Aiming to illustrate simple ingenuity in mathematics. |
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In the supplement of examples of the Key Stage 3 National Strategy Framework for teaching mathematics: Years 7, 8 and 9, (DfEE, 2001) on page 123; under Algebra: Equations, formulae and identities; we have, "As outcomes, Year 8 pupils should, for example:. consolidate forming and solving linear equations with an unknown on one side" There is the following example.
| In an arithmagon, the number in a square is the sum of the numbers in the two circles on either side of it. |
| In this triangular arithmagon, what could the numbers A, B and C be? |
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| Let x stand for the number in the top circle. Form expressions for the numbers in the other circles, (20-x) and (18-x). Then form an equation in x and solve it. |
(20 - x) + (18 - x) = 28
38 - 2x = 28
2x = 10
x = 5
So A = 5, B = 15, C = 13. |
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One pupil presented with this problem without an explanation of how to solve it noticed that the difference between 20 and 18 is 2 so, since A is common to both sides, the difference between B and C must also be 2. For that pupil, the new problem was to find two numbers with a sum of 28 and a difference of 2 with C<B. B and C and then finally A were each evaluated mentally. |
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