Fractions Uncovered

Curriculum Area and Level

NZ Curriculum Learning Area: Mathematics and Statistics
Strand: Number and Algebra
Curriculum Level: Level 3
Focus Achievement Objective:
“Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.”

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Learning Intentions

• Students will understand how to convert decimals and percentages into fractions.
• Students will recognise tenths and hundredths and how they relate across different number representations.
• Students will practise converting familiar decimals and percentages into their fractional equivalents.

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Success Criteria

By the end of this 20-minute session, students will be able to:
✔ Identify simple decimals and percentages and express them as fractions
✔ Simplify fractions where possible
✔ Explain the reasoning behind at least one conversion to a peer or teacher

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Key Competencies

• Thinking: analysing relationships between decimals, percentages, and fractions
• Using language, symbols and texts: interpreting mathematical symbols and notations
• Participating and contributing: engaging in group discussion and numeracy games

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Materials and Set-Up

• Whiteboard and markers
• Printable fraction/decimal/percentage cards (sets of 3 that match: e.g. 0.75 / 75% / ¾)
• Place value mat or number lines (optional for visual anchoring)
• Mini whiteboards and markers (one per student)
• Timer or bell

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Lesson Breakdown (20 minutes)

⏱ 0–3 mins | Whakarongo Mai – Warm-Up Challenge

"What’s the Connection?"

• Teacher quickly displays three numbers on the board (e.g. 0.5, 50%, ½). Ask: “What do you notice? What’s the connection?”
• Encourage brief discussion; highlight that they all represent the same amount in different forms – our big idea for today.
• Voice this Learning Intention: We’re learning how to express percentages and decimals as fractions – and spot the patterns in how they’re all related.

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⏱ 3–10 mins | Ako Time – Guided Practice

"Match Me If You Can!"

• Distribute sets of 3 matching cards (e.g. 0.2, 20%, ⅕) to each pair (two students per group).
• Their challenge: Match the decimals, percentages, and fractions correctly within two minutes per set.
• As they work, circulate the room and prompt with questions like:
  • “What does 0.2 mean in words?”
  • “If 20% is 20 out of 100, can we simplify that?”
• Together as a class, check one or two sample matches on the board. Clarify any misconceptions while modelling fraction simplification on the whiteboard.

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⏱ 10–16 mins | Play & Practise – Think Fast Round

"Decimal Duel!"

• Students grab their mini whiteboards.
• Teacher calls out a decimal or percentage (e.g. 0.4 or 60%), and students race to write the fraction version (simplified).
• Optional: Play as 'Teacher vs Class' – if 10 or more students get it right and hold up boards in time, they score a point.
• Use these examples:
  • 0.25 → ¼
  • 75% → ¾
  • 0.1 → ¹⁄₁₀
  • 40% → ²⁄₅
• Ensure to pause at least twice and ask students to 'turn and talk' to explain how they got their answer.

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⏱ 16–18 mins | Student Reflection

Ask:

• “Which conversions do you find easiest? Why?”
• “Which ones look tricky or confusing?”
  Ask 2–3 volunteers to share strategies they used.

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⏱ 18–20 mins | Quick Post-it Exit Task

Each student writes down:

1. One fraction they learned today
2. One decimal or percentage they want to understand better
   They stick it on the ‘Learning Ladder’ chart or class wall.

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Assessment for Learning (AfL)

• Informal observation during card sort and whiteboard activity
• Check for approximately correct matches and correct simplification
• Note students who need additional support with hundredths vs tenths conversions

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Extensions / Early Finishers

• Challenge: Convert 1.2 and 120% to improper fractions
• Apply: How would you show 33% as a fraction?

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Support & Differentiation

• Use visuals such as number lines or pie charts for learners who prefer concrete models
• Scaffold with sentence starters during peer-talks:
  “I know that 0.5 = ½ because…”

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Reflective Teacher Notes

• Which misconceptions emerged about tenths vs hundredths?
• Did students use place value knowledge effectively?
• For next time: Consider linking fractions to measurement in real contexts (e.g. baking or class surveys)

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Impressively combining speed, pattern recognition, and peer dialogue, this lesson promotes confidence with foundational numeracy using engaging kinaesthetic tools and collaboration – all underpinning Level 3 of the NZ Curriculum.