The post How to use an average: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Averages are a staple of a student’s’ mathematics education. They encounter them for the first time around Year 4, and yet they are still plugging away at them in Year 11 and beyond. Averages are also a strange topic in the sense that whilst students have covered most of the basics early on, they are not really mastered by many students until much later, if ever. Finally, averages represent a substantial challenge to us teachers for the very reason that we need to teach them each and every year. This often means we have to come up with novel ways to present material to students to keep them interested and keep their understanding developing. To cut a long story short – those are three reasons why I love this resource. It tackles what can be one of the most complicated and often abstract concepts in the entire topic – the appropriateness of averages.

**How can it be used?**

This is a PowerPoint presentation that is intended to be used as a lesson, and the structure of the lesson is superb. There is a starter activity which sets up the ambiguities presented by using averages perfectly. Then comes my favourite part – lots of scenarios that present great discussion opportunities. The house price example is particularly powerful and well illustrated. Then we have a very clear way of tackling the pros and cons of each average for a number of situations, before finally looking at some real-life misuses of average. In short, this is just about the best lesson on the concept of appropriateness of averages that I have ever seen on TES. However, as with all resources, it should first be checked out, edited and adapted to suit the needs of your students.

Thanks so much for sharing

Craig Barton

Download: **How to use an average**

View the **author’s other resources**

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]]>The post Carl Hendrick and Robin Macpherson: What does this look like in the classroom? appeared first on Mr Barton Maths Blog.

]]>Robin is a history teacher and currently an Assistant Rector at Dollar Academy in Scotland. Carl is an English teacher completing PhD at King’s College in English education, and is also head of Learning and Research at Wellington College. They have both worked on the Telegraph Festival of Education, and speak regularly at education conferences like researchED.

Now, the reason I wanted to get both Carl and Robin on the show is that firstly we have an inclusive policy here on the Mr Barton Maths podcasts – both mathematicians and non-mathematicians are welcome – and secondly, because they are the co-authors of what is probably my favourite book of 2017 – **What does this look like in the classroom?** It is one of the most successful attempt to bridge the gap between research and practice, and the lineup of contributors is, quite frankly, ridiculous. Are you ready for this? We have fellow podcast guests **Dylan Wiliam**, **Daisy Christodoulou**, **Doug Lemov**, **Tom Bennett** and **Nick Rose**, together with Lucy Crehan, Martin Robinson, David Didau, and more. It is like the Ocean’s 11 of education books, only there’s 18 of them.

I love the way the book is written, with the contributors responding to pertinent questions posed by teachers, such as “I want to improve my questioning style, what three bits of advice would you give me?”, and “what is the best way to deal with low-level disruption?”

Throughout the interview I tried to dig into the key takeaways from the book, and much more besides:

- During the maths speed dating we learn about Carl’s experiences at school with maths, and I ask him what would have made things turn out differently?
- Carl and Robin both talk us through lessons they have taught that went badly, and the lessons they learned from the experience
- We ponder why there has been such a surge in interest in education research recently
- They then each pick out one of their favourite strategies from the book, and what ensues is a fascinating discussion about marking, feedback, workload, and much more
- We consider how past papers can be used most effectively in the run up to an exam?
- Then Carl and Robin reflect on the most important and surprising research they have seen, before sharing some great blogs for us to check out

This episode is definitely one to share with your non-maths colleagues, with Carl and Robin sharing the kind of strategies that any teacher can benefit from. I hope the episode also provides a good overview of what I genuinely think is a superb and very important book.

A podcast about a book would not be complete without a plug about a book, so here it comes, as subtle as ever. My own book, **How I wish I’d taught maths: lessons learned from research, conversations with experts, and 12 years of mistakes**, published by John Catt Education, is released in January 2018. It is a collection of all the things I have learned over the last two years, looking back on the mistakes I have made, and what I now do differently in the classroom. In her review of the book, Jo Morgan says: Craig summarises the key points of the relevant research succinctly and his advice to teachers is perfectly pitched and instantly transferable to any maths classroom. For the sake of our current and future students, I certainly hope that this book becomes essential reading for maths teachers – and she wasn’t even under that much duress from me when she wrote it. Anyway, I hope you find the book useful.

