Dead Ends Are Clues · Goblin Detective Agency

Goblin says

Here is a secret most people never get told: getting it wrong is where the learning actually happens. The trick is not to rub it out and feel bad. The trick is to turn detective on your own working and find out what past-you was thinking.

So. No rubbing out yet. Let's investigate.

First, always this

Find the slip

Read your own working back, out loud, line by line. Don't start again. Hunt for the exact spot where past-you took a wrong turn. Finding your own mistake is a bigger win than getting it right first go, honestly.

Then: what kind of wrong was it?

Tap the one that sounds like you. Each one tells you your next move. (Not sure? Try the top one first.)

🔍 "I didn't really get what it was asking"

Your move: Read it twice, once for the story, once for the maths. Underline the actual question. Watch for a sneaky number that does not matter. Then look at your answer: did you answer that question, or a different one?

🧰 "I had no idea where to start"

Your move: Pick a gadget. Draw the situation, or make a little table, or try a tiny version with small friendly numbers first. Once the tiny one works, copy the same steps onto the real one.

🚪 "I knew what to do but made a slip"

Your move: Knock three times and redo it slowly, one line at a time. Most slips hide in a single step. Check: did you finish the whole question, or stop one step early?

🧮 "My adding or times tables let me down"

Your move: That is a quick fix, not a fail, your thinking was right. Just redo that one sum carefully (use the calculator on your iPad if you like). The detective work was already good.

👃 "I forgot to check if it made sense"

Your move: Do the Sniff Test now. Right size? Right units? Could it really happen in the story? If the answer smells weird, you have just caught the mistake yourself.

Last, try a cousin

🧪 Warm up on a cousin question

Once you have found the slip, do not just stare at the same problem. Grab a cousin: the same kind of case with friendlier numbers (your tutor or the goblin can hand you one). Crack the cousin, then come back and the original suddenly looks easier. That is your brain building the pattern.

Spot the Goblin's Mistake

The goblin is a Certified Maths Messer. In each one below, she has made a very common mistake. Can you be the detective and find the slip before you peek?

🕵️ Mistake 1

A pizza is cut into 8 slices. Sam eats 3 slices. What fraction of the pizza is left?

🥴 Goblin's working

"Easy! Sam ate 3 out of 8 slices."

So the answer is 3/8. Done!

🔍 Where did the goblin slip?

She answered the wrong question. 3/8 is the fraction Sam ate. The question asked what is left.

Left = 8 − 3 = 5 slices, so 5/8 is left. Classic decode slip: read the question twice and underline the important word.

🕵️ Mistake 2

A $60 jumper is 20% off in the sale. You also have a card that takes another $5 off. How much do you pay?

🥴 Goblin's working

"20% of 60 is 12. So 60 − 12 = 48."

You pay $48!

🔍 Where did the goblin slip?

She stopped one step early. She did the 20% off, but forgot the $5 card.

48 − 5 = 43, so you pay $43. Monitor slip: always ask "did I finish the whole question?"

🕵️ Mistake 3

A recipe for 4 people uses 200 g of pasta. How much pasta for 2 people?

🥴 Goblin's working

"2 people... so I'll do 200 × 2 = 400."

400 g of pasta!

🔍 Where did the goblin slip?

No sniff test. Fewer people should need less pasta, not more, so 400 g is obviously too much. She multiplied when she should have halved.

Half of 4 is 2, so use half the pasta: 200 ÷ 2 = 100, giving 100 g. Evaluate slip: the answer failed the smell test.

Goblin says

Spotting a mistake (mine or yours) is the exact same skill that stops you making it next time. Every dead end you investigate makes you a sharper detective. So go easy on yourself, and stay curious.