Apr

30

The Englishman Who Went Up a Hill But Came Down a Mountain.

Filed Under Challenging the students to come up with questions for them to answer. | Leave a Comment

“The Englishman Who Went Up a Hill But Came Down a Mountain”  is a 1995 film … based on a story heard by Christopher Monger from his grandfather about the real village of Taff’s Well (Ffynnon Taf in Welsh), Rhondda Cynon Taff, Wales and its neighbouring Garth Hill.

The movie is set in 1917 (with World War I in the background), and revolves around two English cartographers, the pompous Garrad and his junior, Anson. They arrive at the fictional Welsh village of Ffynnon Garw (“Rough Fountain” or “Rough Spring” in Welsh) to measure its “mountain” – only to cause outrage when they conclude that it is only a hill because it is slightly short of the required 1000 feet. The villagers, aided and abetted by the wily Morgan the Goat and the Reverend Jones (who after initially opposing the scheme, grasps its symbolism in restoring the community’s war-damaged self-esteem), conspire with Morgan to delay the cartographers’ departure while they build an earth cairn on top of the hill to make it high enough to be considered a mountain.” (Wikipedia)

It can be seen on YouTube.

After showing parts of the film, ask the students for math related questions it arises.

If they don’t suggest any questions wait for five minutes in silence. If nothing appears after five minutes wait another five. And so on.

Sooner ot later the students will realise that their task is not to guess the questions you find interesting, but to think about what they find interesting.

Here are the questions I find interesting:

  1. When does a hill become a mountain?
  2. How may the height of a mountain be measured?
  3. What is the volume of a cone of soil h feet tall?
  4. How many buckets are needed to create the cone just mentioned?
  5. How much time is needed to make the cone?
  6. The hill is measured using the previously measured heights of two other hills. One of the men in the village asks, ‘how were the heights of these hills measured?’ and gets the answer ‘using two previously measured hills’ to which he replies ‘how was the first hill measured?’. This is a good question in itself and is analog to the interplay between axioms and theorems.

Here are some ideas for answering these questions I would think about before presenting the task.

  1. relevant factors: objective: height, slope, subjective: local use, elevations nearby
  2. pedometer (mentioned in the film), clinometer, barometers, triangulation
    “the surveyors used a clinometer and stepped-off distances, from which the elevation was calculated. They acknowledged this method was lacking in accuracy. In the second measurement they used barometers. This was less than successful because a low-pressure front flowed through the area, causing the base barometer to change while the observing barometer was carried to the top. The third measurement was made by triangulation with two nearby peaks for which the elevation was known. I wonder how accurate that was.”  (source)
  3. what is the slope of the cone? what if sand was used instead? when you know the slop how do you find the volume, how good is a cone as a model for the real mound?
  4. what is the volume of a bucket? lower and upper estimate? soil is not water, how much soil will go in a bucket with given volume?5. how many buckets can be poured on the top of the mound in an hour? how can it be done? how many people are needed? what is the distance to the place where the buckets are filled?

There are enough questions here for several weeks of work. I suggest one should vote on the questions the students propose and do them in order of popularity. To promote discussions the most popular questions should be done by all. Later the students should be allowed to investigate and report back to the class what they found, how they found it, what further question arose.

Mathbits has made a worksheet for the film, but I would rather ask the students to find questions.