Tools - Math 'Creating Measures' Steep-ness Task, Example #2

Square-ness, Example #1 (solution) || Steep-ness, Example #2 (solution)
Compact-ness, Example #3 (solution) || Crowded-ness, Example #4 (solution)
Awkward-ness, Example #5 (solution) || Sharp-ness, 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 "steep-ness" invent your own ways of measuring this concept examine the advantages and disadvantages of different methods.

Warm-up

Without measuring anything, put the above staircases in order of "steep-ness."

1. Someone has suggested that a good measure of "steep-ness" is to calculate the difference:

Height of step - length of step

for each staircase. Use this definition to put the staircases in order of "steep-ness." Show all your work.

2. Using your results, give reasons why Height of step - length of step is not a suitable measure for "steep-ness."

3. Invent a better way of measuring "steep-ness." Describe your method carefully below:

4. Place the staircases in order of "steep-ness" using your method. Show all your work.

5. Do you think your measure is a good way of measuring "steep-ness?" Explain your reasoning carefully.

6. Describe a different way of measuring "steep-ness."
Compare the two methods you invented. Which is best? Why?

Square-ness, Example #1 (solution) || Steep-ness, Example #2 (solution)
Compact-ness, Example #3 (solution) || Crowded-ness, Example #4 (solution)
Awkward-ness, Example #5 (solution) || Sharp-ness, Example #6 (solution)

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