Sharing Fairly

Overview

Students explore fractions as equal parts of one whole through practical sharing and folding activities. The lesson builds on familiar ideas of sharing equally and describing quantities using everyday language such as half and whole.

Learning intentions

• WALT share one whole into equal parts.
• WALT recognise and describe halves and quarters.
• WALT explain how we know parts are equal.
• WALT represent a fraction using objects, pictures and words.

Success criteria

• I can show one whole and split it into equal parts.
• I can identify a half and a quarter.
• I can use the words whole, half, quarter and equal.
• I can explain why a share is or is not fair.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Mathsteasers: challenging learners to deepen mathematical understanding through higher-order thinking.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Te Mātaiaho Mathematics and Statistics — Mathsteasers alignment: connecting mathematical ideas with relevant representations and problem-solving.
• Early mathematics learning: developing part–whole understanding, equal sharing and mathematical communication.

Lesson structure (20 minutes)

1. 0–3 min · Hook: Fair or unfair? Teacher displays the fair-sharing hook slides and shows one paper “pizza” shared between two children, with one large piece and one small piece. Ask, “Is this fair? How do you know?” Students turn and talk, then share ideas using the words whole, part and equal.

2. 3–6 min · Model a half. Teacher folds a paper circle carefully in half, opens it and traces the fold, explaining that two equal parts make one whole and each equal part is one half. Students copy the fold with their own paper circle and touch or colour one half when prompted by the whole-and-half teaching slide.

3. 6–10 min · Make quarters. Teacher demonstrates folding a new circle in half, then in half again, checking that four parts are equal. Students fold, open and count the four parts, then colour one quarter and two quarters. Prompt: “What do you notice about two quarters compared with one half?” Use the quarter demonstration and discussion slide to support the visual explanation.

4. 10–15 min · Hands-on sharing challenge. In seven pairs, students use paper circles and classroom counters or toy food to solve the challenges shown on the hands-on challenge slide: “Share one whole fairly between two people”; “Share one whole fairly between four people”; and “Show one half and one quarter.” Teacher circulates, asking, “How can you check the parts are equal?” Students explain their models to their partner and use the worksheet to draw one completed example.

5. 15–18 min · Compare and discuss. Teacher brings the class together and displays two student models: one with equal parts and one with unequal parts. Students use thumbs up/down to decide whether each shows a fraction, then justify their decision. Record key language on the reasoning and vocabulary slide: whole, part, equal, half and quarter.

6. 18–20 min · Exit check and review. Distribute the fraction sharing check. Students complete the two quick tasks: circle the picture showing a fair half and draw lines to split a shape into four equal parts. Teacher revisits the final review slide and asks students to complete the sentence, “A quarter is one of ___ equal parts of a whole.”

Resources

• the fair-sharing and fractions slide deck
• the fraction sharing check
• Paper circles, one or two per student
• Pencils, crayons or felt pens
• Classroom counters, blocks or toy food
• One large demonstration paper circle
• Magnetic board or whiteboard for recording vocabulary

Assessment

• Listen for students using “equal”, “whole”, “part”, “half” and “quarter” accurately during partner talk and practical sharing.
• Observe whether students fold and model two or four equal parts rather than simply making any number of pieces.
• Use the exit check to identify students who can recognise a half and represent quarters; photograph or retain models for follow-up grouping.

Differentiation

• Support learners with pre-drawn fold lines, larger paper circles, repeated teacher modelling and sentence starters: “This is a ___ because…” and “The parts are equal because…”.
• Pair students strategically and provide counters or toy food so learners can physically share before drawing or naming the fraction. Accept oral explanations, pointing and gestures alongside written responses.
• For EAL learners, use gestures and visual examples for whole, part, equal, half and quarter; say each word slowly and revisit it throughout the lesson.
• For learners needing additional sensory or motor support, offer thicker paper, pre-folded examples and the option to show their answer with objects rather than colouring or drawing.
• Advanced learners can investigate whether three quarters is more or less than one half, show two different ways to make one whole using halves and quarters, and explain their reasoning without being given a model.