Adding and Subtracting Fractions

Overview

This 40-minute lesson for 7th-grade students focuses on finding a common denominator to add and subtract fractions, designed in accordance with the British Columbia Mathematics Curriculum (Grade 7). The lesson incorporates hands-on, collaborative activities to engage students actively in learning and consolidating their understanding of equivalent fractions and fraction operations.

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Curriculum Alignment

Mathematics – Number

• Learning Standards:
  • Develop fluency in computing with rational numbers (fractions, decimals, integers)
  • Understand and apply the concept of least common multiple (LCM) to find common denominators
  • Represent and solve problems involving addition and subtraction of fractions
• Competencies:
  • Reasoning and analyzing
  • Communicating and representing
  • Connecting and reflecting

Reference: BC Ministry of Education – Mathematics Grade 7 Curriculum:

• Represent and explain adding and subtracting of fractions with unlike denominators by finding equivalent fractions (Number 7)
• Apply the concepts and skills of decomposing numbers and using equivalencies to solve problems (Number 1, 7)

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Learning Objectives

By the end of this lesson, students will be able to:

• Identify and find the least common denominator (LCD) for two or more fractions
• Convert fractions to equivalent fractions with the LCD
• Perform addition and subtraction of fractions with unlike denominators
• Explain their reasoning using visual and numerical representations

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Materials

• Fraction tiles or fraction circles (physical manipulatives, enough sets for groups of 4)
• Whiteboards and markers (one per student pair)
• Printed handouts with fraction addition and subtraction problems
• LCM charts or tables (optional, as support)
• Timer or clock

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Lesson Structure

1. Introduction (5 minutes)

• Begin with a brief review and discussion:
  • Ask: “What happens when we add fractions with the same denominator?”
  • Introduce the challenge: “How about when the denominators are different?”
• Explain that to add or subtract such fractions, we need to find a common denominator (often the least common denominator) and convert the fractions accordingly.

2. Guided Exploration with Manipulatives (15 minutes)

• Group Activity (Groups of 4):
  • Each group receives fraction tiles representing different denominators (e.g., 1/2, 1/3, 1/4, 1/6)
  • Task 1: Using tiles, students explore combining 1/2 + 1/3 by finding a common denominator visually.
  • Prompt Questions:
    • Can you make 1/2 and 1/3 the same size fraction using your tiles?
    • What denominator works? How do you know?
  • Students physically rearrange tiles to make equivalent fractions with a common denominator (e.g., 3/6 + 2/6).
  • Record these fractions on their whiteboards and then perform the addition or subtraction.
• Circulate and scaffold as needed, prompting students to verbalise their reasoning.

3. Consolidation Practice (10 minutes)

• Provide individual problem sheets with 5 problems involving adding and subtracting fractions with different denominators.
• Students work independently or in pairs to:
  • Find the LCD
  • Convert fractions
  • Calculate the sum or difference
• Encourage showing all steps clearly on paper or whiteboards.

4. Class Discussion and Reflection (7 minutes)

• Invite a few students/groups to present their problem-solving approach to the class.
• Highlight strategies for finding the LCD efficiently (e.g., listing multiples, prime factorization).
• Discuss common errors and misconceptions, focusing on the importance of equivalent fractions.
• Ask reflection questions:
  • Why is finding a common denominator necessary?
  • How did the manipulative activity help your understanding?

5. Exit Ticket (3 minutes)

• On a small slip or mini-whiteboard, each student writes one addition or subtraction fraction problem with unlike denominators and solves it, showing the common denominator step.
• Collect or review quickly to assess understanding and inform next steps.

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Assessment

• Formative: Observe group discussions and manipulative use to check understanding of equivalent fractions and LCD.
• Whiteboard responses and individual worksheets provide immediate feedback during the lesson.
• Exit ticket to evaluate each student’s grasp of the core skill.

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Extensions and Differentiation

• Extension: Provide word problems involving fractions in real-life contexts (e.g., recipe adjustments).
• Support: Use LCM charts or calculators for students requiring additional help with finding common denominators.
• Offer guided notes with step-by-step method visuals for visual learners.

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Teacher Reflection

Ask yourself after the lesson:

• Did students engage effectively with the hands-on manipulatives?
• Were students able to articulate why we find a common denominator?
• Which students need further support with equivalent fractions or operations?
• How can this lesson integrate with future topics such as multiplying or dividing fractions?

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This lesson emphasises active exploration linked directly to the British Columbia Grade 7 Mathematics curriculum, promoting deep conceptual understanding through collaborative, tactile learning experiences.