On Twitter, Carl is **@C_Hendrick**

His website is **chronotopeblog.com**

On Twitter, Robin is **@robin_macp**

His website is **robin-macpherson.com**

What does this look like in the classroom? is available **from Amazon here**

Links to the books Carl and Robin recommend teachers read can be **found here**, along with the recommendations of all my other guests.

Carl Hendrick’s Big 3

1. **Ben Newmark’s blog**

2. **Michael Fordham’s blog**

3. **Doug Lemov field notes**

Bonus: **Becky Allen for Data Lab**

Robin Macpherson’s Big 3

1. **Learning scientists blog**

2. **Tom Sherrington’s blog**

3. **Mark Healy’s blog**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:**mrbartonnmaths.com**

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]]>The post GCSE Revision Masters: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

This is a phenomenal collection of homeworks. They have been designed for the 9 to 1 GCSE Maths specification and cover Foundation, Foundation/Higher and Higher. They are really nicely laid out, making them very easy to mark, and the choice of questions is superb. They also share two features that always go down a storm with me and my colleagues. Firstly, the answers are provided (woo hoo!). Secondly, they are in Word format, meaning they can be easily edited, giving you the option to remove questions you deem not suitable for your students, or make copies of the homework, change a few numbers, and voila you have another one good to go.

**How can it be used?**

There are two main ways I will be using these wonderful resources. The first is for homeworks. These days I am a great believer that wherever possible homeworks should not be topic based. Instead they should encompass a wide range of topics so students can benefit from spacing and interleaving, and these homeworks certainly tick that box. The second is for low-stakes quizzes. One of the most significant changes to my teaching that I have made this year is the inclusion of a low-stakes quiz every single lesson, and I am always on the lookout for good content for these quizzes. This resource is superb, in both the challenge and variety of the questions, and fact students can mark it easily due to the lovely way it is laid out. It’s a cracker!

Thanks so much for sharing

Craig Barton

Download: **GCSE Maths 9-1 Revision Masters
**View the

The post GCSE Revision Masters: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Fractions Connect 4: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Students first encounter operations with fractions in primary school, and yet I have taught many Year 11s who still require practice some seven years later. In such situations, it is important to keep the practice as varied as possible, so that students who have had bad experiences with fractions in the past do not immediately assume that they also will not be able to do it this time around. That is why I love this resource. Students have the opportunity to practice all four operations – first with proper fractions, then with mixed number fractions – in the context of a gem of Connect 4. There is an answer grid provided, but students are not told which answer goes with which question, hence the opponent has every incentive to carefully check their rival’s work.

**How can it be used?**

An activity like this would work really well at the end of a unit on fraction operations, or as a revision activity for a class who have studied this in the past. The danger with games is that students think more about the game than the maths involved, but this should not be the case here. Reminding students that they need to check each other’s work is a good way to ensure both parties pay full attention for all of the game, instead of each merely being interested in their own move. I also like to give each student a Calculator Token, which can be exchanged one to check an opponent’s answer. This has the added advantage of encouraging students to carefully consider when best to use this support, which helps them evaluate the complexity of each question.

Thanks so much for sharing

Craig Barton

Download: **Fractions Connect 4**

View the **author’s other resources**

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]]>The post Colin Foster: Mathematical Etudes, Confidence and Questioning appeared first on Mr Barton Maths Blog.

]]>Colin is a former maths teacher who is now an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham. He is an author, has written numerous research papers, and is the creator of three outstanding websites: **foster77**, **mathematical etudes** and **mathematical beginnings**.

Colin shares a keen interest in three areas that I am more than a little obsessed about – purposeful practice (or what Colin refers to as a mathematical etude), measuring students’ confidence in their answers, and effective questioning. If any of those area peak your interest too, then I can promise you are in for an absolute treat.

