After Easter I am introducing my Year 7 class to the idea of how the equation of a graph tells us information about that graph (in essence y=mx+c, but not in that language). We have already seen how to come up with an equation for a line by spotting a pattern between the coordinates, and we shall first be looking at how to draw graphs from equations using a table of values.
I was thinking how best to approach this. Previously I have done this using Autograph (which works very well when they have already met the idea of gradient and intercept), and also getting students to draw out loads of graphs until they spot the different relationships. But this group are a bright bunch, and drawing hundreds of graphs will be of no benefit to them.
I decided I wanted them to do something in groups and to discuss the ideas they cameup with. I came up with the set of sheets shown below (available for download here).
My plan is to split them into eight groups of 3 or 4 and give each group one of the different sheets. They will then have some time to work through the sheet, drawing 6 different graphs (practising their skills at drawing from a table). They are asked to discuss what they notice about their graphs, and make a prediction for a seventh graph, without doing a table. This should get them noticing the parallel lines or the same intercept (depending on the sheet they have).
Once they have had a chance to discuss what they have found in their groups, I am going to split them up into different groups, so that the four groups with the gradient sheets are rearranged so that one from each original group is in each new group (if it was the groups AAAA, BBBB, CCCC, DDDD it will now be ABCD, ABCD, ABCD, ABCD). Similarly for the four intercept groups.
In the new groups, they will discuss what they found, and more importantly compare their ideas with the other groups. Hopefully this will lead them to realising the different gradients (and maybe how they are related), and the different intercepts.
Finally, as a plenary, we shall have a whole class discussion about the different things they have spotted, and what information we can deduce about a graph from its equation. This will be followed by a short homework to consolidate the learning.
I think for this group, the discussion element will allow them to get a lot more ideas than they would by the other ways I have taught this, but we shall see...
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.