Fair Sharing Problems

This is lesson 4 of 5 in the unit "Fair Sharing: Hautau". Lesson Title: Fair-Sharing Problems Lesson Description: Learning intention: We are learning to solve fair-sharing problems involving halves and quarters of pizza and toast. Success criteria: I can decide how many equal parts are needed, represent the sharing with a model or drawing, and explain whether the sharing is fair. Curriculum alignment: NZ-TMOA-PANG-T1-03—solve simple equal-sharing situations; NZ-TMOA-PANG-T2-04—use halves and quarters in practical contexts. Present story problems connected to classroom and whānau-style sharing, for example: “Two tamariki share one toast equally,” “Four friends share one pizza,” and “A pizza has four quarters and two are eaten.” Invite students to use respectful names or invented characters and avoid assuming all families eat pizza or toast; offer culturally familiar alternatives such as flatbread or other kai while retaining the mathematics. Key vocabulary: tohatoha—share/distribute, tika—fair/correct, haurua—half, hauwhā—quarter, katoa—whole, remaining—e toe ana, equal, explain, solve. Year 2: use paper food models and counters to solve one-step sharing tasks with two or four people, draw the result, and state “each gets one half/one quarter.” Year 3: solve multi-step tasks involving 2/4, 1/2, and remaining quarters, record equations or labelled diagrams, and extend to thirds or tenths only if equal partitioning is secure. Resources: paper/cardboard pizza and toast, character cards, counters, story-problem cards, recording sheets, fraction strips, pencils. Teacher prompts: “How many people are sharing?” “What must be equal?” “How will your diagram show each person’s share?” “What fraction is left?” Formative assessment: teacher conference checklist for equal partitioning, representation, vocabulary, and explanation; students complete one independent exit problem. Misconceptions: distributing unequal topping amounts while ignoring piece size; confusing number of people with fraction denominator; reinforce by physically matching each share.

Overview

Lesson 4 of 5 in Fair Sharing: Hautau. Students solve practical sharing problems involving wholes, halves and quarters using paper kai models, counters, drawings and mathematical explanations. Use respectful names or invented characters, and offer pizza, toast, flatbread or another familiar kai without assuming every whānau eats the same foods.

Learning intentions

WALT solve simple equal-sharing problems.
WALT recognise and use haurua (half) and hauwhā (quarter).
WALT represent sharing with materials, drawings or equations.
WALT explain why a sharing arrangement is tika (fair/correct).

Success criteria

I can decide how many equal parts are needed.
I can model or draw each person’s equal share.
I can name the share as a half or quarter.
I can explain what remains and why the sharing is fair.

Curriculum links

Equal sharing and early division in practical situations.
Using halves and quarters to describe equal parts of a whole.
Developing mathematical language, reasoning and communication.
Connecting mathematical ideas to everyday classroom and whānau contexts.

Lesson structure (50 minutes)

0–5 minutes – Reconnect and introduce the problem Open with the hook and learning intention slides. Show one whole paper toast and ask: “Two tamariki share this equally. What must be equal?” Introduce tohatoha (share/distribute), katoa (whole), haurua (half), hauwhā (quarter), tika (fair/correct) and e toe ana (remaining).
5–13 minutes – Teacher modelling Model “Two friends share one toast” using a paper food model. Fold or mark it into two equal parts, match one part to each character, and label each share “one half”. Then model “Four friends share one pizza” as four equal parts. Ask: “How many people are sharing?” and “How will your diagram show each person’s share?” Refer to the modelling and questioning slides.
13–18 minutes – Fair or unfair? Display two examples: equal-sized pieces with different toppings, and unequal-sized pieces with similar toppings. Students use thumb signals, then explain their thinking to a partner. Emphasise that the size of the kai piece must be equal; toppings do not determine whether the share is fair. Physically match pieces to characters to check.
18–33 minutes – Collaborative problem solving Arrange 25 students in mixed-ability pairs, with one group of three. Give each group paper/cardboard pizza and toast, counters, character cards and story-problem cards. Provide the Division Sharing Mats to support the sharing routine, and distribute the fair-sharing recording sheet for recording drawings and explanations. Year 2 students solve one-step problems with two or four people, using models and the sentence “Each person gets one half/one quarter.” Year 3 students solve problems such as: “Four friends share one pizza. Two quarters are eaten. What fraction remains?” They record an equation or labelled diagram. Circulate and ask: “What must be equal?” and “What fraction is left?”
33–41 minutes – Share strategies Select two or three groups to present different representations. Compare folding, cutting, counters and labelled drawings. Invite students to explain how they know the sharing is fair. Revisit haurua, hauwhā, equal, remaining and explain on the discussion and vocabulary slides.
41–48 minutes – Independent check Students complete the final problem on the independent check section: “Four tamariki share one flatbread equally. Draw the shares and write what each person gets.” Year 3 students also answer: “One quarter is eaten. How many quarters remain?” Encourage a labelled diagram, equation or sentence.
48–50 minutes – Exit and preview Invite two students to complete the sentence: “Sharing is fair when…” Collect the independent check for assessment. Preview the final unit lesson, where students will explain and compare different fair-sharing solutions.

Resources

the fair-sharing lesson deck with hook, modelling, prompts, activity instructions, discussion and plenary.
the fair-sharing recording sheet with differentiated problems and an independent check.
Paper or cardboard pizza, toast and flatbread shapes.
Character cards with invented names or respectful local names.
Counters for matching each share to a person.
Story-problem cards.
Pencils, crayons and scissors.
Fraction strips or teacher-made half and quarter guides.
the Division Sharing Mats for the collaborative sharing routine.

Assessment

During group work, use a conference checklist for equal partitioning, accurate representation, fraction vocabulary and explanation.
Ask students to physically match each piece to a character to identify confusion between the number of people and the denominator.
Collect the independent check: look for equal parts, a correct half or quarter, and an explanation of fairness or what remains.

Differentiation

Support Year 2 learners with pre-marked halves and quarters, fewer choices, counters and oral sentence frames: “There are ___ people, so I need ___ equal parts.”
Provide enlarged models, cutting or folding support, a partner rehearsal and vocabulary cards for learners with fine-motor, language or learning needs.
For EAL learners, use gestures, visuals and repeated sentence frames: “Each person gets ___.” “It is fair because ___.”
Extend secure Year 3 learners with two-step problems involving remaining quarters, or ask them to create a fair-sharing problem. Explore thirds or tenths only when equal partitioning is secure.

Teaching Instructions