Understanding Fractions

Overview

This 45-minute lesson introduces Year 5 students to fractions using simple and relatable examples. Activities are designed to engage students actively, using hands-on materials and visual aids to develop understanding, aligned with the New Zealand Curriculum Refresh for Mathematics under the Number and Algebra strand, specifically focusing on developing understanding of rational numbers including fractions.

Curriculum References

• Strand: Number and Algebra
• Achievement Objectives:
  • Year 5: Identify, read, write, and represent halves, thirds, quarters, fifths, sixths, and eighths as fractions of sets and regions, using equal parts of the whole and by positioning on a number line.
  • Find a fraction of a whole number, using understanding of multiplication and division facts to solve problems where the answer is a whole number.
  • Add and subtract fractions with the same denominator, including to make more than one whole.
• Key Competencies: Thinking, Using Language, Symbols and Texts, Managing Self, Relating to Others
• Mathematics Dimensions: Developing number sense and multiplicative thinking with fractions.
• Teaching Considerations: Use concrete materials (fraction walls, paper strips), real-world examples, and rich mathematical language such as numerator, denominator, equivalent, partition, equal parts.

Learning Intentions

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

• Understand fractions as parts of a whole.
• Identify and name simple fractions (½, ⅓, ¼, ⅕, ⅙, ⅛) using physical and visual models.
• Represent fractions on a number line.
• Use correct mathematical language (numerator, denominator, whole, equal parts).
• Solve simple problems involving finding a fraction of a set or whole.

Resources

• Fraction walls (paper or digital)
• Paper strips or rectangles to fold and cut into equal parts
• Whiteboards and markers
• Number lines marked 0 to 1
• Counters or blocks for sets
• Worksheet with fraction identification and problem-solving tasks
• Real-world objects (e.g., sliced fruit, chocolate bars, money as sets)

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Lesson Plan Breakdown

1. Introduction & Activation (5 minutes)

• Hook: Show a chocolate bar or a sliced fruit (like an apple) and ask: "If I eat one part, what fraction of the chocolate/apple is left?"
• Establish prior knowledge by asking if students have heard of fractions and what they think they mean.
• Introduce vocabulary: numerator (top number), denominator (bottom number), whole, part.
• Explain that a fraction represents "part of a whole"—the whole can be one object or a group/set.

2. Concrete Exploration (15 minutes)

• Distribute paper strips shaped as rectangles.
• Teacher models folding strips into equal parts representing the fractions ½, ⅓, ¼, ⅕, ⅙, and ⅛, and labels the parts.
• Students fold their own strips and label the parts with numerator and denominator.
• Use fraction walls to visually compare fractions: Which fraction is bigger/smaller? Why?
• Use counters in small groups to form sets; demonstrate finding ⅓ or ⅕ of a set by grouping equally.
• Support students to say the fractions aloud in words and symbols.

3. Visual and Number Line Representation (10 minutes)

• Display a number line from 0 to 1.
• Teacher plots fractions—½, ⅓, ¼, etc.—on the number line while explaining the process.
• Students draw their own number lines on whiteboards and place fractions.
• Discuss how fractions fit between whole numbers and what happens if fractions are equal (equivalent fractions).

4. Problem Solving & Application (10 minutes)

• Pose problems like: "If there are 12 muffins and we want to share them equally between 4 friends, what fraction does each friend get?"
• Students use paper strips, counters, or drawings to solve.
• Encourage students to explain their reasoning using fraction language.
• Provide worksheet activities for students to practice identifying fractions of shapes and sets.

5. Reflection & Assessment (5 minutes)

• Group discussion: What have we learned about fractions today?
• Ask students to write or say what a fraction is and name 3 fractions learned.
• Quick quiz: Show fraction images or sets and have students identify the fraction.
• Teacher notes informal observations for assessment of understanding.

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Differentiation & Extension

• Support: Provide extra hands-on materials and one-on-one assistance. Use more familiar fractions (½, ¼).
• Extension: Challenge students to find fractions larger than one whole (improper fractions) or to add fractions with like denominators.

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Teacher Notes

• Use culturally relevant and engaging contexts for examples.
• Encourage use of students' heritage languages to describe fractions.
• Emphasise mathematical language consistently.
• Allow students to learn through talking, doing, and reflecting.

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This lesson plan focuses on foundational fraction understanding through tactile and visual learning, essential for the year 5 stage in the New Zealand Curriculum Refresh. It aligns explicitly with achievement objectives related to rational numbers and fraction concepts, ensuring students build a strong conceptual grounding for future fraction work.