Simplify by Common Factors

Overview

In this lesson, Year 4 pupils simplify fractions by finding common factors in the numerator and denominator. They will build on earlier fraction work (including recognizing equivalent fractions) and use diagrams and reasoning to reduce fractions to their simplest form.

Learning intentions

• Students will find the highest common factor (HCF) of the numerator and denominator.
• Students will divide both parts of a fraction by the same common factor to simplify.
• Students will justify why the simplified fraction is equivalent to the original.
• Students will apply simplification to increasingly challenging fraction problems.

Success criteria

• I can identify a common factor of the numerator and denominator.
• I can choose the correct factor to divide both parts by.
• I can simplify the fraction to its simplest form.
• I can explain (orally and in writing) why the simplified fraction is equivalent.

Curriculum links

• Number – fractions (including decimals): recognize and show families of common equivalent fractions (simplifying using common factors).
• Number – fractions (including decimals): solve problems involving increasingly harder fractions and calculate quantities (simplification supports answering problems).
• Number – fractions (including decimals): add and subtract fractions with the same denominator (simplified fractions help accuracy later).
• Number – fractions (including decimals): solve measure and money problems involving fractions and decimals to two decimal places (simplifying supports these contexts).

Lesson structure (30 minutes)

1. 0–5 min · Hook: “Prove it’s the same.” Teacher shows a large fraction strip: 6/8 shaded and asks students to look for “what can be divided” on both parts.

• Targeted whole-class questioning (with hands up + Think-Pair-Share):
• Remember/Understand: “What do you notice about 6 and 8 that could help us simplify?”
• Apply: “If we divide both numbers by 2, what becomes of the numerator and denominator?”
• Analyse (Layered): “How would you show that 6/8 and 3/4 are equivalent using your words (or a quick sketch)?”
• Evaluate: “Which factor should we try first—2, 3, or 4? Explain why your choice makes sense.”
• Create: “Can you make up another fraction with the same value as 6/8 and explain how you know?” Students respond using mini-whiteboards for factor guesses; teacher listens for reasoning, not just answers.

2. 5–12 min · Modelling: HCF-based simplification Teacher models a copy-in-book example while narrating reasoning and showing a fraction bar or circle divided into equal parts.

• Model example to copy:
• Simplify 10/20
• Step 1: “Find a common factor: 10 and 20 are both divisible by 10, but let’s check 5 too.”
• Step 2: “The largest common factor is 10.”
• Step 3: “Divide numerator and denominator by 10: 10 ÷ 10 = 1, 20 ÷ 10 = 2.”
• Final: 10/20 = 1/2
• Reasoning/Verbal first (timer): Teacher uses a “Prove it” sentence stem and a 20-second timer.
• Sentence stems (displayed):
• “I simplified by dividing both parts by ___ because ___.”
• “The simplified fraction is equivalent because each part represents the same size of the whole.”
• “I chose that factor because it is the highest common factor.”
• Active reasoning mini-check: After verbal responses, teacher asks one student to repeat with precise division wording before writing.

AfL during modelling (teacher notes):

• Use a quick teacher glance + 1 “reasoning check” question to 5 students: “Which factor did you use and why—what is the HCF?”
• Track common errors (see Misconceptions).

3. 12–20 min · Guided practice (layered questioning + scaffolded success) Students work on 3 fractions on worksheets/mini-whiteboards, increasing complexity. Teacher circulates with targeted prompts.

• Task set (gradual complexity):
• A: 6/9
• B: 14/21
• C: 8/12 (challenge level: ask pupils to confirm simplest form)
• Layered whole-class questions while pausing for feedback:
• Understand: “What common factor could you use first for 6 and 9?”
• Apply: “If you divide by that factor, what happens to the fraction?”
• Analyse: “How can you be sure you’ve finished simplifying—how do you know the denominator no longer shares a common factor with the numerator?”
• Evaluate: “Did anyone choose 3 first instead of 1 or 2? Is there any other valid path? Explain.”
• Create: “Write a ‘prove it’ sentence for your answer.”
• AFL points (where to use them):
• Collect 6 mini-whiteboards (mixed ability) at the end of A and B; check whether pupils divided both parts by the same factor and whether they justify it.
• Use a “Reasoning meter” (teacher uses quick labels): All correct with explanation / Correct answer only / Common-factor missing / Simplified but not simplest.

4. 20–27 min · Independent work: Simplify and justify Students complete a structured set (4 items). They must show working and include one written sentence using stems.

• Items:

1. Simplify 9/18
2. Simplify 16/24
3. Simplify 18/30
4. Reasoning: “Simplify 12/18. Prove your answer is simplest.”

• Teacher prompts during circulation (active reasoning):
• “Show me the factor you picked and what it means.”
• “What common factor did you test first? Why?”
• “If we tried a different factor, would we still end at the simplest fraction? What would change?”

AFL during independent work:

• Use a 30-second conference with 3 groups:
• Group 1: check HCF selection
• Group 2: check dividing numerator and denominator consistently
• Group 3: check “simplest form” reasoning (not just stopping early)
• Mark for the presence of a correct “both parts divided by ___” statement.

5. 27–30 min · Plenary: “Which simplification is correct?” Teacher shows two student-style responses for the same fraction 15/25:

• Response A: “15/25 = 3/5 (divided by 5)”
• Response B: “15/25 = 1/3 (divided by 15)” Students decide which is correct and must explain using sentence stems.
• Targeted questions (Bloom layered):
• Analyse: “What common factor does 15 and 25 share? What would dividing by that factor do?”
• Evaluate: “Why is Response B incorrect—what step breaks?”
• Create: “Write a short prove-it sentence for the correct answer.”
• Quick exit: each pupil writes on a slip: “The HCF is ___, so / becomes /.”

Resources

• Fraction strips/circles (paper or visual)
• Mini-whiteboards and pens
• Worksheet with layered task sets
• Copy-in-book example (10/20 → 1/2)
• Sentence stem cards
• Timer (visible to students)
• Visual prompts for HCF (divisibility cues: halves, thirds, etc.)

Assessment

• Formative: teacher questions during hook and modelling (prioritise explanations).
• Formative: mini-whiteboard checks for correct factor choice and consistent division.
• Formative: written “prove it” sentence in independent work and exit slip confirming simplest form.
• Use success criteria to code answers: factor correct, both divided, simplest, reasoning stated.

Differentiation

• Support:
• Provide a factor choice chart (2, 3, 4, 5) and divisibility reminders.
• Sentence starters and partially completed examples (e.g., “Divide numerator by __ and denominator by __.”).
• Use fraction visuals for pupils who struggle to find HCF.
• On-task challenge:
• Ask pupils to explain whether simplifying in a different valid order still leads to the same simplest fraction.
• Add an extra reasoning prompt: “How can you tell without calculating every step?”
• SEN/EAL considerations:
• Encourage verbal rehearsing before writing (timer + stems).
• Offer an “explain in a sentence” alternative to full working for some pupils.

Common misconceptions to address

• Dividing only one part (e.g., halving the numerator but not the denominator).
• Stopping early (e.g., simplifying to an equivalent fraction but not the simplest form).
• Using the wrong factor (e.g., choosing a factor that divides one number but not the other).
• Thinking the denominator must always become 10 or a fixed target rather than being reduced by the same factor.
• Believing that “any common factor” will always give the simplest immediately—clarify: choose the HCF to reach simplest in fewer steps.