Proportion means that things happen at the same rate.

If the number of hours sleep you get is directly proportional to how happy you are in the morning, then we can deduce that if you have 8 hours kip you'll be quite jolly in the morning and if you have 4 hours kip then you'll be seriously grumpy.

There is a special symbol which means proportional to:

If x y, this means that as x increases y increases also in the same proportion.

The opposite of being proportional to is being inversely proportional to:

If x is inversely proportional to y this is represented as x 1/y.

If x is inversely proportional to y, this means that as x increases then y decreases in the same proportion.

You could say that the reliabilty of your mountain bike is inversely proportional to the amount of thrashing it gets whilst off-roading.

If you know (from experiment) that two things are proportional then you can create a formula to represent this relation:

e.g. You discover that Sunflower growth is directly proportional to the number of hours sunlight per day the Sunflower receives. If we let Growth per day (in mm) = G and let the time (in hours) = t , we can produce the statement:

G t

We can actually convert this statement into an equation which can be used to make estimates of Sunflower growth by inserting a constant (we'll call this k). We can insert a constant because growth and time are directly proportional.

So, we can now say that G = kt

If we find out that when time = 4 hours, growth = 3mm.