Blob: area and accuracy investigation
You can download a Word file containing an investigation based on finding the area of an irregular shape by two methods.
The investigation assumes students can find the area of a trapezium. They will find the area of the blob by counting squares and by adding up the areas of trapezoidal slices of the shape.
You can download a Word file containing the task.
- The squares method hinges on the choice of square size and I have usually asked students to work with different sizes (some 1cm, some 0.5cm and some 0.2 cm but with 'clever' counting by using rectangles).
- Students are asked to try to predict the accuracy of the squares (will it be to the nearest square - what about the rule for counting a square more than half inside as a whole one? What balances out that rule?)
- This investigation follows area work based on triangles, rectangles, trapeziums and some compound shapes in previous weeks.
- Differentiation: There is scope for quite a sophisticated response to the topic ('I found that using a square size of 0.5 cm gave a similar accuracy to using a trapezium of 2 cm thickness') but less confident students can complete the task and feel they have done a good few hours of work.
- Very few students suss the advantage of using the 2cm spacing for the parallel lines of the trapezium without prompting!
- One day, I really must book the precision balances in the Chemistry lab and weigh a cut out of the shape and then weigh an A4 sheet and find the area that way. My own middle school chemistry teacher had us weighing our signatures on filter paper so the accuracy will probably be high. A piece of A4 photocopying paper weighs about 5g (80g/sq m and 16 A4 sheets in a square metre) and scales resolve to three decimal places.
- How about scanning the shape into a computer at 300 dots per inch and finding a way of counting the coloured pixels inside the contour of the shape?
- Challenge students to devise shapes with exagerated curves so the rounding of the squares up or down no longer balances. Perhaps they can find curves that favour the squares method over the trapeziums.
Originally added on Wednesday, April 9, 03
in category: lesson ideas
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