Making Fair Halves

Overview

In this second lesson of Sharing Fairly: Halves and Quarters, students make and recognise halves in shapes and collections. They build on the idea that sharing must be fair, focusing on two parts that are equal in size or number.

Learning intentions

• WALT make halves in different shapes and collections.
• WALT recognise halves even when they look different.
• WALT explain how we know two parts are equal.

Success criteria

• I can partition a shape or collection into two equal parts.
• I can recognise halves, even when the parts look different.
• I can explain how I know the parts are equal.

Curriculum links

• Mathematics and Statistics — Number: sharing and partitioning collections into equal groups.
• Mathematics and Statistics — Number: recognising and describing halves as two equal parts of one whole.
• Mathematics and Statistics — reasoning: explaining, comparing and checking mathematical ideas.
• Supports the refreshed curriculum emphasis on practical materials, mathematical talk and representations.

Lesson structure (30 minutes)

1. 0–4 min · Welcome and hook. Display a picture of two children sharing one sandwich and ask, “How can we make sure each person gets a fair share?” Open with the fair-sharing hook and learning intention. Students think, share an idea with a partner, and explain what “fair” might mean.

2. 4–9 min · Model equal parts. Use a paper circle and rectangle to model folding each shape into two matching parts, then show an irregular shape that can also be split fairly. Use the teacher modelling slides to show examples of equal and unequal parts. Students use the words half, equal, whole and part as they describe what they notice.

3. 9–16 min · Fold and investigate. Give each student paper circles, rectangles and irregular shape templates. Students fold, press along the fold and cut or tear carefully on the fold to make two parts. They compare the parts by placing one on top of the other and decide whether each shape has been halved. Record examples on the halves investigation sheet. Pause to ask, “Do the parts have to look the same?” and “How could we check?”

4. 16–23 min · Share collections fairly. Place collections of 4, 6, 8 and 10 counters where all students can see. Invite students to share each collection between two people, moving one counter at a time to each group. Students use the sharing mats shown in the fair-sharing activity slides or draw two circles on their worksheet, then say how many counters are in each half. Include one unequal example for students to correct.

5. 23–27 min · Compare and explain. Show two shapes or collections: one divided into equal halves and one divided unequally. Students show thumbs up or down, then explain their decision using the sentence stem, “I know these are halves because …” Use the discussion and comparison slides to reveal each answer only after students have justified it.

6. 27–30 min · Plenary and check. Revisit the WALT on the plenary slide. Each student completes the final box on the halves investigation sheet by drawing one whole shape split into halves and finishing the sentence, “The parts are equal because …” Invite two students to share their explanation.

Resources

• Paper circles, rectangles and irregular shape templates
• Child-safe scissors
• Coloured paper and pencils
• Counters, with collections of 4, 6, 8 and 10
• the complete halves teaching deck
• the halves investigation sheet
• A small plate or tray for modelling a whole shape
• Whiteboard and marker

Assessment

• Observe whether students fold shapes accurately and check parts by matching or overlapping them.
• Listen for correct use of whole, part, half and equal, and note whether students can explain why a share is fair.
• Use the final drawing and explanation as an exit check. Record students who can partition independently, those needing prompts, and those who still confuse equal and unequal parts.

Differentiation

• Support learners with symmetrical shapes first, clearly marked fold lines, smaller even collections and repeated teacher modelling. Offer hand-over-hand support with folding or cutting where appropriate.
• Provide partner support, counters in two labelled hoops and the sentence stem, “Each person gets ___ because ___.”
• For learners developing English, use gestures and real objects alongside the words whole, half, equal, share and same. Accept oral explanations, pointing or drawing as evidence.
• Challenge learners to find more than one way to split a shape into halves, or to explain why a visually unusual division can still be fair.

Extension

• Investigate whether a circle, rectangle or irregular shape can be split into halves in more than one way.
• Draw or paste the different solutions on the worksheet and explain how each pair of parts is equal.
• Create a collection that can be shared fairly between two people, then create one that cannot and explain why.