GCSE Mathematics Resources

# A touch of density: 8 things I taught and 1 amazing thing I learned while teaching density

You can always tell which topics I enjoy teaching by the number of resources I create for it.  Density is definitely one of my favourites to teach, to any age group, possibly because it links in so nicely with ‘real world science’.  I can include apple bobbing in lessons, melt snowballs on the radiator, and discuss why a 12,000-tonne iron ship doesn’t sink.

1. Set a few things straight: “Which is heavier – gold or paper?” *compares wedding ring to pile of books* “Oh, so you need to compare the same amount of each?”  The classic ‘pound of gold or pound of feathers’ normally makes an appearance here.  The key thing to get across is that the more closely packed a particular material is, the heavier each cubic centimetre will be.  Then grams per cubic centimetre will make as much sense as miles per hour.  I have some 1cm dice handy for anything to do with volume: “If this were water, it would weigh 1g.  If it were gold, it would weigh about 20g.”

2. Get a feel for density: Start off with some common materials, and think in terms of ‘sink/float’.  A nice way to begin is my Density Ordering cards.  Did you realise that glass is more dense than granite?  Or that balsa wood is less dense even than freshly fallen snow?  This normally drags me off on a bit of a science tangent (why is ice less dense than water?  And what is up with platinum??)

3. Do a practical experiment: drop things in water, or weigh and measure some objects.  If there’s no snow around, show a video:

4. Tell a story: The classic Archimedes Eureka story may, it turns out, be a bit of an oversimplification due to the tiny tolerances involved (but don’t worry: Wikipedia gives a suggestion of some even cooler maths involving buoyancy that is probably closer to the truth, and can form extension work), but the story is useful nonetheless, and could easily be turned into a Eureka activity.

5. Talk about gold: For some reason we love to think about expensive things.  The value of gold per gram, coupled with its high density, make it very valuable in small amounts.  A pencil made of gold would cost you upwards of £300.  Have them measure an eraser and work out how much it would be worth in solid gold.  A 6-inch diameter sphere is worth £1 million.  And if you want to go really big, consider All the Gold in the World.

6.  Conduct devastating thought experiments: Not content with melting all the gold in the world into a big lump (which, by the way, would be a cube barely 20m to a side), let’s Melt the Eiffel Tower.  This one is crazy: due to the highly efficient wrought-iron lattice structure, it’s incredibly light for its size.  And since it also has quite a wide base, if you melted it down to form a cuboid with the same square footprint the height would be a mere 2 inches.  7300 tonnes may seem a lot, but if you scaled it down perfectly to fit in a classroom it would weigh around 3kg (the same as a large laptop).  The metalwork this model requires would be ludicrously thin (think 3 layers of tinfoil).

7.  And what’s the atmosphere like at this point in the lesson?  Denser than you thought?  At 1.225 kg per cubic metre it may well be.  Remember a cubic metre of water weighs a tonne, though, for comparison.  Students may be surprised to calculate that the air in their classroom weighs as much as them.  Bring it back to the Eiffel Tower and compare the weight of the iron (7300 tonnes) to the weight of the air within (modelled as a pyramid I get the air to weigh 2000 tonnes).  Not the same, as some websites would have you believe (and blithely tell your class for years before doing the maths yourself…) but pretty close!

8.  Shoe-horn density into other topics: When you’re doing volume of cylinders, have students work out the weight of a dug-out canoe.  Combine volume of a pyramid with the volume, and density, of The Great Pyramid (answers on a PowerPoint).

And finally – enough about what I’ve taught, how about what I learnt?  While estimating the weights of mobile phones by holding one in each hand my class kept thinking the lighter one was heavier.  Turns out, our brains were tricking us into comparing density rather than weight!  An iphone was smaller than a Samsung, but denser.  Still weighed about the same, but I’d have sworn it felt heavier.  Try it yourself – your brain is automatically adjusting for volume!  Hold them in bags so you can’t tell the size, and suddenly you can compare weights accurately again!

The Samsung Galaxy Ace weighs almost exactly the same (in fact, slightly more), but because its density is 25% lower, it feels lighter!

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