Why Are Castles So Tall?

Encouraging a Mathematical Mindset

Ask your math students this question: Why are castles so tall? Students of all ages and grades can provide an answer, and while the goal isn’t to get a mathematical answer from your students, it provides an opportunity to frame a mathematical question.

All children are familiar with castles from fairy tales, as well as from myths and legends. Cultures around the world have different types of castles. Show your students pictures of castles from different parts of the world. Here are some examples.

Himeji Castle, Japan

Neuschwanstein Castle, Germany

Château de Pierrefonds, France

The castle shown at the top of this blog is Edinburgh Castle in Scotland. Ask your students what all the castles shown have in common. Don’t immediately go to height as a common characteristic, or you may miss some interesting observations from your students.

You can also show them this Google Earth tree view from the top of Edinburgh Castle in Scotland (view in Chrome): Click here.

Media4Math Classroom has a lesson module on this that explores castle height from the standpoint of indirect measurement. In particular, a castle’s defenses would have required as much advance notice of an approaching army and a tall castle provides a line of sight that reveals longer distances. This module uses trig ratios as a means of calculating distances.

But the topic of castle height isn’t restricted to the province of trig. Here are some ideas that you can use to incorporate this topic of castle height into your math instruction.

Low Floor-High Ceiling Ideas: Castle Height

• Create a castle tower using Lego blocks. Count the number of blocks needed to build the tower. Math question: How many Lego blocks would it take to build a tower ten times taller?
• Create a castle tower from available classroom materials. Measure the angle the tower makes with the floor.

Math questions:

— How does the angle change as the tower increases in height? 

— What would you need to do to maintain the angle measure for a taller tower?

• Look at the triangle formed by the height of the tower, its distance from an observer, and the top of the tower.

— Math question: What kind of triangle is this? 

• This is the view from the top of Neueschwanstein Castle. The castle is 213 feet tall and  provides a panoramic view.

— Math investigation: Estimate how far into the distance you can see from the top of the castle.