In a wide-ranging interview we covered the following, and more:

- We spoke about a man we both admire and who has had a significant influence on us, the great Malcolm Swan, who sadly passed away earlier this year
- Colin then describes a fascinating occasion where a mistake he made could have been turned into a really valuable learning opportunity
- We then move on to discussing mathematical etudes, with Colin sharing a lovely one with us
- Can mathematical etudes replace drills?
- How about other rich tasks?
- I ask Colin my current favourite question – can you teach problem solving, and his answers is fascinating
- Then it is time for a discussion about confidence, with me and Colin sharing our strategies for getting a measure of students’ confidence in their answers and why this is a simple, and potentially valuable thing to do.
- We discuss questions, starting with what makes a good question?
- When should – and just as importantly when should not – students be encouraged to ask questions?
- Finally, Colin reflects on research and books he would recommend to teachers, along with what he wish he knew when he first started teaching

This is one of my favourite interviews I have ever done. Colin is incredibly passionate and knowledgeable, and it was just such a pleasure to discuss and debate with him over subjects that fascinate me. I learned so much. I really hope you find it as useful and enjoyable as I did.

A quick mention that depending on when you listen to this podcast my book – **How I wish I taught maths** – may be either about to be released, available for pre-order, ready to buy, or sent to the pulping factory due to lack of sales, Alan Partridge style. It is a collection of all the things I have learned from two years of talking to the world’s leading experts, and reading all the research I could get my hands on. Some would say it is the ideal Christmas present, but I could not possibly comment.

On Twitter, Colin is **@colinfoster77**

The EEF report “Improving Mathematics at Key Stage 2 and 3″ is available to download **here**

Links to the books Colin recommends teachers read can be **found here**, along with the recommendations of all my other guests.

Colin’s main website is **foster77.co.uk**

His Mathematical Etudes website is **mathematicaletudes.com**

His Mathematical Beginnings website is **foster77.co.uk/mathematicalbeginnings**

Colin Foster’s Big 3

1. **mathshell**

2. **Cambridge maths espressos**

3. **Daniel Willingham Articles**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:**mrbartonnmaths.com**

Book: How I wish I’d taught maths

The post Colin Foster: Mathematical Etudes, Confidence and Questioning appeared first on Mr Barton Maths Blog.

]]>The post Measurement – Metric and Imperial: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?
**This is a beautifully designed and presented history of metric and imperial measurements. Students are shown the history of inches, feet and yards, including some royal interference that I was not aware of. Later on in the PowerPoint we are introduced to metric and imperial conversions, which provides opportunities to recap work on ratio, decimals and general arithmetic. My favourite part is the final slide, which explains:

8 furlongs made a mile,

40 poles made a furlong,

100 links made a chain,

10 chains made a furlong.

6 feet made a fathom,

100 fathoms made a cable

Thank God we went metric!

**How can it be used?**

Whilst the formal requirement for students to know the full set of metric and imperial conversion rates no longer exists at GCSE, that does not make such a wonderful resource redundant. I am a great believer in showing kids the history of our wonderful subject, and its applications and relevance to the world they live in. Here is a rare example of where we do not have to show-hour in some faux real-life context. We can show students how things used to be, and throughout this journey they can do a fair amount of maths along the way.

Thanks so much for sharing

Craig Barton

Download: **Measurement – Metric and Imperial**

View the **author’s other resources**

The post Measurement – Metric and Imperial: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Dog Transformations: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

If you and your students have transformed more quadrilaterals than you care to remember, then this is the resource for you. For, what better thing in the world is there to transform but everyone’s favourite canine friend? Translate the wandering dog, reflect the ice skating dog, rotate the Aussie dog, and enlarge the greedy dog, all whilst practising the fundamental transformation skills students will need for GCSE maths. There are more vertices than on standard shapes that students usually transform, so the challenge all the better. Full answers are provided, along with the original Excel file that allows you to easily adapt each of the transformations to produce an infinite number of varieties.

