'Creating Measures' Steep-ness Task - Example #2
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.
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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?