Using a Risp: What Can Go Wrong...

3. Risps Presentation

One major theme in this site is how a slight tweak in approach can bring a question to life.
Most commonly the shift from a closed question to an open question will accomplish this.
But even open questions need to be presented in the right way.
It is that final sprinkling of parmesan and black pepper that makes the dish that little bit more exciting and which draws one in.

Take Risp 1. The original version of this asked:

"When is the difference between two triangle numbers prime?"

I guess as stated this is rather a closed question.
It is also a little unwelcoming for students.
The word 'prime' has to be attached to 'difference' which is a whole five words away.
The phrase 'prime number' will be a lot more accessible to students than the adjective 'prime' on its own.
They also need to recall the meaning of 'triangle number' at the same time as everything else.
The question is too dense and a little off-putting.

After working through this with a couple of classes, the risp became this:

Pick two whole numbers between 1 and 10 inclusive, and call them a and b.

Say that Tn is the nth triangle number.
Find Ta and Tb.

What is the difference between Ta and Tb?
Is this a prime number?

When is the difference between two triangle numbers a prime number?

When is the difference between two square numbers a prime number?
How about the difference between two cube numbers?

The first line is now a task that any student can accomplish.
Every student experiences a feeling of partial success on this problem that no-one can take away!

The second line leads students gently into algebra, while testing their understanding of 'triangle number'.
The next line asks for diagrams, which must be a good idea.
Each step is essential and yet accessible too.
Then comes the revision of the idea of a prime number, at which point everything is in place to make sense of the main question.
This can then be opened out in a variety of ways.

There are many times when I have come close to discarding a risp,
only to discover that a slightly different way into the question can revitalise it.