magic squares

these task sheets (and solutions) can be clicked to produce and save larger images
easier tasks are in the older posts and become more demanding towards more recent posts
hopefully the resources illustrate that 'magic' squares provide a context for a variety of skill practice - with:
- some form of problem solving requested;
- considerations about relationships, justification and proof;
- extending work to an involvement of symbols;
- developing to quite complex uses of algebra.

I am indebted to Martin Hansen, whose articles in Maths in School (march 2010, sept 2010 and and nov 2010) provided much clarity on a possible teaching sequence and an understanding of relationships and solution techniques

Sunday, 3 July 2011

harder magic squares

this work explores how squares can be produced from just 3 given numbers, that are not in a line

note that no other relationships are to be used in developing this work (e.g. the line total being 3 x middle number and the leading diagonal going up in a linear sequence are not to be used)






 students might need help in appreciating that when a column and a diagonal line have a common 'intersection' then the other pairs of numbers must have the same total




once a line of 3 has been found the square is usually easy to complete

find two reasons why the bottom right number must be 4 then complete the remainder...





























students could go on to explore what happens when 3 (different) numbers are placed anywhere on the grid (but not in a line)...
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