The Fair-Share Farm

Overview

Lesson 1 of 10 in Fraction Detectives in Action. Students explore fractions as equal parts of one whole, using familiar North Otago farm contexts such as kūmara, paddocks, sheep pens and dams. The class works in teams of three; the plan is suitable for 22 students and can be adjusted for a class of 18.

Learning intentions

• WALT recognise a fraction as equal parts of one whole.
• WALT make and describe halves, thirds and quarters.
• WALT explain why equal parts are needed for a fair share.
• WALT use mathematical language, models and drawings to explain our thinking.

Success criteria

• I can divide a whole shape or object into equal parts.
• I can name halves, thirds and quarters.
• I can show fair shares using materials, drawings or words.
• I can explain why unequal parts are not fair fractions.

Curriculum links

• Number: recognise, represent and describe simple fractions as equal parts of a whole.
• Number: use halves, thirds and quarters in familiar sharing situations.
• Mathematical language and communication: explain ideas using models, drawings and words.
• Key competencies: thinking; using language, symbols and texts; relating to others; participating and contributing.

Lesson structure (60 minutes)

1. 0–7 minutes – Hook: Is it fair? Open with the farm fairness hook. Show a picture or simple diagram of a kūmara divided into equal pieces and another divided unevenly. Ask: “Which share would you choose? Is it fair? How do you know?” Accept informal language before introducing whole, part and equal.

2. 7–17 minutes – Explicit teaching and modelling Use the equal-parts teaching slides to model folding or drawing one whole paddock into two, three and four equal parts. Name the parts as halves, thirds and quarters. Deliberately model an unequal partition and ask students to explain why it is not a fair fraction. Emphasise that the parts must be the same size, even when their shapes look different.

3. 17–22 minutes – Movement check Give each student a small imaginary “farm whole”. Call “halves”, “thirds” or “quarters”; students use their arms or body positions to show the number of equal parts. Briefly discuss: “How many equal parts make one whole?” Use this as a quick check for understanding before group work.

4. 22–40 minutes – Team fair-share investigation Organise students into teams of three: a builder, a checker and an explainer. Rotate roles. Give each team hoops, ropes, chalk and paper shapes representing kūmara, paddocks, sheep pens and dams. Teams create fair halves, thirds and quarters, then test each partition by matching, folding, comparing or explaining. Distribute the Fair-Share Farm recording sheet for students to draw one model, label it and complete the sentence: “It is fair because…”. Students may choose a challenge: design two different equal partitions of the same whole, or make an unequal partition and explain how to fix it. The teacher circulates, asking: “How do you know the parts are equal?” and “What would happen if one sheep received this larger part?”

5. 40–50 minutes – Partner explanations and gallery walk Teams leave one model on display. Students visit another team’s work and explain or listen to an explanation using the prompts on the partner-talk and gallery-walk slides: “This whole is divided into…”, “Each part is called…”, and “It is fair because…”. Encourage students to draw, point or speak rather than relying only on writing.

6. 50–56 minutes – Class discussion and address misconceptions Share two or three examples, including one unequal model. Discuss whether differently shaped parts can still be equal and whether more parts always means larger parts. Revisit the words whole, equal parts, half, third and quarter using gestures and student models.

7. 56–60 minutes – Exit reflection Use the reflection and exit prompt. Students complete the final box on the Fair-Share Farm recording sheet or respond orally: “A quarter means…” and “Unequal parts are not fair because…”. Collect sheets to identify students ready for thirds and quarters and those needing further concrete modelling.

Resources

• the Fair-Share Farm teaching deck
• the Fair-Share Farm recording sheet
• Hoops, ropes or skipping ropes
• Chalk or whiteboard markers
• Paper shapes: kūmara, paddocks, sheep pens and dam shapes
• Scissors and glue, if needed
• Fraction circles for teams: the fraction circles cut-out pack
• Large, uncluttered word cards: whole, equal, half, third, quarter
• Open floor or outdoor space for building and movement

Assessment

• Observe whether students make equal-sized parts and correctly use half, third and quarter.
• Listen to explanations during team and partner talk, noting whether students justify fairness rather than simply naming a fraction.
• Review the worksheet and oral exit responses to group students for the next lesson: concrete support, guided practice or extension.

Differentiation

• Support: provide pre-divided shapes, fraction circles, folding demonstrations and a completed example. Work with a teacher-led group on halves before moving to thirds or quarters.
• Use partner talk, role cards and sentence frames: “The whole is divided into ___ equal parts”; “It is not fair because ___.”
• Dyslexia-friendly options: large uncluttered print, sans-serif font, short read-aloud instructions, limited text, visual models and permission to draw, point, build or respond orally.
• Extension: ask students to design two different equal partitions of one whole, compare the size of a half, third and quarter, or create a “not fair” model and explain how to repair it.