Graphs of linear equations - a useful resource

Yay for straight line graphs!

This was a topic that I used to dread teaching, but I've had much more success recently so I thought I'd reflect on why that was.

Straight line graphs are an excellent topic to get students to investigate things for themselves. Give them some y = mx +c type functions, ask them to plot them and tell you what they notice.

Aha! The ones that end in a 5 all cross the y axis at 5. What a coincidence! And the ones that all start with a 2 go up in 2s! Amazing!  etc etc.

I used this approach right from the beginning of my teaching practice, but I still found that some students struggled to understand the generalised form of the equation. Some of them noticed the links straight away and the whole class moved on, but a significant minority were left with only a superficial understanding and they got very stressed out when they couldn't understand something that appeared to be so easy for the others.

I'm sure there are lots of things that I could do to improve my pedagogy for this topic, but I kept having the same response with different classes ...... until...... I made some laminated copies of a 10x10 coordainte grid to use for these lessons. I made 32 (1 for each student) and made sure they were big enough for me to see which coordinates students had plotted when they held them up from the back of the room.

Well the simple ideas are often the best and this turned out to make a big difference.

Firstly, using whiteboard pens on these grids encourages those students who are terrified of making a mistake to just experiment and stop worrying. And those kids who get angry easily - the ones who rip up their pages when they make one error - it calms them down completely. None of them mind rubbing out something written with a whiteboard marker.

But most importantly, it allowed me to use QUESTIONS much more effectively. I could get the whole class, or just a small group to show me this sort of thing:

the coordinate (0,3)
a line that intercepts the y axis at (0,7)
any line with a gradient of 2
another line parallel to your previous one that passes through the point (0,5)

and then:

the line y = 2x + 5
a line with a gradient of -3 or 4/5
a line that is perpendicular to y = 2x + 5


I could straight away see which students were getting muddled up and why. I could set different tasks for different students and I knew exctly who needed what level of challenge. I wasn't moving the whole class on anymore when only half of them were really ready.

 Our HoD has made laminated coordinate grids for eveyone in the department now.
Not rocket science. But pretty darn useful.