From Kindergarten to Grade 12, students use seven critical processes to build their understanding of mathematics and to support lifelong learning.

Communication – read about, represent, view, write about, listen to, and discuss mathematical ideas.
Connections – connect to other mathematical ideas, to real-world phenomena, to personal experiences
Mental Math and Estimation – calculate mentally without the use of external memory aids and make mathematical judgements based on useful, flexible, and efficient mathematical strategies.
Problem Solving – develop creative and innovative solutions through listening, discussing, and trying different strategies to get from what is known to what is sought.
Reasoning – think logically and make sense of mathematics to become confident in their mathematical thinking.
Technology – explore and create patterns, examine relationships, test conjectures, and solve problems through calculator and computer use.
Visualization – think in pictures and images to reason with numbers, measurements, and geometry in order to describe relationships among concepts.

 

Kindergarten students:

Number	Count from 1 to 30 and 10 to 1 starting from anywhere. Subitize (determining the quantity a small group of items without counting) an arrangement of 1 to 6 dots or objects. Describe and compare quantities to 10. Show the numbers 2 to 10 as two parts.
Patterns and Relations	Identify, reproduce, extend, and create repeating patterns using objects, sounds and actions.
Shape and Space	Demonstrate awareness of measurement through comparison. Sort, classify, and build 3-D real-world objects.

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Grade 1 students:

Number	Be able to count by: - 1s forward and backward starting from anywhere - forward by 2s to 30 - 5s and 10s to 100. Subitize (determining the quantity a small group of items without counting) an arrangement of 1 to 10 dots or objects. Represent, describe and compare quantities to 20. Describe and use mental mathematics strategies (memorization not intended) to determine basic addition and related subtraction facts to 18.
Patterns and Relations	Describe, reproduce, extend, create and translate repeating patterns using objects, pictures, sounds and actions. Determine and describe how two sets up to 20, are equal and unequal.
Shape and Space	Demonstrate an understanding of measurement through comparison, filling, covering and matching objects. Sort (using one characteristic), replicate and compare 2-D shapes and 3-D objects.

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Grade 2 students:

Number	Be able to count from 0 to 100 by: - multiples of 2s, 5s and 10s forward and backward, starting from anywhere - 10s using starting points from 1 to 9 - 2s starting from 1. Represent, describe and compare numbers to 100. Use personal strategies to add and subtract numbers to 100 in problem solving situations. Apply mental mathematics strategies to develop recall of basic addition and related subtraction facts to 18.
Patterns and Relations	Predict the object or number in a repeating pattern. Describe, reproduce, extend, and create increasing patterns using objects, pictures, sounds and actions. Demonstrate, explain and record how two sets are equal and unequal.
Shape and Space	Read and understand a calendar. Estimate, measure, and compare measurements using non-standard units. Sort, describe, compare, and build different 2-D shapes and 3-D objects.
Statistics and Probability	Independently ask questions and gather information. Answer questions about information collected. Collect, display and understand information in concrete and picture graphs.

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Grade 3 students:

Number	Be able to count from 0 to 1 000 forward and backward by: - multiples of 10s or 100s, starting from anywhere - multiples of 5s - multiple of 25s. Represent, describe, compare, and estimate quantities to 1 000. Use personal strategies to add and subtract numbers to 100 in problem solving situations. Demonstrate an understanding of addition and subtraction of numbers with answers to 1 000 (limited to 1-, 2-, and 3- digit numerals). Describe mental mathematics strategies to determine basic addition and related subtraction facts to 18. Demonstrate an understanding of multiplication to 5 x 5 and division(limited to division related to multiplication facts up to 5 x 5) by using different strategies to determine answers. Demonstrate an understanding of fractions.
Patterns and Relations	Describe, reproduce, extend, compare, and create increasing patterns using objects, pictures, and numbers. Describe, extend, compare, and create decreasing patterns using objects, pictures, and numbers (to 1000). Solve addition and subtraction sentences involving symbols such as a triangle or square to represent the unknown quantity.
Shape and Space	Measure the passage of time using non-standard and standard units of measurement. Estimate and compare measurements. Identify and describe 3-D objects. Sort polygons.
Statistics and Probability	Collect and display information in different ways. Make, label and understand bar graphs.

