## Why sketching is important

I wrote a while ago about how important diagrams can be using this Chessboard puzzle as an example. Last week I happened across another example while helping a year 12 student complete some exam questions on coordinate geometry.

The question was this:

A relatively easy past paper question, but one that is quite fun nontheless. The student had completed a correctly and got the correct equation for l2 in part b but had gone wrong finding the point of intersection. She hadn’t noticed and hence had lost all the rest of the marks.

Part a was relatively straightforward:

And part b should have been too:

But she hadn’t got that. She’d made a transcription sign error and had the x value as -7. I knew her answer was incorrect as soon as I saw it because I had sketched the lines. She spotted that it must be wrong as soon as she saw my sketch:

Had she sketched the lines out she would have known that the point of intersection was clearly in the first quadrant and couldn’t have had a negative x value. This self checking mechanism is just one of the any reasons I try to get my students to sketch everything. I don’t understand their reluctance to do it, it makes the questions so much simpler and allows you to spot your mistakes. I’ll just have to keep highlighting these examples to them and trying to get them to see how foolish it is to avoid the sketching.

*Have you any ideas of how to instill the knowledge that a sketch is majorly important? If so, I’d love to hear them.*

Incidentally, here’s the rest of my solution.

And in full:

I like to have a specific class activity where the sole aim is to draw diagrams from exam questions. This comes up in so many topics, from AS Core to Mechanics (force diagrams) and Stats (eg sketching and shading a Normal pdf). Project an exam q; all students draw own diagram on mini w/b; then select 4-6 or so to hold at the front for discussion and questioning. Repeat.

Often students will think work on a mini w/b doesn’t need to be neat, but for this activity it does.

I always insist on diagrams, probably chiefly because I am too thick to solve problems without them, as sxpmaths says, even with Normal Distribution.

Drawing diagrams also has the benefit of slowing down the solving process, forcing students to slowly absorb the information and thereby get a good grasp of the problem before trying to rush into a solution.

It’s so difficult to solve many A Level problems without a sketch. You’re right though, I’ve never met a student that wanted to draw the sketch.

Even for trig equations I use the graphs rather than the CAST diagram I was taught. When drawing the graph I can have full confidence in getting the correct answer, even if the graph is transformed.

I use the Solomon question sheets to show how the last set of questions can become trivial ‘with’ a sketch but are extremely difficult without them. Really it’s about visualising your work and whether your method and answer make any sense.

I can’t remember what I was like as a student at that age so I can’t empathise with them from that point of view but in a Maths exam it can be so difficult to know whether you are correct that they should use every effort or technique available to them.