Understanding Fractions Deeply

Overview

This 45-minute lesson introduces Year 5 students to fractions aligned specifically with the New Zealand Curriculum (NZC) refresh, focusing on rational numbers and fraction concepts appropriate for this stage. The lesson emphasises developing students' ability to identify, read, write, and represent fractions including halves, thirds, quarters, fifths, sixths, and eighths both as parts of sets and regions, including placements on number lines. The lesson also introduces equivalence of simple fractions and starts to engage students in comparing and ordering fractions. This ties with the NZC learning area of Mathematics, within Number and Algebra, particularly the strand of Rational Numbers.

Curriculum Alignment

Learning Objectives (Year 5, NZC Phase 2/3 Rational Numbers)

• Identify, read, write (using symbols and words), and represent halves, thirds, quarters, fifths, sixths, and eighths as fractions of sets and regions, using equal parts of the whole and positioning on a number line.
• Directly compare two fractions involving halves, quarters, and eighths.
• Compare and order fractions involving halves, quarters, and eighths and identify when two fractions are equivalent.
• Find a unit fraction and other fractions of whole numbers using multiplication or division facts where the answers are whole numbers.
• Represent fractions using concrete materials (bar models, fraction walls, paper strips), drawings, and number lines.
• Use mathematical language such as numerator, denominator, denominator, partition, and equal parts.

Key Competencies

• Thinking: Use materials and visualisations to understand fractions, compare and order them.
• Using Language, Symbols, and Texts: Read, write, and communicate fraction concepts accurately.
• Relating to Others: Work collaboratively in group activities to discuss and solve fraction problems.
• Managing Self: Persist in solving fraction-related problems, developing conceptual confidence.

Resources Needed

• Paper strips for folding
• Pre-prepared fraction wall posters or fraction wall paper strips
• Whiteboards and markers for student work
• Number lines (classroom size and individual student sheets)
• Sets of objects (e.g., counters or cubes) for grouping activities
• Printed worksheets for practice (optional)

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Lesson Plan

Starter (5 minutes) — Fraction Activation

• Begin by activating prior knowledge: ask students if they know what a fraction is and list everyday examples (e.g., slices of pizza, parts of an orange).
• Introduce fraction vocabulary clearly: numerator, denominator, equal parts, whole.
• Demonstrate folding a paper strip into 2 equal parts — explain numerator and denominator and write the fraction 1/2 on the board.
• Quickly revisit how the denominator tells how many equal parts the whole is divided into and numerator tells how many parts are considered.

Main Teaching and Activities (30 minutes)

Activity 1: Making Fractions (10 minutes)

• Students use paper strips (or pre-cut fraction strips) to fold into halves, thirds, quarters, fifths, sixths, and eighths.
• Label parts with fraction symbols (e.g., 1/3), using both words and numeric symbols.
• Build a class fraction wall on the board or wall using paper strips to visually compare fractions.
• Discuss which fractions are bigger/smaller and ask students why (connect to denominator size).

Activity 2: Fractions on a Number Line (10 minutes)

• Show a number line marked from 0 to 1 on the board.
• Place fractions (halves, quarters, eighths) visually on it using coloured markers or stickers.
• Give students handouts with blank number lines and fraction cards to place fractions in the correct positions themselves.
• Encourage them to discuss with a partner which fractions are equivalent or which fraction is larger.

Activity 3: Comparing and Ordering Fractions (10 minutes)

• Provide scenarios or sets of fractions (particularly halves, quarters, eighths) to order from smallest to largest.
• Use fraction walls and number lines as comparisons.
• Use questioning for deeper reasoning, e.g., "Why is 1/2 more than 1/4? How can we tell?"
• Present simple equivalences visually, e.g., 2/4 = 1/2 using fraction strips.

Plenary (5 minutes) — Reflection and Check for Understanding

• Quick-fire questioning: verbally give fractions and ask if students can say the numerator, denominator and position fraction on a number line.
• Invite a few students to explain what makes two fractions equivalent.
• Briefly introduce the idea that we will learn how to add and subtract fractions with the same denominator in future lessons.

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Assessment for Learning

• Observe students during activities, listening for correct usage of fraction language.
• Review fraction placement on number lines for accuracy.
• Use formative questioning throughout to assess conceptual understanding.
• Optionally, collect and mark students' number line sheets and fraction wall folding for feedback.

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Differentiation

• Support: Provide fraction strips with marked sections for struggling learners. Use real objects like fruit slices for concrete understanding.
• Extension: Challenge advanced learners to find equivalent fractions or to identify fractions with denominators such as 5 or 6.

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Reflection Notes

• Emphasise practical and visual materials as fractions can be abstract.
• Link fractions to everyday contexts students relate to.
• Ensure fraction vocabulary is consistently used.
• Use questioning techniques to deepen conceptual understanding rather than procedural knowledge only.

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This lesson plan is designed to meet NZC Year 5 curriculum expectations with a focus on rational numbers and fractions, introducing fractions through concrete materials, number lines, and visual comparisons, while embedding mathematical language and reasoning for deep understanding.