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How Steep Is the Slope?

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
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How Steep is the Slope? printable sheet
How Steep is the Slope? printable grid

 

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 $-\frac{2}{3}$

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.

 

Related Collections

  • Functions and Graphs - Stage 3

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How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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