular and irregular polygons.

  • Math 6 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Shape and Space (Transformations) > Specific Outcome 6

    6. Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.

  • Math 6 > Shape and Space (Transformations) > Specific Outcome 7

    7. Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.

  • Math 6 > Shape and Space (Transformations) > Specific Outcome 8

    8. Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.

  • Math 6 > Shape and Space (Transformations) > Specific Outcome 9

    9. Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).

  • Math 6 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Create, label and interpret line graphs to draw conclusions.

  • Math 6 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Select, justify and use appropriate methods of collecting data, including:
    • questionnaires
    • experiments
    • databases
    • electronic media.

  • Math 6 > Statistics and Probability (Data Analysis) > Specific Outcome 3

    3. Graph collected data, and analyze the graph to solve problems.

  • Math 6 >

    Statistics and Probability (Chance and Uncertainty)

    Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.
    • Math 6 PAT with Mr. MacKay
      Explains each PAT question and from unit it comes from.
      assignment
      Website

  • Math 6 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 4

    4. Demonstrate an understanding of probability by:
    • identifying all possible outcomes of a probability experiment
    • differentiating between experimental and theoretical probability
    • determining the theoretical probability of outcomes in a probability experiment
    • determining the experimental probability of outcomes in a probability experiment
    • comparing experimental results with the theoretical probability for an experiment.

  • Math 7

    Learning about statistics. Your child will learn and explain the divisibility rules, solve problems involving percent, and add and subtract integers. They will add and subtract fractions and mixed numbers. Your child will model and solve one-step equations and two-step equations, and solve problems involving area. They will understand the mean, median and mode for a set of data and create and interpret circle graphs.

  • Math 7 >

    Number

    Develop number sense.

  • Math 7 > Number > Specific Outcome 1

    1. Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10, and why a number cannot be divided by 0.

  • Math 7 > Number > Specific Outcome 2

    2. Demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, the use of technology is expected).

  • Math 7 > Number > Specific Outcome 3

    3. Solve problems involving percents from 1% to 100%.

  • Math 7 > Number > Specific Outcome 4

    4. Demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals and positive fractions.

  • Math 7 > Number > Specific Outcome 5

    5. Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences).

  • Math 7 > Number > Specific Outcome 6

    6. Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolically.

  • Math 7 > Number > Specific Outcome 7

    7. Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using:
    • benchmarks
    • place value
    • equivalent fractions and/or decimals.

  • Math 7 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 7 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Demonstrate an understanding of oral and written patterns and their equivalent linear relations.

  • Math 7 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.

  • Math 7 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 7 > Patterns and Relations (Variables and Equations) > Specific Outcome 3

    3. Demonstrate an understanding of preservation of equality by:
    • modelling preservation of equality, concretely, pictorially and symbolically
    • applying preservation of equality to solve equations.

  • Math 7 > Patterns and Relations (Variables and Equations) > Specific Outcome 4

    4. Explain the difference between an expression and an equation.

  • Math 7 > Patterns and Relations (Variables and Equations) > Specific Outcome 5

    5. Evaluate an expression, given the value of the variable(s).

  • Math 7 > Patterns and Relations (Variables and Equations) > Specific Outcome 6

    6. Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and b are integers.

  • Math 7 > Patterns and Relations (Variables and Equations) > Specific Outcome 7

    7. Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:
    • ax + b = c
    • ax = b
    • x/a = b , a ≠ 0
    where a, b and c are whole numbers.

  • Math 7 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 7 > Shape and Space (Measurement) > Specific Outcome 1

    1. Demonstrate an understanding of circles by:
    • describing the relationships among radius, diameter and circumference
    • relating circumference to pi
    • determining the sum of the central angles
    • constructing circles with a given radius or diameter
    • solving problems involving the radii, diameters and circumferences of circles.

  • Math 7 > Shape and Space (Measurement) > Specific Outcome 2

    2. Develop and apply a formula for determining the area of:
    • triangles
    • parallelograms
    • circles.

  • Math 7 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 7 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 3

    3. Perform geometric constructions, including:
    • perpendicular line segments
    • parallel line segments
    • perpendicular bisectors
    • angle bisectors.

  • Math 7 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.

  • Math 7 > Shape and Space (Transformations) > Specific Outcome 4

    4. Identify and plot points in the four quadrants of a Cartesian plane, using integral ordered pairs.

  • Math 7 > Shape and Space (Transformations) > Specific Outcome 5

    5. Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).

  • Math 7 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 7 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Demonstrate an understanding of central tendency and range by:
    • determining the measures of central tendency (mean, median, mode) and range
    • determining the most appropriate measures of central tendency to report findings.

  • Math 7 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Determine the effect on the mean, median and mode when an outlier is included in a data set.

  • Math 7 > Statistics and Probability (Data Analysis) > Specific Outcome 3

    3. Construct, label and interpret circle graphs to solve problems.

  • Math 7 >

    Statistics and Probability (Chance and Uncertainty)

    Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

  • Math 7 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 4

    4. Express probabilities as ratios, fractions and percents.

  • Math 7 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 5

    5. Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.

  • Math 7 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 6

    6. Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table or other graphic organizer) and experimental probability of two independent events.

  • Math 8

    Understanding ratios, rates and proportions. Your teen will understand perfect squares and square roots, and solve problems involving percents, rates, ratios and proportions. They will multiply and divide positive fractions, mixed numbers and integers. Your teen will solve problems involving the Pythagorean theorem, surface area, volume and probability of independent events.

  • Math 8 >

    Number

    Develop number sense.

  • Math 8 > Number > Specific Outcome 1

    1. Demonstrate an understanding of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers).

  • Math 8 > Number > Specific Outcome 2

    2. Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).

  • Math 8 > Number > Specific Outcome 3

    3. Demonstrate an understanding of percents greater than or equal to 0%, including greater than 100%.

  • Math 8 > Number > Specific Outcome 4

    4. Demonstrate an understanding of ratio and rate.

  • Math 8 > Number > Specific Outcome 5

    5. Solve problems that involve rates, ratios and proportional reasoning.

  • Math 8 > Number > Specific Outcome 6

    6. Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically.

  • Math 8 > Number > Specific Outcome 7

    7. Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically.

  • Math 8 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 8 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Graph and analyze two-variable linear relations.

  • Math 8 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 8 > Patterns and Relations (Variables and Equations) > Specific Outcome 2

    2. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form:
    • ax = b
    • x/a = b , a ≠ 0
    • ax + b = c
    • x/a + b = c , a ≠ 0
    • a(x + b) = c
    where a, b and c are integers.

  • Math 8 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 8 > Shape and Space (Measurement) > Specific Outcome 1

    1. Develop and apply the Pythagorean theorem to solve problems.

  • Math 8 > Shape and Space (Measurement) > Specific Outcome 2

    2. Draw and construct nets for 3-D objects.

  • Math 8 > Shape and Space (Measurement) > Specific Outcome 3

    3. Determine the surface area of:
    • right rectangular prisms
    • right triangular prisms
    • right cylinders
    to solve problems.

  • Math 8 > Shape and Space (Measurement) > Specific Outcome 4

    4. Develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms and right cylinders.

  • Math 8 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 8 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 5

    5. Draw and interpret top, front and side views of 3-D objects composed of right rectangular prisms.

  • Math 8 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.

  • Math 8 > Shape and Space (Transformations) > Specific Outcome 6

    6. Demonstrate an understanding of the congruence of polygons.

  • Math 8 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 8 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Critique ways in which data is presented in circle graphs, line graphs, bar graphs and pictographs.

  • Math 8 >

    Statistics and Probability (Chance and Uncertainty)

    Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

  • Math 8 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 2

    2. Solve problems involving the probability of independent events.

  • Math 9

    Working with powers and polynomials. Your teen will solve problems involving powers and apply the order of operations, including exponents. They will solve problems involving operations on positive and negative fractions and decimals, and understand square roots of positive numbers. They will model and solve problems using linear equations and linear inequalities in one variable. They will also be introduced to polynomials and solve problems involving circle geometry and scale diagrams.

  • Math 9 >

    Number

    Develop number sense.

  • Math 9 > Number > Specific Outcome 1

    1. Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by:
    • representing repeated multiplication, using powers
    • using patterns to show that a power with an exponent of zero is equal to one
    • solving problems involving powers.

  • Math 9 > Number > Specific Outcome 2

    2. Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents:
    • (a^m)(a^n) = a^m +n
    • a^m / a^n = a^m-n, m > n
    • (a^m)^n = a^mn
    • (a/b)^m = a^m b^m
    • (a/b)^n = a^n / b^n, b ≠ 0.
    • Exponent Laws
      This assignment has students work through questions to discover the patterns behind the exponent laws.
      assignment
      Website

  • Math 9 > Number > Specific Outcome 3

    3. Demonstrate an understanding of rational numbers by:
    • comparing and ordering rational numbers
    • solving problems that involve arithmetic operations on rational numbers.

  • Math 9 > Number > Specific Outcome 4

    4. Explain and apply the order of operations, including exponents, with and without technology.

  • Math 9 > Number > Specific Outcome 5

    5. Determine the square root of positive rational numbers that are perfect squares.

  • Math 9 > Number > Specific Outcome 6

    6. Determine an approximate square root of positive rational numbers that are non-perfect squares.

  • Math 9 >

    Patterns and Relations (Patterns)

    Use patterns to describe the world and to solve problems.

  • Math 9 > Patterns and Relations (Patterns) > Specific Outcome 1

    1. Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution.

  • Math 9 > Patterns and Relations (Patterns) > Specific Outcome 2

    2. Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.

  • Math 9 >

    Patterns and Relations (Variables and Equations)

    Represent algebraic expressions in multiple ways.

  • Math 9 > Patterns and Relations (Variables and Equations) > Specific Outcome 3

    3. Model and solve problems, using linear equations of the form:
    • ax = b
    • x/a = b, a ≠ 0
    • ax + b = c
    • x/a + b = c, a ≠ 0
    • ax = b + cx
    • a(x + b) = c
    • ax + b = cx + d
    • a(bx + c) = d(ex + f)
    • a/x = b, x ≠ 0
    where a, b, c, d, e and f are rational numbers.

