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Magic Squares

You will need to be able to:

  • perform the basic spreadsheet skills

Language used:

toolbar standard toolbar
functions sigma.
sigma sum
summation  

Spreadsheet Skills

  • Enter the numbers 1 to 9 in any order into the cell range A2:C4. This region is shown shaded in the diagram below.
  • Select A5, then write the formula = A2+A3+A4
    which will add together the contents of cells A2, A3 and A4.
  • Move to cell D2 and add the contents of A2, B2 and C2.

 

A

B

C

D

1

 

      

2

        

3

        

4

        

5

        

The standard toolbar, as shown at the bottom of this page, allows you to use the mouse to directly select some useful functions.

  • Select cell B5, then press the S button on the standard toolbar. A formula appears

    = SUM(B2:B4)

  • The cells B2, B3 and B4 are highlighted with a moving dashed line.

  1. What happens when you press return?

  2. What does this do?

  3. What is the name of the symbol sigma. ?

  • Select C5 then write the formula

    =SUM(C2:C4)
    taking careful note of what happens when you type in the second bracket.

  • Press return.

This is a different way of entering the same summation formula.

  1. What happened when you typed in the second bracket?

  • Select D4 then type =SUM(
  • Select A4 then drag across to C
  • Press return.

  1. What happens?

You will need to type in the final bracket and press return.

Introductory Investigation

  1. What happens if you interchange one or more of the numbers in the cells A2:C4?

  2. What happens if you change the numbers to the arrangement shown below?

6

7

2

1

5

9

8

3

4

  • Enter a formula into D5 to find the sum of cells A2, B3 and C4.
  • Enter a formula to do the same along the other diagonal.

  1. What do you notice?

This is known as a magic square.

Further Investigation

Try to construct a 5 x 5 magic square using the numbers 1 to 25. The rows, columns and diagonals should add to 65. Make a copy of your completed square.

Try to construct a 4 x 4 magic square with rows, columns and diagonals summing to 34.

You should now know how to:

  • calculate sums using at least two different methods
  • recognise the standard toolbar and use the sigma. function button.
  • construct and define a magic square.

Spreadsheet Summary

  • Write a sentence on methods to calculate sums using a spreadsheet. Include the use of the sigma.  function button on the standard toolbar.
  • In your own words define what a magic square is.