Simplifying Fractions

Overview

In this 30-minute lesson, students learn to simplify fractions by using common factors to find equivalent fractions in lowest terms. They recognise that simplifying keeps the same value while reducing the numerator and denominator.

Learning intentions

Students will be able to:

• explain what it means to simplify a fraction
• identify common factors of the numerator and denominator
• rewrite fractions as equivalent fractions with the smallest possible denominator (lowest terms)
• recognise when two fractions are equivalent by using simplified forms

Success criteria

Students can:

• simplify a fraction correctly by dividing numerator and denominator by a common factor
• justify their simplification using common factors (e.g. “6 and 8 share a factor of 2”)
• compare two fractions and state which is equivalent after simplifying
• check their answer by confirming they have not changed the fraction’s value (using a quick model or equivalent step)

Curriculum links

• Number: apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
• Number: solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
• Number: approximate numerical solutions to problems involving rational numbers and percentages, including financial contexts (used for quick checking/estimation only)
• Number: identify and describe properties of prime, composite and square numbers and use these properties to solve problems and simplify calculations (used to identify when a fraction cannot be simplified further)

Lesson structure (30 minutes)

1. 0–5 min · Warm-up (equivalence idea). Teacher writes two pairs on the board: 2/4 and 1/2, 3/6 and 1/2, and asks: “Do these fractions represent the same amount? How do you know?” Students quick-think and share with a partner, then volunteer a method (circling the idea of “same value, different fraction form”).

2. 5–10 min · Mini direct teach (what “simplest form” means). Teacher models simplifying one fraction step-by-step using factors: e.g. 6/8 → divide both by 2 → 3/4; then check: 3 and 4 share no common factor other than 1. Students copy the method frame: “Find common factor → divide top and bottom → write equivalent fraction → stop when no common factors.”

3. 10–16 min · Guided practice (common factors). Teacher gives three “factor journeys” on the board and works through the first together, then prompts through the next two:

• 8/12: common factor 4 (or 2 then 2), simplify to 2/3
• 10/20: common factor 10, simplify to 1/2
• 9/12: common factor 3, simplify to 3/4 Students complete a short response on mini-whiteboards for each: show one working line and the final simplified fraction.

4. 16–22 min · Guided practice (spot equivalent fractions). Teacher displays a mix of fractions in two columns: Left: 4/8, 5/10, 6/9 Right: 1/2, 1/2, 2/3, 3/4, 3/6 Teacher instructs: “Match each left fraction to an equivalent one by simplifying.” Students solve by simplifying the left fractions and selecting the correct equivalent from the right (no need to simplify the already-given targets, but they must justify matches verbally).

5. 22–30 min · Independent practice (10 questions). Teacher distributes an independent worksheet (or prints) with 10 simplification questions. Students work individually, showing factor steps for each. Teacher circulates and gives targeted prompts: “What factors do the numerator and denominator share?” “Can you divide both by the same number?” Students complete all 10 questions and submit for quick marking.

Resources

• Board/markers
• Mini-whiteboards and pens for guided practice
• Worksheet (10-question set) on simplifying fractions in lowest terms
• Fraction cards or fraction strips (optional for checks, especially for visual learners)
• Factor chart up to 12 or 20 (teacher-provided reference sheet)
• Timer for structured segments

Assessment

• Formative check during warm-up: ability to explain equivalence (same value, different form)
• Formative checks during guided practice: correct common factor identification and correct simplified fraction on mini-whiteboards
• Teacher observation in independent practice: whether students show dividing numerator and denominator by the same factor
• Quick exit check (part of the 10 questions): at least 2 items should include “cannot be simplified further” so teacher can assess understanding of lowest terms

Differentiation

• Support: provide a “factor step” scaffold sentence starter: “The common factor is __, so I divide __ and __ by __.” Include a small factor chart on the worksheet.
• Support: allow fraction strip/fold model for one question if needed (students must still write the factor-based simplification).
• Extension: include one question where simplification requires choosing between multiple common factors (e.g. 12/18 or 24/36) and ask students to simplify in one or two stages and compare their working.
• EAL/SEN: accept oral justification in the first language if needed, but require the written factor step and final fraction in simplest form.

Independent practice: 10 questions (simplify in lowest terms)

1. 6/9
2. 8/10
3. 12/16
4. 14/21
5. 9/18
6. 10/15
7. 7/14
8. 16/24
9. 25/30
10. 11/22 (include a “lowest terms” check)

(Students must show at least one line of working: divide numerator and denominator by the common factor.)