  • Math 9 > Patterns and Relations (Variables and Equations) > Specific Outcome 4

    4. Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

  • Math 9 > Patterns and Relations (Variables and Equations) > Specific Outcome 5

    5. Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).

  • Math 9 > Patterns and Relations (Variables and Equations) > Specific Outcome 6

    6. Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree less than or equal to 2).

  • Math 9 > Patterns and Relations (Variables and Equations) > Specific Outcome 7

    7. Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially and symbolically.

  • Math 9 >

    Shape and Space (Measurement)

    Use direct and indirect measurement to solve problems.

  • Math 9 > Shape and Space (Measurement) > Specific Outcome 1

    1. Solve problems and justify the solution strategy, using the following circle properties:
    • the perpendicular from the centre of a circle to a chord bisects the chord
    • the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc
    • the inscribed angles subtended by the same arc are congruent
    • a tangent to a circle is perpendicular to the radius at the point of tangency.

  • Math 9 >

    Shape and Space (3-D Objects and 2-D Shapes)

    Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

  • Math 9 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 2

    2. Determine the surface area of composite 3-D objects to solve problems.

  • Math 9 > Shape and Space (3-D Objects and 2-D Shapes) > Specific Outcome 3

    3. Demonstrate an understanding of similarity of polygons.

  • Math 9 >

    Shape and Space (Transformations)

    Describe and analyze position and motion of objects and shapes.

  • Math 9 > Shape and Space (Transformations) > Specific Outcome 4

    4. Draw and interpret scale diagrams of 2-D shapes.

  • Math 9 > Shape and Space (Transformations) > Specific Outcome 5

    5. Demonstrate an understanding of line and rotation symmetry.

  • Math 9 >

    Statistics and Probability (Data Analysis)

    Collect, display and analyze data to solve problems.

  • Math 9 > Statistics and Probability (Data Analysis) > Specific Outcome 1

    1. Describe the effect of:
    • bias
    • use of language
    • ethics
    • cost
    • time and timing
    • privacy
    • cultural sensitivity
    on the collection of data.

  • Math 9 > Statistics and Probability (Data Analysis) > Specific Outcome 2

    2. Select and defend the choice of using either a population or a sample of a population to answer a question.

  • Math 9 > Statistics and Probability (Data Analysis) > Specific Outcome 3

    3. Develop and implement a project plan for the collection, display and analysis of data by:
    • formulating a question for investigation
    • choosing a data collection method that includes social considerations
    • selecting a population or a sample
    • collecting the data
    • displaying the collected data in an appropriate manner
    • drawing conclusions to answer the question.

  • Math 9 >

    Statistics and Probability (Chance and Uncertainty)

    Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

  • Math 9 > Statistics and Probability (Chance and Uncertainty) > Specific Outcome 4

    4. Demonstrate an understanding of the role of probability in society.

  • Math 10C

    Mathematics 10C students determine the surface area and volume of 3-D objects and use trigonometric ratios to solve problems involving right triangles. They simplify expressions that involve powers with integral and rational exponents and simplify or factor polynomial expressions. At this level, students also analyze linear relations, solve systems of linear equations and solve problems related to both of these sets of skills.

  • Math 10C >

    Measurement

    Develop spatial sense and proportional reasoning.

  • Math 10C > Measurement > Specific Outcome 1

    1. Solve problems that involve linear measurement, using:
    • SI and imperial units of measure
    • estimation strategies
    • measurement strategies.

  • Math 10C > Measurement > Specific Outcome 2

    2. Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.

  • Math 10C > Measurement > Specific Outcome 3

    3. Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including:
    • right cones
    • right cylinders
    • right prisms
    • right pyramids
    • spheres.

  • Math 10C > Measurement > Specific Outcome 4

    4. Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
    • Math 10C Trigonometry Group Review - PART B
      Google form used by students to check sum of solutions for each set
      assignment
      Website
    • Math 10C Trigonometry Group Review - PART A
      Group trig review to be used in conjunction with Google Forms named "Math 10C Trigonometry Group Review - PART B"
      assignment
      Website

  • Math 10C >

    Algebra and Number

    Develop algebraic reasoning and number sense.

  • Math 10C > Algebra and Number > Specific Outcome 1

    1. Demonstrate an understanding of factors of whole numbers by determining the:
    • prime factors
    • greatest common factor
    • least common multiple
    • square root
    • cube root.

  • Math 10C > Algebra and Number > Specific Outcome 2

    2. Demonstrate an understanding of irrational numbers by:
    • representing, identifying and simplifying irrational numbers
    • ordering irrational numbers.

  • Math 10C > Algebra and Number > Specific Outcome 3

    3. Demonstrate an understanding of powers with integral and rational exponents.

  • Math 10C > Algebra and Number > Specific Outcome 4

    4. Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.

  • Math 10C > Algebra and Number > Specific Outcome 5

    5. Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.

  • Math 10C >

    Relations and Functions

    Develop algebraic and graphical reasoning through the study of relations.

  • Math 10C > Relations and Functions > Specific Outcome 1

    1. Interpret and explain the relationships among data, graphs and situations.

  • Math 10C > Relations and Functions > Specific Outcome 2

    2. Demonstrate an understanding of relations and functions.

  • Math 10C > Relations and Functions > Specific Outcome 3

    3. Demonstrate an understanding of slope with respect to:
    • rise and run
    • line segments and lines
    • rate of change
    • parallel lines
    • perpendicular lines.
    • Graphing with Slope Y-Intercept Form
      Students graph lines and use their graphs to solve a riddle
      assignment
      Website
    • Counting for Slope
      Walks students through the process of finding slope of a linear function
      assignment
      Website

  • Math 10C > Relations and Functions > Specific Outcome 4

    4. Describe and represent linear relations, using:
    • words
    • ordered pairs
    • tables of values
    • graphs
    • equations.

  • Math 10C > Relations and Functions > Specific Outcome 5

    5. Determine the characteristics of the graphs of linear relations, including the:
    • intercepts
    • slope
    • domain
    • range.

  • Math 10C > Relations and Functions > Specific Outcome 6

    6. Relate linear relations expressed in:
    • slope–intercept form (y = mx + b)
    • general form (Ax + By + C = 0)
    • slope–point form (y – y1 = m(x – x1))
    to their graphs.

  • Math 10C > Relations and Functions > Specific Outcome 7

    7. Determine the equation of a linear relation, given:
    • a graph
    • a point and the slope
    • two points
    • a point and the equation of a parallel or perpendicular line
    to solve problems.

  • Math 10C > Relations and Functions > Specific Outcome 8

    8. Represent a linear function, using function notation.

  • Math 10C > Relations and Functions > Specific Outcome 9

    9. Solve problems that involve systems of linear equations in two variables, graphically and algebraically.

  • Math 10-3

    Mathematics 10-3 students solve linear and area measurement problems of 2-D shapes and 3-D objects using SI and imperial units. They use spatial reasoning to solve puzzles; solve problems involving right triangles and angles; solve unit pricing, currency exchange and income problems; and manipulate formulas to solve problems. They also use scale factors and parallel and perpendicular lines to solve problems.

  • Math 10-3 >

    Measurement

    Develop spatial sense through direct and indirect measurement.

  • Math 10-3 > Measurement > Specific Outcome 1

    1. Demonstrate an understanding of the Système International (SI) by:
    • describing the relationships of the units for length, area, volume, capacity, mass and temperature
    • applying strategies to convert SI units to imperial units.

  • Math 10-3 > Measurement > Specific Outcome 2

    2. Demonstrate an understanding of the imperial system by:
    • describing the relationships of the units for length, area, volume, capacity, mass and temperature
    • comparing the American and British imperial units for capacity
    • applying strategies to convert imperial units to SI units.

  • Math 10-3 > Measurement > Specific Outcome 3

    3. Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.

  • Math 10-3 > Measurement > Specific Outcome 4

    4. Solve problems that involve SI and imperial area measurements of regular, composite and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions.

  • Math 10-3 >

    Geometry

    Develop spatial sense.

  • Math 10-3 > Geometry > Specific Outcome 1

    1. Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

  • Math 10-3 > Geometry > Specific Outcome 2

    2. Demonstrate an understanding of the Pythagorean theorem by:
    • identifying situations that involve right triangles
    • verifying the formula
    • applying the formula
    • solving problems.

  • Math 10-3 > Geometry > Specific Outcome 3

    3. Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.

  • Math 10-3 > Geometry > Specific Outcome 4

    4. Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by:
    • applying similarity to right triangles
    • generalizing patterns from similar right triangles
    • applying the primary trigonometric ratios
    • solving problems.

  • Math 10-3 > Geometry > Specific Outcome 5

    5. Solve problems that involve parallel, perpendicular and transversal lines, and pairs of angles formed between them.

  • Math 10-3 > Geometry > Specific Outcome 6

    6. Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by:
    • drawing
    • replicating and constructing
    • bisecting
    • solving problems.

  • Math 10-3 >

    Number

    Develop number sense and critical thinking skills.

  • Math 10-3 > Number > Specific Outcome 1

    1. Solve problems that involve unit pricing and currency exchange, using proportional reasoning.

  • Math 10-3 > Number > Specific Outcome 2

    2. Demonstrate an understanding of income, including:
    • wages
    • salary
    • contracts
    • commissions
    • piecework
    to calculate gross pay and net pay.

  • Math 10-3 >

    Algebra

    Develop algebraic reasoning.

  • Math 10-3 > Algebra > Specific Outcome 1

    1. Solve problems that require the manipulation and application of formulas related to:
    • perimeter
    • area
    • the Pythagorean theorem
    • primary trigonometric ratios
    • income.

  • Math 10-4

    Knowledge and Employability Mathematics 10-4 students solve everyday problems involving numbers and percents; explore patterns, variables, expressions and equations to solve problems; and solve problems involving estimation, measurement and comparison of objects. Students use visualization and symmetry to explore objects, shapes, patterns and designs; develop and apply a plan to collect, display and analyze data and information; and connect mathematical ideas to their everyday lives. Students who have experienced challenges or difficulty with their skills will be provided with additional strategies for success in the Knowledge and Employability -4 course sequence.

