Understanding Fractions

Overview

This 45-minute lesson introduces Year 5 students (age 9-10) to fractions following the NZ Curriculum Refresh (Te Mātaiaho). It aligns with the "Rational Numbers" progression, focusing on identifying, reading, writing, and representing fractions with denominators such as 2, 3, 4, 5, 6, 8, 10 (that is, halves, thirds, quarters, fifths, sixths, eighths, tenths). The emphasis is on conceptual understanding and visual representation to deepen students' fraction sense in meaningful contexts.

Curriculum References

• Mathematics and Statistics | Number and Algebra: Rational Numbers
  • Identify, read, write and represent fractions of sets and regions using equal parts of the whole.
  • Compare and order fractions involving halves, quarters, and eighths and identify equivalence.
  • Find fractions of a whole number using multiplication or division facts where answers are whole numbers.
  • Connect symbolic fractions to visual and physical representations such as fraction walls, paper strips, and bar models.
  • Develop mathematical language (numerator, denominator, equal parts, fraction, etc.).
  • Use number lines to place and order fractions.
• Key Competencies: Thinking, Using Language, Symbols and Texts, Relating to Others
• Achievement Objective: Engage students in understanding fractions as numbers that can be represented and compared.

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Learning Objectives

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

1. Identify and name fractions such as halves, quarters, and eighths in everyday contexts.
2. Represent fractions visually using paper strips and fraction walls.
3. Understand that the numerator represents parts counted and the denominator the total equal parts of the whole.
4. Place simple fractions on a number line and compare their sizes.
5. Use the terms numerator and denominator confidently and explain what each means.

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Resources Needed

• Pre-cut coloured paper strips divided into halves, quarters, eighths
• Fraction walls (poster or digital)
• Large number line on the board or floor mat
• Whiteboards and markers for students
• Printed fraction word cards (e.g. "one half", "two quarters" etc.)
• Real-life objects for fraction sharing (e.g., a chocolate bar or pizza slices)

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Lesson Activities

1. Introduction and Engagement (10 mins)

• Begin with a quick discussion: “What is a fraction?” Engage students to share prior knowledge or guesses.
• Use real-life examples (sharing a chocolate bar or pizza) to introduce the idea of equal parts and fractions.
• Introduce fraction terms numerator (top number) and denominator (bottom number). Use simple visuals (e.g. circle divided in 4 parts, shade 1 part; write 1/4).

2. Visual Representation (10 mins)

• Demonstrate folding a paper strip to make halves, then quarters, then eighths. Label each section with numerator and denominator.
• Show a fraction wall and ask students to identify fractions they see, encouraging recognition of equivalent fractions (e.g., 2/4 = 1/2).
• Group students and provide paper strips to fold and label their own fractions.

3. Number Line Activity (10 mins)

• Draw a large number line from 0 to 1. Mark fractions like 1/2, 1/4, 3/4, 1/8, 5/8.
• Invite students to place fraction cards on the correct points on the number line.
• Discuss ordering: Which fractions are bigger or smaller and why, linking to the sizes of shaded paper strip parts.

4. Fraction Word and Symbol Practice (5 mins)

• Use word cards and fraction symbol cards. Ask students to match the word to the correct symbol and draw a quick visual representation on mini-whiteboards.
• Encourage reading fractions aloud correctly (e.g., "two fifths", "three quarters").

5. Application and Sharing Task (5 mins)

• In pairs, give students a real object to share fairly (e.g., 8 counters to share equally between 4 people).
• Ask: “What fraction of the whole does each person get?” Students explain verbally and write the fraction.

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Assessment for Learning

• Observe students folding and labelling fractions (formative).
• Listen to students explaining numerator and denominator during number line activity.
• Check students’ whiteboard drawings to see accurate fraction representation.
• Use quick exit tickets: write or say one fraction they learnt today and where it goes on a number line.

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Differentiation

• Support: Use concrete materials throughout; one-on-one help with paper folding; pair low literacy learners with confident peers for language support.
• Challenge: Extend to comparing fractions with different denominators using fraction walls; begin exploring equivalent fractions.

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Reflection and Extension Ideas

• How well did students grasp that fractions are numbers that can be located on a number line?
• Could students identify and write fractions symbolically and verbally?
• Extension: Use digital fraction games or apps to extend learning interactively.
• Plan follow-up lessons on simplifying fractions and adding/subtracting fractions with like denominators.

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This plan follows the NZC refresh closely, focusing on rational numbers at Year 5 as specified, utilising materials and language recommended by the curriculum documents. It provides a balanced mix of concrete, visual, verbal and symbolic learning with clear, curriculum-aligned learning objectives and assessment opportunities.