Mental Mondays #17

mental and oral maths

I always loved the idea of using the Magic Square concept with children since it offers so many opportunities to get to grips with problem solving. However, it always seemed to me that Magic Squares on their own lacked a sense of purpose; if they were set into a historical context, then that seemed fine - but purely as maths puzzles, they only ever seemed to interest a small number of children.

Magic Square Grid

This Mental and Oral idea give Magic Squares a new lease of life by making the activity a 'team event'. Basically, the children have a blank 3 by 3 grid (the Magic Square grid) and a set of six clue cards. They must work as a team to complete the Magic Square according to the usual rule: all rows, columns and diagonals sum to the same value.

As they are working on the problem they need to share the clue cards with each other and determine the best possible value of each cell in the grid. There will be a degree of trial and error involved, as well as a good deal of explanatory talk. All perfect ways to boost mental and oral mathematical strategies.


Here's an example.

The children look at the six clue cards and decide that these two seem most useful:

magic square maths activity

The first clue here clearly gives the parameters for the Magic Square - now all other numbers can be safely ignored.

The second clue tells the children that the number in cell C3 is a multiple of 4, and (when used in conjunction with the first one) , that A1 must be either a 1 or a 2

Searching through the six clues, the children find:

Magic Square teaching maths

From the first clue here, we now know that A1 must be a 2, consequently C3 must be an 8. So that's two cells in the grid completed.

... and from the following clue...

maths activity - magic square

It is a simple task to identify that the central number (B2) must be a 5. The remaining clues help tie the missing numbers into place and the children will find that, if they approach the problem methodically all of the cell numbers can be identified.

The activity enables children to discuss and share problem solving strategies and mathematical facts and ideas. It can be used as a starter activity with the children sharing ideas with the whole class, or as a small-group task in its own right.

The downloadable file includes three Magic Square Clue problems, together with a 3 by 3 grid and a set of number tiles for each problem.

Magic Square maths

As always, we would love to hear what you think of this in the comments and would appreciate your likes, tweets and Pluses if you enjoy it! .


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kerys's picture

Excellent resource.  I am

Excellent resource.  I am trying to prepare for my first term at a new school and I've not seen the curriculum or met the kids yet, so open ended, engaging activities like this are perfect. 
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tizgale's picture

A super way to help qith

A super way to help qith mathematical thinking.  Thank you
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Steve Jubb's picture

Hi Tizgale I hope you will

Hi Tizgale I hope you will not be offended, but I think you have invented a useful new word: Qith. Qith means to calculate mentally, quickly. Regards Steve Jubb
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mjackson174's picture

Very good resource. Really

Very good resource. Really looking forward to using this with my class.
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mjackson174's picture

Fantastic. Thank you. This

Fantastic. Thank you. This will really stretch my MA!
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daisycat's picture

An interesting way to make

An interesting way to make magic square problems more interesting for pupils -I am looking forward to trying them with my class.
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jenblum30's picture

Awesome site! One discovery

Awesome site! One discovery after another!!!
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johdu's picture

I'm glad you like our maths

I'm glad you like our maths resources - sounds like you are having fun looking around. Thanks for the good feedback.
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Pennfold's picture

A lovely way to support and

A lovely way to support and extend the children's mathematical thinking.
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The Chief's picture

 Good bit of fun, the kids

 Good bit of fun, the kids enjoyed it.  I found it worked really well with my MA because they'd not stretched their brains that way before.  Half of my LA gave the usual "too hard" noises and promptly started colouring in whiteboards though. 
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