I have been looking over this old image I made back in 2016. I wanted to look at different ways of viewing square numbers. The image at the top right is one of my favourite and I first saw it on the nrich website: https://nrich.maths.org/2275
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.
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.
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
I 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.
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.
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.