Friday Hotspot: Teaching the Surface Area of a Cylinder

Every Friday, the maths department at Sidney Stringer have a "briefing" with a focus on teaching and learning. We try to run it so that each week a different maths teacher shares a resource or lesson idea.

Last week one of my colleagues shared with us his way of getting students to discover and remember the surface area of a cylinder.

Each student would be given one of these open cylinders. Of course, you could provide students with matching lids too.

Around the top of the cylinder it says "circumference". By wrapping the text around like this, I think it makes it obvious that the length all the way around the cylinder is the circumference of the top circle.

In the middle it says height. Some arrows would be good here to show exactly which measurement we mean.

You would discuss with the students ways of working out the area of the curved surface. Hopefully a student will have the idea of unfolding it to make a net. At this point the scissors would come out.

 

Annoyingly Steve (head of department) chose to cut this one down the middle, breaking up the words. I would have cut it just before the "c". But I'm that kind of person.

Students will recognise this shape as a rectangle. They can see that the width is the height of the cylinder, and the length is the same as the circumference. They can then change this into a formula involving pi, r, and h.

I think the best thing about this is the student can stick it in their book, or better: slip it into a pouch at the back of their book, so whenever they need it, they can get it out, fold it and unfold it, and remind themselves of where the formula comes from. Far better than referring to a formula in a neat little box somewhere in their notes.

Each week I will be sharing our Friday hotspot with you on this blog. I will probably share this on a Monday rather than a Friday, which I hope doesn't really annoy you! It's the kind of thing that would bug me. But again, I'm that kind of person.

This post was written by Emma Cooke, Sidney Stringer Academy, Coventry

Moral Aspects of Maths

Leading on from my last post about SMSC, I have produced another useful document all about moral aspects of mathematics.

This document can also be downloaded from the TES website: Moral Aspects of Maths.

This post was written by Emma Cooke, Sidney Stringer Academy, Coventry

Awe and Wonder in Maths Lessons

OfSTED are really hot on SMSC these days. That's Spiritual, Moral, Social and Cultural aspects of learning.

 

The spiritual side of things is covered in maths, as far as I'm concerned, because there are so many things in maths that just make you go: woah!

 

This can be nicely summed up as "awe and wonder". Think golden ratio. Think zero divided by zero. Seriously: woah!

 

I created a document along with a colleague all about that kind of thing for my department. I enjoyed writing it, and some people have told me they enjoyed reading it (and they didn't even look like they were lying) so I decided to make the document publicly viewable. I hope other maths departments across the country find it useful for injecting a bit of "woah" into their maths lessons.

 

So I have uploaded it to the TES resources website. Here it is: awe and wonder.

 

This post was written by Emma Cooke, Sidney Stringer Academy, Coventry

Further Maths Level 2 (GCSE) Resources

At Sidney Stringer Academy, our students take their maths GCSE at the end of year 10. Those who don't get a C can spend year 11 working towards it. Those who do get above a C will do either Statistics GCSE or, for our most talented mathematicians, Further Maths GCSE.

Further Maths is not really a GCSE but it is a level two qualification, making it the same level of challenge as a GCSE. Many schools offer Additional Maths, which is a level three qualification. Having done Additional Maths in the past with our brightest students, we found it was an excellent preparation for A-Level, as well as a good indicator of who is suitable to take A-Level maths. However, students found it very difficult and the grades were not what we would hope for (students only have two hours of maths per week in year eleven). So we decided that this level two qualification would be perfect.

More details about AQA Further Maths Level 2 qualification can be found here.

I put together a sort of checklist of all of the topics covered in Further Maths, to give my students an overview of the course, and to give them something they can tick off as they go along so they know whether they're on track. I have uploaded this to the TES resources website and you can get it by clicking here: Further Maths Student Plan.

Over the next year I will be sharing more resources for Further Maths, so keep checking back!

 

This post was written by Emma Cooke, Sidney Stringer Academy, Coventry

A New Way to Teach Dividing Fractions

How do you divide a fraction by another fraction?

For example, how would you do something like this:

My guess is you would flip the second fraction upside down and then multiply like so:

If you are a maths teacher, is this how you teach students?

Do you think your students understand why this method works? And, be honest, do you understand why it works?

Well recently in the maths office one of my colleagues showed us a new method he'd thought of.

It works like this:

I think this is a little bit more intuitive.

My colleague got the idea from one of his year sevens who had answered this question without showing any working out:

The answer is quite obviously three. How many quarters are there in three quarters? Three, duh. But I am quite certain many  A* students would perform the technique of flipping and timesing without even thinking.  My colleague was impressed that this student had used some common sense. He wondered whether the same idea could be applied to fractions with different denominators. It is a little bit less obvious that 21/28 divided by 20/28 is 21/20, but it's not entirely unbelievable. Whereas the "trick" of flipping and timesing can look a little bit like magic to some students.

I haven't tried teaching this method so I can't comment on its effectiveness yet. But as a mathematician it appeals to me. It's quite neat. And in case you were wondering, yes this works with algebraic fractions too.

If you're going to be teaching fractions soon, why not try this out? If you do, please let me know how it goes.

Do you think this is a good method?

 

This post was written by Emma Cooke, Sidney Stringer Academy, Coventry