🏰 Maths Castle Multi‑Step Quest

Master multi‑step word problems with discounts, VAT, scaling recipes and journey calculations.

🧙 Welcome, brave apprentice, to the towering Maths Castle! Imagine you’re at a bustling market stall buying a sparkling new wand. The price tag reads £48, but the merchant offers a 25 % discount and then adds 20 % VAT. You need to know exactly how many gold coins to hand over before the dragon awakens. Multi‑step word problems are the secret maps that turn everyday shopping, cooking and travelling into puzzles you can solve with confidence. Every time you crack one, you earn a glittering gem for your wizard’s staff — and the more gems you collect, the closer you get to the Grand Archive of Knowledge. Ready to begin?

A multi‑step word problem is a short story that hides **more than one mathematical operation** inside everyday language. Think of it like a layered cake: the first layer might be a discount (subtraction or percentage), the second layer could be tax (addition or another percentage), and a third layer might ask you to split the total among friends (division). The words “after”, “then”, “finally” and “each” are your clues that a new step is waiting. By learning to spot these signposts, you turn a tangled paragraph into a clear, step‑by‑step plan.

The core rule is **‘read, translate, calculate, check’**. First, read the whole problem twice — once for the story, once for the numbers. Next, translate each sentence into a mathematical expression: “25 % off £48” becomes 0.25 × 48 = £12 discount, so the reduced price is 48 − 12 = £36. Then “add 20 % VAT” means 0.20 × 36 = £7.20, giving a final cost of 36 + 7.20 = £43.20. Finally, check that your answer makes sense in the story (the price should be higher than the discounted price but lower than the original plus full VAT). This cycle works for any multi‑step scenario.

Follow this **four‑step method** every time you face a multi‑step puzzle: 1️⃣ **Highlight** all numbers and keywords (discount, VAT, each, total). 2️⃣ **Write** a short equation for each step in order. 3️⃣ **Solve** each equation carefully, keeping units (pounds, minutes, grams). 4️⃣ **Review** the final answer against the question — does it answer exactly what was asked? Practise this rhythm until it feels like a spell you can cast without thinking.

Let’s walk through an easy quest: *A book costs £8. You have a voucher for 10 % off. How much do you pay?* Step 1 — Highlight: £8, 10 % off. Step 2 — Equation: discount = 0.10 × 8 = £0.80; price = 8 − 0.80 = £7.20. Step 3 — Solve: £7.20. Step 4 — Check: the price is less than £8, which matches a discount. ✅ You hand over £7.20 and the book is yours!

Now a medium challenge: *A recipe needs 300 g flour for 4 people. You’re cooking for 10 people. How much flour do you need?* Step 1 — Highlight: 300 g, 4 people, 10 people. Step 2 — Find the per‑person amount: 300 ÷ 4 = 75 g per person. Step 3 — Scale up: 75 × 10 = 750 g. Step 4 — Check: 750 g is more than 300 g, which makes sense for more diners. 🎯 You measure 750 g and the cake rises perfectly.

Exam‑level example (GL style): *A train travels 120 km in 1 hour 30 minutes. It then continues at the same speed for another 45 minutes. How far does it travel in total?* Options: A 150 km, B 180 km, C 210 km, D 240 km. First, convert times: 1 h 30 min = 1.5 h; 45 min = 0.75 h. Speed = distance ÷ time = 120 ÷ 1.5 = 80 km/h. Second leg distance = 80 × 0.75 = 60 km. Total = 120 + 60 = 180 km → **B**. Why the traps? A forgets the second leg; C adds 120 + 90 (using 1.5 h again); D doubles the first leg. Spotting the unit conversion is the key.

🧙 **Common mistakes & power tips**: 1️⃣ *Skipping a step* — pupils often solve the first operation and stop. Fix: **tick each keyword** as you finish its calculation. 2️⃣ *Mixing units* — minutes vs hours, grams vs kilograms. Fix: **convert all units first**, write them down. 3️⃣ *Misreading “each”* — dividing when you should multiply, or vice‑versa. Fix: draw a quick **bar model** to visualise sharing vs grouping. 🧙 **Wizard’s #1 power tip**: on exam day, **underline the question’s final ask** (e.g., “total distance”, “cost per person”) before you start — it keeps your spell aimed at the right target! 🏆

Common mistakes

• Wrong: £8 − 10 % = £7.20 (forgetting to calculate 10 % of £8 first) — Right: 10 % of £8 = £0.80 → £8 − £0.80 = £7.20. Always work out the percentage amount before subtracting.
• Wrong: 300 g ÷ 10 = 30 g (dividing by the new number of people) — Right: 300 g ÷ 4 = 75 g per person → 75 g × 10 = 750 g. Find the unit amount first, then scale.
• Wrong: Speed = 120 km ÷ 1 h 30 min = 80 km/h → second leg = 80 × 45 = 3600 km (using minutes) — Right: Convert 45 min to 0.75 h → 80 × 0.75 = 60 km; total = 180 km. Never mix hours and minutes in the same calculation.
• Wrong: Discount 20 % on £50 = £10 → price £40; VAT 20 % on £40 = £8 → final £48 (correct) — Right: Discount 20 % on £50 = £10 → price £40; VAT 20 % on £40 = £8 → final £48. This one is actually correct — watch for questions that ask for the VAT amount only!
• Wrong: A box holds 12 eggs. 5 boxes = 5 × 12 = 60 eggs. If 3 eggs break, 60 − 3 = 57 eggs left (but the question asks how many *full* boxes remain) — Right: 57 eggs ÷ 12 = 4 full boxes with 9 eggs spare. Read the final question carefully — ‘full boxes’ changes the operation.

Frequently asked questions

Why do I have to do so many steps instead of one big calculation?

Each step represents a real‑world action (discount, tax, sharing). Doing them separately keeps the magic clear and prevents mistakes. You’ve got this! ✨

What if I forget the order of operations?

Follow the story order — first event, then next, then last. Underlining keywords creates a map you can’t lose. Keep practising! 🌟

How do I know when to multiply or divide with ‘each’?

Draw a quick bar model: sharing = divide, groups of = multiply. Visuals turn confusion into confidence. 🎨

Can I use a calculator in the exam?

Most 11+ papers are non‑calculator, so practise mental and written methods. Your brain is the best wand! 🧠

What’s the trickiest part about VAT?

VAT is always calculated on the **discounted** price, not the original. Remember: discount first, then tax. You’ll master it! 💷

How can I speed up without rushing?

Practise the four‑step rhythm until it feels automatic. Speed comes from fluency, not panic. Stay calm, stay magical! 🏰