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.

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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

Pattern Blocks

I bought my child a set of pattern blocks a few years ago and she has played with them on several occasions. She made pictures; cats, houses, stars and flowers. Sometimes she attempted patterns. She once attempted to create the images that came with the set but got a little bored with those and preferred to make her own designs. I recently bought Simon Greggs ATM Book about Patterns Blocks and spent time playing around with the blocks myself. I like the idea of cutting a gap for my child to fill and thought she would enjoy this (she did)

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I gave her the hexagon first and she quickly made this pattern below and said “this looks like a button to get into a fancy building” and explained that she would push this and then the doors would open and you had to push each hexagon with a different finger and it would check if you could come in.

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Next we tried the Octagon and she enjoyed putting in pieces and then looking at the space remaining and looking over the pieces she had and deciding what could fit. She restarted a few times and the image below is at the point before she emptied the template of pieces and started again. She said she wished there was a shape that “had a pointed end but looked like an arrow so it could fit in the gap”

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Here is another attempt. She said the image looked like a man and wanted to give it a red head and orange hat. She wanted to include a hexagon but after many failed attempts to fill the gaps she removed it.

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Sometimes she started at one end and others at the other end. She made estimations on what piece might fit and which couldn’t. She also said, when picking up the green rhombus “this piece is pointier so can’t fit this gap”

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When she was finally able to fill the template she was really pleased with herself. She tried to find an image within the design and tried picking out 3 small orange triangles to replace with the trapezium but didn’t like it so replaced the triangles.

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I enjoyed watching her play with the pieces and look forward to getting them out again.