Fractions in Our World

Overview

Lesson 1 of 10. Students explore fractions through fair sharing of familiar kai, then diagnose and represent fractions as equal parts of a whole, set and measure using concrete materials, pictures, symbols and words.

Learning intentions

• WALT describe and represent fractions in different ways.
• WALT identify the whole and partition it into equal parts.
• WALT use the numerator and denominator to communicate a fraction.
• WALT explain what a fraction means in a sharing, set or measurement context.

Success criteria

• I can identify the whole and divide it into equal parts.
• I can name the numerator and denominator.
• I can represent a fraction with materials, a picture, a symbol and words.
• I can explain why the whole must be specified and why the parts must be equal.

Curriculum links

• Rational numbers: recognise, represent and communicate fractions as equal parts of a whole, set and measure.
• Number: connect concrete, visual, oral and symbolic representations of fractions.
• Mathematical communication: explain thinking, listen to others and use mathematical vocabulary.
• Problem-solving: apply fractions to fair sharing and familiar everyday situations.

Lesson structure (60 minutes)

1. 0–10 min – Launch: fair sharing Open with the kai-sharing hook and learning intention slides. Show a circular plate or card model of a kūmara, pizza or fruit and ask: “How can we share this fairly?” Invite students to describe equal parts using familiar whānau kai-sharing situations. Establish that a fraction describes equal parts of a specified whole, set or measure. Introduce whole, equal parts, fraction, numerator, denominator and unit fraction.

2. 10–20 min – Individual diagnostic Distribute the fraction diagnosis worksheet and ask students to work independently and show their thinking. Tasks include shading or drawing simple fractions, identifying the numerator and denominator, locating familiar fractions on a number line, and explaining which of two representations is incorrect. Include a misconception prompt: “Which is larger, one-third or one-eighth? Explain.” Do not correct every response yet; collect evidence of current understanding.

3. 20–25 min – Model the representations Open the representation and misconception slides. Model one-half and three-quarters with fraction pieces, a drawing, words and symbols. Explicitly compare one-third and one-eighth: although eight is larger than three, each eighth is a smaller part because the same whole has been divided into more equal parts. Clarify that the bottom number tells how many equal parts make the whole and the top number tells how many parts are being considered.

4. 25–40 min – Hands-on investigation stations Set up mixed-ability groups of four and rotate or assign stations. At the fraction pieces station, students build unit and non-unit fractions using the fraction circles cut-out pack and fraction strips. At the folding station, students fold paper into halves, quarters or eighths and label the parts. At the sets station, students use counters to find fractions of groups, such as one-half of 12 or three-quarters of 8. At the measure station, students use measuring cups to represent fractions of one cup. Students record one example from each station on the representation recording section. Circulate, observe equal partitioning and ask: “What is the whole?” and “How do you know the parts are equal?”

5. 40–52 min – Create a fraction story Open the fraction-story instructions and discussion prompts. Pairs create a short story about sharing kai fairly, such as sharing three-quarters of a fruit platter or one-half of a cup of ingredients. They must show the whole, an image or model, the fraction symbol, the fraction in words and an explanation of its meaning. Invite several pairs to share. Ask classmates to identify the numerator, denominator and whole, and to check whether the parts are equal.

6. 52–60 min – Exit ticket and reflection Finish with the fraction wall and strip cards as a quick visual reflection: students choose one fraction they can represent and explain how the wall or strip shows its equal parts. On the final section of the exit-ticket questions, students draw and label two-thirds, name the numerator and denominator, and answer: “Why must we know the whole?” Collect the worksheets and ask students to self-assess against the success criteria.

Resources

• the complete fractions introduction and teaching deck
• the fraction diagnosis and recording worksheet
• the fraction circles cut-out pack
• the fraction wall and strip cards
• Fraction strips or teacher-made fraction pieces
• Plain paper for folding
• Counters
• Circular plates or card kai models
• Measuring cups and water or dry rice
• Mini-whiteboards and pens

Assessment

• Collect the individual diagnostic and exit ticket to identify understanding of wholes, equal parts, notation and common denominator misconceptions.
• Observe station work: note whether students partition equally, identify the whole, connect representations and use numerator/denominator accurately.
• Listen to fraction stories and explanations, recording students ready for Year 6 work with non-unit fractions, fractions of sets and fractions greater than one.

Differentiation

• Support learners with halves, thirds and quarters, pre-partitioned shapes, fraction circles, oral rehearsal and buddy modelling. Provide sentence frames: “The whole is…”, “The denominator tells…”, and “This fraction means…”.
• Use mixed-ability pairs and allow students to explain orally, draw or build before writing. Pre-teach vocabulary with gestures and displayed examples for EAL learners.
• For learners needing additional support, work with a small teacher group using one whole plate and repeated equal-sharing demonstrations. Reduce the number range in set and measure tasks.
• Extend confident Year 6 learners by representing tenths, fractions of sets and lengths, and fractions greater than one. Ask them to justify why changing the whole changes the meaning of the fraction and to compare fractions with different denominators.