Fractions Three Ways

Overview

Students recall that fractions can be represented using numerals, positions on a number line, and shaded shapes. They connect these representations by explaining how the numerator, denominator, equal parts and whole relate to one another.

Learning intentions

• WALT recognise and describe fractions in different representations.
• WALT connect a fraction numeral to a shaded shape and a point on a number line.
• WALT explain how the denominator and numerator help us interpret a fraction.
• WALT use mathematical language to justify our thinking.

Success criteria

• I can identify the whole and the equal parts in a shape.
• I can explain what the numerator and denominator tell me.
• I can place familiar fractions on a number line between 0 and 1.
• I can match a fraction numeral, shape and number-line position and explain why they match.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen understanding for advanced learners.
• Mathsteasers — Additional resources for advanced learners: rich tasks that encourage reasoning and challenge.
• Mathsteasers — Alignment: connecting representations and challenge activities with classroom mathematics learning.
• Key competencies: thinking; using language, symbols and texts; managing self; participating and contributing.

Lesson structure (40 minutes)

1. 0–5 min · Hook and recall. Teacher displays a rectangle divided into equal parts, a number line from 0 to 1, and the numerals (1/2), (3/4) and (2/3) using the fraction hook and recall slides. Students silently decide which representation matches each numeral, then share one reason with a partner.

2. 5–12 min · Make the connections. Teacher models (3/4), showing four equal parts with three shaded, three equal intervals from 0 to 1, and the numeral (3/4); explicitly identifies the denominator as the number of equal parts and numerator as the parts considered. Students help label the three representations and explain what would change for (1/4) and (4/4).

3. 12–20 min · Hands-on matching. Teacher places pairs in groups of three or four and distributes the fraction wall and strip cards and the fractions on a number line matching cards. Students build or compare fraction strips, match fractions to number-line points, and use the sentence frame “These match because…”; the teacher listens for misconceptions such as unequal parts or reversing numerator and denominator.

4. 20–31 min · Independent application. Teacher distributes the fractions in three representations worksheet and reminds students to show or annotate their thinking. Students complete matching, drawing and number-line tasks, including (1/2), (1/3), (2/3), (3/4), (1/4), (2/4) and (4/4), then answer one explanation question: “How do you know the shape and number line show the same fraction?”

5. 31–36 min · Reasoning challenge. Teacher displays two statements from the reasoning and discussion slides: “(1/3) is greater than (1/2) because 3 is greater than 2” and “(2/4) and (1/2) can represent the same amount.” Students use a shape, fraction wall or number line to decide whether each statement is true, false or needs explaining, then justify their decision.

6. 36–40 min · Plenary and exit check. Teacher revisits the success criteria with the plenary slides and asks students to complete the final task on the fractions in three representations worksheet: draw a shape and mark a number line to represent (2/3), then label the numerator and denominator. Students share one useful strategy or correction before handing in their work.

Resources

• the fraction representations slide deck
• the fractions in three representations worksheet
• the fraction wall and strip cards
• the fractions on a number line matching cards
• Mini-whiteboards and pens
• Pencils, rulers and coloured pencils
• Large number line from 0 to 1
• Display screen or interactive whiteboard

Assessment

• During modelling, check whether students identify equal parts, the whole, numerator and denominator accurately.
• During group work, question students: “Where is the whole?”, “How many equal intervals are there?” and “How does the shape prove your answer?”
• Collect the worksheet and use the final (2/3) task as an exit check. Sort responses into secure, developing and requiring further teaching.

Differentiation

• Support learners with pre-drawn shapes, a clearly labelled 0–1 number line, the fraction wall, reduced choices and the sentence frame “The fraction is ___ because ___ of ___ equal parts are ___.”
• Model each instruction orally and visually. Offer dyslexia-friendly options: use a clear sans-serif font, uncluttered worksheet layout, large print, high contrast, short lines of text and the option to respond by drawing or explaining aloud.
• Pair students strategically and allow students to handle the strips before recording. Revisit the meaning of “equal parts” using concrete examples if needed.
• Extension learners can find more than one representation for (2/4), explain its relationship to (1/2), or create a new “true, false or explain” fraction statement for another group.