Can you work out how many squares can be found in this diagram? Can you be sure you haven't missed any? Can you be sure you haven't counted any twice?
Show Some CluesTopics: Starter  Puzzles  Shape
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Previous Day  This starter is for 27 December  Next Day
There is a printable worksheet to go with this activity.
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The important thing is not the answer but the method you used to arrive at the answer. Did you have a structured approach? Were you sure that you had the right answer? Can you make up a puzzle like this for others to solve?
How many squares are there on a chess board?
A more difficult extension challenge would be to work out how many rectangles are on a chess board. The use of a spreadsheet might be useful when working on this problem.
Other shape counting starters:
How Many Squares 1?
 How Many Squares 2?
How Many Triangles 1?

How Many Triangles 2?  How Many Triangles 3?
How Many Rectangles?
 Rectangles Investigation 
Icosahedron 
Mystic Rose
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Educational Technology on Amazon
Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=December27 However it would be better to assign one of the student interactive activities below. 

Here is the URL which will take them to another systematic listing activity.
Transum Shop :: Laptops aid Learning :: School Books :: Tablets :: Educational Toys :: STEM Books