9 November 2014

5 Maths Gems #13

In my gems posts I share some of the best teaching ideas I've seen on Twitter each week. This is my 13th gems post. I hope you're not triskaidekaphobic.

1. Flying Numbers
At Julia Smith's (@tessmaths) creativity workshop at the last maths conference, she shared an activity in which students make 'Flying Numbers' to hang from the ceiling in the classroom or corridor. It works like this: they choose a number and make that number from wood in Design & Technology (drill a hole at the top for hanging). They paint their number then use fine markers or chalk pens to decorate it with facts about that number. This is a lovely opportunity for students to use the internet to explore number properties and find out all sorts of wonderful mathematical things that are not on the curriculum. The examples below were made at the maths conference - it was a really enjoyable exercise.
Ed Southall (@solvemymaths) suggests using numbergossip.com and numdic.com for researching number properties. Of course it's important that students understand the properties they choose - do they know the meaning of all the words they use to describe their number? Prime, square, perfect, palindromic, narcissistic, repdigit... And do they know about different number systems? For example, you could make a whole lesson out of binary (see my earlier post about teaching a binary lesson).

Ed also created some brilliant 1 - 9 number posters this week - your students could create posters like this as an alternative to the 'flying numbers' activity.

Here's a related idea - Number Experts. When you get your new Year 7 class next year, assign a number to each student and tell them that during the year they will become an 'expert' in that number. For example student number 25 would accumulate interesting facts about the number 25 throughout the year, sometimes making connections to the topics they cover in maths lessons, and at the end of the year they could produce a display piece about that number. Your class could even present their number facts in a school assembly. In this enriching exercise students are given a rare opportunity to step into the amazing world of numbers and perhaps it will give them a greater appreciation for the beauty of mathematics.
Source: The Value of Teaching Mathematics, Philipp Legner, Mathigon
2. Mathigon
Speaking of beautiful mathematics, the Mathigon website is amazing! Parts of it are still under development but new stuff is added all the time - the quality is superb. The website says, "Mathigon wants to improve the public understanding of Mathematics, why it is exciting and why it is important. And there is no better place to do that than in schools! Teachers are encouraged to use the resources on this site to enrich the mathematics curriculum and show children how fun and beautiful mathematics can be". Inspiring stuff. Check out the website for yourself (the ebook is excellent!) - here's a few features to get you started:
  • Alice in FractalLand is a stunning animated slideshow. Show it to your class and explore sequences, fractals, the golden ratio and more. The text at the bottom explains each concept very clearly. I love this! This is exactly the sort of thing I was referring to in my post 'A place for gimmicks?' when I said that we should make time to enrich our students' education with interesting mathematics that is not on the GCSE syllabus.
  • The Primary and Secondary Treasure Hunts are very well designed. Full instructions are included and there are questions on areas of mathematics such as cryptography, primes and probability. The questions are rather challenging for the intended age groups - if I was organising an inter-school maths contest then I might use these questions.
  • The video collection is due to grow - an exciting prospect if this two minute wordless video exploring triangles is a taste of things to come. 

3. Imbalance Problems
If you're not familiar with Don Steward's resources then stop reading this post immediately and check out his Median blog. Mr Steward posts new resources all the time - his last few posts have had a 'balancing' theme. First there was this post 'mobiles', then 'mobile inequalities' and finally 'mobile moments'.

In mobiles, the activities start with number problems that get progressively harder, then move on to algebraic balancing problems. Here's a numerical example which can be solved with arithmetic and logic (fill in the missing weights so that everything balances correctly). 
There are lots of variations, such as this one where the weights must add up to the number in the triangle (this is a straightforward example):
The algebraic problems develop skills in writing algebraically and simplifying expressions. In the problem below, students have to complete the missing weights to make the combined hanging weight equal to 8n.
These are great problems. Check out all three posts to see how Mr Steward developed the idea. It's also worth reading Paul Salomon's (@lostinrecursion) post 'More Imbalance Problems' about students creating their own imbalance problems. Thanks to John Golden (@mathhombre) for sharing this link.

