The following question is taken from my website Diagnostic Questions. Here you will find 1000s of high quality maths questions, ideal for assessment for learning, which have been created and shared by maths teachers all over the world.

This is proving a very popular question on the website. Now, I will have to be careful giving this question too much praise seeing as I wrote it, but I will try to let you know my thinking.

Firstly, I have found that one of the biggest misconceptions students have with multiples is muddling them up with factors. Therefore, I felt it was crucial to include a factor or two in there.

Secondly, I have known some students who think that multiples of a number just end in the number, so I wanted to include that misconception in there as well.

So, here is what you might learn from students' answers:

Answer a)
might indicate that a students is mistaking mutliples with factors

Answer b)
might also imply the same. And it will be interesting to hear students who have voted for b) try to convince students who voted for a) that they are wrong, and vice-versa

Answer c)
is the correct answer

Answer d)
may suggest students believe that if a number ends in a 9 then it is a multiple of a 9

As ever, asking students to explain the misconception that lie behind each incorrect answer and then to go ahead and design their own question really challenges them and leads to a deeper understanding. I have found that asking them to design a question to check understanding of Factors immediately after asking them this question is also a fruitful exercise.

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