Understanding Fractions

Overview

This 45-minute lesson introduces Year 5 students in Australia to fractions, aligned firmly with the New Zealand Curriculum Refresh (NZC Refresh) Phase 2 for Mathematics. The lesson focuses on foundational fraction concepts including identification, representation, and comparison of fractions, specifically halves, quarters, thirds, fifths, sixths, and eighths — using concrete and visual materials such as fraction walls and number lines.

This lesson is crafted based on NZC Refresh learning objectives and teaching considerations, adapted specifically for Australian Year 5 students (typically 9–10 years old). It uses active, scaffolded learning and formative assessment to ensure deep understanding.

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Learning Objectives

Students will be able to:

• Identify, read, write (using words and symbols), and represent common fractions (1/2, 1/3, 1/4, 1/5, 1/6, 1/8) as parts of sets and regions (bar models, paper strips, fraction walls).
• Compare and order fractions with like denominators and simple related denominators (e.g., 1/4 and 1/2).
• Recognise and explain equivalence between fractions by using fraction walls and verbal reasoning (e.g., 3/6 = 1/2).
• Locate fractions on a marked and unmarked number line.
• Use correct mathematical language related to fractions (numerator, denominator, unit fraction).
• Find a unit fraction of a whole number and explain its meaning in context (e.g., 1/5 of 40).
• Engage confidently with simple fraction problems connecting visual materials to symbolic notation.

(These objectives align with those described in the NZC Refresh Phase 2 documents for Year 5 mathematics rational numbers strand .)

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Curriculum Links

• NZC Refresh Phase 2: Rational Numbers (Years 5–6)
  • Represent and identify fractions with denominators including 2,3,4,5,6,8 etc.
  • Compare, order and recognise equivalent fractions.
  • Represent fractions on number lines and with models.
  • Find fractions of whole numbers using multiplication or division where results are whole numbers.
  • Use fraction walls and diagrams as equivalence materials.
• Cross-cutting competencies:
  • Mathematical reasoning and communication.
  • Problem solving and making connections with known facts (e.g., halving).

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Resources Required

• Fraction walls or printable fraction strips (coloured)
• Paper strips for folding
• Whiteboards and markers for each student
• Large number line (floor or board) marked 0 to 1
• Visual fraction cards
• Counters or small objects for creating sets
• Worksheets with fraction identification and ordering tasks

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Lesson Structure (45 minutes)

1. Introduction & Warm-up (5 minutes)

• Engage students with a relate-to-life question: "Have you ever shared a pizza or chocolate bar? What does ‘half’ or ‘quarter’ mean when we share?"
• Quick revision of halves and quarters by showing a pizza diagram and folding paper strips.
• Introduce terms numerator and denominator clearly, using simple fractions (e.g., 1/2, 1/4).

Purpose: Activate prior knowledge and introduce vocabulary aligned with curriculum expectations.

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2. Hands-on Fraction Exploration (15 minutes)

• Activity: Use paper strips folded into equal parts to demonstrate halves, thirds, quarters, fifths, sixths, eighths.
• Students fold their own strips; count parts, label numerator/denominator.
• Use fraction walls to visually compare fractions; ask students to identify which fraction is bigger or equivalent.
• Model fraction equivalence via fraction wall (e.g., show 2/4 is same as 1/2).

Teacher’s role:

• Guide counting and labelling.
• Encourage verbal expression: “This part is one out of four equal parts, so it is one quarter.”
• Discuss why some fractions are equivalent by visually overlaying parts.

NZC Alignment:

• Use equivalence materials to explore relationships between numerator and denominator.
• Make connections with known facts like halving and dividing by 4.

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3. Number Line Placement (8 minutes)

• Use a large number line from 0 to 1.
• Demonstrate marking simple fractions on the number line. For example, divide into quarters or eighths using number line segments.
• Students come up one-by-one to place fraction cards on the line (for denominators: 2,3,4,5,6,8).
• Ask students to explain their reasoning aloud.

NZC Focus: Count forward and backwards in fractions and place fractions on marked and unmarked number lines.

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4. Apply and Find Fractions of Whole Numbers (10 minutes)

• Present whole number scenarios (e.g., 40 marbles).
• Guided whole class activity: "What is 1/5 of 40? How can we find it?"
• Model using division or multiplication facts (40 ÷ 5 or 40 × 1/5).
• Students work in pairs or individually to find fractions of given whole numbers (1/3 of 24, 2/3 of 24).
• Use counters or dots to represent parts of the whole set.

NZC Intent: Find a unit fraction of a whole number using multiplication and division facts where the answer is whole .

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5. Consolidation & Formative Assessment (7 minutes)

• Quick quiz/discussion with each student writing a fraction answer on mini whiteboards:
  • “Write the fraction that shows half a circle.”
  • “Which is bigger: 1/3 or 1/4? Show with a drawing or fraction wall.”
  • “Find 1/4 of 20.”
• Review responses, provide instant feedback.
• Reflect on learning: orally summarise why fractions are important and everyday examples.

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Extension / Differentiation

• Support for struggling students:
  • More physical manipulatives & discrete objects rather than abstract symbols.
  • One-on-one or small group guidance during number line activity.
• Extension for advanced learners:
  • Challenge with identifying and explaining equivalence beyond halves and quarters (e.g., 3/6 = 1/2).
  • Introduce improper fractions and mixed numbers as a teaser for future lessons.

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Teacher Reflection Prompts

• Were students able to use correct fraction terminology confidently?
• Did students understand equivalence visually and verbally?
• Are students able to place fractions accurately on the number line?
• How effectively did students apply multiplication/division to find fractions of whole numbers?

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This lesson plan integrates visual, tactile, and verbal methods deeply emphasised in the NZC Refresh while introducing foundational fraction concepts for Year 5 Australian students. It strikes balance between concrete understanding and symbolic reasoning as recommended by the Te Mātaiaho Maths framework.