'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. ____________________________________________________ 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?