I have been looking at Pythagoras with year 11 and also looking at Pythagoras in context questions. When we looked at question with a Pythagorean triple, I drew an square with length 5cm with a square of length 4cm cut away, next to it I drew a square with length 3cm. We discussed why the two shapes equalled. This left me thinking about other shapes with equal areas.
I have used geometer sketch pad for a number of years to create tessellations. I made this about 10 years ago and I still use it now
I have been looking at questions that involve multiples and LCM
I will add more when I get a chance to add the ones I’ve been compiling.
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
It led me to think about the difference of two consecutive squares and the questions below.
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.
Area and Perimeter of shape problems
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.
I have looked at some variations of this idea
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.