**How can it be used?**

It will come as no surprise that I am going to suggest using the worksheets to help students practice the basics of transformations. The fact that the object being transformed is different to usual may inject a bit of much needed variety into the world of transformations. But with the accompanying Excel file, you can take things even further. Being able to project the dog onto the interactive whiteboard allows you to ask questions such as: if I add one the the number at the bottom of the vector, what will happen to the dog? What would I need to change the translation to so the dog’s nose is at (4, -3)? Or, what if I change the angle of rotation to 180°? Students can then consider the answer, discuss it with their partner, and then you can reveal it stantly, without the need to print out extra sheets. This resource really is the top dog.

Thanks so much for sharing

Craig Barton

Download: **Dog Transformations**

View the **author’s other resources**

The post Dog Transformations: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Doug Lemov: Teach like a Champion and Top Tips for delivering training appeared first on Mr Barton Maths Blog.

]]>Let’s be honest, Doug is a legend. He is probably best known as the author of **Teach like a Champion** – a book which has had a huge influence on the last few years of my teaching and thinking, and which I believe is a must for all teachers to read, jam-packed as it is with loads of practical, easy to implement strategies that can be truly transformative. Doug is also the coauthor, along with his Teach like a Champion colleagues, of **Practice Perfect** and **Reading Reconsidered: A Practical Guide to Rigorous Literacy Instruction**. He is a former teacher, the former Managing Director of Uncommon Schools (something we talk about in the interview), and his CPD sessions are regarded as some of the very best in the world.

In a wide-ranging interview we covered the following, and more:

- Where did the idea for Teach like a Champion come from?
- Doug and I share our past mistakes with regard to “tells” in the classroom
- Doug picks out one strategy from Teach like a Champion that everyone listening can use right away, and it is a classic
- Then we get a world exclusive look at some strategies that will be included in Teach like a Champion 3.0
- I then ask Doug about professional development, and he shares some outstanding, practical advice for anyone giving any form of training to their colleagues
- Doug then reflects on what he feels is the most important finding from educational research that all teachers should be aware of
- Before finally sharing some book recommendations and blogs to check out

I’ll be honest, I was incredibly nervous in the build up to the interview. I even had to knock back two cups of Mellow Birds coffee to take the edge off. I guess I should be used to talking to my heroes on this show by now, but Doug was someone I had wanted to have on for so long. But I need not have worried – Doug was humble, knowledgeable, engaging, and just a superb guest. This is another of those interviews to share with your non-maths colleagues, as the ideas and insights Doug shares are incredibly useful no matter what subject you teach. Oh, and if you haven’t snapped up **Teach Like a Champion 2.0**, then I promise you will not be disappointed.

Speaking of books – notice the seamless transition there – let me quickly take this opportunity to mention – and when I say mention, I of course mean shamelessly plug – my book. In tribute to Doug, perhaps I should have called it Teach like a maths teacher who has been getting it completely wrong for 86% of his career, but in the end I went for How I wish I’d taught maths. It is based on my thoughts from two years of interviewing the world’s leading educational experts on this podcast – including **Dylan Wiliam**, **Robert and Elizabeth Bjork**, **Daisy Christodoulou**, **Greg Ashman**, **Kris Boulton**, Doug, and many more – reading over 200 research papers and books, and most importantly of all, trying, failing and modifying the strategies based on the experiences of my students. It is published by John Catt Education, and it should be out in time for Christmas 2017 – just in case you are short of gift ideas for your mum, son, Granny, dog, etc.

On Twitter, Doug is **@Doug_Lemov**

His website is **teachlikeachmpion.com**

Teach like a Champion 2.0 is available **from Amazon here**

Links to the books Doug recommends teachers read can be **found here**, along with the recommendations of all my other guests.

Doug Lemov’s Big 3

1. **Harry Fletcher Wood’s blog**

2. **Jo Facer’s blog**

3. **Carl Hendrick’s blog**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:**mrbartonnmaths.com**

The post Doug Lemov: Teach like a Champion and Top Tips for delivering training appeared first on Mr Barton Maths Blog.

