Last week I saw a tweet from @Maths_Master (Will Emeny) linking to an 'apeeling' lesson on his 'greatmathsteachingideas' website. As soon as I saw it I was waiting for a reason to do this lesson with my Y10 class - I loved the idea!
It can be seen here... http://www.greatmathsteachingideas.com/2012/11/28/surface-area-of-spheres-an-apeeling-lesson/
Luckily, on Thursday, it was Pi Day. Naturally I started my lesson on Thursday by showing my class my Pi Day '4 pics 1 word' resource I had created especially for that day. My resource can be downloaded from the TES here. This lead to a discussion as to what Pi was and then gave me a natural link into looking at finding the area and circumference of circles and then looking at areas of sectors and lengths of arcs. Near to the end of the lesson I had given some of the students who were ready to move on some volume of cylinder questions to attempt. Having looked over the METHODS of Mathematics SoW for the Unit 2 topics I remembered that the volumes of cones, cylinders and spheres were near to the end of this and would be needed to be taught too. So, rather than waiting til the end of the SoW to cover this I decided to do this in our next lesson, building on our work involving Pi.
The start of our next lesson began with the class working out the volume of cylinders picking up from where we left off. I had a picture up at the start of the lesson too, to hint at what we would be doing for the bulk of the lesson, here was the pic I used (you've probably seen this before, I was reminded of it at our INSET session last Fri, which was delivered by @vicgoddard!)
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Here's where @Maths_Master's brilliant lesson idea came into play. I went through the answers to the volume of cylinder questions and then referred the class to the formula sheets in their mock papers they had just completed. I highlighted on here the volume of a prism and then the formulae for the volume of a sphere and cone (I purposely, at this point, left out the curved surface area formulae out). I gave the class 3 questions of each to apply the formulae too and then checked, as they worked they were able to use their calculators correctly. After the answers were displayed and learning checked I got out the oranges I had rushed to Tesco to get the previous evening!
I then explained to the class what I wanted them to do in their pairs - and followed the details as per @Maths_Master's idea linked above. The class then, in pairs (after I had read the riot in terms of ensuring I wasn't going to find orange peel in all crevices in my room later that day) starting to draw around their orange and then peel their orange and sculpt the pieces into the circles they had created. This then proved the curved surface area of the sphere being 4 x Pi x r x r. Here's some of the class' work as they were doing it...
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Students started by filling, as completely as they could, one of the drawn circles with the orange peel
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They then continued to fill in as many of the other circles that they could. They drew as many circles as they could on their pieces of paper.
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Eventually, students found that the orange peel fitted 4 of their circles. So 4 x the area of one of the circles = 4 x Pi x r x r. This works as the radius of the circles is (practically) the same as the radius of the sphere (orange).
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One of my students managed to peel the orange in one go - this I found rather impressive!
The class then worked out the curved surface area of the spheres they were asked to work out the volumes for earlier in the lesson - this formed the plenary for our lesson.
Note to self...make sure you remember some kitchen towel next time to clear up the small amount of juice that will end up on the tables, oh...and for those kids that will complain that their hands are 'sticky'.
It can be seen here... http://www.greatmathsteachingideas.com/2012/11/28/surface-area-of-spheres-an-apeeling-lesson/
Luckily, on Thursday, it was Pi Day. Naturally I started my lesson on Thursday by showing my class my Pi Day '4 pics 1 word' resource I had created especially for that day. My resource can be downloaded from the TES here. This lead to a discussion as to what Pi was and then gave me a natural link into looking at finding the area and circumference of circles and then looking at areas of sectors and lengths of arcs. Near to the end of the lesson I had given some of the students who were ready to move on some volume of cylinder questions to attempt. Having looked over the METHODS of Mathematics SoW for the Unit 2 topics I remembered that the volumes of cones, cylinders and spheres were near to the end of this and would be needed to be taught too. So, rather than waiting til the end of the SoW to cover this I decided to do this in our next lesson, building on our work involving Pi.
The start of our next lesson began with the class working out the volume of cylinders picking up from where we left off. I had a picture up at the start of the lesson too, to hint at what we would be doing for the bulk of the lesson, here was the pic I used (you've probably seen this before, I was reminded of it at our INSET session last Fri, which was delivered by @vicgoddard!)
Here's where @Maths_Master's brilliant lesson idea came into play. I went through the answers to the volume of cylinder questions and then referred the class to the formula sheets in their mock papers they had just completed. I highlighted on here the volume of a prism and then the formulae for the volume of a sphere and cone (I purposely, at this point, left out the curved surface area formulae out). I gave the class 3 questions of each to apply the formulae too and then checked, as they worked they were able to use their calculators correctly. After the answers were displayed and learning checked I got out the oranges I had rushed to Tesco to get the previous evening!
I then explained to the class what I wanted them to do in their pairs - and followed the details as per @Maths_Master's idea linked above. The class then, in pairs (after I had read the riot in terms of ensuring I wasn't going to find orange peel in all crevices in my room later that day) starting to draw around their orange and then peel their orange and sculpt the pieces into the circles they had created. This then proved the curved surface area of the sphere being 4 x Pi x r x r. Here's some of the class' work as they were doing it...
They then continued to fill in as many of the other circles that they could. They drew as many circles as they could on their pieces of paper.
The class then worked out the curved surface area of the spheres they were asked to work out the volumes for earlier in the lesson - this formed the plenary for our lesson.
Note to self...make sure you remember some kitchen towel next time to clear up the small amount of juice that will end up on the tables, oh...and for those kids that will complain that their hands are 'sticky'.