Comparing Equal Parts

Overview

This is lesson 8 of 10 in the unit “Sharing Halves and Quarters”. Students use identical paper shapes to build wholes from halves and quarters, then compare one half with one quarter of the same whole. The lesson develops mathematical language, visual reasoning and explanation through practical investigation and discussion.

Learning intentions

• WALT compare halves and quarters of the same whole.
• WALT build a whole from two halves or four quarters.
• WALT use pictures, objects and spoken explanations to show which part is larger.
• WALT notice that equal parts must come from the same whole when comparing.

Success criteria

• I can make a whole from equal parts.
• I can show that two quarters make one half.
• I can explain which is larger and why.
• I can use a drawing, model or words to explain my thinking.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenging mathematical thinking connected to relevant learning.
• Mathematical reasoning, communicating ideas and using representations to make sense of quantity and relationships.
• Participation and contribution through partner talk, collaborative problem-solving and respectful listening.

Lesson structure (60 minutes)

1. 0–7 min · Hook and revisit. Open with the comparison hook and learning intention. Show two identical paper circles: one divided into two equal parts and one into four equal parts. Ask, “Which single piece is larger? How could we prove it?” Students quietly choose, then explain their first idea to a partner. Revisit that a whole is one complete shape and that parts must be equal.

2. 7–17 min · Teacher modelling. Use identical paper circles or squares and the halves-and-quarters modelling slides. Fold or display one shape in halves and another in quarters. Place one half over one quarter and think aloud: “The pieces come from the same-sized whole. The half covers more, so one half is larger than one quarter.” Build the whole with two halves, then with four quarters. Students copy the actions with their own pieces and respond orally to quick prompts: “How many halves make a whole?” and “How many quarters make a whole?”

3. 17–32 min · Build and compare. Give each pair identical paper shapes, pre-cut halves and quarters, and coloured overlays. Display the partner investigation instructions. Students first make a whole from two halves, then make a whole from four quarters. They place one half beside or over one quarter and decide which is larger. They match two quarters to one half and say the relationship aloud. Encourage students to check by joining pieces or overlaying them rather than relying only on appearance.

4. 32–44 min · Explain and record. Distribute the halves-and-quarters comparison sheet. Model one example without completing the students’ work. Students match pictures, colour one half and one quarter of identical shapes, draw two quarters making one half, and complete oral or written explanations. Partners use the sentence frame, “___ is larger because ___.” Accept drawing, pointing, arranging pieces, dictation or oral recording instead of copying lengthy text.

5. 44–54 min · Reasoning circle. Return to the discussion and reasoning slides. Show several comparisons using the same whole and ask: “Do two quarters cover the same amount as one half?” and “Why is one quarter smaller than one half?” Invite pairs to demonstrate with their pieces. Include one deliberately misleading example where the shapes are different sizes; guide students to explain that comparisons are fair only when the wholes are the same size. Revoice precise language such as “equal parts”, “same whole”, “half”, “quarter” and “larger”.

6. 54–60 min · Plenary and exit check. Use the final review and exit prompt. Each student shows, draws or tells a partner how to make a whole from quarters and answers, “Which is larger: one half or one quarter? How do you know?” Collect a quick response on the worksheet or make a brief teacher note from the student’s demonstration.

Resources

• the complete comparison deck
• the halves-and-quarters comparison sheet
• Identical paper circles or squares
• Pre-cut halves and quarters
• Coloured pencils or crayons
• Transparent plastic sheets or paper overlays
• Glue sticks, if students assemble a whole
• Whiteboard and marker
• Teacher observation checklist

Assessment

• Observe whether students make wholes from two halves and four quarters using equal parts.
• Listen for explanations that compare pieces from the same whole and use “larger”, “smaller”, “half” and “quarter” meaningfully.
• Use the final demonstration or worksheet response to identify students who can show that two quarters equal one half and those needing further practical modelling.

Differentiation

• Support learners with identical shapes, colour-coded pieces, overlay comparisons and repeated oral modelling. Keep the whole visible while students build and compare.
• Provide sentence frames such as “___ is larger because ___” and “Two quarters make ___.” Allow students to answer by pointing, matching, arranging, drawing, speaking or dictating.
• For dyslexia-friendly access, use large clear visuals, limited written text, uncluttered worksheet sections, repeated vocabulary and partner rehearsal before recording.
• Extend confident learners by asking them to investigate and draw how many quarters equal one half and how many quarters equal a whole. Ask them to prove each answer in more than one way.