Do you remember how you were taught to tell the time in the old fashion way … you know, with an analogue clock face using phrases like “It is just after ten past 3”? Do you ever think about the concepts and numeracy skills involved in what may seem to you a trivial exercise, but to a child might as well be the toughest Mensa challenge? No, well – nor did I until I attempted to impart this skill on J2.
I’ve itemised below the learning elements that I believe need to be understood in order to tell time in this way. I’ve also made some assumptions that your child already understands basic number sequencing (i.e. can count upto 60) and has the ability to distinguish size and movement (the long, short hands and which one is visibly moving). Ok, looking at my digital watch, the time is 19:43 and the analogue equivalent answer we are seeking is “It is almost a quarter to 8 in the evening”. So, how do you go about instructing your child to arrive at this answer?
i) Modulo 12 arithmetic – there are 24 hours in the day and the day starts at midnight, but at midday, the hour goes back to 12 again. Get your child to look at the clock face and establish where the short (hour) hand is pointing. With any luck, he/she should respond “Between 7 and 8”.
ii) Latin – in the English speaking world one adds “ante meridian”or “post meridian” in order to make the distinction clear between an hour that falls before midday (AM), and an hour that falls after midday, but before midnight (PM). Now ask your child if he/she has had lunch (yes, I’m making the bold assumption here that lunch is still served around midday). Hopefully, the answer should be positive so you add to the confusion with some additional rules – if it’s before lunch, say “in the morning” but if it’s after 5, say “in the evening”, otherwise say “in the afternoon”.
Still with me … good, now let’s try to read the minute hand.
iii) Modulo 60 arithmetic – there are 60 seconds in a minute, and 60 minutes make an hour. On some clocks, the minute segments are marked, but more often than not, only the hour delimiters are marked 1 to 12, leading to the common mistake of calling “It’s 2 minutes past six” when the time is actually indicating “10 minutes past six”.
iv) enter the 5 times table – multiply the number on the clock face by 5 to get the value of the minute, e.g when the minute hand is on the number ‘4’, the minute value is really 20 (4 x 5). In our case, the minute hand is nearer the number ‘9’, so the answer we are looking for is “45 minutes” (9 x 5).
v) roman numerals – if that wasn’t challenging enough, on some clock faces, the hour segments are marked in roman numerals. so teach your child (parrot-fashion if that’s easiest) to convert between roman and arabic numerical notation – sorry, that’s out of scope for this tutorial 😉
v) being able to distinguish your right from your left (you’ll be surprised how many grown-ups still struggle with this concept!) – it is considered clumsy to say “45 minutes past” the hour, so we need to split the clock face vertically down the middle into two halves. The ability to differentiate right and left is needed to establish whether time is ‘past’ the hour (the long minute hand is on the right half of the clock-face) or moving towards i.e. ‘to’ the next hour (left hand side of the clock face).
But we now have to introduce the concept of …
vi) symmetry – having split the clockface into two halves, persuade your child to look at left hand side of the clock face as a mirror image of the right i.e. substitute 11 with 1, 10 with 2 and 9 with 3 etc etc. Now, get your child to confirm that the minute hand is on the left hand side, in which case apply the 5 times table to re-evaluate the minute value as “15 minutes to”.
vii) approximation – it seems anachronistic in this day and age to approximate time when we have the technology to put accuracy of +/- 5 seconds drift per annum on a quartz wristwatch! Nevertheless, this is an exercise in mental gymnastics and not a scientific experiment. So, instruct your child to add the words “almost” or “just after”, depending on whether the minute hand is closer to and approaching the hour segment or just departed, respectively.
viii) higher or lower – now go back to the answer in part i) and apply an additional rule based on the position of the minute hand. If it’s on the left hand side, make the hour the higher number i.e. ‘8’. Otherwise, use the lower number. So, putting it together, we should now have assembled “It is almost 15 minutes to 8 in the evening”.
ix) fractions – this is still clumsy, so we approximate time further by cutting the clockface again, horizontally to produce 4 quarters of a pie. Now, instruct your child to substitute “15 minutes” with the phrase “quarter” and “o ‘clock” and “half” when the minute hand is closer to or at the hour markers of ’12’ and ‘6’ respectively.
“It is almost a quarter to 8 in the evening”. QED … actually, it is 20:47 and boys and girls, tomorrow’s mathematical problem is to evaluate the time taken for me to write this blog in Martian hours so sharpen your pencils and stand ready …