  • Math 10-4 >

    Number (Number Concepts & Number Operations)

    Students will develop and demonstrate a number sense for whole numbers, common fractions, decimals, percents and integers and apply arithmetic operations to solve everyday problems.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 1

    1. Use estimation strategies to estimate and round numbers to the nearest unit, tenth and hundredth to solve problems in everyday contexts

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 2

    2. Represent and describe the relationships between proper/improper fractions, equivalent fractions and mixed numbers concretely, pictorially and symbolically.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 3

    3. Convert among fractions, decimals and percents concretely, pictorially and symbolically to facilitate the solving of problems.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 4

    4. Represent and explain the meaning of integers in everyday contexts concretely, pictorially and symbolically.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 5

    5. Estimate and apply arithmetic operations to solve everyday problems, using:
    • whole numbers
    • decimals
    • fractions
    • mixed numbers
    • percents.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 6

    6. Estimate, add and subtract integers concretely, pictorially and symbolically in everyday contexts.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 7

    7. Assess the reasonableness of applied calculations and problem-solving strategies, using a variety of tools and/or strategies, e.g., estimation, charts, graphs, calculators and/or computers.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 8

    8. Calculate and compare rates and unit prices by writing ratios that involve numbers with different units.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 9

    9. Determine the value of a power, using a whole number base with exponents of 2 and 3.

  • Math 10-4 > Number (Number Concepts & Number Operations) > Specific Outcome 10

    10. Recognize and explain numbers in scientific notation form.

  • Math 10-4 >

    Patterns & Relations (Patterns & Relationships)

    Students will express and use patterns, variables and expressions, including those used in business and industry, with graphs to solve problems at home, in the community and in the workplace.

  • Math 10-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 1

    1. Identify, describe and draw conclusions about patterns and relationships, in oral and written form, in nature and everyday contexts.

  • Math 10-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 2

    2. Create expressions, make predictions and develop rules to describe, complete and extend patterns and relationships in everyday contexts.

  • Math 10-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 3

    3. Distinguish between the use of variables and constants in everyday situations.

  • Math 10-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 4

    4. Graph relationships using everyday home, community and workplace contexts and draw conclusions using patterns and relationships.

  • Math 10-4 >

    Patterns & Relations (Variables & Equations)

    Students will use variables and equations to express, summarize and apply relationships as problem-solving tools in a restricted range of contexts.

  • Math 10-4 > Patterns & Relations (Variables & Equations) > Specific Outcome 5

    5. Use variables, formulas and/or substitutions to solve problems in practical situations.

  • Math 10-4 > Patterns & Relations (Variables & Equations) > Specific Outcome 6

    6. Substitute numbers for variables in expressions and graph and examine the relationship.

  • Math 10-4 >

    Shape & Space (Measurement)

    Students will estimate, measure and compare using whole numbers, decimals, fractions and metric (SI) and Imperial units of measure to solve everyday problems.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 1

    1. Select and use appropriate metric (SI) and Imperial measuring devices and units to take measurements in home and work-related contexts, including:
    • length
    • mass (weight)
    • volume (capacity).

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 2

    2. Measure within acceptable degrees of accuracy.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 3

    3. Compare, convert and apply metric (SI) and Imperial units of measure, as appropriate in everyday contexts.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 4

    4. Solve problems involving perimeter, area, mass (weight) and volume (capacity).

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 5

    5. Use conversion charts, calculators and/or other tools to compare and convert common metric (SI) and Imperial units of measure, as required in everyday contexts.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 6

    6. Estimate the measurements of angles in a diagram and in various environments.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 7

    7. Measure and draw angles using a straight edge, protractor and other technology.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 8

    8. Estimate, measure and calculate the area of a circle.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 9

    9. Calculate the unknown when given the circumference, diameter and/or radii of a circle to solve everyday problems.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 10

    10. Estimate and calculate the area of a circle to solve problems in everyday contexts.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 11

    11. Estimate and apply a variety of arithmetic operations, using hours and minutes, in everyday applications.

  • Math 10-4 > Shape & Space (Measurement) > Specific Outcome 12

    12. Estimate and measure temperature and calculate changes in temperature.

  • Math 10-4 >

    Shape & Space (3-D Objects & 2-D Shapes & Transformations)

    Students will use visualization and symmetry to:
    • extend their awareness of objects and shapes
    • create and examine patterns and designs using congruence, symmetry, translation, rotation and reflection.

  • Math 10-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 13

    13. Measure and classify pairs of angles as either complementary or supplementary.

  • Math 10-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 14

    14. Represent, examine and describe enlargements and reductions.

  • Math 10-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 15

    15. Interpret scale models and identify the geometric properties associated with figures and shapes used in representations.

  • Math 10-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 16

    16. Reproduce drawings or objects to scale, using a variety of strategies; e.g., grid paper, dot paper and/or computer software.

  • Math 10-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 17

    17. Draw designs, using ordered pairs, in all four quadrants of a coordinate grid, with translation and reflection images.

  • Math 10-4 >

    Statistics & Probability (Collecting & Analyzing Information)

    Students will develop and implement a plan for the collection, display and examination of data and information, using technology and other strategies as required.

  • Math 10-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 1

    1. Predict, interpret, make comparisons and communicate information from graphs, tables, charts and other sources at home and in the workplace.

  • Math 10-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 2

    2. Recognize the uses of data and data collection and display tools in life- and work-related situations.

  • Math 10-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 3

    3. Record information and organize files and directories, using computers and/or other tools.

  • Math 10-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 4

    4. Examine a plan for collecting and processing information and modify as appropriate for everyday situations.

  • Math 20-1

    Mathematics 20-1 students investigate arithmetic and geometric patterns and use the sine and cosine laws to solve problems involving triangles. They investigate the properties of radicals and rational expressions. Mathematics 20-1 students also analyze the characteristics of absolute value functions and quadratic functions, solve quadratic equations and systems of equations in various ways, and analyze the relationship between a function and its reciprocal.

  • Math 20-1 >

    Algebra and Number

    Develop algebraic reasoning and number sense.

  • Math 20-1 > Algebra and Number > Specific Outcome 1

    1. Demonstrate an understanding of the absolute value of real numbers.

  • Math 20-1 > Algebra and Number > Specific Outcome 2

    2. Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.

  • Math 20-1 > Algebra and Number > Specific Outcome 3

    3. Solve problems that involve radical equations (limited to square roots).

  • Math 20-1 > Algebra and Number > Specific Outcome 4

    4. Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

  • Math 20-1 > Algebra and Number > Specific Outcome 5

    5. Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).

  • Math 20-1 > Algebra and Number > Specific Outcome 6

    6. Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials).

  • Math 20-1 >

    Trigonometry

    Develop trigonometric reasoning.

  • Math 20-1 > Trigonometry > Specific Outcome 1

    1. Demonstrate an understanding of angles in standard position (0° to 360°).

  • Math 20-1 > Trigonometry > Specific Outcome 2

    2. Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.

  • Math 20-1 > Trigonometry > Specific Outcome 3

    3. Solve problems, using the cosine law and sine law, including the ambiguous case.

  • Math 20-1 >

    Relations and Functions

    Develop algebraic and graphical reasoning through the study of relations.

  • Math 20-1 > Relations and Functions > Specific Outcome 1

    1. Factor polynomial expressions of the form:
    • ax^2 + bx + c , a ≠ 0
    • a^2x^2 - b^2y^2 + c , a ≠ 0, b ≠ 0
    • a(f(x))^2 - b(f(x)) + c, a ≠ 0
    • a(f(x))^2 - b^2(g(y))^2, a ≠ 0, b ≠ 0
    where a, b and c are rational numbers.

  • Math 20-1 > Relations and Functions > Specific Outcome 2

    2. Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.

  • Math 20-1 > Relations and Functions > Specific Outcome 3

    3. Analyze quadratic functions of the form y = a(x - p)^2 + q and determine the:
    • vertex
    • domain and range
    • direction of opening
    • axis of symmetry
    • x- and y-intercepts.

  • Math 20-1 > Relations and Functions > Specific Outcome 4

    4. Analyze quadratic functions of the form y = ax^2 + bx + c to identify characteristics of the corresponding graph, including:
    • vertex
    • domain and range
    • direction of opening
    • axis of symmetry
    • x- and y-intercepts
    and to solve problems.

  • Math 20-1 > Relations and Functions > Specific Outcome 5

    5. Solve problems that involve quadratic equations.

  • Math 20-1 > Relations and Functions > Specific Outcome 6

    6. Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.

  • Math 20-1 > Relations and Functions > Specific Outcome 7

    7. Solve problems that involve linear and quadratic inequalities in two variables.

  • Math 20-1 > Relations and Functions > Specific Outcome 8

    8. Solve problems that involve quadratic inequalities in one variable.

  • Math 20-1 > Relations and Functions > Specific Outcome 9

    9. Analyze arithmetic sequences and series to solve problems.

  • Math 20-1 > Relations and Functions > Specific Outcome 10

    10. Analyze geometric sequences and series to solve problems.

  • Math 20-1 > Relations and Functions > Specific Outcome 11

    11. Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).

  • Math 20-2

    Mathematics 20-2 students use proportional reasoning to solve real-life problems involving 2-D shapes and 3-D objects. They use the properties of angles and triangles, including the sine and cosine laws, to solve problems; use reasoning to prove conjectures; use spatial reasoning to solve puzzles; and solve problems that involve radicals. They interpret statistical data, solve problems involving quadratics and research and present a mathematical topic of their choice.

  • Math 20-2 >

    Measurement

    Develop spatial sense and proportional reasoning.

  • Math 20-2 > Measurement > Specific Outcome 1

    1. Solve problems that involve the application of rates.

  • Math 20-2 > Measurement > Specific Outcome 2

    2. Solve problems that involve scale diagrams, using proportional reasoning.

  • Math 20-2 > Measurement > Specific Outcome 3

    3. Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects.

  • Math 20-2 >

    Geometry

    Develop spatial sense.

  • Math 20-2 > Geometry > Specific Outcome 1

    1. Derive proofs that involve the properties of angles and triangles.

  • Math 20-2 > Geometry > Specific Outcome 2

    2. Solve problems that involve properties of angles and triangles.

  • Math 20-2 > Geometry > Specific Outcome 3

    3. Solve problems that involve the cosine law and the sine law, excluding the ambiguous case.

  • Math 20-2 >

    Number and Logic

    Develop number sense and logical reasoning.

