Sharing Parts Fairly

Overview

This 45-minute lesson introduces Year 5 students to the concept of fractions using simple examples aligned with the New Zealand Curriculum Refresh. It focuses on understanding fractions as parts of a whole and develops students' ability to read, write, and represent simple fractions such as halves, quarters, and eighths. The lesson incorporates hands-on activities and visuals to engage students and build foundational knowledge.

Curriculum Links

• Learning Area: Mathematics and Statistics
• Strand: Number and Algebra — Rational Numbers
• Level: Level 3 (Years 5–6)
• Achievement Objectives:
  • Identify, read, write, and represent halves, quarters, and eighths as fractions of sets and regions, using equal parts of a whole and positioning on a number line.
  • Use mathematical language for fractions (numerator, denominator, equal parts, share equally).
  • Connect visual, symbolic, and practical representations of fractions.
• Key Competencies:
  • Thinking (problem-solving through practical activities)
  • Using language, symbols, and text (reading/writing fractions)
  • Relating to others (collaborative group work)
• Mathematical Processes:
  • Symbolic reasoning
  • Visualisation and representation

Learning Objectives

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

1. Explain what a fraction represents using simple terms.
2. Identify numerator and denominator in a fraction.
3. Represent halves, quarters, and eighths using paper folding and objects.
4. Read and write basic fractions using symbols and words.
5. Place simple fractions correctly on a number line.
6. Compare simple fractions involving halves, quarters, and eighths.

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Resources

• Strips of paper for folding (enough for each student)
• Fraction walls visuals (large chart or digital projection)
• Pre-cut circle shapes (e.g., paper pizzas)
• Whiteboard and markers
• Number lines drawn on paper or projected
• Counters or small objects for grouping

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Lesson Sequence

1. Warm-up and Engagement (5 minutes)

• Begin with a simple sharing scenario: "If I have one chocolate bar and I want to share it equally with my friend, how can I do this?"
• Use paper strip to fold in half and show concept of halves visually.
• Discuss everyday examples of sharing and dividing (pizza slices, chocolate bars).

2. Vocabulary Introduction (5 minutes)

• Introduce the key terms:
  • Fraction: a number that shows one or more parts of a whole.
  • Numerator: the top number showing how many parts we have.
  • Denominator: the bottom number showing how many equal parts the whole is split into.
• Show symbols for ½, ¼, ⅛ on the whiteboard.
• Use fraction walls to visually show these fractions.

3. Hands-On Activity: Folding and Representing Fractions (15 minutes)

• Distribute paper strips to each student.
• Guide students to fold their paper into halves, then quarters, then eighths.
• Have students label the parts with numerator and denominator using sticky notes or markers.
• Encourage students to say the fractions aloud (e.g., "one half," "one quarter," "three eighths").
• In pairs, have students check each other’s paper folds for equal parts.

4. Representing Fractions on a Number Line (10 minutes)

• Display a large number line from 0 to 1 on the whiteboard or using a projected image.
• Model how to place 0, ½, ¼, ¾, and ⅛ on this line.
• Invite students to place their fingers or counters on the number line at the correct fraction positions.
• Discuss how the fractions compare (is ¼ less than ½?).

5. Group Challenge – Comparing Fractions (5 minutes)

• Divide the class into small groups.
• Give each group a set of fraction cards (½, ¼, ⅛, ¾).
• Have groups put the cards in order from smallest to largest.
• Discuss as a class the different strategies they used.

6. Reflect and Consolidate (5 minutes)

• Review what fractions are and the meaning of numerator and denominator.
• Ask students to explain in their own words what they learned today.
• Quickly assess understanding with a few on-the-spot questions:
  • "What fraction is half of a circle?"
  • "What does the denominator tell you?"
• Explain where fractions could connect to future learning (adding fractions, fractions as decimals).

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Assessment for Learning

• Observations during hands-on activities: Do students fold paper strips into equal parts correctly? Can they identify numerator/denominator?
• Questioning during number line and group challenges to check for conceptual understanding.
• Exit ticket: Each student writes a fraction they learned today and draws a picture representing it.
• Use this information to plan next steps (e.g., expanding to other fractions, equivalence).

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Differentiation

• Support: Provide larger paper strips, use concrete objects to represent fractions.
• Extension: Challenge students to find fractions of different objects (e.g., 3/4 of 20 counters).
• Use digital fraction tools for visualising more complex fractions for advanced learners.

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Teaching Tips

• Engage multiple senses: see, say, fold, place, and write fractions.
• Use clear, consistent mathematical language as specified in the NZ curriculum.
• Encourage collaboration and discussion for deeper understanding.
• Reinforce that fractions represent parts of a whole and can be placed on a number line.

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This lesson plan adheres closely to the New Zealand Curriculum Refresh for Year 5 mathematics rational numbers, emphasising active learning and visualisation to build a strong foundation in fractions .