How much does an apple weigh? How wide is a typical family car (not an SUV or a campervan)? How far is 100 metres, and how fast can you run it? These are the kind of things that children should know (or at least have an idea of) by a certain age, preferably around the age my children are now (10 and 12). Even if you’ve never weighed an apple or taken a tape measure to a car you should be able to work these things out. This piece has grown to over 1600 words, but there are headings to guide you through.

The weight of an apple

Nearly 20 years ago I coached a member of my family through some entrance exams, similar to the old 11+ exams. She did very well. The first two questions in the opening paragraph above (about apples and cars) were given as examples of the things children should know. I discussed them with a work colleague, who expressed contempt that children should need to be taught these things. “Everybody knows that,” she said. “Okay, how much does an apple weigh?” I asked her. “30 grams?” was her reply. I talked her through it. “Okay, so there are around 450 grams in a pound. If an apple weighed 30 grams I’d get 15 apples to the pound, or over 30 to the kilo. Is that right?” No. Not all apples are the same size and weight but you’d expect to get around 8-9 in a kilo, or 4 apples to the pound. This means that a regular-sized apple weighs around 120 grams. Anything lower than 50g or higher than 180g is probably a wrong answer (though a monster-sized cooking apple might conceivably top 180g).

Kilos and pounds

Part of the difficulty with weights and measures here in Europe, for adults as well as children, is dealing with imperial and metric measurements (pounds and ounces along with kilograms and grams). There are plenty of food and drink references to help us out here, and metric measurements help to tie up volumes of liquid with how much they weigh. A litre of water weights 1 kilogram. 1 kilogram is also the standard weight of a bag of sugar these days, and equates to 2.2lb, about 10% heavier than the 2lb bags of sugar we had before the metric system was adopted in the UK. To be even more precise about this 1lb is 454g (or 453.59g if you like things to 2 decimal places).

Litres and pints

To equate litres and pints many of us rely on this rhyme: “A litre of water’s a pint and three quarters” (it’s 1.7598 if you want a couple more decimal places). If you have ever looked closely at a pint glass or an old-fashioned bottle of milk you might have seen that 1 pint = 568ml (568 millilitres, or .568 of a litre). A 1980s beer campaign (for Heineken I think) has always helped me to remember an approximation of this number. The campaign suggested that with the arrival of metric measurements the Great British Pint might have to go, so we’d be drinking .57 of a litre instead. “Heineken,” my memory tells me, “It’s a great .57 of a litre.”

I would like my children to feel confident about these sorts of numbers. They’re getting there. They know what a 2-litre bottle of water looks like and feels like, and it weighs 2 kilograms. A 500ml bottle weighs half a kilo, or 500g. They know what a kilo of sugar feels like. Last year, when she was still nine, my daughter had a homework assignment to find liquids around the house in as many different sized containers as possible. Just to complicate things, the same measurement could appear three different ways: 50cl, 0.5l or 500ml, it’s all the same amount of liquid (half a litre). A carton of juice is typically 200ml. A can of soft drink is 330ml. A can of Guinness is 440ml. A bottle of wine is 750ml (or 75cl). We tried to make sure that there weren’t too many examples of alcoholic drinks in her completed homework.

Distance

When it comes to how long or how far things are I have found that many adults have difficulty visualizing a full range of distances, from an inch or a centimetre to 100 yards or 100 metres or a couple of miles. The plastic rulers we had as kids are always a good starting point. Typically they are 6 inches long (15cm) or 12 inches long (30cm). Most of us can also picture what someone who’s 6 feet tall looks like. A general rule of thumb, for men at least, is that your “wingspan” (the distance from the end of one middle finger to the end of the other middle finger, when your arms are stretched out wide) is the same as your height. For me that equates to 6 feet (or 2 yards, or 72 inches, or 1.83m).

The width of a car

To return to the second question in the opening paragraph: How wide is a typical family car? The answer is between 5 and 6 feet. It is unlikely to be wider than 6 feet (or 1.83m). Our Peugeot 307 SW is 1.73m (about 68 inches, or 5’8”). The width of a Mini Cooper is 1.4m (well under 5 feet). If I sit in the middle of the back seat of any car and stretch my arms out wide both hands will touch the windows.

