My wife and I visited family in in England, Scotland and South Wales, and so had opportunities to visit various sites near where family members live. Two of these locations are featured in this week's podcast.


Stonehenge, Wiltshire, UKFirst, Stonehenge, in Wiltshire. This site was built in pre-historic times, meaning that its precise origins were not recorded in writing and so working out why it is there, how it was constructed and what it meant at the time can only be deduced by experts in archaeology and history.

I had hoped that the experts had agreed by now what the site was used for and what it looked like when it was in use. Sadly, the experts can't agree (do they ever?), and so debate continues about whether it was primarily a religious site, or one connected to astronomical observations and the science of the day. My view is that it was probably both, and that if we could see it in use today we wouldn't be all that impressed with the significance attached to it. Yes, the technology used to quarry, cut and transport the stones and then to construct the site are really impressive. But the science of lining points up with the rising sun? Whereas in its day the fact that the movement of sun, moon and stars was highly predictable was a major discovery, nowadays we take it all for granted and have so many other ways to check the movement of "heavenly" bodies that Stonehenge gets left behind as a sort of "quaint" calendar-calibrating device.

What can students learn from this? Most people have a pretty fuzzy understanding of movement of sun, moon and the earth, so studying more precisely how the apparent movement of the sun and moon changes over time is a worthwhile exercise for our students in understanding basic astronomy. This site illustrates the idea that if you know about astronomical dates and directions you can predict with a high degree of accuracy where the sun will appear to be at certain times, every year. The math behind all this can get really complicated, but the basics are worth investigating for middle school students.

Cardiff Castle

Later in our trip, we had a trip to Cardiff, and a local historical site, Cardiff Castle. I can thoroughly recommend it as a fun day out for families or couples. The main castle building itself has some beautifully furnished rooms, and, for royal watchers, some nice connections with the Royal Family.Cardiff Castle, Wales, UK

Outside there is a Keep (small tower) on top of a steep mound, called a "motte", which the energetic can climb up, including climbing some really steep stairs to the top of the keep.

Now, in the grounds of the castle is a working trebuchet, which apparently was constructed for use in the 2011 movie Ironclad (click to see trailers - including shots of the trebuchets). The castle asked if they could have it when the movie was finished, and there it is. The machine is "fired" (is that what you call it?) periodically for the public. We missed seeing it shot by one day - what a shame. Still, I got to stand in front of it uninterrupted to talk about science, technology and math.


Google Maps of Video Locations

Here is a Google Map view of the location at Stonehenge where I shot the video:

View Stonehenge, Wiltshire, UK in a larger map

This is the location of the second exterior segment, at Cardiff Castle in South Wales:

View Cardiff Castle, Wales, UK in a larger map

Teaching Opportunities

How does a visit to a site such as these help you to teach mathematics? There are lots of directions you could take this, but my approach is to connect science, technology and math together, in the context of what those in the past invented and constructed. Sites like these are truly rich with opportunities for teaching possibilities. Some suggestions from me for suitable topics:

  • observing the sun over time - note the direction of rising and setting during a year
  • the angle of the sun's rays at different times and on different dates
  • connections between the sun's elevation and the latitude of the observer; differences in different locations around the globe
  • the physics of propelling a heavy projectile at an enemy without gunpowder or other propellant
  • differences in distance when a projectile is launched at different angles
  • the effects of using heavier masses, different length arms and and so on

Cross-curricular links could also be made to subjects such as:

  • history - especially in the areas of science and technology
  • military technology
  • astronomy before telescopes: what could be observed in ancient times?
  • science - physics of projectiles

What sites are available to you to expand your students' horizons about applications for math? Are there locations near you which offer these sorts of opportunities? Share your thoughts below and encourage other teachers!