Fractions to Decimals

Learning Focus

WALT (We Are Learning To):

• Convert fractions to decimals up to three decimal places.
• Compare, order, and convert between fractions, decimals, and percentages.
• Understand fractions as quotients to aid conversion.

New Zealand Curriculum Links

Mathematics and Statistics | Number and Algebra | Rational Numbers

• Identify, read, write, and represent fractions, decimals (to three decimal places), and percentages.
• Compare, order, and convert between fractions, decimals, and percentages (Year 7 and 8 level), .

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Success Criteria

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

• Convert simple and complex fractions into decimals using division and understand the process as a quotient.
• Compare and order fractions, decimals (up to three decimal places), and percentages using strategies like benchmarks and double number lines.
• Recognise and record decimals accurately, including verbalising decimals correctly using place value language.
• Apply conversions confidently in practical, real-world examples.

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Lesson Duration: 60 minutes

Class Size: 25 students
Year Level: 7 & 8

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Resources Required

• Whiteboard and markers
• Fraction and decimal place value charts (PV Houses)
• Double number lines printed for student pairs/groups
• 100s square manipulatives
• Calculators (optional for checking)
• Printed worksheets with practical problems and conversion tasks
• Dyslexia-friendly font handouts and visual aids

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Lesson Plan Overview

Introduction (10 minutes)

1. Set the scene: Introduce fractions as division (quotients) – e.g. ( \frac{5}{12} = 5 \div 12 ). Demonstrate this using simple division on the board.
2. WALT and Success Criteria: Share learning intentions and success criteria clearly; check for understanding.
3. Activate prior knowledge: Quick review of equivalent fractions, decimals, and percentages with concrete examples (e.g., ( \frac{1}{2} = 0.5 = 50%)). Use 100s squares and fractional bars.
4. Vocabulary focus: Introduce/review key terms like numerator, denominator, decimal place, quotient, percentage — use a Frayer Model for words and dyslexia-friendly visual support .

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Main Activity 1: Converting Fractions to Decimals (15 minutes)

• Use explicit teaching to demonstrate division for conversion of fractions to decimals with examples such as:
  • ( \frac{1}{4} = 1 \div 4 = 0.25 )
  • ( \frac{7}{8} = 7 \div 8 = 0.875 ) (connect to three decimal places)
• Link this procedure back to the idea of fractions as quotients.
• Provide guided practice: Students use number lines, PV charts and calculators to convert given fractions to decimals.
• Emphasise rounding to three decimal places if needed, with examples.

Differentiation:

• Provide fraction-to-decimal conversion charts for students who may struggle with division calculations.
• Use step-by-step pictorial guides and chunking for students with dyslexia or processing challenges.
• Pair lower ability learners with peers for supported practice.

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Main Activity 2: Comparing and Ordering Fractions, Decimals, Percentages (15 minutes)

• Introduce double number lines as a tool to visually compare and order fractions, decimals, and percentages.
• Students work in pairs to place mixed values (fractions, decimals to 3 places, percentages) on the number line and order them.
• Discuss benchmark fractions (e.g., ( \frac{1}{2} )) and decimals to assist comparisons.
• Incorporate practical examples like money, measurements in sports, or timelines.

Differentiation:

• Use larger print and dyslexia-friendly fonts on worksheets and number lines.
• Use colour coding and tactile number lines for kinaesthetic learners.
• For advanced learners: Challenge them to convert non-terminating decimals from fractions like ( \frac{1}{3} ) and discuss repeating decimals.

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Practical Application Task (10 minutes)

• Give students word problems involving conversion between fractions, decimals, and percentages (e.g., recipe adjustments, sports statistics).
• Encourage students to show working clearly, use diagrams/double number lines, and explain their thinking.
• Students share and discuss their reasoning in small groups.

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Extension Activities for Advanced Learners

• Investigate fractions that convert to repeating decimals (e.g., ( \frac{1}{3} = 0.333... )) and explore converting recurring decimals back to fractions.
• Explore connections between multiplying/dividing by powers of 10 and moving decimal places to deepen understanding of decimal place value.
• Use factor trees to simplify fractions before conversion.

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Plenary (10 minutes)

• Roundtable discussion: Each student states one learning takeaway and one question they still have.
• Recap WALT and Success Criteria — self-assessment using thumbs up/down or a simple exit slip:
  • “I can convert and order fractions and decimals confidently”
  • “I need more practice with…”
• Provide feedback and clarify misconceptions.

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Additional Supports and Teaching Considerations

Dyslexia-Friendly Strategies

• Use clear, sans-serif fonts for all visual aids and handouts
• Use colour contrast carefully—avoid red/green combinations
• Present numeric information spaced appropriately (at least 1.5 line spacing)
• Use multi-sensory teaching: combine verbal explanations, diagrams, and physical manipulatives (fraction bars, place value charts)
• Chunk information in small steps; repeat and summarise key points frequently.

Engagement Tips

• Make use of real-life contexts relevant to students’ lives (sharing food, sport timings, shopping discounts).
• Include collaborative discussions and peer teaching for deeper engagement.
• Use digital calculators or apps for checking calculations for some students to reduce cognitive load.

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This detailed 60-minute lesson maximises student understanding of fraction-to-decimal conversion with strong curriculum alignment, inclusive teaching strategies, and depth for all learners according to the New Zealand Curriculum Refresh .