In e-assessment, especially in numerate disciplines, it is often necessary to have many similar questions to enable students to practise their assessments. The most efficient items are created so that one question in the item bank produces many similar instances using randomisation.

To see how efficient question randomisation can be, consider this example:

"If 4 men take 6 hours to paint a wall 48 metres long, how long will it take 3 men to paint a wall the same height but 30 metres long?"

The Numbers

Firstly, we need to know whether the numbers should be restricted to integer values. Clearly that depends on the educational stage at which this question will be used.

Let's suppose that the numbers have to be integers.

We are thinking in man-hours, so we choose an integer number of units of work u to be done in one man-hour. This number could be selected from {1,2,3,4,5} - but the range can be extended if we wish, and you might want to exclude 1.

Let's choose 2 - it takes 1 man-hour to paint 2 metres of wall.

Now we choose the example numbers of men m1 and hours h1. For example: 2<=m1<=10, 2<= h1<=10

If the chosen values are 4 and 6, it takes 4 x 6 = 24 man hours to paint the 2 x 4 x 6 = 48 metre wall.

Next we choose the "answer" numbers of men m2 and hours h2:  2<=m2<=10, 2<= h2<=10

If the chosen values are 3 and 5, it takes 3 x 5 = 15 man hours to paint the 2 x 3 x 5 = 30 metre wall.


The Context

Now consider whether the context of the question can be modified:

• Can we think of alternative "operators" - rather than just "men" could we also use builders, workers, plasterers, children, ... ?

• Are there alternative tasks - plastering ceilings, making coffees, digging holes, painting faces, ... ?


The Answer

In this case we can also choose whether to ask for the number of men or the number of hours, which multiplies the number of possible questions by two.


One algorithmic question produces 5 x 9 x 9 x 5 x 5 x 2 = 2250 different problems.

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