This exploratory problem is a fantastic way to consolidate children's understanding of halving and halves. Pupils will have many ideas of their own when it comes to checking or proving that the squares really are split in half. Some will count squares if drawn on squared paper. Others may want to cut out the squares and physically lay the halves on top of each other. Alternatively, it might be possible in some instances to cut out the square and fold it to show that it has been split in half. You might like to distinguish between the squares that have been divided into two pieces (one red, one white) from those where there are more than two pieces. You could use the PowerPoint presentation which is linked to from this site: http://www.icteachers.co.uk/resources/resources_numeracy.htm in the Number section under "fractions". It shows squares being divided in different ways (although not always in half) and would provoke a nice introductory discussion to this problem.