NRICH: How Steep Is the Slope?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

The gradient of a line tells us how far up or down we go when we take one step to the right:

Gradients
On a grid like the one below we can draw lines through two points with different gradients.
Check you agree that the blue line is one of several that could be drawn with a gradient of 2 and the red line is one of several that could be drawn with a gradient of 23

5 by 5 grid

Picture some more lines with different gradients. You may want to use this sheet to record your working.

How many different gradients can you find? Can you find them all?

Arrange them in order of steepness and list the points each line passes through.

Age 11 to 14


Algebra & Pre-Algebra, Functions & Graphs
Middle School, High School, Educator

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