Grade 8: Mathematics

Here is a comprehensive overview of the Grade 8 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 8 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 units.

Overarching Big Ideas (Themes for the Year)

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

• Spatial Relationships: The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare phenomena.

• Uncertainty: Analyzing data by determining averages and judging the likelihood of outcomes enables us to compare and interpret.

• Relationships: Linear relations can be identified and represented using expressions, tables, and graphs and can be used to form generalizations.

Unit 1: Numbers and Operations (The Integer and Decimal System)

This unit deepens students’ understanding of the number system, focusing on fluency with integers and decimals.

• Key Concepts: Integers, order of operations, perfect squares and square roots, operations with decimals.

• Learning Goals:

  • Demonstrate an understanding of integers, including ordering, comparing, and representing them on a number line.

  • Solve problems involving operations with integers (addition, subtraction, multiplication, division).

  • Apply the order of operations (BEDMAS/PEDMAS) to problems with integers and decimals, with and without brackets.

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

  • Solve problems involving operations with decimals to thousandths.

Unit 2: Patterns and Relations (Introduction to Algebra)

This unit focuses on using algebra to represent, analyze, and solve problems involving linear relationships.

• Key Concepts: Linear relations, algebraic expressions, equations, and graphing.

• Learning Goals:

  • Write and simplify algebraic expressions.

  • Model and solve problems using two-step linear equations of the form ax + b = c and a(x + b) = c, where a, b, and c are integers.

  • Represent and describe linear relations using:

    • Table of Values

    • Graphs

    • Equations

  • Explain and illustrate the connection between a linear equation and its graph on a coordinate plane.

Unit 3: Spatial Relationships (Geometry and Measurement)

This unit explores the properties of 3D objects, focusing on the relationship between their surface area and volume.

• Key Concepts: Surface area, volume, nets of 3D objects.

• Learning Goals:

  • Sketch and construct nets for 3D objects (right prisms, cylinders).

  • Calculate the surface area of right prisms and cylinders.

  • Calculate the volume of right prisms and cylinders.

  • Solve problems involving the surface area and volume of right prisms and cylinders.

  • Describe the relationship between linear dimensions, surface area, and volume (e.g., if you double the dimensions, the surface area increases by a factor of 4, and the volume increases by a factor of 8).

Unit 4: Statistics and Probability (Uncertainty)

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

• Key Concepts: Central tendency, misleading graphs, theoretical probability.

• Learning Goals:

  • Determine the mean, median, and mode for a set of data.

  • Select and defend the choice of using either the mean, median, or mode as a measure of central tendency for a specific data set.

  • Critique ways in which data is presented in circle graphs, line graphs, bar graphs, and pictographs (e.g., identify misleading graphs).

  • Solve problems involving the probability of independent events.

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 and contribute to culture and society.

Sample Real-World Problems (Connecting the Units)

• Problem: “A scuba diver is at -25 meters. She ascends 10 meters, then descends 8 meters. What is her final position?” (Uses Operations with Integers from Unit 1).

• Problem: “A gym membership has a $50 sign-up fee and costs $30 per month. Write an expression for the total cost after ‘m’ months. How many months can you afford if you have $200?” (Uses Algebra from Unit 2 to model and solve with a linear equation).

• Problem: “You are designing a cylindrical can to hold 500 ml of juice. What dimensions would minimize the amount of aluminum (surface area) used?” (Uses Spatial Relationships from Unit 3).

• Problem: “A news article shows a bar graph that makes a 5% salary increase look massive. How was the graph designed to be misleading?” (Uses Statistics from Unit 4).

This framework ensures that BC Grade 8 students develop both the procedural fluency and the conceptual understanding needed to be mathematically literate citizens.