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
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.
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 wanted a series of questions that looked at the effect of double the base number whilst squaring. It makes me think of when we double the lengths of a 2D shape to create similar shapes but the area is 4 times as big. I wanted to look at the idea in this way as a precursor to looking at area and volume.
Scale Factor square numbers
Loci multiple choice questions. ppt above
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.
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