4. Desmos Water Line Activity
I've long been a fan of Desmos for graphing but I've never looked at Desmos activities before. My first introduction to a Desmos activity came from reading Jon Orr's (@MrOrr_geek) post 'Describing Relationships – Active Learning'. In a lesson on what we call 'real-life' graphs in the UK, he starts by showing this video which is low quality but still worth showing.

He then uses the Desmos Water Line activity. It only takes a few seconds to register on this site and then you're ready to go - your students login to Desmos using a four-digit code, they enter their name then complete the activities. They're shown various glasses being filled with water and they have to draw the associated graph. Their answer is then illustrated so they can check its accuracy. This website really is superb and very user-friendly - you must spend a few minutes checking it out so you see what I mean. At the end of the lesson students can create their own glasses and challenge their classmates to graph them. The teacher can see what the students are doing behind the scenes, without any complicated registration process or uploading of student data.
I'm really impressed by this technology and keen to explore Desmos' other activities. The people behind Desmos are experts at creating user-friendly interfaces.

5. Three Apps
I was going to include my thoughts on the value of iPads in mathematics education today, but I've decided that there's too much to say so it deserves its own post - watch out for one in the near future. However, thanks to @Corbettmaths, I've discovered three iPad apps that are worth a mention today. These free apps would be useful in the classroom if your students have access to iPads, but they work well on iPhones too and are utterly addictive for teachers!

First, Angles? - Let's solve figures problems! by Gakko Net Inc. In this app you have to find the marked angles in problems ranging from simple triangles to parallel lines to circle theorems. It's a very simple app that lets you write workings on the screen and enter your answer - if you're correct you move onto the next question. Hints are available. Crucially, it's not necessary to progress through all the questions in a level to move onto the next level so you can jump straight to circle theorems if you want.

The same app developer also brings us Areas? which is equally well designed. Shapes are shown on a grid and you simply have to work out the areas. Again, they start off easy and become quite challenging. For example I enjoyed this question:
You can't tell what the radius is, but you can see it's between 5.5 and 6 units. The key is to realise that the answer only contains integers.

Finally, the same developer brings us Make 10 which is an order of operations game. In each question your task is to make 10 using all four numbers.
Three excellent apps - great fun for both students and teachers.

What I've been up to
My Pret homework collection continues to grow thanks to contributions from twenty helpful maths teachers. New contributors are always welcome! I'm pleased that one of my Pret homeworks featured as Craig Barton's Resource of the Week this week - Kathryn Forster (@DIRT_expert) should be very proud of her creation. If you've not used a Pret homework before then Craig Barton's video guide is worth watching. It's great to hear that the template has been adopted by Science and English teachers too. Marsha Smith (@marshasmith244) had the great idea of giving her students blank templates to create their own Pret homeworks - having created a number of them myself, I've found that creating a Pret homework does help you think about a topic in depth.
Students' Pret homework creations from @marshasmith244
This week I've been busy reading and commenting on interesting blogs - this post about the new GCSEs from Cav (@srcav) is very helpful, especially for Heads of Department who need to start thinking about which exam board they will use from next September. Do have a look at this post from Bruno Reddy (@MrReddyMaths) too - it describes the important work he's doing to transform negative mathematical attitudes.

I'm really pleased to see that the 'hashtag marking' I suggested in last week's gems post has paid off - both Debbie Hart ‏(@Debbie_Hart_UK) and Jane Appleton (‏@JaneAppleton24) have tried it.

I've been busy writing a post about circle theorems which will be ready soon. Also, after seeing some great Halloween and Guy Fawkes maths resources, I've started to collate a 'seasonal resources' page. I've seen so many good Christmas resources, it's hard to choose the best but I'm getting there.

So there you go, my 13th gems post. It wasn't scary at all.

Image source: guernseydonkey.com

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