]]>The post Algebra Exit Tickets: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Exit tickets are a very popular form of formative assessment. They usually consist of a single question given out in the final few minutes of the lesson for the students to complete, which is then handed back to the teacher as students leave the room. The idea is that the answers given by the students help inform the planning of the next maths lesson. For exit tickets to be successful they need to be super-quick to mark, and also kind on the photocopying budget. Fortunately, this wonderful collection of algebra exit tickets is exactly that. The questions are really well chosen, beautifully presented, and organise so four tickets fit on each side of A4.

**How can it be used?**

Exit tickets can certainly be used in the traditional sense, but I have a little twist I like the throw into the mix – the Delayed Exit Ticket. Given the widely cited distinction between learning and performance and the benefits of spaced learning, we can potentially make exit tickets an even more powerful tool by delaying their release. Say I have just taught a sequence of lessons on straight line graphs to my class, and last term we studied solving equations. In the final few minutes of the lesson I might presented them with two exit tickets. The straight line graphs one would give me an indication of how students are performing in the current topic and allow me to identify any misconceptions, whereas the solving equations exit ticket would give me a indication of how much students have retained from that previous topic, whilst also tapping into the benefits of spaced retrieval.

Thanks so much for sharing

Craig Barton

Download: **Algebra Exit Tickets**

View the **author’s other resources**

The post Algebra Exit Tickets: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise appeared first on Mr Barton Maths Blog.

]]>Peps is a former Fasttrack maths teacher and Senior Lecturer in mathematics education. He has been a National Curriculum Advisor for the DfE, External Examiner at the OU, and is the author of Lean **Lesson Planning** and **Memorable Teaching**. Peps has three Masters degrees (in Engineering Design, Educational Leadership, and Educational Research) and holds Fellowship Awards from the University of Brighton and the Young Academy. He now leads on the **Institute for Teaching’s** Masters in Expert Teaching course.

In short – I was once again well out of my depth.

I absolutely love Peps’ books on lesson planning and memorable teaching and I am fascinated by the challenges of developing expertise in teaching. Hence, I had been wanted to get Peps on the show for ages, and he did not disappoint.

In a wide-ranging interview we covered the following, and more:

- Does Peps believe you can teach problem solving, and if so how?
- What are Peps’ 7 habits of highly effective lesson plans, and what are the practical implications of implementing these?
- How can teachers work together to joint-plan effectively?
- What are the key principles of memorable teaching, and how can we design our teaching to lead to more memorable experiences?
- What does Peps think of my ideas about keeping still, teaching in silent, and getting rid of all classroom displays in terms of his understanding of memory?
- How would Peps present a worked example?
- Is there a consensus as to what expert teaching looks like?
- Can you judge how good a teacher is from a lesson?
- Can the principles of deliberate practice be applied to teacher education?
- What would Peps consider to be three essential research findings or principles that all teachers should know?

I don’t want to build this up too much, but I am going to have to. This is one of those special episodes. I reckon I need to listen to it about 48 times to take in all the nuggets. It is also one to share with your non-maths colleagues as the vast majority of Peps’ points about planning, memory and the development of expertise are applicable to all teachers and all subjects. So please spread the word. And if you enjoy this episode, or any of the other 30-odd, then a quick review on iTunes would be hugely appreciated.

I’d also like to take this opportunity to officially announce that I have written a book. It is called “How I wish I’d taught maths”, with the subtitle “reflections on research, interviews with experts, and 12 years of mistakes”, and is being published by John Catt Education, the home of such wonderful books as** What every teacher needs to know about psychology** and the recent

On Twitter, Peps is **@pepsmccrea**

His website is **pepsmccrea.com**

His first book is **Lean Lesson Planning**

His second book is **Memorable Teaching**

Links to the books Peps recommends teachers read can be **found here**, along with the recommendations of all my other guests.

Peps Mccrea’s Big 3

1. **John Sweller TES piece**

2. **David Wees stuff around Instructional Activities **

3. **Keep an eye on the IFT website > going to be publishing some stuff **

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:**mrbartonnmaths.com**

The post Peps Mccrea: Planning, Memorable Teaching and Teacher Expertise appeared first on Mr Barton Maths Blog.

