Venns and the Eleven Plus

At one Venn Diagrams were held to be `New Maths’ and the diagrams were embraced by teachers in Junior and Secondary schools. Times change, new brooms and ideas come in, and old mathematical concepts are thrown out. One of the problems with solving Venn diagrams is that there is an element of problem solving – and all concerned have to think!

A set of objects can have the property of two. There can be one fish in one pond and a second fish in the other pond. It only becomes complicated when we add the third fish. Does Fish Three warrant another pool or can that dear little fishy swim in number of pools? A Venn Diagram can help.

Here is an example:

A group of ten eleven plus students are preparing for the examinations. Six are studying mathematics, five study verbal reasoning and seven non-verbal reasoning. Three study maths and verbal reasoning while two work on verbal reasoning and non-verbal reasoning. Four out of the ten study non-verbal reasoning and mathematics.

Every eleven plus child is working on at least one of the subjects. How many students are preparing for the eleven plus by working through all three disciplines?

This type of question seems to be coming back into fashion. Some eleven plus examinations now have numerical reasoning questions. Venn diagrams can creep into this mixture. How do people solve a problem of this nature?

Some will build a table. The combinations will be recorded.

Others will perform some sort of algebra – along these lines: (x – 1) + (3 – x) + x + (4 – x) + x + (2 – x) + (x + 1) = 10. As x + 9 = 10, so x = 1.

A few may even hold the combinations in their heads and come up with the right answer in a remarkably short time. These are probably the mathematical thinkers who realise that the three children studying maths and verbal reasoning are included in all three subjects.

(So the answer is still 1!)