Grade 6: Mathematics

Here is a comprehensive overview of the Grade 6 Mathematics content, aligned with the British Columbia (BC) Curriculum.

The BC curriculum is structured around “Big Ideas,” “Curricular Competencies,” and “Content,” with a strong focus on reasoning, communicating, and connecting mathematical concepts to the world.

BC Grade 6 Mathematics: At a Glance

The curriculum is designed to develop flexible and creative mathematical thinkers. The content is often integrated but can be broadly categorized into the following areas of focus.

Overarching Big Ideas (Themes for the Year)

• Number: Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.

• Spatial Relationships: The regular change in patterns can be identified and represented using tools and tables.

• Uncertainty: Data from the results of an experiment can be used to predict the theoretical probability of an event happening.

• Relationships: Linear relations can be identified and represented using expressions and tables of values.

Unit 1: Numbers and Operations (Mastering Decimals and Whole Numbers)

This unit solidifies students’ understanding of our number system and builds fluency with larger numbers and decimal operations.

• Key Concepts: Place value to millions, decimal operations, order of operations.

• Learning Goals:

  • Demonstrate an understanding of place value for numbers up to 1,000,000 and decimal numbers to thousandths.

  • Solve problems involving multiplication and division of whole numbers.

  • Solve problems involving addition and subtraction of decimals to thousandths.

  • Apply the order of operations to multi-step problems with whole numbers (excluding exponents).

Unit 2: Patterns and Relations (Introduction to Algebra)

This unit introduces the powerful language of algebra to describe patterns and relationships.

• Key Concepts: Variables, expressions, equations, table of values.

• Learning Goals:

  • Represent and describe patterns and relationships using graphs and tables.

  • Demonstrate understanding of the preservation of equality by solving one-step equations with whole-number coefficients and solutions (e.g., $2x=8$, $x+3=7$).

  • Use variables to write expressions representing mathematical relationships.

Unit 3: Spatial Relationships (Geometry and Measurement)

This unit explores the properties of shapes and objects, focusing on area, volume, and angles.

• Key Concepts: Area, volume, angles, triangles, transformations.

• Learning Goals:

  • Develop and apply formulas for determining the area of triangles, parallelograms, and volume of right rectangular prisms.

  • Perform combinations of transformations (translations, rotations, reflections) on a single 2D shape.

  • Demonstrate understanding of angles by identifying and classifying them as acute, obtuse, right, straight, or reflex.

  • Construct and compare triangles based on side and angle measurements.

Unit 4: Statistics and Probability (Uncertainty)

This unit focuses on using statistics to analyze data and probability to understand chance.

• Key Concepts: Data collection, central tendency, theoretical and experimental probability.

• Learning Goals:

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

  • Determine the theoretical probability of an outcome and experimental probability of an outcome in a given probability experiment.

  • Compare the theoretical and experimental probabilities of an outcome.

Curricular Competencies in Action (The “Habits of a Mathematician”)

The BC curriculum emphasizes how students learn and use mathematics, not just the content. Key competencies include:

• Reasoning and Analyzing: Estimate reasonably, analyze and apply mathematical ideas, develop mental math strategies.

• Understanding and Solving: Develop, demonstrate, and apply conceptual understanding to solve problems.

• Communicating and Representing: Explain and justify mathematical ideas and decisions in multiple ways (orally, visually, in writing). Use mathematical vocabulary and language.

• Connecting and Reflecting: Connect mathematical concepts to each other and to real-life situations. Use mathematics to support personal choices.

Sample Real-World Problems (Connecting the Units)

• Problem: “A sports stadium has 45 sections with 128 seats in each section. What is the total seating capacity?” (Uses Multiplication of Whole Numbers from Unit 1).

• Problem: “A pizza costs $12.50 and a drink costs $1.75. If you pay with a $20 bill, how much change should you get?” (Uses Decimal Operations from Unit 1).

• Problem: “A pattern starts at 3 and increases by 5 each time. Write an expression for the n-th term. What is the 10th term in the pattern?” (Uses Algebra from Unit 2).

• Problem: “You are designing a box to hold 36 cubes. What are the possible dimensions (length, width, height) of the box?” (Uses Volume from Unit 3).

• Problem: “You flip a coin 50 times. It lands on heads 28 times. What is the experimental probability of getting heads? How does it compare to the theoretical probability?” (Uses Statistics and Probability from Unit 4).

This framework ensures that BC Grade 6 students develop both the procedural fluency and the conceptual understanding needed to be mathematically literate citizens, preparing them for the increased abstraction in Grade 7.