Fractions Unpacked

Overview

This 45-minute lesson introduces Year 5 students (ages 9-10) to fractions, focusing on understanding halves, quarters, and eighths using concrete, pictorial, and symbolic representations. The lesson applies the New Zealand Curriculum Refresh (NZC Refresh) mathematics framework with reference to teaching fractions within the Number strand, targeting specific learning objectives on identifying, reading, writing, and representing fractions.

Class size: 20
Subject: Mathematics
Country context: UK (using appropriate spelling and terminology)

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Learning Objectives

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

• Identify and represent halves, quarters, and eighths as fractions of sets and regions using equal parts of the whole.
• Read and write fractions using correct symbols and terminology (numerator, denominator).
• Understand and explain that the denominator shows how many equal parts the whole is divided into, and the numerator shows how many parts are considered.
• Place simple fractions involving halves, quarters, and eighths on a number line.
• Compare two fractions involving halves, quarters, and eighths, and identify when two fractions are equivalent.

These objectives align with NZC Refresh year 5 expectations for rational numbers in mathematics .

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Key Competencies

• Thinking: Develop strategies to understand fractions conceptually and solve problems involving fractions.
• Using language, symbols, and texts: Engage with mathematical language (numerator, denominator) and symbolic representations.
• Managing self: Work independently and collaboratively on fraction tasks.
• Relating to others: Discuss and compare fractions with peers using appropriate language.

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Resources

• Fraction strips/paper strips (folded into halves, quarters, eighths)
• Fraction walls (physical or digital)
• Whiteboard and markers
• Number lines (marked and unmarked)
• Set of small objects (e.g., counters or cubes)
• Worksheets with pictorial fraction problems
• Fraction vocabulary flashcards (numerator, denominator, half, quarter, eighth)

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Lesson Outline

1. Warm-up and Introduction (5 minutes)

• Begin with a brief recall of prior knowledge: ask students if they can name common fractions like ½ or ¼ in everyday life (e.g., cutting an apple, pizza slices).
• Introduce the learning objectives clearly.
• Use correct mathematical language: numerator, denominator, fraction, equal parts.

2. Concrete Exploration: Folding and Sharing (10 minutes)

• Distribute paper strips or rectangles to each student.
• Guide students to fold these into halves, quarters, and eighths, explaining what denominator and numerator mean as they label the parts on the strips (e.g., ¼ means 1 part of 4 equal parts).
• Use physical fraction walls or build one together on the board with the class, labelling each fraction.
• Highlight equal parts and how the denominator shows the total parts of the whole.

3. Pictorial and Symbolic Representations (10 minutes)

• Use fraction walls and number lines to show where halves, quarters, and eighths sit.
• Show symbolic fractions on the board and have students say them aloud (e.g., “three eighths”).
• Ask students to represent fractions with counters - e.g., show ½ of 8 counters.
• Model reading and writing fractions, reinforcing numerator and denominator meanings.

4. Comparing Fractions Activity (10 minutes)

• Using cards with fractions involving halves, quarters, and eighths, have students work in pairs to compare two fractions — using fraction walls, paper strips, or marked number lines.
• Facilitate classroom discussion to explain when two fractions are equivalent (e.g., 4/8 = ½).
• Have students place fractions on unmarked number lines to practise ordering and equivalence recognition.

5. Assessment & Reflection (7 minutes)

• Provide a short worksheet task where students:
  • Identify and colour fractions of shapes.
  • Write the fraction represented.
  • Order three fractions involving halves, quarters, and eighths.
• Gather feedback by discussing with the class what they found easy or difficult.
• Reinforce correct vocabulary and concepts from the lesson.

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Assessment for Learning

• Formative assessment through questioning during activities (checking understanding of numerator, denominator).
• Observation during fold and compare activities to see if students can identify and explain fractions.
• Worksheet completion to assess symbolic recognition and comparison skills.

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Differentiation

• Support: Use concrete manipulatives extensively and provide fraction walls for visual reference.
• Extension: Challenge students to find equivalent fractions beyond halves, quarters, and eighths, and represent them on number lines.

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Teaching Considerations

• Connect fractions to real-life contexts familiar to the students (food, money sharing, time).
• Use clear, age-appropriate mathematical language.
• Ensure visual aids like fraction walls and number lines are large and clear for group viewing.
• Emphasise that fractions represent numbers that can be placed on a number line, linking fractions to the number system.

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By following this plan, teachers can confidently introduce fractions to Year 5 students in a way that is engaginɡ, concrete, and aligned to the latest NZC Refresh curriculum standards while integrating the UK context and terminology.

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References

• NZ Curriculum Refresh mathematics phases and strands, particularly Phase 2 for Year 5 rational numbers.
• Rational numbers – fractions introduction and comparison expectations for years 4–6 from Te Mātaiaho Maths 0-8 documentation .