
Tools  Math 'Creating Measures' Steepness Task, Example #2
Squareness, Example #1 (solution)  Steepness, Example #2 (solution)
Compactness, Example #3 (solution)  Crowdedness, Example #4 (solution)
Awkwardness, Example #5 (solution)  Sharpness, Example #6 (solution)
Malcolm Swan
Mathematics Education
University of Nottingham
Malcolm.Swan@nottingham.ac.uk
Jim Ridgway
School of Education
University of Durham
Jim.Ridgway@durham.ac.uk
This problem gives you the chance to:
 criticise a given measure for the concept of "steepness"
 invent your own ways of measuring this concept
 examine the advantages and disadvantages of different methods.

Warmup
Without measuring anything, put the above staircases in order of "steepness."
 Someone has suggested that a good measure of "steepness" is to calculate the difference:
Height of step  length of step
for each staircase. Use this definition to put the staircases in order of "steepness."
Show all your work.
 Using your results, give reasons why Height of step  length of step is not a suitable measure for "steepness."
 Invent a better way of measuring "steepness." Describe your method carefully below:
 Place the staircases in order of "steepness" using your method. Show all your work.
 Do you think your measure is a good way of measuring "steepness?" Explain your reasoning carefully.
 Describe a different way of measuring "steepness."
Compare the two methods you invented. Which is best? Why?
Squareness, Example #1 (solution)  Steepness, Example #2 (solution)
Compactness, Example #3 (solution)  Crowdedness, Example #4 (solution)
Awkwardness, Example #5 (solution)  Sharpness, Example #6 (solution)
