🔍
Case Cracker
Talan's detective desk
Case file · how to crack any problem

Every problem is a case.

A word problem is just a case waiting to be cracked. The hard part is almost never the maths. It is working out what the question is actually asking. Crack that, and the numbers are easy. Three moves, every time.

📝 Talan: this is your desk. Rename it to whatever you want.
The three moves

Do these in order, every single case. Keep this on your desk so you never have to remember it.

1

Read the case

Read it twice. Once for the story, once for the maths. Find the actual question and underline it. Circle the numbers and write what each one means.

"What is this actually asking me?"
2

Check yourself

Partway through, stop and check you are still on the right track. If your plan is not working, change it. Switching is a smart move, not a fail.

"What am I doing? Is it working?"
3

Close the case

Before you call it done, check the answer makes sense. Right size? Right units? Could it really happen in the story?

"Does that actually make sense?"
If it gets hard

🧱 If you get stuck

Stuck is a clue, not a fail. Re-read the case. Try it with smaller, friendlier numbers first. Still stuck? Grab your help card. Every detective hits dead ends.

🚀 If it feels easy

Explain out loud HOW you cracked it, like you are teaching a rookie detective. Then try the same kind of case with bigger numbers.

Cracked cases

Three real cases, cracked with the three moves, so you can see how it works.

Case 01🏀 Basketball · percentages
Talan's team scored 40 points in the game. Talan scored 25% of them. How many points did Talan score?
1 · Read itIt is asking how many points Talan got. The numbers: 40 points total, and his share is 25%.
2 · Check25% is the same as one quarter. So I need a quarter of 40. That is a divide. 40 ÷ 4 = 10
3 · Close it10 points out of 40 looks about right for a quarter. Makes sense.
AnswerTalan scored 10 points.
Case 02💼 Business · two-step
Each flip book costs $3 to make. Talan sells it for $8. If he sells 6 books, how much profit does he make?
1 · Read itIt is asking for total profit on 6 books. Numbers: costs $3, sells for $8, sells 6.
2 · CheckFirst the profit on ONE book: 8 − 3 = 5. That is two steps, do not stop here. Now 6 books: 5 × 6 = 30
3 · Close it$5 profit each, six books, $30. Makes sense. (Watch out: $5 is the trap if you stop early.)
AnswerTalan makes $30 profit.
Case 03🏀 Free throws · fraction = decimal = percent
Talan made 8 of his 10 free throws at training. Write that as a fraction, a decimal, and a percentage.
1 · Read itIt wants the same number in three outfits: fraction, decimal, percent. The numbers: 8 made out of 10.
2 · CheckFraction first: 8/10, which tidies to 4/5. Out of 10 makes the decimal easy: 0.8. Decimal to percent, slide it: 80%.
3 · Close it8 out of 10 is most of them, and 80% is most of 100%. Makes sense. They are all the same amount.
Answer8/10 = 4/5 = 0.8 = 80%
Your turn

No worked answers this time. Crack each one with the three moves, then check yourself.

Your case 1🏀 Basketball · half time
Your team scored 18 points in the first quarter and 23 in the second. The other team has 35 points in total. By how many points is your team ahead at half time?
Check your answer

Your team: 18 + 23 = 41. Ahead by: 41 − 35 = 6 points.

Move 2 catches this one: do not stop at 41, that is only half the job.
Your case 2💼 Business · who made what
You sell stickers for $2 each. On Monday you sell 7 and on Tuesday you sell 5. Your friend sells 9. How much money did YOU make?
Check your answer

You sold 7 + 5 = 12 stickers. 12 × $2 = $24.

Move 1 catches this one: your friend's 9 is a trap. The question says YOU.
Your case 3🏀 Basketball · there and back
A basketball court is 28 metres long. You run from one end to the other and then all the way back again. How far did you run in total?
Check your answer

One length is 28 m. There and back is two lengths: 28 × 2 = 56 metres.

Move 1 catches this one: "and back again" means you run it twice.
Your case 4🏀 Free throws · fractions
You made 3/4 of your 12 free throws at practice. How many did you make?
Check your answer

A quarter of 12 is 12 ÷ 4 = 3. Three quarters is 3 × 3 = 9 shots.

Move 3 checks it: 9 out of 12 is most of them, which fits "three quarters". Makes sense.
🧭 For Mum · not part of Talan's desk

Taking his baseline, the gentle way

No cold test, that would just trip his anxiety and the Independence Ladder. Instead, over his next couple of Tue/Thu sessions, hand him three or four normal word problems at his level and just watch. Do not help unless he asks, and note when he asks. You are not marking. You are spotting where the chain snaps.

Open his baseline question set →

The six places it can snap

  • Read it — doesn't work out what is being asked, grabs every number, answers a different question.
  • Connect — treats every problem as brand new, doesn't notice two are the same shape.
  • Strategy — no way in, no table or drawing, tries random operations.
  • Check yourself — picks a path and never checks it, or stops one step early.
  • Fundamentals — understands the situation but the actual sum (times tables, %, fractions) is the wall.
  • Close it — writes a number and moves on, never asks if it is reasonable.

Then what

  1. Whichever one snaps most is what his missions lean into for the next few weeks.
  2. Layer the three moves onto his normal numeracy missions (it fits the Grab / Warm-up / If-stuck format). Move 2 "check yourself" is the big one for his working memory, it lives on the card so he does not have to hold it in his head.
  3. If he wobbles, drop a rung without comment, exactly like the ladder. The help card must always work.