Perimeter of semi-circles

It’s funny that sometimes the most straightforward ideas can sometimes be quite surprising (for me anyway) The latest such idea is that the circumference of a circle with diameter 8cm is equal to the length of an arc of a semicircle with diameter of 16cm. I know this to be true but it just surprises me every time I see it.

I’ve added in the slide with AREA of semicircles too but just so students can see that area is affected differently to perimeter when scaling the diameter.

Curves

 

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Circle Theorems

Looking forward to September and I have seen that I will be teaching Circle Theorems in the first term. Its not a topic I’ve taught in a while so I wanted to have a look at some issues that I think may arise (if memory serves me well, students sometimes incorrectly identified some theorems because they ‘looked’ similar to others) so I wanted to create a few resources, that I could use if needed, that hopefully highlighted these errors that students made. 

I decided I’d start with finding missing angles in triangles where two sides are the radii of the circle. We’ve been looking at area of sectors and circles in the previous lesson so they have been exposed to some of the terminology needed. Then after looking at angles in a triangle I would like to look at angles subtended from an arc from the centre… then work my way through angle subtended from an arc at the circumference… and then angles in the same segment. This will be plenty for one lesson and all are linked. The second lesson I’d look at a few more. I want to use questions to build up the ideas after we discuss them and then spend lessons looking at more complex problems.

circle-theorems-1.pptx

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A simple 10 question build up of some of the circle theorems. Students liked using this as a practice starter.

Metric Measures

I used to find converting metric measures really dull but then I realised not only its importance in real life use of Maths but also how we as humans are fascinated by measures. We are always interested in the fastest, oldest, heaviest etc. Many people spend their lives trying to break records. So why are we fascinated by these forms of measure? Possibly because we love to hear about almost impossible feats. We like to know what the extremes are in everything we measure so we can understand where our own measurement fall.

When I ran a Maths club we spent one term trying to draw an outline of the accurate sizes of the worlds largest foot, person, hand etc so we could compare our own with them.

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Today I looked through the Guinness World of Records book with my daughter and I had to explain some of the measurements using objects she could see or touch in person. I made this for use with year 7 or 8 when we return to school.

Guinness Book of Records

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Connected Questions

I started these tasks originally for year 11 where students answer the same questions in different guises. I decided to repeat the idea for my year 9 class as we are setting revision for them. The first two are using basic skills to connect a linear sequence. The third is a look at Factors of 24

Connected Q

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Mandalas

There’s a hashtag called #Maydala that @MissBowkett and @c0mplexnumber began on the 1st May. I’ve never even attempted to draw a Mandala before and my first try wasn’t the best but since then with their Mandalas on Twitter to inspire me and some great links that were shared I was able to create a few I was proud of. I thought it might be nice to put them in this post so I had a place to look back at them