Fraction Connections

Curriculum Information

Subject: Mathematics
Strand: Number and Algebra
Curriculum Level: NZC Level 3 (typically Year 6)
Key Idea: Number strategies and knowledge – understanding equivalent fractions, decimals, and percentages through simplification.
Specific Learning Outcome: Students will simplify fractions and recognise how common percentages and decimals relate to these. (e.g. 20% = 0.2 = 1/5)

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Learning Intention

We are learning to simplify fractions so that we can convert between fractions, decimals and percentages.

Success Criteria

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

• Simplify common fractions to their lowest terms (e.g. 20/100 → 1/5)
• Make connections between fractions, decimals, and percentages
• Explain or show how these numbers represent the same value in different forms

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Timeframe: 30 minutes

Class Size: 20 Year 6 students

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Materials Needed

• Mini whiteboards and markers
• Fraction conversion triangle template
• Simplifying fractions printable (targeted scaffolded exercise sheet)
• A3 laminated "Fraction Pizza" visuals (cut into sections with %/decimal but not simplified fraction)
• Real pie chart printed and segmented
• Interactive Mātauranga Māori context story (optional, to connect with holistic understanding of sharing and parts making a whole)

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Lesson Breakdown

⏱️ 0–5 mins: Warm-Up – Say it Fast!

Activity: "Say That Fraction!"
Teacher flashes percentages/decimals on a mini whiteboard (e.g. 10%, 0.5, 75%)
Students call out the simplest fractional equivalent they know.

Example: Teacher writes “0.25” → Students try “1/4”

Purpose: Sparks prior knowledge and primes students to think in fractional relationships.

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⏱️ 5–15 mins: Interactive Teaching – Linking Forms

Strategy: Visual storytelling and guided modelling

• Use a laminated A3 “Fraction Pizza” visual where each slice has a percentage (e.g. 10%) and decimal (0.1), but the fraction reads e.g. “10/100” — as a class, simplify it together on the board.
• Introduce the concept that these are “different clothes for the same number.”

Teacher Modelling (Use Think Aloud):

• E.g. “We have 20/100. Hmm, what number goes into both 20 and 100? Let’s try 10.”
• Highlight what's happening (20 ÷ 20 = 1, 100 ÷ 20 = 5)
• Write: 20/100 = 1/5 on the board
• Show that 0.2 and 20% are another way to say “1 out of 5 parts”

Key Transition Moment:
Ask students: “So if someone gives you 0.2 of a pie, how much have they really given you?”
Encourage visualisation: use the pie chart or pizza image and shade it.

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⏱️ 15–25 mins: Hands-on Group Challenge – Fraction Triangle Flip

Students work in 4 groups of 5
Each group receives a set of “conversion triangle” templates. Each side of the triangle represents one: fraction, decimal, or percentage. One side is missing (the simplified fraction)

Task: Match the corners.
e.g. 0.2 and 20% → What’s the simplified fraction?

Teacher Circulates: Supports students making connections. Encourages thinking aloud:
“How many 0.2s are in one? Does that help you think in parts?”

Extension: For faster groups, introduce uncommon percentages (e.g. 60% = 3/5).

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⏱️ 25–28 mins: Class Snap Check – Simplify It!

Quick-fire game on whiteboards
Teacher gives a decimal or percentage
Students write the simplest equivalent fraction and hold it up
e.g. Teacher says “75%” → Expected answer “3/4”

Gamify: 1 point per correct answer. Emphasise speed + accuracy.

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⏱️ 28–30 mins: Reflect and Rewind

Class discussion

• What did we learn about fractions today?
• Why is it helpful to know that 0.2 and 20% are really just 1/5?
• Pair talk: Can you explain that to your partner in your own words?

Optionally record one or two confident students giving explanations for a wall display (or for whānau sharing).

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Differentiation

Support:

• Use pictorial representations for early learners (e.g. colour-shaded boxes and circles)
• Provide a multiplication/division table for simplifying assistance

Extension:

• Challenge students with irregular percentages (e.g. 12.5%)
• Introduce percentages over 100% to extend understanding

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Assessment for Learning (AfL)

• Informal formative checks using whiteboard responses
• Observation of triangle matching accuracy
• Ability to explain equivalency clearly in own words during reflection

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Integration Opportunities

• Literacy: Ask students to write a short explanation of how 0.75, 75%, and 3/4 are related
• Social Studies: Connect to real-life contexts like splitting kai or sharing resources equitably
• Mātauranga Māori: Use traditional stories involving sharing food to explore mathematical concepts of fairness and parts of a whole

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Teacher Reflection Prompt

• Did students begin to see the fraction as the “base form” they can convert from and back into?
• Who needs more support in seeing patterns across different forms?

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Suggested Follow-up Activities

• Create a fraction/decimal/percentage number line wall chart with student contributions
• Interactive digital quiz or fraction conversion relay
• Explore this knowledge through real-world data: e.g. class survey results in different form comparisons

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“Learning is strongest when students make connections. Let’s help them see that numbers, like people, wear different outfits but are just showing us the same meaning.”