magic squares

these task sheets (and solutions) can be clicked to produce and savelarger 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

Tuesday, 10 May 2011

finding patterns - swaps

create a magic square using the first nine odd numbers: 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15  and 17

then create a magic square using the first nine even numbers ( 2 up to 18 inclusive)

how is this easy after making one with the odd numbers?


magic square using the first nine odd numbers

















using the first nine even numbers

what happens when you half these?
in these magic squares, 2 of the numbers have been swapped over

without bothering about the middle number, students try to 'unswap' these magic squares




then they look at their squares, sort out what the central number will be and find patterns (there are many)

then they can try to create a different magic square (not a refection or rotation of these) with 10 in the middle:



they can do this by adjusting from the middle number moving outwards along both of the diagonals

what happens if a = 2b?

how can you avoid involving negative numbers?

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