Telling time: clocks to read here or print

How a clock with hands works

• The short hand shows the hour. It moves slowly from one number to the next, so at half past three it sits halfway between the 3 and the 4. The hour is the number it has just passed.
• The long hand shows the minutes. It goes all the way around once in an hour: 60 minutes, and 60 small marks around the edge. Each number is 5 minutes after the one before it, so the long hand on the 3 means 15 minutes and on the 6 means 30.
• Written with two dots: the hour, two dots, then the minutes with two digits. Five minutes after three is 3:05, and three on the dot is 3:00.
• On these clocks the short hand is drawn where the hands of a clock with gears would put it: half a degree further for every minute, while the long hand turns 6 degrees a minute.

The five kinds of sheet

• To the hour: 1:00, 2:00 and so on. There are only 12 such times, so a sheet of 12 has every one of them, in a mixed order.
• To the half hour: the times that end in :00 or :30.
• To the quarter hour: the times that end in :00, :15, :30 or :45.
• To five minutes: the long hand points to one of the twelve numbers.
• To the minute: any of the 720 times a clock can show.
• The sheet number: any whole number from 1 to 999999. The same times and number make the same twelve clocks on any device, so a whole class can have the same sheet, and no two clocks on a sheet show the same time. If we change how the page picks times, a number will make a different sheet.
• How big they print: on a Letter sheet, 6 or 9 clocks are each about 6 cm across and 12 clocks are about 4 cm across.

Every time the page is built, a program makes 2,000 sheets (400 of each kind) and reads all 24,000 clocks back from their pictures, with code written apart from the page’s own: it takes the angles of the two drawn hands and works out the time they show, and that has to be the time on the answer sheet. It does the same for each of the 720 times a clock can show, checks that the four answers on the screen are four different times with the right one among them, and measures the 6 ways the page can lay clocks out on a sheet.

What this page does not do

• It does not say morning or afternoon. A clock with hands looks the same at 3:00 at night and 3:00 in the day, so there is no a.m., no p.m. and no 24-hour time here.
• It does not use words for the time, such as “quarter past” or “half past”. Every answer is written with digits.
• It has no second hand, no Roman numerals and no digital clock to match.
• It does not check hands you draw. On paper, compare with the answer sheet. On the screen there are only clocks to read.
• It does not keep score after you close or reload the page, or pick another sheet. The sheet number brings back the clocks, not your answers.
• It is not a lesson plan and follows no school’s program or grade. It makes no promise about what anyone will know after using it. It is clocks to practice on.
• It cannot be read from the picture by a screen reader. “Where are the hands?” says in words which numbers the two hands point to, and from that the time can be worked out without seeing the clock.
• It cannot see your printer. It has been tried in one browser’s print preview (Chromium, saved as PDF), where each sheet came out on one page; it has not been tried on paper from a real printer.