Look at our school building from the yard. How tall do you think it is, from the ground to the very top of the roof? Now here is the tricky part: nobody has a ladder long enough, and you certainly cannot climb up there with a metre stick. So how could we find out the real height without ever reaching the top?

On a sunny day, everything casts a shadow. We will use a stick and its shadow to work out how tall the school is, then check that height two quick ways. Watch how the stick's shadow and the school's shadow grow in step with their heights.

Counting storeys. Each storey is roughly 3 m tall. Count how many storeys the school has and multiply by about 3 m to get a rough height.

Comparing to a known height. Stand a pupil whose height you know beside or near the feature, and judge how many of that pupil would stack up to reach the top. If a 1.4 m pupil fits about 7 times, that is roughly 1.4 m × 7 ≈ 9.8 m.

Now pick one feature around the school that you cannot reach with a ruler, and estimate its height two different ways. Aim for two estimates that agree to within 10% of each other. Then lightly estimate two more features, one method each, so you have practised more than one strategy.

How to check the 10% rule. Before you go, here is how to tell if two estimates agree closely enough. Take this pair:

• Shadow-and-stick estimate: 10 m
• Storey-count estimate: 9 m

Find the difference: 10 m − 9 m = 1 m.

Find 10% of the larger estimate: 10% of 10 m = 1 m.

Compare: the difference (1 m) is equal to the 10% amount (1 m), so these two estimates agree within 10%. If the difference had been bigger than 1 m, they would not agree closely enough.

Use this same check on your own two estimates for your main feature, and record both methods and both heights in your table.

What we did today

• We found the height of something we could never reach, using shadows, counting and comparison.
• We learned that shadows are in the same ratio as heights when the sun is in the same place.
• We saw that two estimates agreeing to within 10% is what lets us trust a measurement.