Grade 5: Mathematics

Here is the Mathematics curriculum for Grade 5 in British Columbia, presented with the content first, followed by the curricular competencies and big ideas, as you requested.

Grade 5 Mathematics Content (BC Curriculum)

The learning standards for Grade 5 Math are organized into the following content areas.

1. Number: Computational Fluency and Conceptual Understanding

• Multiplication and Division Facts: Extend understanding of multiplication and division to facts with products and dividends to 100 and corresponding multiples.

• Multiplication: Model, record, and explain multiplication with two 2-digit numbers, using flexible computation strategies and algorithms.

• Division: Model, record, and explain division with 2-digit dividends and 1-digit divisors, with and without remainders.

• Fractions and Decimals:

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

  • Compare and order decimals (tenths, hundredths, thousandths).

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

• Equivalency: Demonstrate an understanding of equivalency among fractions, decimals, and whole numbers.

• Order of Operations: Model and explain the meaning of the order of operations, limited to problems involving addition, subtraction, multiplication, and division, with or without parentheses.

2. Number: Financial Literacy

• Financial Calculations: Count and represent different combinations of Canadian coins and bills up to $1000.

• Making Change: Make change for amounts up to $100, using mental math and other strategies.

• Financial Goal Estimation: Estimate sums and differences of different money amounts, and calculate make-change strategies.

3. Patterns and Relations

• Patterns: Describe, extend, and create increasing and decreasing patterns using tables, charts, and diagrams.

• Variables and Equations:

  • Solve one-step equations with a single variable using whole numbers.

  • Represent an unknown number using a symbol or letter (e.g., + 3 = 10, 4 × = 20).

4. Geometry and Measurement

• Length, Mass, and Capacity:

  • Estimate, measure, and compare length (mm), mass (g, kg), and capacity (mL, L) using standard units.

  • Read and write time using both analog and digital clocks.

• Perimeter and Area:

  • Measure and calculate the perimeter of regular and irregular polygons.

  • Measure and calculate the area of rectangles using a formula (Area = length × width).

• Transformations: Perform, describe, and identify single transformations (translations, rotations, and reflections) of 2D shapes.

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

5. Statistics and Probability

• Data Collection and Analysis:

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

  • Construct and interpret double bar graphs to draw conclusions.

• Probability:

  • Describe the likelihood of a single outcome occurring using words such as:

    • Impossible, Possible, Certain

    • Less Likely, Equally Likely, More Likely

  • Compare the likelihood of two possible outcomes occurring.

Curricular Competencies (The “Doing” of Mathematics)

These are the processes students use to engage with the mathematical content.

• Reasoning and Analyzing:

  • Use logic and patterns to solve puzzles and play games.

  • Use reasoning and logic to explore, analyze, and apply mathematical ideas.

  • Estimate reasonably and use tools to check.

• Understanding and Solving:

  • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving.

  • Visualize to explore mathematical concepts.

  • Use multiple strategies to engage with problems in both abstract and contextual situations.

• Communicating and Representing:

  • Explain and justify mathematical ideas and decisions.

  • Communicate mathematical thinking in multiple ways (orally, visually, with numbers and words).

  • Use mathematical vocabulary and language to contribute to mathematical discussions.

• Connecting and Reflecting:

  • Reflect on mathematical thinking.

  • Connect mathematical concepts to each other and to real-life situations.

  • Use mathematical arguments to support personal choices.

Big Ideas (The Core Concepts)

These are the key understandings students should retain from Grade 5 Math.

• Numbers: Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.

• Decimals and Fractions: Decimals and fractions are other ways of representing quantities, and they can be equivalent to each other.

• Patterns and Equations: Regular changes in patterns can be identified and represented using tools and expressions.

• Data: Data represented in graphs can be used to show many-to-one correspondence.

• Geometry: The likelihood of an outcome can be examined, compared, and interpreted.

Key Changes & Focus for Grade 5

• A major shift from basic operations to more complex calculations (2-digit by 2-digit multiplication).

• A deep dive into the relationship between fractions and decimals.

• The introduction of foundational algebraic concepts (variables and equations).

• A move from single bar graphs to more complex double bar graphs.

• The formal introduction of the Cartesian plane and area calculation.