Area and Perimeter of 2D Shapes

I have been playing around with some ideas and questions on Area and Perimeter. I was looking at the changes to the perimeter when I doubled the length of one side and then looked at how it affected the area when a rectangle was enlarged. There is quite a difference in the difficulty of each question. Whilst I was looking at some of these ideas in Geogebra I thought about the idea of moving one vertex of a triangle, whilst maintaining the same area and what the possibilities were. I thought it might make an interesting question when looking at the area of a triangle. I usually start looking at the area of a triangle by using a prompt like the one below. I find it fascinating that moving one vertex of a triangle along the line parallel to the line joining the other two vertices always results in the same area. shaded-shapes

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Screenshot 2020-08-07 at 00.25.00Area and Perimeter of shape problems

Inequalities

I have been looking ahead at some topics I will be teaching in the first term and one of those is inequalities. I wanted to look at some activities where students could identify shaded regions. I thought one activity could be to identify correct inequalities when the co-ordinates were substituted. Then once co-ordinates were identified as lying in a region I thought that then next step was to use this to find the correct inequality.

Inequalities

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Complete the empty boxes (Distributive Law)

I have been playing a game called ‘Cheeky Monkeys’ with my daughter and the winner is the one that has the most bananas (the bananas are being held by the monkeys) I watched how my daughter lined them up in rows and then proceeded to count the bananas. I started counting the 1s and then the 2s and 3s so added 4 and 6 and 9 and made 19 but then considered the fact there was 3 rows of (0+1+2+3) and then an additional 1 too. This made me wonder about how we add up groups of numbers that have repeated rows Empty Boxes

Screenshot 2020-08-03 at 10.40.02I was thinking adding up numbers like these and at first I wanted to group the 8s but then thought that 8+7+3+2 was 20 and then it was just 20 times 6. I often like to check this by doing 48+42+18+12. So I thought it might be a good activity to try with my year 7 class in September. There are lots of ways I could extend it too.

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I have looked at some variations of this idea

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Numeracy

At the school I work at, we have a lot of shared classes because we are a split site school. We often have classes once a week and the other teacher has the class 3 times a week. At KS3, it was decided last year that the once-a-week teacher should work on numeracy skills. I have been playing around with some numeracy resources I wanted to try out with my once-a-week classes based mostly around the Distributive and Associative Laws.

Laws of Arithmetic

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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.

circle-theorems-1.pptx

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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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