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Number Magic
Magic is fascinating. Mystifying pupils with a dazzling piece of mental
conjuring is an excellent way to start a lesson. Typically 'Think of a number,
double it, add 18, halve it and take away 9'. The stunned (stupefied) audience
ends up with the number they first thought of.
How is it done? Can we do it? How does it work?
The worksheet guides the pupil to understand the mechanics of this style of
puzzle. The novelty of the puzzle spurs pupils through several important and
basic algebraic skills. Firstly putting sentences into basic algebraic
expressions and then leading to the concept of brackets.
Forming the expressions is relatively straight forward, but what about doubling
an expression? n doubles to 2n, but how do you double 3n+1 ? Looking at it
diagrammatically
Double 3n+ 1 is n n n 1 and then repeated
n n n 1
hence giving 6n + 2. It is easily
seen that
we double both parts of the expression. Later, after the sheet has been
completed, it can be formalised into 2(3n + 1). We know the answer - so how do
brackets work?
Similarly, halving can be viewed in the same way.
Halve 4n + 10 is n n n n 10
hence giving 2n + 5.
Again this can be formalised into ½(4n + 10) or
4n + 10
2
Pupils can now practise their new found 'magical' skills on unsuspecting
parents.
Ian Fisher
This article is about 10ticks worksheets Level 6 Pack 1 Page 15 and Level 6
Pack 1 Page 16.
Maths in Schools. March 2005. Vol 34 No 2.
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