Building Fraction Meaning

Overview

In this third lesson of the five-lesson unit Fractions: Equal Parts, students move from identifying equal parts to representing unit and non-unit fractions. They use folding, drawing and practical role-based tasks to connect fraction diagrams with notation and explain the meaning of the numerator and denominator.

Learning intentions

• WALT represent unit and non-unit fractions, including ( \frac{2}{3} ) and ( \frac{3}{4} ).
• WALT explain what the numerator and denominator tell us.
• WALT read, write and discuss fraction notation.
• WALT compare fractions that have the same whole divided into equal parts.

Success criteria

• I can identify a unit fraction as one equal part.
• I can represent ( \frac{2}{3} ) and ( \frac{3}{4} ) with a diagram.
• I can read and write fraction notation.
• I can explain the numerator as the selected parts and the denominator as the equal parts in the whole.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge tasks with relevant mathematical learning.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Mathematical practices: representing, communicating, reasoning and comparing mathematical ideas using words, diagrams and symbols.

Lesson structure (60 minutes)

1. 0–7 min · Reconnect and hook. Teacher displays the WALT and asks, “Which is larger: one third or two thirds? How do you know?” using the opening fraction detective slide; students briefly recall that fractions describe equal parts of one whole, then share an initial explanation with a partner.

2. 7–17 min · Fraction detective discussion. Teacher shows examples of ( \frac{1}{3} ), ( \frac{2}{3} ), ( \frac{1}{4} ) and ( \frac{3}{4} ) on the fraction detective examples and deliberately asks, “What is the same? What changes?” Students identify the whole, count the equal parts, count the shaded parts, and read each fraction aloud. Emphasise that a unit fraction names one equal part, while a non-unit fraction names more than one equal part.

3. 17–30 min · Fold, draw and label. Teacher models folding a paper whole into thirds and quarters, shading selected parts, and recording the numerator above the line and denominator below it; then distribute the equal-parts representation sheet and, where useful, the fraction circles cut-out pack. In pairs, students make or draw one whole, partition it into thirds or quarters, shade ( \frac{1}{3} ), ( \frac{2}{3} ), ( \frac{1}{4} ) or ( \frac{3}{4} ), and label the diagram with words and notation.

4. 30–45 min · Build the fraction. Teacher divides the class into two groups of four, provides four role cards, and explains the process on the build-the-fraction instructions: one student draws a whole, one partitions it, one shades the numerator, and one reads and checks the fraction. Students complete several rounds, rotating roles after each round. The checker must ask, “Are the parts equal?” and “Does the notation match the shaded diagram?”

5. 45–54 min · Conference and quick representations. Teacher conferences with pairs, asking them to compare ( \frac{1}{3} ) with ( \frac{2}{3} ), and ( \frac{1}{4} ) with ( \frac{3}{4} ), without requiring a general rule. Students complete four quick representations on the four fraction check tasks and explain one representation orally to the teacher or a partner. Record observations, particularly any confusion between numerator and denominator.

6. 54–60 min · Share and reflect. Teacher revisits the success criteria using the final reflection prompts and asks, “What does the denominator tell us? What does the numerator tell us?” Students share one explanation, self-assess against the criteria, and correct one diagram or label if needed.

Resources

• the unit fraction teaching deck
• the equal-parts representation sheet
• the fraction circles cut-out pack
• Scrap paper or thin paper for folding
• Pencils and coloured pencils
• Four role cards: whole, partition, shade, read and check
• Board and markers
• Teacher observation notes

Assessment

• Listen during the fraction detective discussion for accurate use of “whole”, “equal parts”, “numerator” and “denominator”.
• Observe pair work and the build-the-fraction task, checking whether students partition wholes equally and match notation to shaded parts.
• Use the four quick representations and one oral explanation as formative evidence. Note whether each student can identify the denominator as the number of equal parts and the numerator as the selected parts.

Differentiation

• Support learners with fraction frames, pre-partitioned wholes, paper fraction pieces, colour coding and vocabulary cards showing whole, equal parts, numerator and denominator.
• Accept pointing, folding, drawing and oral explanation before expecting students to independently write notation. Provide sentence stems such as “The denominator tells me…” and “The numerator shows…”.
• Pair students strategically and reduce the choice of fractions to ( \frac{1}{3} ) and ( \frac{2}{3} ) or ( \frac{1}{4} ) and ( \frac{3}{4} ) if needed. Model each role before group work and check understanding privately for learners who need communication or processing support.
• For advanced learners, ask students to represent ( \frac{2}{3} ) and ( \frac{3}{4} ) using different-shaped wholes, then create a fraction riddle for a partner, such as “My whole is split into four equal parts and three are shaded. What fraction am I?”