Here, as promised are instructions for doing the guess the function activity on an Hewlett Packard HP40GS graphing calculator. First press SYMB, enter a function, and press ENTER:

Now click SHIFT and PLOT to enter the plot setup. Click the PAGE down softkey, select AXES and click the CHK softkey to deselect the axes. Click PLOT to make sure you can see the graph properly (you may need to use MENU then ZOOM to set it up, but quicker to choose a function whose graph you can see!)

Now click SHIFT NUM to enter the number setup, select NUMTYPE, click the CHOOS softkey, select BUILD YOUR OWN and click OK. Now click NUM and you are ready to start.

Ask participants to give a value for X and guess the value for F1. Make sure no-one actually guesses the function or that will close down everyone else’s thinking. When you have a few values, ask if we could improve the table and they will say (because they always do!) “put them in order”, so click the SORT softkey. Only when there is enough data and some are struggling, ask if another view would be useful and they’ll say “show us a graph”. So click PLOT, but only very briefly, click NUM again after a couple of seconds. They only need the shape after all. When most participants are able to give a value for X and its corresponding value of F1, ask them what form they think you put the function in. (Entering the quadratic as (X+2)(X-1) is unusual, but very helpful!). Finally, the function can be revealed.

Now, because they have a handheld, pairs can make up their own and try it out on their neighbour … pair work perfection.