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Telling time

Time is the one measurement that does not run in tens. Sixty seconds make a minute and sixty minutes make an hour, so working out how long something lasted means subtracting in sixties — and that is where very nearly every mistake in the topic comes from.

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An hour and a bit

How many minutes is it from 10:40 am to 11:45 am?

  1. Count on from 10:40 to 11:00. That is 20 minutes.
  2. From 11:00 to 11:45 is another 45 minutes.
  3. Add the two: 20 + 45.
  4. The answer is 65 minutes.

Worth knowing. Counting on in steps avoids the borrow altogether. Taking 10:40 from 11:45 in columns gives 1 hour 5 minutes, which is the same answer — but only if you remember that an hour is sixty and not a hundred.

When the minutes borrow

How many minutes is it from 2:40 pm to 4:15 pm?

  1. Count on from 2:40 to 3:00. That is 20 minutes.
  2. From 3:00 to 4:00 is 60 more.
  3. From 4:00 to 4:15 is another 15.
  4. 20 + 60 + 15 is 95 minutes.

Worth knowing. Subtracting the columns here asks for 15 minutes take 40, which is where the borrow comes in: one of the hours becomes 60 minutes, leaving 1 hour 35 — and 95 minutes is that same length of time.

Where it usually goes wrong

  • Treating an hour as 100 minutes, so 2:40 pm to 4:15 pm comes out as 175.
  • Subtracting each column on its own, getting a negative number of minutes, and then writing it down as though it were positive.
  • Losing the midday boundary. 11:30 am to 1:15 pm crosses 12, and counting on through it keeps the am and the pm straight.

The Professor counts on to the next whole hour first, then counts the hours, then counts the last few minutes. Three small steps beat one subtraction he might borrow wrong.

Practise it

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Questions teachers and parents ask

Why is time not in tens like everything else?

It is inherited. Sixties come from Babylonian astronomy and stayed because 60 divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 — inconvenient for arithmetic, convenient for splitting an hour into parts, and about four thousand years old.

Should I count on or subtract?

Counting on is usually safer, because it never asks you to borrow. Subtracting in columns is quicker once you are comfortable that borrowing one hour gives you sixty minutes and not ten.

Are there questions about reading a clock face?

Not yet. Reading an analog clock needs a picture, and pictures are something these worksheets do not carry. The questions here give both times in figures and ask how long something lasted, or ask you to convert between units of time.

When is elapsed time taught?

Telling time to the nearest minute and solving problems about time intervals is grade 3 (3.MD.A.1). Converting between units of time — seconds, minutes, hours, days — sits with the other unit conversions in grade 4 (4.MD.A.1).

Where this shows up

Standards

  • 3.MD · Measurement and data
  • 4.MD · Measurement and data
  • CCSS.MATH.CONTENT.3.MD.A.1 — Tell and write time to the nearest minute, and solve word problems involving addition and subtraction of time intervals in minutes.
  • CCSS.MATH.CONTENT.4.MD.A.1 — Know the relative sizes of measurement units within one system, and express a larger unit in terms of a smaller one.

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