Have a play around with this task, and please share any questions, extensions, simplifications, modifications, or lines of inquiry in the comment box below. The idea is to collect loads of suggestions that can then be used for effective differentiation. The full set of these tasks, along with additional notes, can be found here: http://www.mrbartonmaths.com/richtasks.htm
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Investigate how the number of squares the line passes through changes as the dimensions of the rectangles change<br /> <br /> Prompts for support:<br /> <br /> • Work in a group, and decide who is going to draw which rectangles<br /> • Try keeping the width of the rectangle fixed and changing the height. Can you spot any patterns?<br /> • Keep the difference between the width and the height the same. Can you spot any patterns?<br /> • What happens with squares?<br /> • What happens when the height is double the width?<br /> • What about when it is triple the width?<br /> <br /> Prompts for Extension<br /> <br /> • What happens to the number of squares when the height and width share a common factor?<br /> • Circle sets of dimensions that do not seem to fit the pattern. Do these dimensions have anything in common?<br /> • Look at the intersections of the squares in the diagrams you have drawn. What has this got to do with common factors?<br /> • Can you come up with a rule that will allow you to say how many squares the line will pass through for any set of dimensions?<br /> • Can you explain why this rule works?<br /> • Now investigate the world of 3D, with diagonals through cubes and cuboids!<br />
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