Maths Teachers – Ideas for the New Year and one less lesson to plan!

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

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

Revision Videos

Revision Videos

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

Collaborative ideas

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 herehinge questions

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.

diagnostic questions

Thanks to the brilliant William Emeny @Maths_Master for lots of ideas on his website

Download his newsletter with the link below

I am a huge fan of the work of Dan Meyer @ddmeyer and his blog

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

Nuffield AMP

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)

3 Act Physics – First attempts

These are the first drafts of applying Dan Meyer’s 3 act maths here  into physics having had some previous ideas here and a premise of using intuition here – After all isn’t maths just physics with the toys removed?

Below are act 1s . These are the ‘hooks’ to generate questions that would lead into explorations of act 2. The reveals , act 3 are all on my youtube channel but please dont look until you have really thought the problems through. These will probably be also put on Dan Meyer’s 101QS when/if  I get permission here

Bouncy demolition ball

A great way to break a cup

How to blow a candle out

Suspended ball mystery

Comments, suggestions and contributions as always welcome. This is a non commercial resource, so please keep it that way.

There will be many more to follow

Three Act Science – Collaboration?

Before we start educating them, it makes sense to ask the question what makes a great scientist?


The ability to ask astute questions ?

Being able to consider innovative and divergent strategies for getting the answers?

Having the capability to create valid experiments and spotting flaws in techniques and patterns/ anomalies in results?

Have a sufficient depth of knowledge to connect concepts to reach the Extended Abstract level of SOLO Taxonomy?

To be able to evaluate and extend understanding with more investigations?

How well does our education system facilitate the development of great scientists?

Often very poorly. All too often we teach from the bottom up; tell stories where the answers are already known. In many lessons no conflict is created, nor curiosity excited; no creativity is allowed and students are limited by the outcome.

In short, often students are taught merely to decode exam questions and performance takes the place of real learning.

Teachers complain of students lacking:

  • Initiative
  • Independence
  • Resilience
  • Thinking skills
  • Communication skills

This is not entirely our students fault.  Our education system is not designed to encourage creativity and free thinking, but geared towards conformity and mass production. Complaining that our students lack these skills is the equivalent of moaning that cars don’t fly.

With an education system that is exam orientated and risk averse it is easy to see why students are spoon fed and a cycle of dependency created.

How can we break the cycle and move away from this sanitised science experience?

Using Dan Meyer’s inspirational @ddmeyer  Three Act Maths as a model, we can incorporate multimedia and digital tools to redefine the learning experience. This is one example of transformational practice

What might we do?

  • Use multimedia and digital tools
  • Let them use their intuition
  • Let the students build the problem by asking questions themselves
  • Have them share their discoveries and evaluate each others technique
  • Be less helpful

If you only do one of these do the last: as a teacher it is incredibly difficult to acheive. When delivering teacher training I often use a magic box that there is a strategy to open, which is difficult to discover. I use it to demonstrate that invoking curiosity as a starting point, is much more powerful than the ‘bottom up’ approach. We would normally teach this as ‘here is a box, here is how to open the box, then give it to them and they would be able to open it’. This completely removes the joy of discovery and makes it very boring. The interesting thing when doing this activity with teachers, is that when they learn to  open the box, most immediately feel compelled to tell other people how to do it, thus killing the learning experience. The box is only interesting when you can’t open it. No other group I have tried it with suffers this compulsion. In fact a group of bankers used it to prove their superiority and wouldn’t dream of helping others!

I would like to propose a Three Act model for improving the delivery of science and would welcome collaboration, comments and criticism in the development of this.

The Three Act structure is already used by Screenwriters who know lots about how to engage our interest:

It sounds horribly like the formulaic OFSTED three part lesson , but please bear with me. You break your lesson down intothree parts: Act One, Act Two, Act Three. Beginning, middle, end. Setup, problem solving, resolution.

Act One is the hook. The purpose of the first act is to engage the students. It must be unique, something they haven’t seen or considered before. They are then encouraged to ask questions and build the problem themselves; to make predictions and use their intuition. Most people understand far more physics than they realise – for example: they don’t fall over as they understand centre of mass. What many lack is the ability to communicate this understanding in a conventional scientific way.

An example is here: (The idea is stolen from one of the finest minds in physics I know: Dr  Lawrence Cattermole)


If you cannot see the video there are three cartons of juice: one full, one half full, one empty. The full one is pushed over until it falls.

So what questions does this invoke?

The questions can be narrowed. The highly talented Tom Harbour (a beacon for Teach First ) at a school in Leicester gets his classes to ask superb questions using his “What would happen if…?” format.

Some questions they may come up with:

Which is the most stable? (This then generates more questions – do we mean which falls at the greatest angle, or which needs the biggest force to push them over?)

In which order will they fall over when pushed, from the first to fall over to the last?

Which requires the biggest force to push it over?

How much juice will make it the most stable? (This is massively more complicated than you may think!)

