Scale it Up
… the picture and the maths, that is!
Proportional reasoning is more than abstract ratios on a page and certainly should have in origins in visual strategies. Scale is one of the first proportional ideas that students meet. They meet scale on graphs and maps but on the page a scale of 1cm to 1m doesn’t mean very much to a novice. So why not play around with scale and explore ideas such as twice as wide, 3 times as wide, 10 times as wide, or half as wide, a third as wide.
The original ‘alien’ is drawn on a 1cm square grid, 4 wide by 4 high. It can be stretched in just one direction or in both directions as shown in the drawings. It can be stretched by diﬀerent magnitudes and it is important from a place value and metric conversions perspective to explore enlarging by a magnitude of 10 or 100. Yes that will take you outside with the chalk, so pick a dry day.
Obviously, some modelling of how to locate relevant points and places on the grid will be needed to get the ball rolling. I think something simple such as an archetypal house would work well.
Be nice, give out the grids ready drawn (possibly for younger students). Click here to download grids if you want to.
Be not so nice and expect students to measure and construct their own grids, could be a lot of teaching ‘ruler work’ and how to create squares correctly involved in this part.
Expect students to describe their changes at an appropriate level and in an appropriate way, this could be as simple as ‘this is twice as thin’ or more abstract, such as ‘the ratio is 3:1 wide and 4: 1 tall’.