Exploring fractions deeply

Overview

This 45-minute lesson for Year 5 students in Australia introduces fractions aligned with the New Zealand Curriculum Refresh (NZC Refresh), focusing on understanding, representing, and simple operations with fractions. The lesson leverages hands-on materials and visual models for conceptual understanding, consolidates the language of fractions, and introduces equivalence and ordering of simple fractions.

Curriculum Alignment

• NZC Refresh Years 5–6 Mathematics and Statistics - Rational Numbers:
  • Identify, read, write, and represent fractions involving halves, quarters, eighths, thirds, fifths, sixths, and tenths.
  • Compare and order fractions, identify when two fractions are equivalent.
  • Represent fractions using bar models, fraction walls, and number lines.
  • Find fractions of whole numbers (using multiplication and division facts).
  • Add and subtract fractions with the same denominators, including more than one whole (basic introduction).

Competencies addressed:

• Thinking: Students develop number sense and fraction concepts through hands-on and visual activities.
• Using language, symbols and texts: Learning fraction notation and vocabulary.
• Participating and contributing: Collaborative group work on fraction problems.

All learning objectives and activities are referenced from the NZC Maths Phase 2 documents and Te Mātaiaho Maths 0-8 guidelines .

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Learning Objectives

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

1. Explain what a fraction represents, including numerator and denominator roles.
2. Represent and identify fractions such as 1/2, 1/4, 1/3, 1/5, and 1/10 using visual aids (bar models, fraction walls).
3. Compare and order simple fractions with related denominators (halves, quarters, eighths, thirds).
4. Find a unit fraction of a whole number using multiplication or division (e.g., 1/5 of 40).
5. Recognise and name equivalent fractions such as 3/6 = 1/2.
6. Use correct mathematical vocabulary and notation to describe fractions.
7. Understand the concept of fractions as numbers on a number line.

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Materials

• Fraction walls (pre-made or paper strips students fold)
• Paper strips, whiteboards, markers
• Counters or discrete objects for grouping
• Number line display (marked 0 to 1)
• Worksheets with fraction visuals and simple problems
• Calculators (optional, for checking multiplication/division)

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Lesson Structure (45 minutes)

1. Introduction (5 minutes)

• Begin with a quick brainstorming: "What do you know about fractions?"
• Explain that a fraction shows a part of a whole, defining numerator (parts counted) and denominator (total parts).
• Show fraction notation examples: 1/2, 3/4, 2/5.
• Display a whole shape (e.g., circle or rectangle) divided into equal parts. Colour some parts to illustrate fractions visually.

2. Hands-on Activity: Exploring Fractions Using Paper Strips and Fraction Walls (10 minutes)

• Distribute paper strips folded into halves, quarters, eighths, thirds, and fifths.
• Students label numerators and denominators on each.
• Build a class fraction wall on the board or digitally.
• Discuss the relationship between denominators and number of equal parts.
• Identify equivalent fractions by overlaying strips and noting how some fractions (e.g., 2/4 and 1/2) represent the same length.

3. Visual Representation and Number Lines (8 minutes)

• Introduce fractions on a number line between 0 and 1.
• Students place paper strip fractions or cards on a classroom number line.
• Count forward and backward between fractions.
• Emphasise that fractions are numbers that can be ordered and compared.

4. Finding Fractions of Whole Numbers (10 minutes)

• Use counters or groups of objects.
• Pose problems like “Find 1/3 of 15 counters” and “If 1/4 of a set is 5, what is the whole?”
• Model using multiplication and division facts to find fractions of a set.
• Give students a few problems to solve in pairs.

5. Comparing and Ordering Fractions (7 minutes)

• Use fraction walls and number lines to directly compare fractions with related denominators (halves, quarters, thirds).
• Discuss equivalence: for example, “Does 3/6 equal 1/2?”
• Include simple ordering tasks with fraction cards.
• Engage students in explaining their reasoning aloud.

6. Wrap-Up and Assessment (5 minutes)

• Quick quiz orally or on mini whiteboards: Identify numerator and denominator; write fractions represented visually; order a few simple fractions.
• Ask students to explain one new thing they learned about fractions.
• Collect a worksheet with fraction ordering, equivalence, and fractional part of set questions for formal assessment.

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Teacher Notes and Differentiation

• Support students struggling with fraction language by providing fraction vocabulary cards and one-on-one modelling.
• Extend advanced students by introducing improper fractions and mixed numbers or by exploring fractions with denominators like 10 and 12.
• Use real-life contexts (e.g., sharing food, measuring lengths) to make fractions meaningful.
• Emphasise equivalence and simplest forms using fraction walls and number lines as described in NZC refresh recommendations.

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This lesson integrates visual, tactile, and verbal learning styles, and ensures NZC Refresh Year 5 standards for fractions learning are met, providing a solid foundation for future decimals and percentages work in later years.