Creating and Sharing Fractions

Overview

This is the final lesson of the unit "Understanding Fractions Together" designed for Grade 3 students (ages 8–9) following the British Columbia Mathematics Curriculum. In this 40-minute class, students will work collaboratively in small groups to create their own fraction models using diverse, tactile materials. They will then present their creations to the class, articulating their understanding of fractions and the principle of equal sharing.

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Learning Goals

Curriculum Alignments: British Columbia Mathematics Curriculum (Grade 3, Numbers, and Operations - Fractions & Patterns)

• Learning Standards Addressed:

  • Number Concepts:
    Demonstrate an understanding of fractions as numbers that can represent a part of a whole or part of a collection.
    (Reference: Grade 3 - Numbers, 3.1)

  • Representation & Modelling:
    Represent fractions concretely, pictorially, and symbolically, including through use of manipulatives.
    (Reference: Grade 3 - Numbers, 3.4)

  • Communication & Reasoning:
    Explain mathematical thinking and ideas clearly and in ways that make sense to others.
    (Reference: Grade 3 - Mathematical Processes and Skills)

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Materials Needed

• Fraction strips (paper or plastic)
• Paper circles, rectangle cut-outs (to model pies/pizzas, bars)
• Manipulatives (e.g., counters, coloured blocks)
• Glue sticks and scissors
• Large chart paper for group presentations
• Markers and coloured pencils

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Lesson Structure (40 minutes)

1. Introduction & Review (5 minutes)

• Briefly review what was learned in previous lessons about fractions, focusing on the ideas of:
  • What a fraction represents (part of a whole or a part of a collection).
  • Equal sharing/partitioning.
• Invite a few students to share examples of fractions they remember.

2. Group Activity: Creating Fraction Models (20 minutes)

• Grouping: Students are divided into 5 groups of 4 students.
• Task: Each group will create their own fraction model displaying a fraction with numerator and denominator clearly communicated.
• Materials Usage Suggestions:
  • Use paper circles to create "fraction pies" showing equal parts.
  • Use fraction strips to show different fractions and compare sizes.
  • Use manipulatives to demonstrate sharing (e.g., divide 12 counters equally among 3 parts to show 4/12 = 1/3).
• Guidance:
  • Encourage exploration beyond common fractions (1/2, 1/4), e.g., 3/5, 2/3.
  • Assist with fraction language: numerator (top number), denominator (bottom number), equal parts.
• Students write down the fraction they are modelling and a brief explanation on chart paper.

3. Group Presentations (10 minutes)

• Each group presents their fraction model to the class.
• The presenter explains:
  • What fraction their model represents.
  • How the model shows equal sharing.
  • Why the parts are equal and how the numerator and denominator connect to the model.

4. Whole Class Reflection & Assessment (5 minutes)

• Reflection prompts:
  • What did you learn about fractions today?
  • Why is it important that the parts are equal in a fraction?
• Formative assessment through questioning:
  • Ask students to identify which models represent the same fraction even if they look different.
  • Clarify any misconceptions gently.
• Teacher notes anecdotal observations on students’ understanding and communication skills.

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Differentiation

• For students needing support:

  • Provide simpler fractions (like halves and quarters) with pre-cut materials.
  • Pair with a peer buddy who can assist in the explanation.

• For advanced learners:

  • Challenge to create mixed fractions or improper fractions using the materials.
  • Ask them to compare fractions and discuss equivalency.

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Assessment

• Formative: Observation of group work — participation, engagement, collaboration.
• Oral: Clarity and accuracy during group presentations.
• Written: Group notes on chart paper showing correct fraction notation and explanation.

These assess understanding of fractions as parts of a whole and equal sharing, consistent with BC Grade 3 learning goals.

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Teacher Notes & Suggestions

• Encourage creativity and use of varied materials; empowering students to “own” their fraction models can deepen conceptual understanding.
• Position this final lesson as a celebration of learning, fostering confidence in mathematical communication.
• Optionally, photograph group models and create a visual display in the classroom or a digital portfolio to share with parents.
• Use language consistently: numerator = number of parts taken, denominator = total equal parts.

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Summary

By the end of this lesson, students will have constructed their own fraction models, practised explaining the concept of fractions emphasizing equal sharing, and enhanced their communication skills in line with the British Columbia Curriculum. This active, cooperative learning approach consolidates prior knowledge and fosters positive attitudes towards mathematics.