Fractions Review

Overview

In this lesson (Lesson 4 of 20), students review fractions using proper, improper, and mixed numbers, linking what each representation means and how to compare them. This builds readiness for later work with rational numbers and decimal representations.

Learning intentions

• Students will recognise and use proper, improper and mixed numbers.
• Students will explain how improper fractions can be represented as mixed numbers.
• Students will compare fractions and justify which is larger using visual models.
• Students will use fraction representations to solve short problems accurately.

Success criteria

• I can identify whether a fraction is proper, improper, or a mixed number.
• I can convert an improper fraction to a mixed number using equal groups.
• I can convert a mixed number to an improper fraction.
• I can compare fractions using models and explain my reasoning.

Curriculum links

• Number — recognise terminating and recurring decimals, using digital tools as appropriate: prepares for later converting between fractions and decimal forms.
• Number — use the 4 operations with integers and with rational numbers: supports representing rational numbers consistently (fractions as rational numbers).
• Number — use mathematical modelling to solve practical problems involving rational numbers and percentages: fractions and mixed numbers are used to interpret real situations.

Lesson structure (30 minutes)

1. 0–4 min · Starter: fraction sorting

• Teacher displays three fraction cards (e.g. ( \frac{3}{8} ), ( \frac{11}{4} ), (2\frac{1}{3})) and asks: “Which are proper, improper, and mixed? How do you know?”
• Student responds verbally, then places cards into a simple “proper / improper / mixed” chart on the board.

2. 4–12 min · Direct teach: what each type means

• Teacher draws/uses a rectangle model showing “one whole” split into equal parts (e.g. eighths or fourths), then demonstrates:
• Proper fraction: less than 1 (only part of a whole).
• Improper fraction: equals more than 1 (numerator bigger than denominator).
• Mixed number: whole(s) and part.
• Student watches and answers guided questions: “Where is the ‘extra’ part in an improper fraction?” and “How do we show the extra beyond 1 as whole units?”

3. 12–18 min · Worked example: improper to mixed

• Teacher models converting an improper fraction to a mixed number using repeated partitioning:
• Example: ( \frac{7}{3} ) as ( 2\frac{1}{3} ) by showing 3/3 makes 1 whole, then remaining 1/3.
• Student completes a second example with teacher prompts (e.g. ( \frac{10}{4} ) to mixed number), counting how many “full groups” of the denominator fit into the numerator.

4. 18–25 min · Partner-style check (single student: interactive practice)

• Teacher gives a short set of 4 questions on a worksheet:
• Q1: Classify each fraction as proper, improper, or mixed.
• Q2: Convert one improper fraction to mixed form.
• Q3: Convert one mixed number to improper form.
• Q4: Compare two fractions using models (e.g. ( \frac{3}{5} ) and ( \frac{7}{10} )).
• Student completes questions, showing working with drawn circles/rectangles or using fraction strips where possible.

5. 25–30 min · Exit ticket + quick recap

• Teacher asks one final question: “Write an improper fraction for (1\frac{2}{3})” and a second: “Is ( \frac{9}{9} ) proper, improper, or whole? Explain using a model.”
• Student submits answers and gives a brief explanation of the rule used.

Resources

• Fraction strips or paper rectangles split into equal parts (e.g. thirds, quarters, eighths, tenths)
• Fraction cards for proper/improper/mixed sorting
• Mini-whiteboard or worksheet set with space for diagrams
• Coloured pencils or markers to shade parts and whole units
• Projector/board for the rectangle model
• Timer to keep steps on pace

Assessment

• Observe sorting decisions in the starter: listen for correct identification and justification.
• During conversion tasks, check that the student correctly counts groups of the denominator and creates the right whole/remaining part.
• Exit ticket: verify both conversions/classifications and whether the student explains the reasoning using a model.

Differentiation

• Support:
• Provide sentence starters: “A proper fraction is…”, “I know it’s improper because…”, “To convert, I count…”
• Use consistent denominators (e.g. thirds or quarters) in early practice so visual modelling is easier.
• Extension:
• After accuracy is reached, ask the student to create an example of each type (proper, improper, mixed) and label what part represents.
• EAL/SEN considerations:
• Keep language explicit and repeated (proper = less than 1, improper = more than 1, mixed = whole + part).
• Allow oral responses for one part of each question if writing is a barrier, but require a model sketch.

Extension (optional)

SKIP