Sunday, March 11, 2007

Counting Blessings

“What mathematics books should we use? My son is writing his eleven plus examinations later this year. I know how to work the examples out but my son does not always understand my methods. Please help.”

Oh dear! We all have that problem. Some times it could be that your son does not understand the method you have used. On other occasions he simply does not understand how to approach the question. He may not have been taught the basics of the question. This is not a failure by the school – it is simply that the requirements of the eleven plus examinations are sometimes different to those of the school. The school may simply want to introduce the topic you are trying to cope with at a different time.

Let us take the scenario of a girl living in London and she is trying to win a place at a Grammar School. She and her mother decide to try the route out before pinning their hopes on entry to the new school.

She will need to walk 2 km to a bus stop and then travel by bus to the nearest train station. She will then go by train three times as far as she has already travelled. The total journey is 24km. How long is the bus journey?

Mum: “What are we trying to find?”

Girl: “The length of the bus journey.”

Mum: “Which unit will we need to use?”

Girl: “Oh Mum. It tells you in the question. We need to find the bus journey in kilometres.”

Mum: “How far is the total journey?”

Girl: “Well Mum, the total journey is 24 kilometres. We walk 2 kilometres and then go by bus and then train.”

Mum: “What can we call the length of the bus ride?”

Girl: “We call it “x”. Why do we always call numbers x?”

Mum: “So if you have already walked 2 km you will have travelled 2x km. The bus journey is three times as long as this so you will have travelled 3(x + 2).

The whole journey is then: x + 2 + 3(x+2) and this is equal to 24 km.

x + 2 + 3(x + 2) = 24 km
x + 2 + 3x + 6 = 24 (Brackets first.)
4x + 8 = 24
4x = 16
x = 4

So the bus journey is 4 km."

If this all seems a little far fetched with a girl having to walk, catch a bus and then a train before she reached the school of her choice – we actually discussed a very similar situation with a mother last week.

The lengths some parents will need to go to in order to try to help their children reach the school of their choice always astounds me. We checked the route on one of the journey planners. We are simply in awe of the determination of the mother and the ambition of her daughter.

So to return to the question, “What mathematics books do we need?” You are going to need far more than selection papers. Look at KS2 and KS3 study aid books. They will present the examples logically and clearly. Read through the examples together.

Occasionally think of the mother and daughter we mentioned earlier and be grateful for what you have.