Earlier this week I saw a tweet from Jo Morgan about a broken question that appeared in an end-of-topic test produced by an exam board for KS4 pupils.
Can't believe I used this broken question again! Gave it to my Yr 10s in a test before half-term. Was confused when marking. Vaguely recalled I'd been in this exact situation before & in a quick Twitter search found I tweeted about it five years ago! Doh. https://t.co/FGxJsW1aN5
— Jo Morgan (@mathsjem) October 26, 2021
Clearly, that's not helpful in a test, because it might confuse students, particularly if two friends answer it in different ways and get different, but reasonable answers!
It is, though, a great task to use with A-level students who need to revise the sine rule and cosine rule.
Here is the original question (taken from Jo's tweet):
Yr 12 could be asked about the problem with the original question, or could be told that not only has too much information been provided, but that it is not internally consistent (which is what leads to the problem with different answers being produced/possible).
They could then be told to ignore one piece of information each time and to work out the answer each time. The neat thing about this is that a different strategy is required each time. Here are the six things I could think of to remove:
- Version 1: Remove the 19cm
- Version 2: Remove the right angle
- Version 3: Remove the 35°
- Version 4: Remove the 10cm
- Version 5: Remove the x and the 2x
- Version 6: Remove the need for ADC to be a straight line
To my surprise, two of these gave the same answer for angle y. Can they predict which two?
Then: which two pieces of information can be removed, still leaving a question that can be answered?
This is available as a worksheet (with all eight versions shown with diagrams). I suspect the second page is the only one that is necessary for the students to have.
Here is the final diagram, with two of the original pieces of information removed. (It is still possible to calculate y.)
Version 7: Remove the 10cm and the 19cm
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