The moons of Vuvv
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Problem
The Moons of Vuvv printable sheet
The planet of Vuvv has $7$ moons which lie spread out on one plane in a great disc round it. These Vuvvian moons all have long and confusing names so scientists usually call them by their initials: $A, B, C, D, E, F$ and $G$ starting from the nearest one to the planet.
When two of these moons line up with the planet it is called a 'lunar eclipse'. When three line up with the planet it is called a 'double eclipse', when four do it is a 'triple eclipse' and so on. Once in a while all seven moons line up with the planet and this is called a 'super-eclipse'.
Moon $A$ completes a cycle round the planet in one Vuvvian year, moon $B$ takes two years, moon $C$ takes three years, moon $D$ takes four years and so on.
How long is it between each 'super-eclipse' on the planet of Vuvv?
Getting Started
You could look at just two moons and work out how many years it takes for them to coincide.
Which moons might it be good to look at first?
It might help to use a calculator and to jot your ideas on paper.
Student Solutions
"I enjoy your website", wrote Becky , from Carleton St Hilda's C. of E. Primary School. Becky explained how she began her solution search:
Now, I wonder what Becky changed her search to? If Becky is going to change her search to try and arrive at an answer perhaps she wants to think about this idea.
Alex and her family from Leicester, England worked on this Vuvvian problem. Alex explains how they set about arriving at a solution:
- We started off by doing the seven times table, because that was how long the last moon took to go round Vuvv.
- Next, we checked if the multiples of seven were also in the 2x, 3x, 4x, 5x, 6x tables. This was so we'd know if they (Vuvv moons) would line up.
- We got fed up working out the multiples of seven, because they got way too big. So, we used a calculator! We pressed +7=== to get the multiples of seven.
- We found out that it would take 210 Vuvvian years between each super eclipse.
However, I'm not sure that 210 is a multiple of all of the numbers 2, 3, 4, 5, 6 and 7, is it?
Anita and Jing Jing from Kilvington Girls' Grammar in Australia, think that's only the half of it...in fact, they think that it is 420 year wait between Super-eclipses.
Franco and Jonny from Northamptonshire agree that is it 420. They say:
We started off with 42. Every number goes into 42, except 5, so we multiplied it by 5.
6 doesn't go into 210, so we went back to 42. We then multiplied 42 by 10, to get 420. We checked by dividing 420 by 1, 2, 3, 4, 5, 6 and 7. They are all factors of 420. So the overall answer is 420.
Teachers' Resources
The Moons of Vuvv
The planet of Vuvv has $7$ moons which lie spread out on one plane in a great disc round it. These Vuvvian moons all have long and confusing names so scientists usually call them by their initials: $A, B, C, D, E, F$ and $G$ starting from the nearest one to the planet.
When two of these moons line up with the planet it is called a 'lunar eclipse'. When three line up with the planet it is called a 'double eclipse', when four do it is a 'triple eclipse' and so on. Once in a while all seven moons line up with the planet and this is called a 'super-eclipse'.
Moon $A$ completes a cycle round the planet in one Vuvvian year, moon $B$ takes two years, moon $C$ takes three years, moon $D$ takes four years and so on.
How long is it between each 'super-eclipse' on the planet of Vuvv?
Why do this problem?
This problem offers opportunities for pupils to reinforce their understanding of factors and multiples, and, in a simple example, see an illustration of 'lowest common multiple'. It would fit in well when revising multiplication tables or working on multiples and factors.
Possible approach
Key questions
Do these two moons coincide sooner than that?
Possible extension
Tell the children that more moons have been discovered circling Vuvv. Get them to work out the length of time between the super-eclipses if there are also moons that cycle taking $8, 9, 10 \ldots$ years.
Possible support
Suggest starting with just three or four moons and slowly adding the higher numbers.