Take the Right Angle
Problem
How many times in twelve hours do the hands of a clock form a right angle?
What are these times to the nearest minute?
Getting Started
Count round a clock, or use a geared clock (one where the two hands move together rather than separately).
Student Solutions
Abby, Antony, James and Peter from Gateway school in Carterton wrote to say:
We found 22 right angles in 12 hours. All the right angles are listed below:
12:16 12:49 1:22 1:54 2:27 3:00 3:33 4:05 4:39 5:11 5:44 6:16 6:49 7:22 7:54 8:27 9:00 9:33 10:05 10:39 11:11 11:44.
One of these is a minute out according to the NRICH clock. Can you find which one?
William and Alex at Maadi British International School, Cairo used a wrist watch to work out the problem and agreed there were 22 right angles, so did Eliza and Milli from St Hilda's School.
Teachers' Resources
Take the Right Angle
How many times in twelve hours do the hands of a clock form a right angle?
What are these times to the nearest minute?
Why do this problem?
This problem is one which could be done as an introduction when extending or revising work on time and clocks. It will encourage the use of digital times.
Key questions
At what time is the first right angle after 12 o'clock?
Why is it not just 15 minutes later?
Can you write down these times using digital notation
Why is the number of times not divisible by 4?
Possible extension
Learners could find out the times for 24 hours and record using 24 hour digital notation.
Possible support
Using a geared clock would be helpful. (Some 'play' clocks allow you to move the minute and hour hands separately, which can lead to the hands being placed in an impossible way!)