Teaching graphs I try to focus on linking features of the graph and features of the equation, and piecing together what the graph looks like one clue at a time.

*What type of equation is it?*

Looks like a parabola.

*Is the x positive or negative? What does that tell us?*

It's negative, so it curves down.

*It's got a number added to the end? What does that tell us?*

It moves up the y axis.

I favour matching activities and assigning "possible" equations to graphs rather than dealing with definites where they can check points or use a table of values.

I've also focused on categorising graphs and exploring their features by looking at a lot of graphs and equations to help make those links. There's a great exploration of this idea at exzuberant (A Visit to the Function Zoo). With a lower-achieving General Maths class I've used Geogebra printouts of graphs with their equations on them in a hands-on categorising activity. I just get them to put them into groups of graphs that they think are similar. Then look at what is similar, and what is different. Where do those differences come from in the equation? What do they look like in the graph?

Today I tried another approach. It was with a Year 10 5.1 class, so they don't really need to know about these graph types, but they are supposed to have seen them or graphed them using tables of values or something, so I figured we'd try this anyway. Extra knowledge can't hurt, and lots of them will do General Maths and it might help to have seen these wacky graphs before.

Here's how it worked:

- Students are given a card with a letter-number coordinate. Letters are from A-E and numbers are from 1-5.
- (I was going to add this in but realised there wasn't enough time) Whole class to place a series of images of graphs into 5 categories based on the shape of the graphs.
- Assign a letter to each group of tables.
- Students go to the table with a letter that matches their coordinate. Each table has a different type of graph to become ‘experts’ on. They have a worksheet with questions (each) and a set of graphs (to share) with their equations written on them. Students have to work together (and with the teacher’s help when needed) to answer the questions and learn all about that type of graph. The questions are all about the properties of the graph and links between graph and equation.
- Students now move to tables based on the number in their coordinate. This is arranged in such a way that each table has at least one expert on each type of graph. Each person has 5 minutes to share their knowledge about the graph type.

The Good:

- Some students who were not usually engaged in their work were more serious because they knew they would have to explain it to others.
- Many students benefited from working with people they didn't usually work with.
- Some students made the connections between the transformations of different graph types very well. (and what does adding or subtracting a constant do to
*this*graph? What a surprise.) - It changed our routine up a bit. Always worth doing.

The Bad:

- Some students seemed to understand well enough in their first group, but were not confident enough to explain it to others without any support.

Next Time:

- I think I'd prefer using expert groups for an idea that is well within the ability range of the kids rather than something at the edge of what's expected of them, just for the confidence thing. Although it certainly showed which students could cope with these new and challenging ideas.
- On that note it might also be a good revision activity - break the topics down into small bits and share those around. Then most students should already have some idea of the content and just need the extra time to fine tune their knowledge.
- More time if possible. Maybe a good activity for a double period rather than a single. This would leave time to do some prep activity (like the categorising that I left out) and add other elements.
- After the expert sharing time, I went over things together as a class. This meant that weaker groups had an opportunity to fill in gaps of knowledge, and it acted as a nice summary. I would then like to follow this up with an individual activity like a little quiz or worksheet, to check their understanding. Maybe the group with the highest score could get a prize, to show what good experts and teachers they are.

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