Which is most likely to get knocked over – an empty , full or half full glass, if you knocked them in passing ? (real life example – that gets even more tricky as the shapes of glasses will affect this)

Act Two: Ideas are generated  towards a resolution of the problem. Engagement is increased as the key aspects of motivation are in place: Mastery, Autonomy and Purpose – See Dan Pink here

This is the stage where they can explore their understanding and knowledge can be added if needed. Allow them to make mistakes and follow wrong lines of enquiry.

They can then plan and carry out their investigation into stability to find out answers.

Digital technology used to follow their learning journey can  be transformative. Videos used to show what they predicted, what they did and what they were thinking offer great insight.

Apps such as Socrative, Showbie and Nearpod allow questions from the students to be compiled and progress to be shown. I will be developing examples of these in the future

Act Three is the reveal, the resolution to the dilemma. This ideally should be shown, if possible through the video or demonstration, rather than simply being told the answer. This builds tension and often gets the release – “Yess!!” Though for some of the activities the “right” answer is unknown and there are no limits to what students can achieve.

So what is the solution to the juice carton stability problem?

Find out for yourself!

( Contact me if you haven’t access to a carton!)

Please add comments and feel free to share and collaborate, this is not a commercial product.

Collaboration on Dan Meyer’s 3 Act Maths supported by Technology

Please join us on this collaborative project.

Note all materials are copyright to Dan Meyer – All of this collaborative work is for non commercial purposes and is for us all to share ideas freely

Are you interested in collaborating in a radical way of approaching maths that hits the highest level of SOLO taxonomy ?


and uses Redefinition of SAMR in order to create a set of FREE shared collaborative resources ?


Than please join us

All too often maths is taught as a set of processes to follow . The traditional maths lesson is to give an example showing how to do it and then they repeat this process on similar problems until they have “learned’ it. However learning is something complex and barely measurable and should not be confused with performance.

Robert Bjork – dissociating learning from performance: 

The key point in this is that if students have ‘learned’ something they will not be thrown if the question format is different to what they have seen before. Word problems trip up many students as they are simply following a set of rules and suddenly they don’t seem to apply leading to panic and failure. We need to try and build resilience and the ability to think.

Dan Meyer in his TED Talk – Maths Class needs a makeover makes this point and describes many of his students as having;

Meyer students lack

The eagerness for a formula that will give a solution without any thinking needed is very common.

Probably the most powerful advice given is to ‘Be less helpful’ This is so difficult for many of us to do, it is embedded in our psyche we help them whenever we can. By being too helpful we can foster dependence and a lack of independence.

meyer what to do?

A recent study found that video gamers could cope with persistent  failure as there was constant feedback coupled with renewed opportunities for success.  This resilience that they show outside the classroom is rarely seen in maths. Could we increase the chances of this by allowing our students to make choices based on intuition, to raise their curiosity and to give instant feedback?

Could the way forward be Dan Meyer’s 3 act maths?  (Thanks to Alex Linklater @mrcalculator for introducing me to this.)

Dan Meyer has created a spreadsheet on which he has listed the Three Acts of many math tasks.

Act One is the video or image of a situation that generates questions that can be answered mathematically.  In Act One the student asks a question and then determines what information is needed to answer the question.

Act Two gives further information that may help answer the question.

Act Three shows a video or image that answers the question.

In this spreadsheet, a common question is posed based on Act One and then Acts Two and Three are based on that question.  There may be other questions posed that this particular Act Two and Three do not answer.  That does not mean that the question is not the right question.  It only means that more research will be needed to find the information that will be needed to ask t he question.  (Taken from  here )

It seems to me that this has huge potential for putting curiosity back in the maths classroom and leading to understanding of modelling in an engaging way that should lead to better learning (and hopefully performance)

The first step is a google doc with Dan Meyers current activities that we can all add to. Access is open to anyone with the link and everyone has editing rights (though please add rather than take away) I have added columns for socrative, Nearpod and Padlet  – If you are an organised person please sort the activities into a useful order.

meyer ssheet

The second step is to explore the best way of documenting and choosing the questions to follow and their estimates – I feel Socrative may be the ideal solution to this . Use SOC#: SOC-1406095  to load edit and improve the Socrative popcorn quiz. Please post your Socrative numbers in the shared google spreadsheet above. Create new columns if needed.

soc popcorn

Nearpod is another option that has the videos embedded – A very first draft is available here  or as a homework here

nearpod popcorn 2

To launch this Nearpod Homework, open this link in your iOS device:nearpod://pin=OGJXE; or launch the Nearpod App and enter PIN: OGJXE in the Student box

This is just to give an idea of what could be done – please copy it , improve it  and add comments and suggestions

Padlet – (used to be wallwisher) allows collaboration and a shared wall is

padlet popcorn

Dont worry if you don’t know how to use the technology , please get in contact for support. This is not about technology, it’s about learning. Please add any comments or suggestions