This week I was introducing Yr 8 to linear functions. The textbook does the usual dull thing of showing a table of values like this:
| x | 1 | 2 | 3 | 4 | 5 |
| y | 1 | 3 | 5 | 7 | 9 |
and asking the students to determine the 'rule' that connects x and y.
But I have a laptop and a projector on the ceiling, so let's make it more interesting. Fire up Geogebra, and drop some points onto the cartesian plane like so:
Now I can ask the students some questions: Are these points on a straight line? Does the fact that they are on a straight line mean that there is some connection between the x-coordinate and the y-coordinate for each point? (To which I got the reply, "There must be, or you wouldn't have asked." I didn't mind that, it was the next statement that threw me - "No, Mr D often asks weird questions"!)
Having decided that there may be a connection, the students put there heads together and came up with an answer, which then gave me the opportunity to ask how we would write that as a mathematical statement. Having decided on 'y = 2x -1', Geogebra then allowed to neatly type exactly that into the input field at the bottom of the window - the line appeared on screen passing through all the points, and the students were quite pleased with themselves.
A few more examples done the same way and the students had clearly grasped the concepts I wanted to get across. One boy asked a nice question about expressing one of our 'rules' differently (x in terms of y) which led to some useful discussion.
What I found most pleasing about this was the ease with which I was able to do what I needed. Simply being able to type in the equation as I would write it on the board made the connection all the more obvious to the students. I could have done the same thing with Geometer's SketchPad (and I still like GSP for certain things), but Geogebra seems easier and more intuitive for a lot of this type of work.
Geogebra - my students are going to be seeing a lot more of it.
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