Write down two consecutive numbers.
Square each of them and find the difference.
Do the same for other pairs of consecutive numbers.
What do you notice?
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Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=October10
Here is the URL which will take them to another activity involving square numbers.
See the National Curriculum page for links to related online activities and resources.