How would you define exactly the direction and position of the paths of the differentaircraft (can you name each of these modern aeroplanes?) and the blue whale?

Why might it be important for airports and shipping radars to be able to track anddefine exactly the path they want ships and aeroplanes to take?

What sort of line does y=10x - 3 describe? How does this internationally accepted way of describing lines/relationships compare with the one you designed?

Can you save the planet from missile attacks?

Why we like this activity....
We like this activity because we feel, for many of you, y=mx+c too often has no meaning . The aim of this approach is for you to consider the common sense starting point: “how do I measure the steepness/flatness and, exact position (how do you know that two parallel lines are not exactly the same line?!), of airplanes flight paths (in 2D!), ships positions on the sea etc.

How this activity can be used....
The missile/boat games are a plenary and starter (respectively) which can be used to introduce and review the topic.

Try it as a homework. When you've handed it in, the teacher can collect all the many ingenius ideas the class has had for defining and measuring different paths/lines, and prepare a selection of the best of them to share with you all.

What to expect when using this activity, from our experience...
The teacher will get a very interesting picture of how you all see, describe and make sense of lines and boat/plane etc. pathways. They'll then introduce you to how mathematicians the world over have agreed to describe them: what are the pros & cons of your methods versus these agreed upon methods? Maybe in the future, your method might be used internationally!

Extra notes
Homework feedback can often consist of a photocopy (or scanned file to load onto students itouches etc.) of the most innovative and/or efficient student ideas.

 

Oliver Bowles 17.08.09

Thanks to Jim Noble for the Discovering the meaning of equations for lines worksheet.