Building Fraction Sense

Overview

In this first lesson of a four-lesson unit, students build a conceptual understanding of improper fractions and mixed numbers before adding them. Using fraction strips and number lines, they connect the numerator and denominator to wholes, represent quantities greater than one, and convert between forms.

Learning intentions

• WALT recognise and describe improper fractions and mixed numbers.
• WALT represent improper fractions using fraction strips and number lines.
• WALT compare improper fractions and mixed numbers.
• WALT convert between improper fractions and mixed numbers.

Success criteria

• I can identify the numerator and denominator and explain their roles.
• I can model an improper fraction as more than one whole.
• I can place an improper fraction or mixed number on a number line.
• I can convert between an improper fraction and a mixed number and explain my method.

Curriculum links

• Mathematics and Statistics — Number: develop understanding of fractions, equivalence, comparison and representation.
• Mathematics and Statistics — mathematical and statistical practices: reason, represent, communicate and justify mathematical thinking.
• Mathsteasers: use higher-order thinking questions to challenge learners and deepen understanding.
• Mathsteasers alignment: connect challenge tasks with relevant textbook learning about fractions.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Display the opening question in the fraction mystery hook: “Can a fraction be greater than one?” Students complete a quick think-pair-share, then sketch what they think (5/3) might look like. Invite two contrasting ideas and avoid confirming answers immediately.

2. 5–12 min · Establish key language. Use the numerator and denominator slides and display the fraction vocabulary cards for reference. Teacher revisits numerator, denominator, whole, proper fraction, improper fraction and mixed number, explicitly connecting the denominator to the number of equal parts in one whole. Students identify the numerator and denominator in examples such as (3/4), (7/4) and (2\frac{1}{4}), and explain what each number tells us.

3. 12–22 min · Model with strips and number lines. Give each mixed-ability pair fraction strips and use the visual modelling slides. Teacher models (7/4) by joining seven quarters, regrouping four quarters as one whole, and recording (7/4=1\frac{3}{4}). Model the same quantity on a number line from 0 to 2, then repeat with (9/3) and (11/5). Students build each example, draw or label its number-line position, and explain the conversion to their partner.

4. 22–30 min · Guided examples. Work through the examples on the guided examples slides, pausing for partner reasoning before revealing each step. Include (5/2), (8/3) and (13/4), asking: “How many complete wholes can be made?” and “What fraction remains?” Students record the conversion rule in their own words: divide the numerator by the denominator; the quotient is the whole number and the remainder is the numerator of the fractional part. Check that the denominator stays unchanged.

5. 30–39 min · Paired practice. Distribute the improper fractions and mixed numbers worksheet. Students complete the representation, comparison and conversion questions in pairs, using strips or a number line to justify at least two answers. Teacher circulates, checks language and asks selected pairs to explain why (7/3) is greater than (2), rather than accepting an answer without representation.

6. 39–45 min · Share and exit check. Use the discussion and plenary slides to compare methods and address misconceptions, including confusing the numerator and denominator or changing the denominator during conversion. Students complete the final two questions on the reflection and exit questions: convert (14/5) to a mixed number and represent it on a number line; explain which is greater, (9/4) or (2), and why. Collect responses for grouping in lesson 2.

Resources

• the complete fraction introduction and teaching deck
• the improper fractions and mixed numbers worksheet
• the fraction vocabulary cards
• Fraction strips or paper strips divided into equal parts
• Mini-whiteboards and pens
• Number-line strips from 0 to 3
• Pencils, rulers and coloured pens
• Projector or interactive whiteboard

Assessment

• Listen for accurate use of numerator, denominator, whole, improper fraction and mixed number during partner explanations.
• Check models and number lines during guided and paired work, particularly whether students partition wholes equally and retain the denominator when converting.
• Use the final worksheet questions to identify students who can represent, compare and convert independently; note who needs concrete materials or further teacher modelling next lesson.

Differentiation

• For learners needing support, provide pre-labelled fraction strips and number lines, keep vocabulary cards visible, and use sentence starters such as “The denominator tells me…” and “I made ___ whole(s) because…”.
• Pair students using mixed-ability partnerships, while assigning both partners a role: builder/recorder, then swap roles.
• Reduce the initial task to denominators of 2, 3, 4 and 5; allow students to physically regroup strips before recording symbolic notation. Read worksheet instructions aloud and provide uncluttered working space for learners with dyslexia, ADHD or processing needs.
• For extension, students investigate fractions greater than two wholes, such as (17/6) and (23/8), place them accurately on a number line, compare them with another mixed number, and create a fraction that lies between two given values.