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Grade 4 students:

Number	Represent, describe and compare numbers to 10 000. Demonstrate an understanding of addition and subtraction of numbers with answers to 10 000 (limited to 3-, and 4- digit numerals) by using personal strategies. Demonstrate and apply different mental mathematical strategies to develop recall of basic multiplication facts to 9 x 9 and related division facts. Demonstrate an understanding of multiplication (2- or 3-digit numerals by 1- digit numerals) by using different strategies to determine answers. Demonstrate an understanding of division (1-digit divisor and up to 2- digit dividend) by using different strategies to determine answers. Demonstrate an understanding of fractions and decimals (to hundredths). Use different strategies to add and subtract tenths and hundredths.
Patterns and Relations	Identify, describe and reproduce a pattern found in tables and charts. Express and solve an equation involving symbols such as a triangle or square to represent the unknown quantity.
Shape and Space	Read and record time using digital and analog clocks. Read and record calendar dates in a variety of ways. Solve problems involving 2-D shapes and 3-D objects. Describe and construct rectangular and triangular prisms.
Statistics and Probability	Make and understand pictographs and bar graphs to draw conclusions.

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Grade 5 students:

Number	Represents and describes numbers to 1 000 000. Applies mental math and estimation strategies in problem solving situations. Uses addition, subtraction, multiplication, and division of whole numbers and decimals to solve problems. Understands and relates decimals and fractions in various ways.
Patterns and Relations	Determines a pattern rule and makes predictions. Solves a problem with a variable in one step.
Shape and Space	Makes connections between perimeter and area. Measures in mm and connects to cm and m. Solves problems related to objects and shapes by visualizing, building, sorting, and drawing. Understands volume and capacity. Draws and describes the motion of a 2-D shape.
Statistics and Probability	Understands methods of collecting data. Constructs and solves problems using double bar graphs. Compares and describes the chances of outcome(s) occurring.

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Grade 6 students:

Number	Understands and relates decimals, fractions, ratios, and percents. Understands and solves problems using large numbers, place value, integers, and factors and multiples. Uses the order of operations with whole numbers and decimals to solve problems.
Patterns and Relations	Uses variables to show number patterns. Understands the meaning of preservation of equality.
Shape and Space	Classifies, estimates, determines, draws, and labels angles, triangles, and other polygons. Develops and uses a formula for perimeter, area, and volume of various figures. Draws and describes the motion of a 2-D shape. Solves problems involving the coordinate plane.
Statistics and Probability	Constructs and solves problems using line graphs. Collects, displays, and analyzes data gathered from appropriate samples.   Determines and compares experimental and theoretical probability.

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Grade 7 students:

Number	Uses divisibility rules, addition, subtraction, multiplication, and division of decimals, and percents to solve problems. Shows understanding of the addition and subtraction of fractions and integers in a variety of ways. Compares and orders fractions, decimals, and integers.
Patterns and Relations	Connects patterns to expressions and equations, graphs patterns and analyses the results. Applies preservation of equality to model and solve equations. Evaluates expressions. Solves a problem with a variable in one or two steps.
Shape and Space	Determines the relationships among the properties of circles. Solves problems involving the area of triangles, parallelograms and circles, parallel and perpendicular lines, and bisectors. Draws and describes the motion of a 2-D shape. Solves problems involving the coordinate plane.
Statistics and Probability	Constructs and solves problems using circle graphs. Determines and judges the appropriateness of mean, median, mode, and range. Solve problems using probabilities and represents experimental and theoretical probability as ratios, fractions, and percents.

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Grade 8 students:

Number	Demonstrates number sense for perfect squares, square roots, percents, rate and ratio, fractions, integers, and rational numbers. Shows understanding of the multiplication and division of fractions and integers in a variety of ways. Uses number sense to solve problems using a variety of strategies.
Patterns and Relations	Models, solves, graphs, and understands the meaning of equations.
Shape and Space	Solves problems involving surface area, volume, and the Pythagorean theorem. Draws and interprets nets and views of 3-D objects. Creates, identifies, and explains the properties of tessellation.
Statistics and Probability	Analyses advantages and disadvantages of data presented in a variety of ways. Solves problems involving the probability of independent events.

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