FLAG - Tools: Math 'Creating Measures' Square-ness Task, Example #1

Math 'Creating Measures' Square-ness Task, Example #1

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 "square-ness" invent your own ways of measuring this concept examine the advantages and disadvantages of different methods. Warm-up

Use visual judgements to answer the warm-up questions.
Which rectangle looks the most square?
Which rectangle looks least square?

Without measuring anything, put the rectangles in order of "square-ness."

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

Longest side - shortest side

for each rectangle. Use this definition to put the rectangles in order of "square-ness." Show all your work.

2. Using your results, give one good reason why Longest side - shortest side is not a suitable measure for "square-ness."

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

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

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

6. Find a different way of measuring "square-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) 