Exploring Fractions

Overview

This 45-minute lesson introduces Year 5 students in New Zealand to fractions through simple, tangible examples. The lesson adheres closely to the New Zealand Curriculum Refresh expectations for Year 5 Mathematics, focusing on rational numbers, specifically fractions. Learning experiences use hands-on materials and encourage communication, critical thinking, and connecting representations—key competencies in the NZ curriculum.

Learning Objectives

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

• Understand and explain what a fraction represents (as part of a whole or a set).
• Identify and write simple fractions (halves, quarters, thirds) using correct mathematical language and symbols.
• Use concrete materials to represent fractions of shapes and sets.
• Compare and order simple fractions with denominators 2, 3, and 4.
• Recognise fractions as numbers that can be placed on a number line.

These objectives align with the NZ Curriculum Refresh, specifically under the “Rational Numbers” strand for Year 5:

• "identify, read, write, and represent halves, thirds, quarters as fractions of sets and regions, using equal parts of the whole and by positioning on a number line".
• Compare and order fractions with denominators 2, 3, 4, 5, 6, 8, 10 .
• Use mathematical language such as numerator, denominator, partition, equal parts .

Key Competencies

• Thinking: Making sense of fractions as parts of wholes and sets.
• Using Language, Symbols, and Text: Reading, writing, and interpreting fraction symbols and words.
• Relating to Others: Sharing ideas about fractions and communicating findings.
• Managing Self: Working independently or in pairs to construct and discuss fractions.

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Lesson Outline (45 minutes)

1. Warm-up and Introduction (~5 mins)

• Begin with a quick challenge: Show a whole apple or paper circle, then cut it into two equal pieces and discuss:
  • What do you notice?
  • What do we call one part?
• Introduce the fraction concept: "A fraction represents an equal part of a whole."
• Use simple language: numerator = how many parts you have; denominator = how many parts make the whole.

2. Exploring Fractions with Visuals and Materials (~15 mins)

• Materials: Paper strips, fraction circles, or shapes divided into halves, thirds, and quarters; a fraction wall (created with labelled paper strips).
• Teachers demonstrate folding paper strips into halves, quarters, and thirds, labeling each part with numerator/denominator and corresponding words ("one half," "one quarter").
• Students create their own fraction strips (fold and label).
• Use coloured counters or blocks to represent fractions of a set (e.g., 4 red counters out of 12).
• Discuss: How many equal parts? How many parts are we looking at? Write the fraction.

3. Fraction Number Line Activity (~10 mins)

• Draw a number line from 0 to 1 on the board and mark fractions:
  • Place 1/2, 1/4, and 3/4 on the number line as examples.
• Hand out mini whiteboards or fraction number lines to students.
• Students place fraction markers on their number lines.
• Discuss ordering fractions visually on the line (e.g., which is bigger 1/2 or 1/4?).

4. Comparing and Ordering Fractions Game (~10 mins)

• In pairs, students use fraction cards or strips to compare pairs of fractions.
• Task: Order a small set of fraction cards from smallest to largest.
• Encourage use of fraction wall or number lines to justify their order.
• Prompt discussion with language: "I know 1/2 is bigger than 1/4 because…"

5. Reflection and Assessment (~5 mins)

• Class discussion: What did you learn about fractions today?
• Quick formative quiz:
  • Show shapes or groups of objects and ask students to write the fraction.
  • Students write one fraction they learned today on a sticky note to stick on the board.
• Informally assess understanding through students’ completed tasks and participation.

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Resources Needed

• Paper strips for folding
• Pre-made fraction circles or strips (halves, thirds, quarters)
• Counters or blocks for sets
• Whiteboards and markers for fraction number line activity
• Number line on the board or individual fraction number lines for students
• Fraction cards for comparison game

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Teaching Considerations and Differentiation

• Use concrete materials and visuals to make fractions tangible.
• Encourage use of mathematical vocabulary (numerator, denominator, equal parts).
• Support ELL learners and those needing extra help with labelled visuals and peer support.
• Extend learning by asking students to find fractions in everyday contexts (e.g., sharing food, time).
• For advanced learners, introduce equivalent fractions or fractions greater than one.

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Alignment with New Zealand Curriculum Refresh

Curriculum References

• Number and Algebra > Number and Quantity > Rational Numbers and Proportional Reasoning:
  To "identify, read, write, and represent halves, thirds, quarters as fractions of sets and regions, using equal parts of the whole and by positioning on a number line" .
• Mathematical Competencies: Reasoning, communicating mathematical ideas, and employing strategic thinking to compare and order fractions accurately.
• Encourages mathematical language development and connections between concrete, pictorial, and symbolic forms of fractions.

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This lesson plan combines teacher modelling, hands-on engagement, visual supports, and peer collaboration to build a robust foundational understanding of fractions for Year 5 students within the New Zealand curriculum context. It offers practical and varied approaches to conceptualising fractions, capitalising on the refreshed curriculum's emphasis on both procedural skill and conceptual understanding.

If you would like, I can also create a detailed student activity sheet or a teacher’s guide to accompany this plan.