Scale models.

  Usually in most textbooks I've used, problems involving scale models all seem to revolve around planning a garden, drawing plans for a house, or even figuring out the length of a real car or train based on a scale model but there are other things we can use which might provide students with an understanding of other subjects.

For instance in science, they learn about the layers of the atmosphere, peer at a diagram in the book and move on but what if we took time to help them draw a picture in math while studying it in their science class?  Might that show students there is a connection between the two classes?

Since most of the world uses metric including the science class, its best to draw this on centimeter grid paper so students become used to using metric.   First step is to have students draw a circle with a radius of 6.378 cm in the center of the page.  This represents a scale of 1cm = 1000km so a radius of 6.378cm represents a real radius of 6378 km.

99.999% of the atmosphere is within the first 100 km above the planet so you have students draw a small line about 1 mm above the earth.  That shows the students a reasonable visual of how thick the atmosphere is around the earth.

More specifically if air pressure is 1 kg per square cm at sea level.  If you move upwards to around 5,500 meters or 5.5 km, the pressure drops to half of what it was at sea level.  Go up another 5,500 meters or 5.5 km, its dropped in half to about one fourth of what it was at sea level.  Most planes fly between 11,000 and 13,000 km and if you get up to 30 Km above the earth, you are above 99 percent of the atmosphere.

If you have the students create a thin strip to show the layers of the atmosphere, the tape from an adding machine is great for that purpose or a strip of graph paper with 1 cm = 1 km works equally well.  The layers would be as follows:

1. The troposphere is about 15 km thick.
2. The tropopause is about 5 km thick.
3. The stratosphere is about 30 km thick.
4. The mesosphere is around 40 km thick.
5. The ionosphere is 260 km thick.

This activity shows how the atmosphere is divided up but its nice for students to see that the whole atmosphere is not that thick. 

Each activity involves creating scale models, each with a different scale.  It would be quite difficult to see the different layers of the atmosphere if the scales were the same.  I believe this shows the need for different scales.

Let me know what you think, I'd love to hear.  Have a great day.