Four Fair Pieces

Overview

Lesson 2 of 5 in Fair Sharing: Hautau. Students use folding, sharing and visual models to make and recognise four equal parts, naming one part as one quarter, or hauwhā. Learning is connected to fair sharing and mathematical talk in te reo Māori and English.

Learning intentions

• WALT make and recognise quarters as four equal parts of a whole.
• WALT use the language hauwhā, haurua, hautau, wāhanga, whole and equal.
• WALT connect a whole, halves and quarters.
• WALT explain why fair shares must be equal.

Success criteria

• I can divide a pizza or toast model into four equal parts.
• I can identify one quarter and write or say 1/4.
• I can explain that four quarters make one whole.
• I can show that 2/4 is the same amount as 1/2.

Curriculum links

• Equal sharing and representing simple fractions in practical, familiar contexts.
• Recognising and using halves and quarters, including the relationship between them.
• Communicating mathematical ideas using words, drawings, symbols and objects.
• Developing mathematical thinking through explaining, comparing, justifying and checking.

Lesson structure (50 minutes)

1. 0–5 minutes – Welcome and fair-sharing hook Show a pizza or toast model and ask: “If four people are sharing fairly, what must we do?” Open with the fair-sharing introduction slides. Invite students to use wāhanga, equal, whole and hautau as they explain their ideas.

2. 5–13 minutes – Teacher modelling: folding into quarters Demonstrate folding a circular paper pizza in half, carefully matching the edges, then folding it in half again. Unfold it and discuss the four equal regions. Repeat with a rectangular toast model, asking: “What did you do to make four equal parts?” and “How many quarters make a whole?” Model one region as one quarter, one out of four equal parts, and 1/4. Emphasise that the four parts must be equal, not simply four pieces of any size. Return to the quarter modelling slides for the visual sequence.

3. 13–17 minutes – Hinge question and partner explanation Display four images: a whole divided into four equal parts, a whole divided into unequal parts, a whole divided into two parts, and a whole divided into four parts with one line off-centre. Ask students to show their answer on mini-whiteboards: “Which picture shows quarters? How do you know?” Students use Think–Pair–Share with the Think Pair Share Poster. Listen for the explanation that quarters are four equal parts, not just four parts.

4. 17–37 minutes – Practical station rotations Place students in five groups of five. Groups spend approximately five minutes at each station, moving when signalled. Use the station instruction slides to show the task and rotation order.

• Fold and mark paper pizza circles into four equal quarters. Shade one quarter and say or record 1/4.
• Partition toast rectangles into four equal parts using folding or a ruler. Compare different-looking rectangles.
• Match fraction cards to images of wholes, halves and quarters. Year 3 students identify 2/4 as 1/2 where shown.
• Distribute four equal sets of counters or paper toppings onto four quarter regions. Discuss why unequal amounts are not fair.
• Use mini-whiteboards to draw a whole, two halves and four quarters, then explain the connections to a partner. Adults or capable peers prompt: “How can you prove the parts are equal?” and “What would happen if one piece were bigger?”

5. 37–44 minutes – Compare halves and quarters Gather students with one folded model visible. Fold or cover two quarters to show 2/4, then compare it with 1/2. Ask: “Is 2/4 the same amount as 1/2? How can you prove it?” Year 2 students explain orally using “two of four equal parts”; Year 3 students label 1/2, 2/4 and 4/4, explaining that four quarters make one whole. Address the misconception that 1/4 is larger than 1/2 because four is larger than two: compare pieces from the same whole.

6. 44–50 minutes – Exit ticket and sharing Distribute the quarter exit ticket worksheet. Students draw a shape or pizza, divide it into four equal parts, shade one quarter and label 1/4 or write “one out of four equal parts”. Year 3 students add: “Four quarters make one whole” and “2/4 = 1/2”. Invite two or three students to share their drawings. Close with: “How do we know a share is fair?” Revisit the plenary and exit-question slide.

Resources

• Cardboard or paper pizza circles
• Toast-shaped rectangular card models
• Rulers and paper-folding strips
• Fraction picture and symbol cards
• Counters or paper toppings
• Mini-whiteboards and pens
• the complete Fair Sharing: Hauwhā slide deck
• the quarter exit ticket worksheet
• the Think Pair Share Poster

Assessment

• Use the hinge question to identify students who recognise equal and unequal partitions.
• During stations, listen for accurate use of hauwhā, “four equal parts”, 1/4, 1/2 and 2/4.
• Collect exit tickets to check whether students can draw and label one quarter; note who needs further support with equal partitioning or the relationship between halves and quarters.

Differentiation

• Support learners by providing pre-folded models, bold fold lines, larger shapes and sentence frames: “One quarter is ___ out of ___ equal parts.” Pair students for practical and oral explanations.
• For Year 2, prioritise folding, shading and oral language; accept drawings and spoken explanations instead of written fraction notation when appropriate.
• For Year 3, require labels 1/4, 2/4, 1/2 and 4/4, and ask students to prove equivalence by folding or covering parts.
• Support EAL and SEN learners with real objects, gestures, repeated bilingual vocabulary, visual examples and explicit modelling. Check that shapes are the same whole before comparing piece sizes.