Fraction Shape Builders

Overview

This is lesson 5 of 9 in Rational Numbers in Action. Students use concrete materials and drawings to investigate how equal fractional parts combine to make one whole, focusing on two halves and four quarters. They build on earlier learning about sharing shapes into equal parts and describing halves and quarters.

Learning intentions

• WALT make a whole from equal fractional parts.
• WALT identify and describe halves and quarters.
• WALT explain that two halves or four quarters make one whole.
• WALT communicate mathematical thinking using materials, drawings and words.

Success criteria

• I can build a whole using two equal halves or four equal quarters.
• I can identify whether parts are equal.
• I can explain that two halves or four quarters make one whole.
• I can draw and label my whole.

Curriculum links

• Mathematics and Statistics — Number: recognising, representing and describing halves and quarters of a whole.
• Mathematics and Statistics — Reasoning: noticing that parts can look different while still making the same whole.
• Mathematics and Statistics — Communicating: explaining mathematical ideas using materials, drawings and words.
• Mathsteasers: using rich, higher-order tasks to deepen understanding and challenge advanced learners.

Lesson structure (45 minutes)

1. 0–5 min · Hook and revisit. Display the opening comparison slides showing two shapes divided into halves in different ways, and ask, “Which shape shows one whole? How do you know?” Students turn and talk, then share ideas using the words whole, half and equal.

2. 5–12 min · Model the big idea. Use a fraction circle or paper shape to fold and cut one whole into two equal parts, then four equal parts; show the corresponding slides from the teacher modelling sequence. Teacher emphasises that the parts may have different shapes or directions but must cover the whole with no gaps or overlaps. Students help complete the sentences: “Two halves make ___ whole” and “Four quarters make ___ whole.”

3. 12–25 min · Build and investigate. Organise 25 students into mixed-ability groups of three or four. Provide fraction circles, folded paper shapes, pattern blocks and collage pieces. Groups build as many complete wholes as possible using two halves or four quarters, checking that the parts are equal and cover the whole. Students discuss: “Does it still make one whole if the pieces look different?” Teacher circulates, asks students to justify their choices and photographs or selects examples for sharing.

4. 25–34 min · Record and explain. Distribute the fraction shape builders recording sheet. Students choose one build, draw it, colour the equal parts and label it one whole, two halves or four quarters. They complete the sentence frames: “My whole is made from ___.” and “I know the parts are equal because ___.” Partners explain their drawings to one another while the teacher checks vocabulary and reasoning.

5. 34–40 min · Compare and discuss. Revisit the compare-and-explain slides and display two student examples that look different but cover the same whole. Invite students to compare them using “same because…” and “different because…”. Address the misconception that a part must look a particular way to be a half or quarter.

6. 40–45 min · Demonstrate and reflect. Invite selected students to complete a quick build-and-explain demonstration using materials. Students show either two halves or four quarters, then say how they know it is one whole. Collect the completed labelled drawing section as the individual assessment record and finish with the prompt on the closing reflection slide, “What is one way to make a whole?”

Resources

• the Fraction Shape Builders slide deck
• the fraction shape builders recording sheet
• Fraction circles or pre-cut fraction shapes
• Paper circles and rectangles for folding
• Pattern blocks
• Collage pieces in varied shapes
• Scissors, glue sticks and coloured pencils
• Chart paper or whiteboard
• Containers or trays for group materials

Assessment

• During modelling and group work, check whether students identify equal parts, use whole, half and quarter accurately, and recognise that differently shaped pieces may still make one whole.
• Listen to partner explanations and use questioning: “How do you know the parts are equal?” and “What would happen if one part were bigger?”
• Assess the build-and-explain demonstration and labelled drawing. Look for a complete whole, two equal halves or four equal quarters, accurate labels and a simple explanation.

Differentiation

• Support learners with pre-cut shapes, fraction circles, colour-coded matching parts and a partially completed worksheet. Model one action at a time and use the sentence starters “I made a whole from…” and “The parts are equal because…”.
• Offer tactile resources and allow students to demonstrate understanding by building and speaking before drawing or writing. Pair learners strategically and provide visual cards showing whole, half, quarter and equal.
• For EAL learners, rehearse vocabulary through gestures, repeated oral sentences and partner talk; accept drawing, pointing and oral explanation alongside written responses.
• Extend advanced learners by asking them to design a collage picture made from halves and quarters, then describe several different ways to make one whole. Challenge them to explain why a rearrangement of the pieces does not change the whole.

Extension

• Students create a picture using at least two halves and four quarters, label each part and explain the wholes they made.
• Students find or draw two different-looking arrangements that each make one whole and present their reasoning to the class.