Matching Fraction Models

Overview

In this third lesson of Rational Numbers in Action, students connect familiar equal-part models with the language of halves and quarters. They move between folded shapes, shaded pictures, sets of objects and simple fraction statements, building on earlier experiences of sharing wholes equally.

Learning intentions

• WALT represent halves and quarters in different ways.
• WALT match a fraction model to its fraction name.
• WALT find a half or quarter of a set of objects.
• WALT explain why the parts of a whole or set must be equal.

Success criteria

• I can match a model to the words one-half or one-quarter.
• I can show one-half or one-quarter of a whole or set.
• I can describe the equal parts using mathematical language.
• I can explain how I know my match is correct.

Curriculum links

• Mathematics and Statistics — Rational Numbers: recognising and representing halves and quarters of wholes and sets.
• Mathematics and Statistics — communicating mathematical thinking using drawings, objects, words and symbols.
• Mathematics and Statistics — developing reasoning by identifying equal parts and explaining matches.
• Mathsteasers — deepening understanding through challenge, discussion and higher-order thinking.

Lesson structure (45 minutes)

1. 0–5 min · Reconnect and hook. Display the opening question on the fraction models introduction slides: “Are these both one-half?” Show two shapes divided into parts, including one incorrectly divided into unequal parts. Students quietly decide, then explain their thinking to a partner. Emphasise that fractions describe equal parts and introduce the words whole, half, quarter and equal parts.

2. 5–12 min · Teacher modelling. Use the examples on the modelling slides to fold or draw a rectangle into two equal parts and then four equal parts. Model matching a shaded shape with “one-half” or “one-quarter”, and finding one-half of 8 counters and one-quarter of 12 counters. Students help count the equal groups and rehearse the sentence frames: “The whole is split into __ equal parts. __ part is shaded, so it is __.”

3. 12–17 min · Guided practice. Display three models from the guided practice slides: a shaded shape, a set of objects and a folded paper shape. Ask students to show their answer with fingers or mini-whiteboards before discussing each one. Students identify the fraction, explain whether the parts are equal, and correct any model that does not show a half or quarter.

4. 17–32 min · Matching game. Give each group of four a mixed set of teacher-prepared cards showing folded shapes, shaded pictures, sets of objects and fraction words/statements. Revisit the instructions on the matching game instructions. Students turn cards face up, find groups of matching representations, and record each completed match on the fraction matching record sheet. Students must justify each match to their group before recording it. Include examples such as one-half of 8 counters and one-quarter of 12 counters. Circulate, asking: “What is the whole?”, “How many equal parts are there?” and “How do you know?”

5. 32–40 min · Independent draw and label. Display the task on the draw-and-label task slide. Students complete the fraction matching record sheet by drawing one whole divided into four equal parts, shading one quarter, and labelling it. They then draw or arrange a set of 8 objects to show one-half, labelling the two equal groups. Students explain one drawing to a partner using the sentence frame before handing in their work.

6. 40–45 min · Share and reflect. Use the final prompt on the reflection slide: “How can the same fraction look different?” Invite two or three students to share different representations. Students complete the oral reflection: “I know it is one-half/one-quarter because…” and self-assess against the success criteria with a thumbs signal.

Resources

• the fraction models lesson deck
• the fraction matching record sheet
• Teacher-prepared matching cards: folded shapes, shaded pictures, sets and fraction words
• Paper rectangles for folding
• Counters, 8–12 per group
• Mini-whiteboards and pens
• Pencils, crayons and scissors
• One recording sheet per student

Assessment

• Observe group talk and matching decisions, noting whether students identify the whole, count equal parts and use “half” and “quarter” accurately.
• Check students’ matching records for correct links between concrete, pictorial and word representations.
• Collect the draw-and-label task. Look for equal partitioning, correct shading, accurate labels and a set divided into equal groups.

Differentiation

• Support students with concrete paper folding and counters before asking them to draw. Begin with only one-half and one-quarter choices, and provide a worked example on the table.
• Use reduced card choices, enlarged pictures, repeated modelling and the sentence frames: “I matched __ with __ because…” and “There are __ equal parts.”
• Allow oral explanations, pointing, acting out equal groups or scribing for students with speech, language, fine-motor or literacy needs. Pair EAL learners with supportive peers and use gestures alongside the vocabulary.
• For students ready for challenge, ask them to create a new matching card set with four linked representations. They can also find different wholes that have the same number of shaded quarters, such as one quarter of 8 and one quarter of 12, and explain what changes and what stays the same.

Extension

• Create a new card showing one-half or one-quarter in a context such as fruit, teams or collections, then swap with another group to solve.
• Investigate: “Can different wholes have the same number of shaded quarters?” Draw two examples and explain the answer.