100m and Marathons

To return once again to the opening paragraph, how far is 100m, and how fast can you run it? This piece has been prompted partly by all the years that I have spent trying to explain quantifiable things like weights and measures, and partly because many of the local parks currently have running lanes measured out on them, for school sports days. One set of lanes in our nearest park is a straight 100m, as in an Olympic 100m race. My daughter and I have been practising on it recently. It took us around 18 seconds to run 100m. I might have managed it slightly quicker but am not as fit as I used to be, and I don’t want my hamstring to snap. I managed to stay slightly ahead of her in our last “race” and this is probably the last summer that I will ever be able to run 100m quicker than her. She’s a good runner, though cross-country rather than sprinting is her strength. When she gets to 11 or 12 she’ll be running 100m a second or two faster and I wouldn’t dream of trying to keep up. That’s the way it should be. Aged 11 I could out-run most people who are the age I am now. The quickest time that I ever recorded for 100m when I was a child was 15 seconds. If I ever ran it faster than that (and I hope I did) there is no record of it. Usain Bolt, as you probably know, has run 100m in 9.58 seconds.

If we could run 100m in 18 seconds, how long does it take a medal-winning athlete to run every 100m in a marathon? I suggested this question to my daughter, as a means of tying up her interest in athletics with some practical maths. How would you even begin, and could you do it in your head? As long as you know two key things (how long a marathon is, and what the world or Olympic record is) you should be able to get an approximate answer.

Here’s one way. A marathon is 26 miles and 385 yards. The current world records are around 2 hours 3 minutes for men and 2 hours 17 minutes for women. Anything under 2 hours 10 (men) or 2 hours 25 (women) is an excellent time. If we want to work out an average speed for each 100m, first convert 26 miles 385 yards to metres or kilometres. 5 miles = 8 km, so 26 and a bit miles = about 42 km. (The exact distance in km is 41.95, so 42 is close enough.) 2 hours 10 minutes is 130 minutes, or 7800 seconds. This means that a good runner would run around 42,000 metres in 7800 seconds, or 420m in 78s. If we divide each number by 6 we’ll see that they run 70m in 13s. To work out the time for each 100m, multiply 13 by 10 over 7, which is the same as 130/7 or 18.5. This means that a man running a marathon in 2 hours 10 minutes is covering each 100m (all 420 of them) in 18.5 seconds. And I was catching my breath after running a single 100m in 18 seconds. A marathon time of 2 hours 23 minutes (which is a very good time for a woman, just outside the world record) is only 10% more than this (143 minutes is 13 minutes, or 10%, more than 130 minutes). The time taken for each 100m will be 10% more than 18.5s, which is 20.35s (18.5 + 1.85 = 20.35).

How light is a gram?

To return to weights rather than distances, here’s the most useful tip I have found for teaching children how light a gram is: think of hula-hoops, the potato-based snack. Each hula-hoop weighs around a gram. If you want to check for yourself take a packet of hula-hoops, count out the contents, and compare it with the weight indicated on the packet. I have just emptied out a 24g gram bag and it had around 29 hula-hoops (27 complete ones and enough bits to make up another couple), so each one weighs just under a gram. Recently we have tried the same thing using the corn-based snack Wotsits and have discovered that a Wotsit is even lighter than a hula-hoop, under 1/2 of a gram. The 16.5g packet beside me yielded 44 items. The beauty of hula-hoops and Wotsits over crisps is that each item in a packet is pretty much the same size. Some hula-hoops may be slightly smaller than others, but they all weigh just under a gram. Other corn- and potato-based snacks are available.

Finally, a joke

I feel obliged, whenever weights and measures are being discussed, to tell the following joke.

A man walks into a butcher’s shop and says, “Two pounds of sausages please.”

The butcher replies, “It’s kilos now mate.”

“Alright, I’ll have two pounds of kilos then.”