  • Math 20-2 > Number and Logic > Specific Outcome 1

    1. Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.

  • Math 20-2 > Number and Logic > Specific Outcome 2

    2. Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.

  • Math 20-2 > Number and Logic > Specific Outcome 3

    3. Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands (limited to square roots).

  • Math 20-2 > Number and Logic > Specific Outcome 4

    4. Solve problems that involve radical equations (limited to square roots or cube roots).

  • Math 20-2 >

    Statistics

    Develop statistical reasoning.

  • Math 20-2 > Statistics > Specific Outcome 1

    1. Demonstrate an understanding of normal distribution, including:
    • standard deviation
    • z-scores.

  • Math 20-2 > Statistics > Specific Outcome 2

    2. Interpret statistical data, using:
    • confidence intervals
    • confidence levels
    • margin of error.

  • Math 20-2 >

    Relations and Functions

    Develop algebraic and graphical reasoning through the study of relations.

  • Math 20-2 > Relations and Functions > Specific Outcome 1

    1. Demonstrate an understanding of the characteristics of quadratic functions, including:
    • vertex
    • intercepts
    • domain and range
    • axis of symmetry.

  • Math 20-2 > Relations and Functions > Specific Outcome 2

    2. Solve problems that involve quadratic equations.

  • Math 20-2 >

    Mathematics Research Project

    Develop an appreciation of the role of mathematics in society.

  • Math 20-2 > Mathematics Research Project > Specific Outcome 1

    1. Research and give a presentation on a historical event or an area of interest that involves mathematics.

  • Math 20-3

    Mathematics 20-3 students solve surface area, volume and capacity problems. They use primary trigonometry to solve problems involving two or three right triangles, and model and draw 3-D objects and their views to scale. They use numerical reasoning to solve puzzles; create and analyze personal budgets; use proportional reasoning, unit analysis and manipulation of formulas to solve problems; and create and interpret graphs. Students use their understanding of slope and rate of change to interpret graphs.

  • Math 20-3 >

    Measurement

    Develop spatial sense through direct and indirect measurement.
    • Math 20-3 Workbook Part 3
      assignment
      File
    • Math 20-3 Workbook Part 2
      assignment
      File
    • Math 20-3 Workbook Part 1
      assignment
      File

  • Math 20-3 > Measurement > Specific Outcome 1

    1. Solve problems that involve SI and imperial units in surface area measurements and verify the solutions.
    • Math 20-3 Workbook Part 3
      assignment
      File
    • Math 20-3 Workbook Part 2
      assignment
      File
    • Math 20-3 Workbook Part 1
      assignment
      File

  • Math 20-3 > Measurement > Specific Outcome 2

    2. Solve problems that involve SI and imperial units in volume and capacity measurements.
    • Math 20-3 Workbook Part 3
      assignment
      File
    • Math 20-3 Workbook Part 2
      assignment
      File
    • Math 20-3 Workbook Part 1
      assignment
      File

  • Math 20-3 >

    Geometry

    Develop spatial sense.

  • Math 20-3 > Geometry > Specific Outcome 1

    1. Solve problems that involve two and three right triangles.

  • Math 20-3 > Geometry > Specific Outcome 2

    2. Solve problems that involve scale.

  • Math 20-3 > Geometry > Specific Outcome 3

    3. Model and draw 3-D objects and their views.

  • Math 20-3 > Geometry > Specific Outcome 4

    4. Draw and describe exploded views, component parts and scale diagrams of simple 3-D objects.

  • Math 20-3 >

    Number

    Develop number sense and critical thinking skills.

  • Math 20-3 > Number > Specific Outcome 1

    1. Analyze puzzles and games that involve numerical reasoning, using problem-solving strategies.

  • Math 20-3 > Number > Specific Outcome 2

    2. Solve problems that involve personal budgets.

  • Math 20-3 > Number > Specific Outcome 3

    3. Demonstrate an understanding of compound interest.

  • Math 20-3 > Number > Specific Outcome 4

    4. Demonstrate an understanding of financial institution services used to access and manage finances.

  • Math 20-3 > Number > Specific Outcome 5

    5. Demonstrate an understanding of credit options, including:
    • credit cards
    • loans.

  • Math 20-3 >

    Algebra

    Develop algebraic reasoning.

  • Math 20-3 > Algebra > Specific Outcome 1

    1. Solve problems that require the manipulation and application of formulas related to:
    • volume and capacity
    • surface area
    • slope and rate of change
    • simple interest
    • finance charges.

  • Math 20-3 > Algebra > Specific Outcome 2

    2. Demonstrate an understanding of slope:
    • as rise over run
    • as rate of change
    • by solving problems.

  • Math 20-3 > Algebra > Specific Outcome 3

    3. Solve problems by applying proportional reasoning and unit analysis.

  • Math 20-3 >

    Statistics

    Develop statistical reasoning.

  • Math 20-3 > Statistics > Specific Outcome 1

    1. Solve problems that involve creating and interpreting graphs, including:
    • bar graphs
    • histograms
    • line graphs
    • circle graphs.

  • Math 20-4

    Knowledge and Employability Mathematics 20-4 students solve everyday problems involving numbers and percents, and decide if the processes used are reasonable. They explore patterns, variables and expressions, and interpret variables, equations and relationships, to solve problems in practical situations. They estimate, measure and compare objects; read and interpret scale drawings and maps; develop and apply a plan to collect, display and analyze information; and use probability and statistics to make predictions and decisions. In most of their studies, Mathematics 20-4 students connect mathematical ideas to their everyday lives. Students who have experienced challenges or difficulty with their skills will be provided with additional strategies for success in the Knowledge and Employability -4 course sequence.

  • Math 20-4 >

    Number (Number Concepts & Number Operations)

    Students will solve everyday home, community and workplace problems by applying arithmetic operations to whole numbers, decimals, common fractions, percents and integers.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 1

    1. Use estimation strategies to estimate and apply arithmetic operations to solve everyday problems, using:
    • whole numbers
    • integers (add/subtract only)
    • decimals
    • fractions
    • mixed numbers
    • percents.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 2

    2. Estimate and round numbers and decimals, e.g., money, to the nearest unit, tenth and hundredth to solve problems in everyday contexts.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 3

    3. Assess the reasonableness of applied calculations and problem-solving strategies, using a variety of tools and/or strategies; e.g., estimation, charts, graphs, calculators and/or computers.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 4

    4. Identify and use appropriate tools, e.g., tables, charts, spreadsheets and calculators, to increase accuracy in everyday and/or work-related problem-solving situations.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 5

    5. Create, use and modify a spreadsheet template for a variety of everyday contexts, including the determining of interest rates, vehicle payments, investments or budgets.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 6

    6. Use a variety of methods and tools to convert fractional percents to decimal forms.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 7

    7. Express rates and ratios in equivalent forms to solve problems in everyday contexts.

  • Math 20-4 > Number (Number Concepts & Number Operations) > Specific Outcome 8

    8. Estimate unit costs and compare costs of everyday purchases.

  • Math 20-4 >

    Patterns & Relations (Patterns & Relationships)

    Students will express and use patterns, variables and expressions, including those used in business and industry, with graphs to solve problems at home, in the community and in the workplace.

  • Math 20-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 1

    1. Use relationships and patterns to summarize, generalize and predict when problem solving and decision making in life- and work-related contexts.

  • Math 20-4 > Patterns & Relations (Patterns & Relationships) > Specific Outcome 2

    2. Generalize patterns arising from everyday problem-solving contexts, using mathematical expressions and equations and/or verifying by substitution.

  • Math 20-4 >

    Patterns & Relations (Variables & Equations)

    Students will use variables and equations to express, summarize and apply relationships as problem-solving tools in a restricted range of contexts.

  • Math 20-4 > Patterns & Relations (Variables & Equations) > Specific Outcome 3

    3. Interpret formulas related to practical situations and solve everyday problems using common arithmetic expressions and relationships; e.g., perimeter and area.

  • Math 20-4 >

    Shape & Space (Measurement)

    Students will estimate, measure and compare using whole numbers, decimals, fractions and metric (SI) and Imperial units of measure to solve everyday problems.

  • Math 20-4 > Shape & Space (Measurement) > Specific Outcome 1

    1. use appropriate metric (SI) and Imperial measuring strategies, tools and units to measure:
    • length
    • volume (capacity)
    • mass (weight)
    • angles
    • time
    • temperature.

  • Math 20-4 > Shape & Space (Measurement) > Specific Outcome 2

    2. Measure within acceptable degrees of accuracy as required in life- and work-related situations.

  • Math 20-4 > Shape & Space (Measurement) > Specific Outcome 3

    3. Ccalculate elapsed time in everyday contexts.

  • Math 20-4 > Shape & Space (Measurement) > Specific Outcome 4

    4. Use conversion charts, calculators and/or other tools to compare and convert common metric (SI) and Imperial units of measure, as required in everyday contexts.

  • Math 20-4 > Shape & Space (Measurement) > Specific Outcome 5

    5. Investigate the types and uses of measuring tools and units within the community and workplace.

  • Math 20-4 >

    Shape & Space (3-D Objects & 2-D Shapes & Transformations)

    Students will use visualization and symmetry to:
    • extend their awareness of objects and shapes
    • create and examine patterns and designs using congruence, symmetry, translation, rotation and reflection.

  • Math 20-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 5

    5. Read and interpret scale drawings and models in workplace and community situations.

  • Math 20-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 6

    6. Use scale diagrams, including enlargements and reductions, to solve construction, renovation and other related problems.

  • Math 20-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 7

    7. Give oral and written directions, applying appropriate communication skills.

  • Math 20-4 > Shape & Space (3-D Objects & 2-D Shapes & Transformations) > Specific Outcome 8

    8. Read and interpret maps to locate specific sites, determine distances, give directions or use public transportation

  • Math 20-4 >

    Statistics & Probability (Collecting & Analyzing Information)

    Students will develop and implement a plan for the collection, display and examination of data and information, using technology and other strategies as required.

  • Math 20-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 1

    1. Use information and data from a variety of sources to make comparisons, predictions, inferences, conclusions and/or decisions in everyday situations.

