Area and Volume – Cuboid and Cylinder

16 10 2011

I was tasked by another course leader to do area, shape and size and in particular in relation to circles to assist with her Delphi unit whereby learners were struggling to understand and visualise Pi and its associated formulas.

I realised that I needed an interactive lesson and first of all did the following exercise as an intro into the lesson, one to check prior knowledge and two to see how alert learners were as a first morning lesson. As part of this activity I had a box of a similar shape to the task so learners could actually visualise the position of the boxes inside a box, (as I find with area and volume learners struggle to visualise in their head or on paper).

I briefly covered with the group formula’s for circumference, area and volume and the use of Pi and BIDMAS.

I then wanted to gain interactivity in the lesson and still stay with the visualise theme and asked learners (in groups) to discuss and decided the answer to the following just using their current knowledge and no calculations.

Question: does a sheet of A4 paper have a bigger volume when rolled on its longest length or shortest length, or does it have the same volume. 

It was really good to see some learners arriving at the correct decision (by stating that the one with the biggest circumference will have the biggest volume) but the majority of learners where choosing the wrong answer or remained unsure.

I then used a box of Frosties (this could be rice or pasta, however my IT boys loved the Frosties, so much half the box went missing during the lesson) and asked learners to put the longer tube inside the shorter tube and fill up the longer tube. They then had to life up the longer tube to see if the contents filled or more then filled the shorter tube. It did not and resulted in the shorter tube having the larger volume. I then asked groups why and asked them to back up why, of which then used V = Pi x (rxr) x h. I really enjoyed this lesson and so did the learners. I am definitely going to do this again later in the year for my other groups (but I am going to use uncooked pasta as I do not think they will eat that ensuring that the pasta lasts for all my classes). I just wish I took some photos – learners actively engaged and motivated in a maths lesson.

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2 responses

18 10 2011
stephenhooley

How did you handle their Frosties sugar rush?

19 10 2011
juleskilburn

Good point, well I think the teacher following my lesson took that hit.

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