Should students who struggle with numeracy be learning to solve quadratics? Is rote-learning trigonometry genuinely the best use of our time with every student regardless of ability or aspiration? I’m not sure. I am a firm believer in the utility of my subject, and also in the value of learning things that may never be used again. Moreover, learning for the sake of learning, and curiosity for its own sake is what most often yields the amazing advances that justify our investment in the subject.
I have my own answers to the question “What’s the point of maths?” In fact, if you’re interested, I even made a leaflet for the more skeptical of my students:
However, this post is about one of the (many) topics that is unquestionably applicable to everyday life. Since the dawn of civilization, mankind has wanted to keep track of things; to count our herds, weigh our flour, measure our land. And more recently, compare our smartphone specs, remodel our kitchen or track our puppy’s BMI (is that a thing?)
There is definitely value, I think, in glancing back over the rich tapestry of imperial units. Too often students take things at face value without question, and it’s worth getting them to ask why we have centimetres: Where did they come from? Why are they that size? This is more easily done with the imperial system. Oudated and outrageous in its complexity, its very confusion speaks of its widespread and disparate usage. From farmers to tailors, and from sea-farers to road-builders, the applications come through in the units chosen: feet and hands, shackles and cables, rods and chains, furlongs and barley-corns. The unit chosen is entirely arbitrary – the only value in a given unit is the value people place in it (just like the confidence we have in paper money). So long as everyone used yards, yards were the logical choice. Of course, depending on whether you were at sea or on land, ploughing a field or hemming a skirt, there were dozens of popular alternatives to choose from. I started out the first year 7 lesson of the year with this wonderful video by Matt Parker:
As well as being something of a history lesson, this video – as was its intention, of course – highlights the greatest flaw in the imperial system: it’s a bugger to work with. The system developed organically, over hundreds – if not thousands – of years, so it resembles a sprawling 18th century London – built up over time by separate groups with little cohesive narrative. Until the upheaval of the French Revolution gave us the push we needed to make a drastic change, and along came the meticulously planned Milton Keynes of measurement systems. Taking the most universal thing they could think of as the base unit, they split the circumference of our entire planet into quarters, then broke those quarters into 10 easy pieces. Each of those was broken down into a million (more manageable) lengths (conveniently roughly equivalent to a yard, thus thumbing their noses at its inventor, Henry I, who is credited with defining it as the distance from his outstretched thumb to the tip of his nose). Once the metre was established (even the word was audacious: ‘metre’, of course, meaning ‘measure’), the rest followed in a logical base-10 system: millimetres, kilometres, etc. Of course, their original measurements were a little off (the Earth happens to be 40,075km around, not exactly 40,000km), but, like we said, the choice of unit is not as important as the value we attach to it.
And school children of today don’t know they’re born, with the luxury of only ever having to multiply or divide by 10, 100 or 1000. The system was designed with ease-of-use in mind. Having said that, old habits die hard, and it takes a generation or more before people are more comfortable with the new units than with the old. This worksheet introduces the metric system while highlighting the cultural scenarios when the imperial system is alive and kicking in the UK:
And this one is something of a follow-on, giving details of imperial to metric conversions for students to use throughout:
While our curriculum may be mostly tied up with unit conversion, the skill I am most keen to develop in my students is an intuitive sense of the units they are manipulating. They should know that their iphone weighs 150g and that there’s a 10m drop from the classroom window (those two facts are not necessarily related…). In my opinion, fostering a familiarity with units of measurement is one of the best ways a parent can equip their child to confidently use maths in the so-called ‘real world’. Parents don’t need to love algebra or get all excited about circular motion, but we should all be able to provide opportunities for our children to measure, to estimate, and to budget. This next one is simply an opportunity for students to find examples of what is measured in which units. Just how heavy is that car ferry? How far away is France? What is the width of a pencil line?
At this stage I try my hardest not to get too hung up on the distinction between weight and mass (see ill-concealed rant / A-level info-sheet). Students need to develop a ‘feel’ for this stuff first and foremost. The following match-up activity I enjoy using. Students (individually or as competing teams) have to first choose the most logical thing to measure (do we want temperature or distance for a high-jumper?), then pick a number that fits the given units. Truth be told, some are hard to guess, but there’s a lot of mileage (sorry, km-age) in asking students which answers they’re really confident with – they may surprise you.
And this worksheet encourages rough estimation. Given the number, can you choose the appropriate units? Is a tin of beans more likely to be 415 grams, kilograms or tonnes?
Some quirk of human nature makes my students 12 times more eager to answer questions when I dole out plastic counters for their efforts. Usually given out with no explanation or promise of reward, and collected back at the end with no totting up or declaration of a winner. Competition alone is enough. This next activity is, therefore, in the form of a quiz. Put them in teams, and maybe even save it for the end of term so they view it differently to a normal lesson. This has plenty of scope for curiosity and extra discussion (so read up on it before-hand, or better yet make your own) – students have to guess the big numbers that go with these big things.
Once your students get on to compound measure, test their confidence converting compound units of speed with Speed Conversion, and of course check out my earlier post on density (which packs in a surprising amount, for its size…)