Rich Maths Task 20 - Diagonals of Rectangles

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 />