There are some awesome Maths Practitioners out there sharing some wonderful ideas. Please feel free to add those I have missed and you want to draw attention to. This is not an exhaustive list by any means

First up the very talented Colin Hegarty @hegartymaths and his website www.hegartymaths.com

What’s so great about his website? He is sharing loads of videos that very clearly take students through the thinking process in solving the problems. Visible thinking ideas are outlined here

These videos are ideal if you want to try Flipped Learning as Colin has done very effectively in his own school. Another great practitioner is Dave Ashton ~~@~~DaveAshtonCPD who has created a google doc of collaborative approaches

Using Hinge questions can transform your AfL and impact on progress

What is a hinge question?

A check for understanding at a ‘hinge-point’ in a lesson, so-called because of two inter-linked meanings:

1) It is the point where you move from one key idea/activity/point on to another.

2) Understanding the content before the hinge is a prerequisite for the next chunk of learning.There is an interesting Blog by Nik Doran on hinge questions in maths here

To further develop hinge questions an utterly brilliant website from the wonderful Mr Barton ~~@~~mrbartonmaths is a collaborative diagnostic questions site that uses multiple choice questions to unearth misconceptions as well as the right answers. Possibly the biggest thing in Maths Assessment for learning ever.

Thanks to the brilliant William Emeny ~~@~~Maths_Master for lots of ideas on his website greatmathsteachingideas.com

Download his newsletter with the link below

http://www.greatmathsteachingideas.com/wp-content/uploads/2013/11/Teaching-and-Learning-Focus-11.pdf

I am a huge fan of the work of Dan Meyer ~~@~~ddmeyer and his blog http://blog.mrmeyer.com/

If you want the spreadsheet of ideas you can find it on another blog of mine here an example of one of the tasks is given below

An oldie (and he can annoy some people) but some fantastic ideas from Jonny Heeley from the Masterclass Series are available on Schoolsworld here

I love the Nuffield Foundation Ethos and there are some great activities outlined on their website here

Supermarket Queue

And finally the lesson which is developed from an idea from Dan Meyer on supermarket queues. This is mathematical modelling and is based on the idea that the students already know how to use algebra. I have used it from Year 7 up to Year 12 with more sophisticated answers available from the older students ( though the younger ones have pushed them close) This is an example of the Low Threshold High Ceiling tasks outlined on NRICH Maths site here

You walk towards the checkout in a supermarket and there are 2 queues. One person has 10 items in their trolley, the other 20. Which queue do you join? What maths have you done?

Before you get there someone pushes in so now we have this arrangement. Which Queue now? What maths have you done?

This is quite sophisticated maths – If s = time to scan and p = time to pay The students have worked out that

(10s + 10s + p +p) > 20s + p But most will not have realised that this is what they have done.

So what about this scenario? Which queue now?

We cant work it out as we don’t know s or p. So how can we work it out?

Next step is to model a checkout to determine s, the time to scan. So what variables do you need to consider? How many items do you need to scan to get a reasonable estimate?

You may want to include an origami exercise to make a shopping basket

Now we turn to p, the time to pay. The variables here are massive. Cash, card, cashback, vouchers, age, gender . I’ve heard students suggesting that over 50s take twice as long and women wait until they are told how much before reaching for their purse – be careful not to reinforce stereotypes!) So do we use mean, mode or median ? This is a truly high ceiling task enabling very sophisticated considerations

Then give them the challenge

They are given 5 minutes to calculate the times, put them on a post it note and stick them on the board. There is a large timer projected.

We find the answers by modelling the activity itself. Run one, with the 3 baskets on the left goes smoothly.

Run 2 is the 4 baskets on the right. I am the last customer and I am the customer from hell. “Oh sorry that paint is light blue, I wanted the dark blue, can someone change it for me please. ” “But thats the gloss, I wanted the matt, please get me the right paint” Then I cant remember my pin number etc. The students start losing the plot at this point and getting cross as they see their calculations going ‘wrong’. The point of this is that mathematical modelling tells you what might happen. Not what will happen.

Please try this and let me know how it goes or any additions. Have a great New Year and keep getting better. Not because you are not good enough, because you can be even better! (D.Wiliam)