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

• Communication—showing learning orally, through diagrams, and in writing.
• Connections—making connections among everyday situations, other subject areas, and mathematics concepts.
• Estimation/Mental Mathematics—developing understanding of numbers and quantities.
• Problem Solving—investigating problems, including those with multiple solutions.
• Reasoning—justifying thinking.
• Technology—using technology to enhance problem solving and encourage discovery of number patterns.
• Visualization—drawing on mental images to clarify concepts.

 

Kindergarten students:

Patterns and Relations	Sort collections of objects. Identify, describe, and create patterns from real life.
Statistics and Probability	With help, collect information, display it on object graphs, and compare data. Talk about something happening using the words: never, sometimes, or always.
Shape and Space	Demonstrate awareness of measurement. Sort, classify, and build real-world objects. Describe, orally, the position of objects.
Number	Describe, orally, and compare quantities (0 to 10). Demonstrates awareness of addition and subtraction.

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Grade 1 students:

Patterns and Relations	Sort collections of objects. Compare and create patterns from real life.
Statistics and Probability	With help, collect information in different ways and display it on graphs. Describe and compare data.
Shape and Space	Estimate, measure, and compare using non-standard units. Classify objects according to their characteristics. Describe the relative position of objects and shapes.
Number	Recognize and use numbers from 0 to 100, and explore halves. Use informal ways of solving addition and subtraction problems (0 to 18).

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Grade 2 students:

Patterns and Relations	Sort objects. Compare and create patterns. Change patterns to different forms.
Statistics and Probability	Independently ask questions. Collect and display information in different graphs. Draw conclusions.
Shape and Space	Estimate, measure, and compare lengths (cm/m). Use non-standard units for most other measurements. Name, describe, and build different objects/shapes. Describe changes in position.
Number	Use numbers to 1000. Explore halves, thirds, and quarters. Use different methods to add and subtract numbers to 100 in problems.

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Grade 3 students:

Patterns and Relations	Sort objects using two characteristics. Explain pattern rules and make predictions.
Statistics and Probability	Collect and display information in different ways. Interpret data to make predictions.
Shape and Space	Estimate and compare measurements using mostly standard units of measure. Classify objects and connect shapes to objects. Use numbers and direction words to describe position.
Number	Develop understanding of numbers to 1000. Explore fifths and tenths. Use all operations to solve and create problems.

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Grade 4 students:

Patterns and Relations	Explain relationships and justify predictions about patterns.
Statistics and Probability	Choose a sample or population. Gather data and display them in different ways.
Shape and Space	Estimate, compare, and solve problems in measurement, using decimal numbers/standard units. Compare objects, sort shapes, and recognize different lines. Write directions for a given path.
Number	Understand numbers to 10 000. Explore fractions and decimals. Use all operations to solve and create problems. Use concrete materials to add and subtract tenths and hundredths.

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Grade 5 students:

Patterns and Relations	Extend, create, and explain the growth of patterns using everyday language, charts, and rules.
Statistics and Probability	Develop and use a plan to answer a question. Gather, display, and interpret data. Predict outcomes, conduct probability experiments, and communicate the results.
Shape and Space	Solve everyday problems using measurement concepts, appropriate tools, and results of measurements. Solve probems related to objects and shapes by visualizing, building, and drawing. Use coordinates to describe position. Describe motion as flips, slides, or turns.
Number	Understand numbers to 100 000. Demonstrate number sense for fractions and decimals. Solve problems using a combination of arithmetic operations on decimals and whole numbers.

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Grade 6 students:

Patterns and Relations	Explain, generalize, and extend patterns using relationships. Solve equations with one unknown using informal strategies.
Statistics and Probability	Develop and use a plan to collect, display, and analyze data gathered from appropriate samples. Use numbers to communicate the probability of single events from experiments.
Shape and Space	Solve problems involving perimeter, area, surface area, volume, and angle measurement. Solve problems using symmetry and visualization. Create patterns and designs using symmetry, slides, and flips.
Number	Develop a number sense for decimals and common fractions, explore integers, and demonstrate a number sense for large numbers. Add, subtract, multiply, and divide whole numbers and decimals to solve and create problems.

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Grade 7 students:

Patterns and Relations	Use expressions containing unknowns to represent patterns and to make predictions. Solve problems by using unknowns and equations.
Statistics and Probability	Develop and defend a plan to collect, display, and analyze data (using median, mode, mean, range, extremes, and quartiles). Create and solve problems using probability.
Shape and Space	Solve problems involving circles, time zones, perimeter, and area. Link angles and properties of parallel lines. Create and analyze patterns and designs, using congruence, symmetry, slides, flips, and turns.
Number	Demonstrate a number sense for decimals, fractions, integers, and whole numbers. Add, subtract, multiply, and divide decimals and integers to solve problems. Use rates, ratios, and percentages to solve problems.

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Grade 8 students:

Patterns and Relations	Solve problems using patterns, unknowns, algebraic expressions, and graphs. Solve and verify two-step linear equations.
Statistics and Probability	Develop and use a plan to collect and display data, using technology. Analyze the effect of changes in data. Compare theoretical and experimental probability of independent events.
Shape and Space	Generalize relationships in measurement. Solve problems involving area, perimeter, surface area, and volume. Link angle measures and parallel lines to the classification of four-sided shapes. Create and analyze patterns in designs and architecture. Solve problems using proportion, scale, and networks.
Number	Demonstrate a number sense for decimals, fractions, integers, and whole numbers. Add, subtract, multiply, and divide fractions to solve problems. Use rates, ratios, percentages, and proportion to solve problems.

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