Concept 9 of 9
Spot the Odd Figure: Undo the Turn, Then Compare
Today's big idea
Undo the turn before comparing, or every part will look out of place.
Straightened, the second square matches the first exactly, so it is no difference.
How it works
👀 What's going on?
Two figures can look completely different and be the same figure. They can also look nearly identical and be genuinely different. At Class 5 you have to tell those two cases apart.
💡 Here's the trick
Look at the pair above. The second figure looks wrong until you turn it a quarter turn, and then every part lines up with the first. A turn is not a difference. Undo the turn first, and only then compare the figures part by part.
🪄 How to do it
- 1.Ask whether one figure is simply the other turned, as the pair above is.
- 2.Undo that turn in your head so both figures sit the same way up.
- 3.Now compare part by part, because any difference left is a real one.
✍️ Try it
A shape and its copy, turned a quarter turn, with every mark in the same place. Then the same pair, but with one mark moved to another corner.
The first pair is the same figure, because undoing the turn makes them match exactly. The second pair is genuinely different, because the mark is still in the wrong corner after the turn is undone.
⚠️ Watch out
You might be thinking a mirror image is the same as a turn. It is not. Under a turn the parts keep their order as you travel round the figure, and under a mirror that order reverses.
🌟 Why this matters
Deciding whether two things really differ or are just held differently is a daily job. A map, a jigsaw piece and a part that will not fit all need it. It saves a lot of forcing.
Exam tip: Undo the turn before you compare anything, or every part will look wrong.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“After turning one figure a quarter turn, every line matches its twin but one extra dot remains. Are the two figures truly different?”
- 1
Undo the turn first
Straighten the turned figure so nothing is misplaced by the spin alone.
- 2
Now compare part by part
Every line lines up, but one figure carries an extra dot.
- 3
A turn hides nothing real
The extra dot cannot be turned away, so it is a genuine difference.
- 4
Answer ✓
Yes — the extra dot is a real difference
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Straighten them first. A turn is not a difference.
TURN UNDOER · ROUND 1 OF 3
Step 1 · what is this pair?
Quick check
✅ VERIFICATION
Two figures look different. After turning one a quarter turn they match exactly. Are they different figures?
⚡ Finish the activity above first to answer.
Keep going!