Seven lessons on scaling in Year 4

The idea of scaling is really important in mathematics, and everywhere in the world, so in Year 4 we've spent seven days exploring it in different ways.

❶ We started off by scaling up shapes drawn on grids. We looked at this:

This is what Rod drew

Then we made some scaled up shapes ourselves.  And we had lots of them (sometimes it went wrong the first time, an we had to re-do it):

❷ The next day we made designs with pattern blocks, with a certain ratio: two triangles to one square. (Thanks to John Golden for this idea.)

There were streets, cats

Here are some of them put on a graph:

and two charts made on paper:

What about a pattern that could carry on forever with the same ratio!

❸ Next up, we looked at A-sizes of paper. We use A4 most of the time, but the wonderful thing about this shape rectangle is that you can cut it in half and it's just the same shape scaled down. So, that's what we did, starting at A2 paper:

❹ In our fourth lesson, we looked at two models of the A380. The real A380 is one hundred times longer than the big model, and five hundred times longer than the small one.

Taking the small one, how long would the runway at Blagnac need to be to be the same scale?

We looked on Google maps:

So, about 4km. We divided this by 500 together, and got...

8 metres!

We made some 8 metre runways (they're a bit too thin, but never mind):

❺ Another approach was to scale up squares of Cuisenaire rods:

  ❻ Next we made chocolate cornflake cupcakes. But we needed to scale up the recipe to make the right number of cupcakes.

We also had a go at scaling up with this website

and scaling down with this:

❼ This one was a bit of a challenge. We looked at a clip from Zoolander:

Thanks to Robert Kaplinski for this lesson.

The real question is how many times would you need to scale this model up to make the real school?
And.... how can you work this out?

We thought about this in groups, and came up with different ideas. But it was a hard question!