  • Math 20-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 2

    2. Record and organize information and data as appropriate in life- and work-related situations.

  • Math 20-4 > Statistics & Probability (Collecting & Analyzing Information) > Specific Outcome 3

    3. Use probability and statistics to predict upcoming events and to make decisions in everyday life.

  • Math 30-1

    Mathematics 30-1 students investigate the properties of logarithms; study the characteristics and transformations of trigonometric, polynomial, exponential and logarithmic functions by sketching and analyzing their graphs; and solve equations and problems related to these functions. Students also use basic counting principles to determine the number of permutations or combinations of the elements of a set to solve problems.

  • Math 30-1 >

    Trigonometry

    Develop trigonometric reasoning.
    • Math 30-1 Trigonometry and the Unit Circle Review
      A chapter review for math 30-1 trigonometry and the unit circle
      assignment
      Website

  • Math 30-1 > Trigonometry > Specific Outcome 1

    1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

  • Math 30-1 > Trigonometry > Specific Outcome 2

    2. Develop and apply the equation of the unit circle.

  • Math 30-1 > Trigonometry > Specific Outcome 3

    3. Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.

  • Math 30-1 > Trigonometry > Specific Outcome 4

    4. Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.

  • Math 30-1 > Trigonometry > Specific Outcome 5

    5. Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.

  • Math 30-1 > Trigonometry > Specific Outcome 6

    6. Prove trigonometric identities, using:
    • reciprocal identities
    • quotient identities
    • Pythagorean identities
    • sum or difference identities (restricted to sine, cosine and tangent)
    • double-angle identities (restricted to sine, cosine and tangent).

  • Math 30-1 >

    Relations and Functions

    Develop algebraic and graphical reasoning through the study of relations.

  • Math 30-1 > Relations and Functions > Specific Outcome 1

    1. Demonstrate an understanding of operations on, and compositions of, functions.

  • Math 30-1 > Relations and Functions > Specific Outcome 2

    2. Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.

  • Math 30-1 > Relations and Functions > Specific Outcome 3

    3. Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.

  • Math 30-1 > Relations and Functions > Specific Outcome 4

    4. Apply translations and stretches to the graphs and equations of functions.

  • Math 30-1 > Relations and Functions > Specific Outcome 5

    5. Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the:
    • x-axis
    • y-axis
    • line y = x.

  • Math 30-1 > Relations and Functions > Specific Outcome 6

    6. Demonstrate an understanding of inverses of relations.

  • Math 30-1 > Relations and Functions > Specific Outcome 7

    7. Demonstrate an understanding of logarithms.

  • Math 30-1 > Relations and Functions > Specific Outcome 8

    8. Demonstrate an understanding of the product, quotient and power laws of logarithms.

  • Math 30-1 > Relations and Functions > Specific Outcome 9

    9. Graph and analyze exponential and logarithmic functions.

  • Math 30-1 > Relations and Functions > Specific Outcome 10

    10. Solve problems that involve exponential and logarithmic equations.

  • Math 30-1 > Relations and Functions > Specific Outcome 11

    11. Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree 5 with integral coefficients).
    • Math 30-1 Polynomial Functions Review
      A math 30-1 chapter review for polynomial functions
      assignment
      Website

  • Math 30-1 > Relations and Functions > Specific Outcome 12

    12. Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
    • Math 30-1 Polynomial Functions Review
      A math 30-1 chapter review for polynomial functions
      assignment
      Website

  • Math 30-1 > Relations and Functions > Specific Outcome 13

    13. Graph and analyze radical functions (limited to functions involving one radical).

  • Math 30-1 > Relations and Functions > Specific Outcome 14

    14. Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

  • Math 30-1 >

    Specific Outcome 14

    Develop algebraic and numeric reasoning that involves combinatorics.

  • Math 30-1 > Specific Outcome 14 > Specific Outcome 1

    1. Apply the fundamental counting principle to solve problems.

  • Math 30-1 > Specific Outcome 14 > Specific Outcome 2

    2. Determine the number of permutations of n elements taken r at a time to solve problems.

  • Math 30-1 > Specific Outcome 14 > Specific Outcome 3

    3. Determine the number of combinations of n different elements taken r at a time to solve problems.

  • Math 30-1 > Specific Outcome 14 > Specific Outcome 4

    4. Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).

  • Math 30-2

    Mathematics 30-2 students use numerical and logical reasoning to solve puzzles, and solve real-life problems about the probability of events occurring. They solve problems algebraically involving rational equations; investigate exponential, logarithmic, polynomial and sinusoidal functions; and research and present a mathematical topic of their choice.

  • Math 30-2 >

    Logical Reasoning

    Develop logical reasoning.

  • Math 30-2 > Logical Reasoning > Specific Outcome 1

    1. Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.

  • Math 30-2 > Logical Reasoning > Specific Outcome 2

    2. Solve problems that involve the application of set theory.

  • Math 30-2 >

    Probability

    Develop critical thinking skills related to uncertainty.

  • Math 30-2 > Probability > Specific Outcome 1

    1. Interpret and assess the validity of odds and probability statements.

  • Math 30-2 > Probability > Specific Outcome 2

    2. Solve problems that involve the probability of mutually exclusive and non–mutually exclusive events.

  • Math 30-2 > Probability > Specific Outcome 3

    3. Solve problems that involve the probability of two events.

  • Math 30-2 > Probability > Specific Outcome 4

    4. Solve problems that involve the fundamental counting principle.

  • Math 30-2 > Probability > Specific Outcome 5

    5. Solve problems that involve permutations.

  • Math 30-2 > Probability > Specific Outcome 6

    6. Solve problems that involve combinations.

  • Math 30-2 >

    Relations and Functions

    Develop algebraic and graphical reasoning through the study of relations.

  • Math 30-2 > Relations and Functions > Specific Outcome 1

    1. Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).

  • Math 30-2 > Relations and Functions > Specific Outcome 2

    2. Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials).

  • Math 30-2 > Relations and Functions > Specific Outcome 3

    3. Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials).

  • Math 30-2 > Relations and Functions > Specific Outcome 4

    4. Demonstrate an understanding of logarithms and the laws of logarithms.

  • Math 30-2 > Relations and Functions > Specific Outcome 5

    5. Solve problems that involve exponential equations.

  • Math 30-2 > Relations and Functions > Specific Outcome 6

    6. Represent data, using exponential and logarithmic functions, to solve problems.

  • Math 30-2 > Relations and Functions > Specific Outcome 7

    7. Represent data, using polynomial functions (of degree ≤ 3), to solve problems.

  • Math 30-2 > Relations and Functions > Specific Outcome 8

    8. Represent data, using sinusoidal functions, to solve problems.

  • Math 30-2 >

    Mathematics Research Project

    Develop an appreciation of the role of mathematics in society.

  • Math 30-2 > Mathematics Research Project > Specific Outcome 1

    1. Research and give a presentation on a current event or an area of interest that involves mathematics.

  • Math 30-3

    Mathematics 30-3 students investigate the limitations of measuring instruments, use trigonometry to solve problems involving triangles, and describe and illustrate properties of polygons. They investigate slides, rotations, flips and size changes of 2-D shapes or 3-D objects; they use logical reasoning to solve puzzles; and they solve various other problems involving financial situations, linear relations and probability.

  • Math 30-3 >

    Measurement

    Develop spatial sense through direct and indirect measurement.

  • Math 30-3 > Measurement > Specific Outcome 1

    1. Demonstrate an understanding of the limitations of measuring instruments, including:
    • precision
    • accuracy
    • uncertainty
    • tolerance
    and solve problems.

  • Math 30-3 >

    Geometry

    Develop spatial sense.

  • Math 30-3 > Geometry > Specific Outcome 1

    1. Solve problems by using the sine law and cosine law, excluding the ambiguous case.

  • Math 30-3 > Geometry > Specific Outcome 2

    2. Solve problems that involve:
    • triangles
    • quadrilaterals
    • regular polygons.

  • Math 30-3 > Geometry > Specific Outcome 3

    3. Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including:
    • translations
    • rotations
    • reflections
    • dilations.

  • Math 30-3 >

    Number

    Develop number sense and critical thinking skills.

  • Math 30-3 > Number > Specific Outcome 1

    1. Analyze puzzles and games that involve logical reasoning, using problem-solving strategies.

  • Math 30-3 > Number > Specific Outcome 2

    2. Solve problems that involve the acquisition of a vehicle by:
    • buying
    • leasing
    • leasing to buy.

  • Math 30-3 > Number > Specific Outcome 3

    3. Critique the viability of small business options by considering:
    • expenses
    • sales
    • profit or loss.

  • Math 30-3 >

    Algebra

    Develop algebraic reasoning.

  • Math 30-3 > Algebra > Specific Outcome 1

    1. Demonstrate an understanding of linear relations by:
    • recognizing patterns and trends
    • graphing
    • creating tables of values
    • writing equations
    • interpolating and extrapolating
    • solving problems.

  • Math 30-3 >

    Statistics

    Develop statistical reasoning.

  • Math 30-3 > Statistics > Specific Outcome 1

    1. Solve problems that involve measures of central tendency, including:
    • mean
    • median
    • mode
    • weighted mean
    • trimmed mean.

  • Math 30-3 > Statistics > Specific Outcome 2

    2. Analyze and describe percentiles.

  • Math 30-3 >

    Probability

    Develop critical thinking skills related to uncertainty.

  • Math 30-3 > Probability > Specific Outcome 1

    1. Analyze and interpret problems that involve probability.

  • Math 31

    Mathematics 31 students determine the limit of a function at finite or infinite values of the independent variable. They use derivative theorems to determine the derivative of a function, either explicitly or implicitly, and use derivatives to sketch graphs of functions and solve optimization problems. They also investigate the relationship between differentiation and integration.

