This year with my Year 10 class I decided to build a fractal christmas tree as given on Think Maths. However, before getting into the making, I wanted to explore the world of fractals with the class a little bit first. I started by looking at the Koch Snowflake, and we found this by constructing it. We started with an equilateral triangle that had side length 9cm (a little revision of constructions), and then split each side into three 3cm sections. On the middle of each of these sections, we constructed a new 3cm equilateral triangle. Now we split each 3cm side into three 1cm sides, and again constructed a 1cm equilateral triangle in the middle section on each side. We then discussed the nature of fractals and their selfsimilarity, and their applications to things such as coastlines.
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With open day fast approaching, it has been that time of the year when all the displays get a revamp. I like to do lots of posters and displays anyway, but in the run up to Open Day, I wanted to something a little bit special. And this year I devises a project for my Year 7 class which ran over a couple of weeks on the different types of numbers. We had started by looking at various types of numbers, starting with the usual suspects such as Primes, Factors, Multiples, etc. But we diverged into some other nice types of numbers as well, such as Perfect Numbers and Happy Numbers. I used this PowerPoint (shown below) to deliver the lessons, and talk through the different properties. With my Year 7 class we have recently been studying various aspects of data handling, including averages (including from frequency tables) and a variety of graphical representations. With the end of term drawing near, and having completed the scheme of work ahead of schedule, I decided to do one of my favourite projects with the: the Average Student (available to download from TES). This project uses many areas of the data handling cycle, and in my opinion is an excellent way to get them to see the whole process. Once I had introduced the task to them, we started off by discussing what kinds of information we could collect about the class. There were lots of good ideas, and a few more abstract ones as well, and we started to build up a spreadsheet of all the data that we wanted to include. It is really important (in my opinion) to let them decide which information it is that we should collect to give them more ownership over the task. I would recommend having a few ideas to include if they don't come up with any though. Height, eye colour, shoe size, number in family, etc are good ones, as they cover the different types of data. The idea of NonTransitive Dice has been around for a while. The basic premise is that Red beats Blue, and Blue beats Green, so we expect that Red will beat Green. However, as the NonTransitive suggests, this is not the case, and actually Green beats Red. There are many sets of 3 NonTransitive Dice, and one way to introduce them would be to use the trusty NRICH. This introduces the idea to students, and lets them play around with them a little bit. However, as interesting as the Dice are in themselves, we want to get at the maths behind them. The video below is of James Grime of the University of Cambridge. He starts by explaining a 3 NonTransitive Dice game, and goes on to look at a 5 Dice game that he has invented. There is also his full article on the Grime Dice as well. And you can buy an amazing set of the dice from mathsgear. I love the end of term, as it always brings the chance to dive off the scheme if work a little bit and do something a bit different. Here are a few ideas that I have used just before the Easter holidays, and have always gone down well. The first is Easter Egg Tangrams. This is a spin on the classic tangram puzzle, where the pieces are made by cutting up an egg rather than a square. Students have to follow some detailed instructions to first create the egg (using lots of compass skills). Once they have the pieces, they have to arrange them to make some different birds.
It always amazes me some of the things you can find on www.tes.co.uk and yesterday I found a real gem. For those of you that haven't read "17 Equations that Changed the World" by Ian Stewart, it is definitely one that you should read. This wonderful resource sees the 17 equations turned into simple but effective posters. They are eyecatching, and bound to spark the interest of a few students in the corridor. The user who uploaded them suggests they are the perfect way to reply to the ageold question "Why do we need algebra?", but I think these posters have so much more to them. They are of varying levels, and so can interest any secondary age group, and they give students a nudge towards going to look something up themselves, as well as how far mathematics can really take you. I'm going to be printing them off, laminating and putting them up next week, and I look forward to the responses from the kids. I know this is an idea that has been around for a while, but as a relatively new teacher, it is the first time I have got round to actually doing it this way. I have done the challenge in class before, but this term I am opening it up to the whole school! For those who don't know, the Four 4s challenge asks students to use the digit 4 four times along with any mathematical operations to make the numbers 1 to 100. They can combine the digits to make 44, and can use any operations they can think of, including factorials, powers and roots (as long as they make the power using 4's!) I have put the display in the main maths corridor, which is in a fairly central location in the school. Rather than have students write their own answers on the display, and to allow the activity to continue when I am not there to check and write up immediately, I have come up with a system where they submit their solutions on a named slip, which they hand in to be checked. If correct, I will then add their solution and name to the display for everyone to see. To add another edge to the problem, I will also be allowing them to submit "better" solutions for numbers which have already been solved. By better, I mean more efficient, which will be measured by the number of key presses on a calculator it takes to input the calculation. I am hoping that the location and input method will get the whole school involved in the problem, from Year 7 to ALevel. I am also going to award prizes for completing "random" numbers, which I have prechosen as winning numbers, but have not told them which ones they are. I put up the display on the last afternoon of school, after the students left, before Christmas, and I am looking forward to getting underway with finding them all!

Dan RodriguezClark
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice. Categories
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December 2018
