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Magic Squares.
Over this publication's history it has dealt with Magic Squares from virtually
every angle possible so I don't expect to reveal any deep, dark secrets here.
The worksheet Make a Magic Square derives from a mention in the Year 7
Framework and deserves a two page spread from the diversification of the
mathematics it derives. It is one of those worksheets that after writing I
couldn't wait to get into a classroom to teach. It was then used with Years 7,
8 and 9! The mathematics involved brings in substitution; addition/subtraction
involving whole numbers, negative numbers and decimals; innate forming and
solving equations; problem solving and inequalities. By the end of the
worksheet pupils have a good knowledge of the workings of a Magic Square. Using
a phrase from previous editions of MiS the sheet differentiates by fallout. The
more able complete the sheet, whilst some may only partially complete the
sheet.
The first page is purely a substitution exercise, building on previous
knowledge of negative and decimal numbers. For Questions 16 - 21 I get the
class to solve them mentally first, but then to return and write down the
equation they formed in solving the problem. Encouraging them to find more than
just one equation for solving the same letter makes them think about all the
terms used, rather than returning to the same term for each question. This is
an important algebraic step and fairly easy in this context. Finding a is
obvious, and thus the other equations stem from this.
The rest of the questions concern the make up of a magic square. How can we set
up an inequality to create only positive numbers? (Does this work for negative
numbers?). Why is the Magic Number 3a? There's plenty of scope to extend the
sheet into more complex areas!
Ian Fisher
This article is about 10ticks worksheets Level 5 Pack 5 Page 20 and Level 5
Pack 5 Page 21.
Maths in Schools. March 2002. Vol 31 No 2.
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