  • Math 31 >

    PRECALCULUS AND LIMITS

    Students are expected to understand that functions, as well as variables, can be combined, using operations, such as addition and multiplication, and demonstrate this, by:
    • describing the relationship among functions after performing translations, reflections, stretches and compositions on a variety of functions
    • drawing the graphs of functions by applying transformations to the graphs of known functions
    • expressing final algebraic and trigonometric answers in a variety of equivalent forms, with the form chosen to be the most suitable form for the task at hand
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the algebra of functions, by:
    • illustrating different notations that describe functions and intervals
    • expressing, in interval notation, the domain and range of functions
    • expressing the sum, product, difference and quotient, algebraically and graphically, given any two functions
    • expressing, algebraically and graphically, the composition of two or more functions
    • illustrating the solution sets for linear, quadratic and absolute value inequalities |P(x)| >= a, |P(x)| = d
    • illustrating the difference between the concepts of equation and identity in trigonometric contexts.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 2

    2. Conceptual Understanding - Students will demonstrate conceptual understanding of the transformation of functions, by:
    • describing the similarities and differences between the graphs of y = f(x) and y = af[k(x+c)]+d, where a, k, c and d are real numbers
    • describing the effects of the reflection of the graphs of algebraic and trigonometric functions across any of the lines y = x, y = 0, or x = 0
    • describing the effects of the parameters a, b, c and d on the trigonometric function f (x) = a sin [b(x+c)]+d
    • describing the relationship between parallel and perpendicular lines
    • describing the condition for tangent, normal and secant lines to a curve
    • linking two problem conditions to a system of two equations for two unknowns.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 3

    3. Conceptual Understanding - Students will demonstrate conceptual understanding of equivalent forms, by:
    • describing what it means for two algebraic or trigonometric expressions to be equivalent.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 4

    4. Conceptual Understanding - Students will demonstrate conceptual understanding of limits and limit theorems, by:
    • explaining the concept of a limit
    • giving examples of functions with limits, with lefthand or right-hand limits, or with no limit
    • giving examples of bounded and unbounded functions, and of bounded functions with no limit
    • explaining, and giving examples of, continuous and discontinuous functions
    • defining the limit of an infinite sequence and an infinite series
    • explaining the limit theorems for sum, difference, multiple, product, quotient and power
    • illustrating, using suitable examples, the limit theorems for sum, difference, multiple, product, quotient and power.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 5

    5. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the algebra of functions, by:
    • using open, closed and semi-open interval notation
    • finding the sum, difference, product, quotient and composition of functions
    • solving inequalities of the types: |P(x)| >= a, |P(x)| / |Q(x)| >= a, |P(x)| = a, ax^2 + bx + c >= d
    • using the following trigonometric identities: primary and double reciprocal ratio, and half reciprocal ratio angle, and Pythagorean, sum and difference sin (A±B) and cos (A±B), to simplify expressions and solve equations, express sums and differences as products, and rewrite expressions in a variety of equivalent forms.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 6

    6. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the transformation of functions, by:
    • sketching the graph of, and describing algebraically, the effects of any translation, reflection or dilatation on any of the following functions or their inverses: linear, quadratic or cubic polynomial, absolute value, reciprocal, exponential, step
    • sketching and describing, algebraically, the effects of any combination of translation, reflection or dilatation on the following functions: f (x) = a sin [b(x+c)]+d, f (x) = a cos [b(x+c)]+d, f (x) = a tan [b(x+c)]
    • finding the equation of a line, given any two conditions that serve to define it
    • solving systems of linear–linear, linear–quadratic or quadratic–quadratic equations.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 7

    7. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the construction of equivalent forms, by:
    • factoring expressions with integral and rational exponents, using a variety of techniques
    • rationalizing expressions containing a numerator or a denominator that contains a radical
    • simplifying rational expressions, using any of the four basic operations.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 8

    8. Procedural Knowledge - Students will demonstrate competence in the procedures associated with limits and limit theorems, by:
    • determining the limit of any algebraic function as the independent variable approaches finite or infinite values for continuous and discontinuous functions
    • sketching continuous and discontinuous functions, using limits, intercepts and symmetry
    • calculating the sum of an infinite convergent geometric series
    • using definitions and limit theorems to determine the limit of any algebraic function as the independent variable approaches a fixed value
    • using definitions and limit theorems to determine the limit of any algebraic function as the independent variable approaches ± infinity.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 9

    9. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • modelling problem situations, using sums, differences, products and quotients of functions
    • investigating the connections between the algebraic form of a function f(x) and the symmetries of its graph.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 10

    10. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • translating problem conditions into equation or inequality form.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 11

    11. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • illustrating the difference between verification and proof in the comparison of two algebraic or trigonometric expressions.

  • Math 31 > PRECALCULUS AND LIMITS > Specific Outcome 12

    12. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • proving and illustrating geometrically, the following trigonometric limits: lim x -> 0, sin x / x, or lim x -> 0, x / sin x = 1, and lim x -> 0, cos x - 1 / x = 0
    • using the basic trigonometric limits, combined with limit theorems, to determine the limits of more complex trigonometric expressions
    • comparing numerical and algebraic processes for the determination of algebraic and trigonometric limits

  • Math 31 >

    DERIVATIVES AND DERIVATIVE THEOREMS

    Students are expected to understand that the derivative of a function is a limit that can be found, using first principles, and demonstrate this, by:
    • giving examples of the differences between intuitive and rigorous proofs in the context of limits, derivatives and integrals
    • connecting the derivative with a particular limit, and expressing this limit in situations like secant and tangent lines to a curve
    • computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of derivatives, by:
    • showing that the slope of a tangent line is a limit
    • explaining how the derivative of a polynomial function can be approximated, using a sequence of secant lines
    • explaining how the derivative is connected to the slope of the tangent line
    • recognizing that f (x) = x^n can be differentiated where n∈R
    • identifying the notations f(x), y^f, and dy / dx as alternative notations for the first derivative of a function
    • explaining the derivative theorems for sum and difference (f + g)(x) = f(x) + g(x)
    • explaining the sense of the derivative theorems for sum and difference, using practical examples.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 2

    2. Conceptual Understanding - Students will demonstrate conceptual understanding of derivative theorems, by:
    • demonstrating that the chain, power, product and quotient rules are aids to differentiate complicated functions
    • identifying implicit differentiation as a tool to differentiate functions where one variable is difficult to isolate
    • explaining the relationship between implicit differentiation and the chain rule
    • comparing the sum, difference, product and quotient theorems for limits and derivatives
    • explaining the derivation of the derivative theorems for product and quotient
    • explaining the derivative theorems for product and quotient, using practical examples
    • illustrating second, third and higher derivatives of algebraic functions
    describing the second derivative geometrically.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 3

    3. Conceptual Understanding - Students will demonstrate conceptual understanding of the derivatives of trigonometric functions, by:
    • demonstrating that the three primary trigonometric functions have derivatives at all points where the functions are defined
    • explaining how the derivative of a trigonometric function can be approximated, using a sequence of secant lines.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 4

    4. Procedural Knowledge - Students will demonstrate competence in the procedures associated with derivatives, by:
    • finding the slopes and equations of tangent lines at given points on a curve, using the definition of the derivative
    • estimating the numerical value of the derivative of a polynomial function at a point, using a sequence of secant lines
    • using the definition of the derivative to determine the derivative of f (x) = xn where n is a positive integer
    • differentiating polynomial functions, using the derivative theorems for sum and difference
    • differentiating functions that are single terms of the form xn where n is rational.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 5

    5. Procedural Knowledge - Students will demonstrate competence in the procedures associated with derivative theorems, by:
    • finding the derivative of a polynomial, power, product or quotient function
    • applying the chain rule in combination with the product and quotient rule
    • using the technique of implicit differentiation
    • writing final answers in factored form
    • finding the slope and equations of tangent lines at given points on a curve
    • finding the second and third derivatives of functions.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 6

    6. Procedural Knowledge - Students will demonstrate competence in the procedures associated with derivatives of trigonometric functions, by:
    • calculating the derivatives of the three primary and three reciprocal trigonometric functions
    • estimating the numerical value of the derivative of a trigonometric function at a point, using a sequence of secant lines
    • using the power, chain, product and quotient rules to find the derivatives of more complicated trigonometric functions
    • using the derivative of a trigonometric function to calculate its slope at a point, and the equation of the tangent at that point.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 7

    7. Problem Solving Context - Students will demonstrate problem-solving skills, by:
    • deriving f x ′( ) for polynomial functions up to the third degree, using the definition of the derivative
    • using the definition of the derivative to find f(x) for f(x) = (ax + c)^n where n = -1 or n = 1/2.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 8

    8. Problem Solving Context - Students will demonstrate problem-solving skills, by:
    • deriving the quotient rule from the productrule
    • showing that equivalent forms of thederivative of a rational function can be foundby using the product and the quotient rules
    • determining the derivative of a functionexpressed as a product of more than twofactors
    • determining the second derivative of animplicitly defined function
    AND, in one or more of the following, by:
    • showing the derivative for a relation found byboth implicit and explicit differentiation to bethe same
    • finding the equations of tangent lines to thestandard conics.

  • Math 31 > DERIVATIVES AND DERIVATIVE THEOREMS > Specific Outcome 9

    9. Problem Solving Context - Students will demonstrate problem-solving skills, by:
    • using the definition of the derivative to find thederivative for the sine and cosine functions
    • explaining why radian measure has to be usedin the calculus of trigonometric functions.

