Fractions Word Problems

Overview

Today you will solve multi-step word problems with fractions where the denominators match. You will build on adding and subtracting fractions, finding fractions of amounts, and you will work with improper fractions and mixed numbers, explaining your reasoning clearly at each step.

Learning intentions

• Add and subtract fractions with the same denominator in multi-step contexts.
• Find a fraction of an amount accurately to support solving word problems.
• Convert between improper fractions and mixed numbers when answers require it.
• Explain and justify each step of a fraction calculation using correct mathematical language.

Success criteria

• I can identify the fraction operation(s) needed in a word problem.
• I can show my working for each step (including common denominators and simplifying).
• I can convert answers between improper fractions and mixed numbers correctly.
• I can explain my reasoning using sentence stems and justify why my steps make sense.

Curriculum links

• Number — fractions (including decimals): add and subtract fractions with the same denominator.
• Number — fractions (including decimals): solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number.
• Number — fractions (including decimals): solve simple measure and money problems involving fractions and decimals to two decimal places (as an optional check within reasoning, if time).

Lesson structure (35 minutes)

1. 0–4 min · Hook & retrieval (Active reasoning). Teacher displays a short word problem: “Mia has 3/4 of a pizza. She eats 1/2 of the pizza. What fraction of the pizza is left?” Students give a first prediction: “What do you think the answer will be and why?” (No solving yet—focus on reasoning.)

• Targeted whole-class questions (layered):
• Remembering/Understanding: “What information is given, and what are we being asked for?”
• Applying: “Which operation(s) might you need—add, subtract, or find a fraction of a fraction? How do you know?”
• AfL: Teacher listens for whether pupils recognise “1/2 of the pizza” means subtracting 1/2 from 3/4.

2. 4–10 min · Model a prove-it (copy example). Teacher models a slightly more complex multi-step problem, thinking aloud with a clear structure. Example to copy into books (same structure used today): “A rope is 2 1/4 m long. You cut off 3/4 m. Then you use 1/2 of what remains to make a bookmark. How long is the bookmark material?” Teacher modelling steps (show, don’t rush):

• Convert mixed number: (2 1/4 = 9/4).
• Subtract cut length: (9/4 - 3/4 = 6/4 = 1 2/4 = 1 1/2). (Explain simplification.)
• Find half of what remains: (1/2 \times 1 1/2 = 1/2 \times 3/2 = 3/4) m.
• Final answer: ( \boxed{3/4 \text{ m}} ).
• Timer + verbal before written: “For 30 seconds, turn and tell your partner the next step and the reason. Then write.”
• Sentence stems for reasoning (display):
• “I converted because the denominators need to match when subtracting.”
• “I subtracted the fractions to find what remains.”
• “I found a fraction of an amount by multiplying by the numerator/denominator.”
• AfL: During partner verbal rehearsal, teacher checks whether pupils can say why conversions and the fraction-of-amount step are needed.

3. 10–16 min · Targeted whole-class questions (deepen reasoning). Teacher presents three quick prompts. Pupils answer using reasoning sentences, not just numbers.

• Q1 (Understanding → Apply): “In the example, why did we convert (2 1/4) to an improper fraction before subtracting?”
• Q2 (Applying → Analyse): “Show how (9/4 - 3/4) uses the ‘same denominator’ rule. What stays the same and what changes?”
• Q3 (Create/Evaluate): “Could we get (3/4) m any other way? What would be the first step, and why would it still work?”
• AfL: Use thumbs (secure/explaining/unsure) plus a call-and-respond: pupils must add the “because…” to their answer.

4. 16–28 min · Guided practice task (layered complexity). Students work independently then brief teacher checks at set points.

• Task set (increase complexity): Level 1 (single multi-step, one mixed number): “A cake is 1 3/4 kg. You remove 2/4 kg. Then you take 1/2 of what remains. How much is left for the recipe?” Level 2 (same denominator operations, requires simplification): “A tank has 3/2 L. You pour out 1/4 L. Then you fill back using 3/4 of a 1/4 L amount. How much liquid is in the tank now?” Level 3 (improper to mixed at the end + explain): “A ribbon is 5/4 m long. You cut off 3/4 m. Then you use 3/2 of the remaining length to wrap gifts. Give your final answer as a mixed number and explain each step.”
• Reasoning requirement: Every answer must include one written “because” statement, e.g., “I subtracted because…”, “I converted because…”.
• Teacher monitoring (AfL):
• Check for common denominators before adding/subtracting.
• Look for correct conversion of improper fractions ↔ mixed numbers.
• Listen for whether pupils are mistakenly adding numerators directly when denominators don’t match (or failing to simplify).

5. 28–34 min · Plenary (prove-it share & misconceptions). Teacher displays two student-style attempts (one correct reasoning, one incorrect).

• Misconception focus (choose based on what you saw during monitoring):
• Pupils subtract numerators only without keeping the denominator rule.
• Pupils treat “1/2 of what remains” as subtracting 1/2 rather than finding a fraction of an amount.
• Pupils leave answers as improper fractions when mixed numbers are expected (or forget simplification).
• Layered questions for whole-class:
• “Which step is the mistake: converting, subtracting, or finding the fraction of an amount? How do you know?”
• “What evidence from the working proves your answer makes sense?”
• AfL: Quick “Reasoning check” on whiteboards: “Write one sentence starting ‘I know… because…’ for why your final step is correct.”

6. 34–35 min · Exit ticket (quick AfL). Prompt: “A loaf is 1 1/2. You use 1/4 to make toast. Then you use 3/4 of what remains. Give your final answer as a mixed number.” Pupils must also add: “Because I…” (one sentence).

• AfL: Collect to assess accuracy and reasoning quality.

Resources

• Example worked solution (teacher copy) shown on board for students to copy.
• Fraction strips/paper circles for quick visual checking of “fraction of an amount”.
• Whiteboards or mini A4 sheets for Q&A and plenary.
• Sentence stem cards for reasoning.
• Timers (phone/clock) for verbal-first moments.
• Printed task sheet with Levels 1–3.

Assessment

• Formative during hooks and model: teacher listens for correct operation choice and “because” reasoning.
• During guided practice: teacher uses an observation checklist (conversion, same-denominator subtraction, fraction-of-amount, simplification).
• Exit ticket: checks both method accuracy and written justification.

Differentiation

• Support: Provide partially completed frames (e.g., “Convert first: ___. Then subtract: ___.”). Offer extra fraction strips for the “fraction of an amount” step.
• Support sentence starters: “I converted because…”, “I subtracted because…”, “To find 1/2 of… I multiplied by…”.
• Extension: Ask pupils to create their own multi-step word problem with the same-denominator subtraction and a fraction-of-an-amount step, then include a “because…” explanation.
• EAL/SEN: Allow verbal reasoning recorded as a single key sentence or diagram first; provide word banks (convert, subtract, remain, half of, simplify).