This is the first in the ALL ABOUT SCALE sequence of lesson packs.

Watch the video http://bit.ly/ScalePaperAirplanes. The video gives instructions for making the planes but you can use your own design. Using scrap paper is more planet friendly.

The pictures show one paper airplane made with ordinary A4 printing paper and another bigger airplane.

Two sheets of A4 paper make a similar rectangle with double the area that we call A3. Two sheets of A3 double the area again making A2 size paper, so the area scale factor is 2. What is the liner scale factor?

We can fold an A4 sheet in half to make a similar A5 sheet and then fold again and again and again to make A6, A7 and A8 paper and make each sheet into a smaller and smaller and smaller scale model airplane. What are the scale factors for area and for edge lengths?

Make your own airplanes and investigate how far they fly. Change the design and find out how the change affects the performance of your planes. For example, you could add a small paper clip in different places to weight the plane and see what happens when you fly it. Try flying your planes out of an upstairs window and aim them upwards to try to catch a gust of air and make the plane fly further.

If you are in the USA, or if your paper is not A4, then fold a sheet of your standard printing paper in half. Is the smaller rectangle mathematically similar to your original piece of paper? If not then you need to cut your paper down so the edges are in the ratio $\sqrt {2}:1$ For example, the edge lengths of A4 paper are 297 millimetres by 210 millimetres.