  • Math 31 >

    APPLICATIONS OF DERIVATIVES

    Students are expected to understand that calculus is a powerful tool in determining maximum and minimum points and in sketching of curves, and demonstrate this, by:
    • relating the zeros of the derivative function to the critical points on the original curve
    • using the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable
    • determining the optimum values of a variable in various contexts, using the concepts of maximum and minimum values of a function
    • using the concept of critical values to sketch the graphs of functions, and comparing these sketches to computergenerated plots of the same functions
    • fitting mathematical models to situations described by data sets.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of maxima and minima, by:
    • identifying, from a graph sketch, locations at which the first and second derivative are zero
    • illustrating under what conditions symmetry about the x-axis, y-axis or the origin will occur
    • explaining how the sign of the first derivative indicates whether or not a curve is rising or falling; and by explaining how the sign of the second derivative indicates the concavity of the graph
    • illustrating, by examples, that a first derivative of zero is one possible condition for a maximum or a minimum to occur
    • explaining circumstances wherein maximum and minimum values occur when f x ′( ) is not zero
    • illustrating, by examples, that a second derivative of zero is one possible condition for an inflection point to occur
    • explaining the differences between local maxima and minima and absolute maxima and minima in an interval
    • explaining when finding a maximum value is appropriate and when finding a minimum value is appropriate.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 2

    2. Conceptual Understanding - Students will demonstrate conceptual understanding of related rates, by:
    • illustrating how the chain rule can be used to represent the relationship between two or more rates of change
    • explaining the clarity that Leibnitz’s notation gives to expressing related rates
    • illustrating the time rate of change of a function y = f (x) or a relation R(x, y) = 0.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 3

    3. Procedural Knowledge - Students will demonstrate competence in the procedures associated with maxima and minima, by:
    • sketching the graphs of the first and second derivative of a function, given its algebraic form or its graph
    • using zeros and intercepts to aid in graph sketching
    • using the first and second derivatives to find maxima, minima and inflection points to aid in graph sketching
    • determining vertical, horizontal and oblique asymptotes, and domains and ranges of a function
    • finding intervals where the derivative is greater than zero or less than zero in order to predict where the function is increasing or decreasing
    • verifying whether or not a critical point is a maximum or a minimum
    • using a given model, in equation or graph form, to find maxima or minima that solve a problem.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 4

    4. Procedural Knowledge - Students will demonstrate competence in the procedures associated with related rates, by:
    • using the chain rule to find the derivative of a function with respect to an external variable, such as time
    • using Leibnitz’s notation to illustrate related rates
    • constructing a chain rule of related rates, using appropriate variables
    • calculating related rates for the time derivatives of areas, volumes, surface areas and relative motion
    • calculating related rates of change with respect to time, given an equation that models electronic circuits or other engineering situations
    • using the chain rule to derive an acceleration function in terms of position, given a velocity function expressed in terms of position.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 5

    5. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • employing a systematic calculus procedure to sketch algebraic and trigonometric functions
    • comparing and contrasting graphs plotted on a calculator and graphs sketched, using a systematic calculus procedure
    • calculating maxima and minima for such quantities as volumes, areas, perimeters and costs
    • illustrating the connections among geometric, economic or motion problems, the modelling equations of these problems, the resulting critical points on the graphs and their solutions, using derivatives
    AND, in one or more of the following, by:
    • constructing a mathematical model to represent a geometric problem, and using the model to find maxima and/or minima
    • constructing a mathematical model to represent a problem in economics, and using the model to find maximum profits or minimum cost
    • constructing a mathematical model to represent a motion problem, and using the model to find maximum or minimum time or distance.

  • Math 31 > APPLICATIONS OF DERIVATIVES > Specific Outcome 6

    6. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • constructing a mathematical model to represent time rates of change of linear measures, areas, volumes, surface areas, etc.
    • solving related rate problems that use models containing primary trigonometric functions.

  • Math 31 >

    INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS

    Students are expected to understand that the operation of finding a derivative has an inverse operation of finding an antiderivative, and demonstrate this, by:
    • giving examples of the differences between intuitive and rigorous proofs in the context of limits, derivatives and integrals
    • recognizing that integration can be thought of as an inverse operation to that of finding derivatives
    • computing definite and indefinite integrals of simple functions, using antiderivatives, integral theorems and calculator/computer methods
    • using the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of antiderivatives, by:
    • explaining how differentiation can have an inverse operation
    • showing that many different functions can have the same derivative
    • representing, on the same grid, a family of curves that form a sequence of functions, all having the same derivative.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 2

    2. Conceptual Understanding - Students will demonstrate conceptual understanding of area limits, by:
    • defining the area under a curve as a limit of the sums of the areas of rectangles
    • establishing the existence of upper and lower bounds for the area under a curve.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 3

    3. Conceptual Understanding - Students will demonstrate conceptual understanding of definite integrals, by:
    • identifying the indefinite integral f(x)dx as a sum of an antiderivative F (x) and a constant c
    • explaining how the definite integral between fixed limits a and b is a number whose value is F(b) – F(a)
    • explaining the connection between the numerical values of the area and the definite integral for functions f of a constant sign and a variable sign
    • illustrating the following properties of integrals
    • describing the sense of the fundamental theorem of calculus
    • explaining how the fundamental theorem of calculus relates the area limit to the antiderivative of a function describing a curve.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 4

    4. Procedural Knowledge - Students will demonstrate competence in the procedures associated with antiderivatives, by:
    • finding the antiderivatives of polynomials, rational algebraic functions and trigonometric functions
    • finding the family of curves whose first derivative has been given
    • solving separable first order differential equations for general and specific solutions.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 5

    5. Procedural Knowledge - Students will demonstrate competence in the procedures associated with area limits, by:
    • sketching the area under a curve (polynomials, rational, trigonometric) over a given interval, and approximating the area as the sum of individual rectangles.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 6

    6. Procedural Knowledge - Students will demonstrate competence in the procedures associated with definite integrals, by:
    • calculating the definite integral for polynomial, rational and trigonometric functions
    • determining the area between a curve and the x-axis over a given domain
    • determining the area between a curve and the x-axis: if f(x) has a constant sign over a given interval, if f(x) has a change in sign over a given interval
    • determining the area between curves over a given interval
    • determining the area between intersecting curves.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 7

    7. Procedural Knowledge - Students will demonstrate competence in the procedures associated with displacement, velocity and acceleration, by:
    • estimating an instantaneous velocity, using slopes of secant lines to represent average velocities
    • finding the first and second derivatives of a position function to get instantaneous velocity and instantaneous acceleration functions, where the position function is an algebraic function or a trigonometric function of time
    • using antiderivatives of acceleration and velocity functions to get velocity and displacement functions.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 8

    8. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • finding the antiderivatives of rational functions and polynomial powers by comparison and inspection methods
    • determining antiderivatives for polynomial, rational and trigonometric functions

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 9

    9. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • communicating the similarities and differences between definite integrals and areas under curves.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 10

    10. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • relating the value of the integral between x = a and x = b to the area between the curve and the x-axis over the interval [a, b]
    • using integration theorems, such as those listed below, to simplify definite integrals
    • using integral theorems to simplify more complicated integrals
    • illustrating the conditions necessary for a function to be differentiable, or able to be integrated.

  • Math 31 > INTEGRALS, INTEGRAL THEOREMS AND INTEGRAL APPLICATIONS > Specific Outcome 11

    11. Problem-Solving Contexts - Students will demonstrate problem-solving skills, by:
    • solving problems associated with distance, velocity and acceleration whose models are restricted to those of the forms y(t) = f(t) and y^n(t) = f(t)
    • deriving the following kinematic equations, starting from the expression a = constant: v = at + v0, v^2 = v0^2 + 2ad, d = 1/2at2 + v0 t + d0
    • determining the equations of velocity and acceleration in simple harmonic motion, starting from the displacement equation: x = A cos (kt + c).

  • Math 31 >

    CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS

    Students are expected to understand that exponential and logarithmic functions have limits, derivatives and integrals that obey the same theorems as do algebraic and trigonometric functions, and demonstrate this, by:
    • computing limits of functions, using definitions, limit theorems and calculator/ computer methods
    • computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods
    • computing definite and indefinite integrals of simple functions, using antiderivatives, integral theorems and calculator/computer methods
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable
    • fitting mathematical models to situations described by data sets.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the calculus of exponential and logarithmic functions, by:
    • defining exponential and logarithmic functions as inverse functions
    • explaining the special properties of the number e, together with a definition of e as a limit
    • illustrating that the derivative of an exponential or logarithmic function may be derived from the definition of the derivative
    • illustrating that base-e exponential and logarithmic functions form a convenient framework within which the calculus of similar functions in any base may be developed
    • illustrating how exponential and logarithmic functions may be used to model certain natural problems involving growth, decay and return to equilibrium.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the calculus of exponential and logarithmic functions, by:
    • estimating the values of the limits e and e^x
    • approximating the slopes of y = ex and y = ln x for some specific value of x
    • finding the derivative and antiderivative of the base-e exponential function
    • using limit theorems to evaluate the limits of simple exponential and logarithmic functions
    • finding the derivative of the natural logarithmic function
    • finding the derivatives of logarithmic functions having bases other than e
    • finding the derivatives and antiderivatives of exponential functions having bases other than e
    • solving the differential equations y = ky and y = k(y - y0).

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, by:
    • evaluating maxima and minima of given functions involving exponential and logarithmic functions
    • finding areas bounded by exponential, logarithmic or reciprocal functions
    AND, in one or more of the following, by:
    • relating natural growth, natural decay and return to equilibrium to the differential equations y = ky or y = k(y - y0)
    • solving natural growth and decay problems, starting from the equations y = ky or y = k(y - y0)
    • fitting exponential models to observed data
    • calculating distance, velocity and acceleration for falling bodies, with air resistance present as part of the model
    • connecting the integral a b dx px q ∫ + with the integral

  • Math 31 >

    CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS

    Students are expected to understand that many limits, derivatives, equation roots and definite integrals can be found numerically, and demonstrate this, by:
    • identifying and giving examples of the strengths and limitations of the use of technology in the computation of limits, derivatives and integrals
    • computing limits of functions, using definitions, limit theorems and calculator/ computer methods
    • computing derivatives of functions, using definitions, derivative theorems and calculator/computer methods
    • computing definite and indefinite integrals of simple functions, using antiderivatives, integral theorems and calculator/computer methods.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the calculus of exponential and logarithmic functions, by:
    • defining exponential and logarithmic functions as inverse functions
    • explaining the special properties of the number e, together with a definition of e as a limit
    • illustrating that the derivative of an exponential or logarithmic function may be derived from the definition of the derivative
    • illustrating that base-e exponential and logarithmic functions form a convenient framework within which the calculus of similar functions in any base may be developed
    • illustrating how exponential and logarithmic functions may be used to model certain natural problems involving growth, decay and return to equilibrium.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the calculus of exponential and logarithmic functions, by:
    • estimating the values of the limits e and e^x
    • approximating the slopes of y = ex and y = ln x for some specific value of x
    • finding the derivative and antiderivative of the base-e exponential function
    • using limit theorems to evaluate the limits of simple exponential and logarithmic functions
    • finding the derivative of the natural logarithmic function
    • finding the derivatives of logarithmic functions having bases other than e
    • finding the derivatives and antiderivatives of exponential functions having bases other than e
    • computing
    • solving the differential equations y = ky and y = k(y - y0).

