Scale modeling the Great Wall of China.

How long is the Great Wall of China?

A simple question you would think, a quick check on the internet and you have your answer.  Not so.
The Great Wall of China is a series of walls built at different times.  When the children were researching in groups they found all sorts of lengths and answers.  It was wonderful to see them automatically check multiple websites for their answers, and indeed to check with each other.

We got all sorts of answers ranging from 5,500 miles to 13, 000 or so miles.  So what to do?
Well, we decided to settle on the Ming section of the wall which is 5,500 miles or 8,850 km. They are into the Ming dynasty right now from their investigation into the Forbidden City.

Can we build a model?

The first thing I did was to stand back, to let the students figure it out, how would they go about building a model?  One group started building with blocks, their main goal to build an aesthetically pleasing wall that looks like the great wall, complete with watch towers.

Another group decided to use a scale - one cm to one mile in length and then one cm to one foot for the height - this of course ran them into problems.

The idea of scale was there for most of the students but I soon realized that the sense of length was proving to be a difficulty.

So we slowed down.

The next day in math we looked at both standard and metric measurements.  Scales mixing the two measuring units were common and I wanted them to stick with one set of units.  We went with metric and decided on a length scale of 1mm = 1km.  They easily worked out that the wall needed to be 8,850 mm long.   Easy!  I then asked how much space does 8,850 mm take up, is it as long as the trailer?

This proved to be a fascinating glimpse into the students ideas of length and measuring units. As they were studying rulers, it was soon obvious that mm were foreign for many of the students and they explored the idea in detail.

They first looked on rulers to try and find the part that was mm.  They all knew that mm were small but were not sure whether they were part of inches or cm.  We started with that, then moved to how many mm in a cm?  Some said 10, some 11.  It all depends on knowing how to read a ruler.  This led to a great discussion. Then some groups looked into how many mm in a ruler. (standard 12 inch ruler) Next was how many in a meter.  Even though we slowed down, it was amazing quickly the children took themselves step by step to solve the problem.

Think of the math involved, converting mm/cm/m using multiplication and division, the powers of ten.
Reading a ruler, investigating the sense of length and size, making comparisons.

It is one thing to say 8,850 mm = 885 cm or 1 meter 85 cm but it another to really understand how the system works and to get the sense of the scale of the measurement units.

I was so impressed with their enthusiasm and the speed of their understanding.
One group took a long tape measure outside to get a sense of the scale.

So, next:
Will this scale work?  What about the wall height?  With 1mm = 1km, getting the height of only 15 meters is going to be tough.  Let's see what happens.