Flashing lights
Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?
Problem
Flashing Lights printable sheet
Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Norrie then watches a third light. He sees it flash at the same time as the other two, then it flashes every 7th second. How many minutes will it be before this light flashes again at exactly the same time as the other two?
Getting Started
When will the first light flash?
When will the second light flash?
So when will they flash together?
Could you predict when they would next flash together? How?
Student Solutions
(Thank you to Norrie McKay and the lights over Tokyo Bay for this problem)
There were many correct answers sent in for this problem. As Primary Maths Club (International School of Toulouse) pointed out, it helps if you start counting seconds from the first time the two lights flashed together (at zero seconds).
Some people thought about a number line, others looked for a number that both of the numbers of seconds (4 and 5) would divide into (common multiple). Here are two very well explained solutions.
Holly, Harriette, Caroline, Florence and Rebecca from The Mount School, York:
1st light 0 - 4 - 8 - 12 - 16 - 20 - 24 - ......
2nd light 0 - 5 - 10 - 15 - 20 - 25 - ........
They flash at the same time every 20 seconds 0 - 20 - 40 - 60
That's four times in all.
For two lights the pattern was every 20 seconds and 4 x 5 = 20
For the three lights it is going to be 4 x 5 x 7 = 140 seconds or 2 minutes 20 seconds
Christina from Marlborough Primary School :
To work this out you need to find a multiple of both 5 and 4 which is 20. So the lights flash together every 20 seconds and to find out how many times they flash in one minute you need to do 60/20 = 3 which means that they flash together 3 times a minute.
You need to find a multiple of 20 and seven to work out how many minutes before all of the lights flash together. 20 x 7 = 140 sec = 2 mins 20 sec
Well done to all of the following people: Jesse, Edward, Daniel and Thomas from Tattingstone School who did some very good work with finding the multiples. Lily from Sotogrande International School, Daniel from Anglo-Chinese School, Singapore, Abigail, Charles and David from Moorgate Primary School, Staffordshire, Jason from Priory School, Thomas from St Francis School, Maldon and Ashley.
Teachers' Resources
Flashing Lights
Flashing Lights printable sheet
Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Norrie then watches a third light. He sees it flash at the same time as the other two, then it flashes every 7th second. How many minutes will it be before this light flashes again at exactly the same time as the other two?
Why do this problem?
This problem is a good way of introducing children to common multiples and it is also a useful context for looking at different recording methods.
Possible approach
As a starter, you could split the class into two groups. One group will clap every 3 beats and the other every 6 beats, while you count the beats. Ask them to predict on which beats they will all be clapping. Try other rhythms in the same way e.g. 3 and 4. Can they explain why everyone will be clapping on certain beats? How would they work out which beats these were without clapping?
In the plenary, you can specifically introduce the vocabulary of common multiples if you haven't done so already.
Key questions
Possible extension
Music to My Ears would be a good problem for children to try next as it places greater emphasis on predicting when common multiples occur.
Possible support
Some learners might find Clapping Times a good problem to try before this one.