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, by:
    • evaluating maxima and minima of given functions involving exponential and logarithmic functions
    • finding areas bounded by exponential, logarithmic or reciprocal functions
    AND, in one or more of the following, by:
    • relating natural growth, natural decay and return to equilibrium to the differential equations y = ky or y = k(y - y0)
    • solving natural growth and decay problems, starting from the equations y = ky or y = k(y - y0)
    • fitting exponential models to observed data
    • calculating distance, velocity and acceleration for falling bodies, with air resistance present as part of the model.

  • Math 31 >

    CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS

    Students are expected to understand that volumes of revolution may be considered as the limiting sum of smaller volumes and can be related to definite integrals, and demonstrate this, by:
    • describing the connections between the operation of integration and the finding of areas and averages
    • combining and modifying familiar solution procedures to form a new solution procedure to a related problem
    • computing definite and indefinite integrals of simple functions, using antiderivatives, integral theorems and calculator/computer methods
    • using the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the principles of numerical analysis, by:
    • describing the difference between an exact solution and an approximate solution
    • identifying when a particular numerical method is likely to give poor results
    • explaining the difference between iterative and noniterative procedures
    • explaining the basis of the Newton–Raphson procedure for determining the roots of f(x) = 0
    • describing the basis of a limit, derivative, equation root or integral procedure in geometric terms
    • connecting the number of subdivisions of the range of integration with the accuracy of the estimate for the integral
    • showing that all numerical integration formulas are procedures that interpolate between the lower and upper Riemann sums for the integral.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with numerical methods, by:
    • estimating the value of a limit by systematic trial and error
    • calculating the numerical value of the derivative at a point on a curve, whether or not there is a defining formula for the curve
    • solving the equation f(x) = 0 by systematic trial and error, and by the Newton– Raphson method
    • calculating the upper and lower Riemann sums for a definite integral
    • calculating the value of a definite integral, using the midpoint rule
    • calculating the value of a definite integral, using the trapezoidal rule
    • calculating the value of a definite integral, using Simpson’s rule.

  • Math 31 > CALCULUS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, in one or more of the following:
    • comparing the errors in computing definite integrals when using different procedures
    • writing computer software for the computation of limits, equation roots or definite integrals
    • reconstructing limit processes so that numerical evaluations can be efficient and reliable
    • evaluating the reliability of a numerical procedure for finding a limit, an equation root or a definite integral.

  • Math 31 >

    APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING

    Students are expected to understand that most of the important equations of physics are differential equations, and calculus provides the most efficient solution method, and demonstrate this, by:
    • linking displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity
    • describing the connections between the operation of integration with the finding of areas and averages
    • calculating the displacement, velocity and acceleration of an object moving in a straight line with nonuniform velocity
    • calculating the mean value of a function over an interval
    • producing approximate answers to complex calculations by simplifying the models used
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable
    • fitting mathematical models to situations described by data sets.

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of volumes of revolution, by:
    • identifying the solid generated by the rotation of the graph of a function, either between two boundary values, or between two graphs
    • explaining the connection between the volume of revolution and the volume of a cylindrical disc
    • demonstrating how the formula for the volume of revolution by the disc method could be generated.

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with volumes of revolution, by:
    • using the relationship to find the volume of revolution between the boundaries of a and b for polynomial and trigonometric functions
    • finding the volume of revolution between two polynomial or trigonometric functions by first finding the intersection points of the graphs of the two functions

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, in one or both of the following, by:
    • deriving formulas for the volume of a cylinder, cone and sphere
    • revolving the graph of a function about a horizontal or vertical line, other than the x- or y-axis, and finding the resulting volume of revolution.

  • Math 31 >

    APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING

    Students are expected to understand that many important biological applications of calculus are connected with models involving the solution of the differential equation f(x) = kf(x), and demonstrate this, by:
    • combining and modifying familiar solution procedures to form a new solution procedure to a related problem
    • using the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem
    • producing approximate answers to complex calculations by simplifying the models used
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable
    • fitting mathematical models to situations described by data sets.

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the links among calculus, the physical sciences and engineering, by:
    • illustrating situations in which differential equations are required to represent problems
    • developing one or more differential equations in the areas of linear motion, simple harmonic motion, work, hydrostatic force, moments of inertia, radioactive decay or similar situations
    • showing that the concept of mean value can be applied to situations where the quantity varies with time, or where a range of values exists in a system of multiple bodies.

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the application of calculus to the physical sciences and engineering, by:
    • solving differential equations of type y^n(t) = f(t)
    • solving differential equations of type y^n(t) = -k^2y
    • calculating the work done by any nonuniform force f(x) using W = f(x)dx
    • determining root–mean–square values for sinusoidal functions.

  • Math 31 > APPLICATIONS OF CALCULUS TO PHYSICAL SCIENCES AND ENGINEERING > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, in one or both of the following, by:
    • determining the half-life, the decay rate, and the activity as a function of time for a radioisotope
    • analyzing the motion and energy in an oscillating spring system (Hooke’s law)
    • analyzing hydrostatic forces on the surface of submerged objects
    • determining the moment of inertia for rigid bodies
    • determining the centre of mass for individual bodies and for systems of bodies
    • integrating Newton’s second law when expressed in the form mx^n(t) = f(x)

  • Math 31 >

    APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS

    Students are expected to understand that calculus may be used as a tool to analyze situations in business and economics that involve revenue, profit and cost, and demonstrate this, by:
    • relating the zeros of the derivative function to the critical points on the original curve
    • producing approximate answers to complex calculations by simplifying the models used
    • constructing mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable
    • determining the optimum values of a variable in various contexts, using the concepts of maximum and minimum values of a function
    • using the concept of critical values to sketch the graphs of functions, and comparing these sketches to computergenerated plots of the same functions
    • fitting mathematical models to situations described by data sets.

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the links between calculus and the biological sciences, by:
    • defining exponential and logarithmic functions as inverse functions
    • explaining the special properties of the number e, together with a definition of e as a limit
    • illustrating that the derivative of an exponential or logarithmic function may be derived from the definition of the derivative
    • illustrating how differential equations may be used to model certain biological problems involving growth, decay and movement across a boundary.

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the application of calculus to the biological sciences, by:
    • estimating the values of the limits e and e^x
    • using limit theorems to evaluate the limits of simple exponential and logarithmic functions
    • approximating the slopes of y = e^x and y = ln x for some specific value of x
    • finding the derivative of the natural logarithmic function
    • finding the derivative and antiderivative of the base-e exponential function
    • using methods of guess-and-test, and comparing coefficients to solve the differential equations y = ky and y = k(y - y0)
    • verifying that y = Ae^kx satisfies the differential equation y = ky

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, by:
    • relating natural growth, natural decay and return to equilibrium to the differential equations y = ky or y =(y - y0)
    • solving natural growth and decay problems starting from the equations y = ky or y =(y - y0)
    AND, either, by:
    • fitting differential equation models to observed biological data
    OR, both of the following, by:
    • relating growth subject to limits to the logistic equation y = ky(L - y)
    • solving logistic equation models, and estimating values for the parameters k and L, from experimental data.

  • Math 31 >

    APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS

    Students are expected to understand that limit, derivative and integral theorems can be proved at different levels of rigor, from intuitive to analytic, and demonstrate this, by:
    • giving examples of the differences between intuitive and rigorous proofs in the context of limits, derivatives and integrals
    • calculating the mean value of a function over an interval
    • constructing geometrical proofs at an intuitive level that generalize the concepts of slope, area, average and rate of change.

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the links among calculus, business and economics, by:
    • explaining how calculus procedures frequently arise in models used in business and economics
    • explaining how both maximum and minimum values are important in the making of business and economic decisions.

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the application of calculus to business and economics, by:
    • sketching polynomial, exponential and trigonometric functions of one variable
    • using a given revenue, profit or cost function to calculate and justify optimum values
    • finding the maximum of a revenue or profit function that is expressed as a function of price or number sold
    • finding the minimum of a cost function that is expressed as a function of price or number sold.

  • Math 31 > APPLICATIONS OF CALCULUS TO BUSINESS AND ECONOMICS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, in one or both of the following, by:
    • determining a revenue, profit or cost function from a problem situation that can be modelled, using polynomial functions
    • modelling the business cycle, using trigonometric functions.

  • Math 31 >

    CALCULUS THEOREMS

    Students are expected to understand that limit, derivative and integral theorems can be proved at different levels of rigor, from intuitive to analytic, and demonstrate this, by:
    • giving examples of the differences between intuitive and rigorous proofs in the context of limits, derivatives and integrals
    • calculating the mean value of a function over an interval
    • constructing geometrical proofs at an intuitive level that generalize the concepts of slope, area, average and rate of change

  • Math 31 > CALCULUS THEOREMS > Specific Outcome 1

    1. Conceptual Understanding - Students will demonstrate conceptual understanding of the nature of proof in the context of limit, derivative and integral theorems, by:
    • proving the equivalence of the product and the quotient rule for derivatives
    • comparing the nature of intuitive and rigorous proofs knowing the conditions under which a theorem is true
    • explaining what is an example, and what is a counterexample
    • illustrating the intermediate value theorem, Rolle’s theorem, the mean value theorem and the fundamental theorem of calculus, by examples and counterexamples, using both graphical and algebraic formulations.

  • Math 31 > CALCULUS THEOREMS > Specific Outcome 2

    2. Procedural Knowledge - Students will demonstrate competence in the procedures associated with the construction of proofs of limit, derivative and integral theorems, by:
    • using specific functions to illustrate the equivalence of the product and quotient rules
    • locating an error in a given proof of a calculus theorem
    • verifying the mean value theorem and the fundamental theorem of calculus for specific examples.

  • Math 31 > CALCULUS THEOREMS > Specific Outcome 3

    3. Problem Solving - Students will demonstrate problem-solving skills, by:
    • composing rigorous proofs for derivative theorems, starting from the corresponding limit theorems
    AND, in one of the following, by:
    • deriving formulas for the derivatives of complicated functions, using the basic rules; e.g., functions, such as y = ( f(x)g(x) / h(x) ) or y = f(g(h(x)))
    • proving that a differentiable function satisfies the mean value theorem
    • constructing, and justifying, an iterative solution procedure for the equation f(x) = c, using the intermediate value theorem.

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