]]>The post Mean from a Frequency Table Generator: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

You know sometimes you are looking for something very specific, to suit a certain need, and then you find it, and life is good? Well, that happened with this resource, and so I could not resist making it my Resource of the Week. I was planning a lesson on calculating an estimation of the mean from a frequency table for my Year 9 class, and I simply wanted some examples that they could do – lots of them. And this resource does just that. It is an Excel mean from a frequency table generator. Every time you hit “new question” you get a brand new table to complete, and best of all you can reveal the necessary steps to the solution step-by-step.

**How can it be used?**

I used this resource four ways:

1. I used it when going through a worked example. I took a screenshot of the incomplete table, pasted it onto a PowerPoint, and used this to talk students through the necessary steps. I was then free to flick back to the Excel version to check my calculations.

2. I next used it to generate examples for the students to practice. Again, the facility to check solutions at the click of a button was brilliant. And as a top-tip, I would recommend saving 4 versions of the resource, and then you can project 4 questions on the board at any one time. I show you what I mean in the video.

3. I used this resource to create practice questions and answers for my students’ homework

4. Finally, I have this resource saved on my desktop so I can quickly project a question at any stage to ensure students have never gone more than a month without practising this key skill

Thanks so much for sharing

Craig Barton

Download: **Mean from a Frequency Table Generator**

View the **author’s other resources**

The post Mean from a Frequency Table Generator: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables and Anxiety appeared first on Mr Barton Maths Blog.

]]>Lucy is a former maths teacher and head of maths, who is now the Research and Communications Officer at Cambridge Mathematics.

The reason I wanted to have Lucy on the show is that I am a little bit addicted to her espressos. Now, anyone who knows me will know my chosen brand of coffee is a very milky and pathetically weak cup of Mellow Birds, but these are mathematical espressos – bite-sized chunks of mathematical research into key areas. I originally planned to ask Lucy about five of these areas, and have everything wrapped up in under an hour – just in time for my evening Mellow Birds, in fact. But once we started talking, we could not stop, as Lucy dropped nugget after nugget.

So, in a wide-ranging interview we covered the following, and more:

- How did Lucy deal with poor behaviour during her time as head of maths?
- Would Lucy have advocated centrally planned lessons in her department?
- Why did many of Lucy’s maths lessons go wrong, and what did she learn from them?
- Why is the quest for engagement in mathematics a problematic one?
- Then we hit the espressos – and we cover five key questions:
- What are the effects of attainment grouping on mathematics learning?
- What are the issues in learning and assessing times tables?
- How does maths anxiety affect mathematics learning?
- How does assessing confidence affect learning and testing in mathematics?
- How can mathematics teaching be measured?
- Finally Lucy reflects on the most important research she has read, books she would recommend, and what she wishes she knew when she first started teaching that she knows now

I promise you, this episode is gold – and it is absolutely nothing to do with me. Lucy is incredibly well-read, but has the impressive ability to relate all of the research to experiences she has had during her many years in the classroom. This leads to a series of fascinating and practical takeaways that you can build directly into your teaching.

Lucy mentions lots of papers, and there are links to everything on the podcast page, along with a link to my own research page in case this has left you wanting more. Also, Lucy forgot to mention Black Mathematicians Month, which is happening in October. Again, there are links to this on the podcast page.

And just before we crack on, my podcast hit a significant milestone just before I recorded this episode – 100,000 downloads. Thank you so much to all my guests who have helped transform the way I teach and continually make me strive to be better. And thank you to all of you who listen and who have helped spread the word about this podcast. I cannot tell you how much it means to me to know people find these interviews as useful as I do. Long may they continue.

On Twitter, Lucy is **@honeypisquared **

Cambridge Maths can be found at **cambridgemaths.org
**On Twitter, they are:

The books Lucy recommends, along with recommendations from all previous guests, can be found

Other links from the episode:

**Expectancy effects**

**TRU framework **

Black Mathematician month **here** and **here **

Lucy Rycroft-Smith’s Big 3

1. Cambridge Mathematics **salad** and **espressos**

2. **Chalk Dust Magazine**

3. **Aperiodical **

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

I am a maths teacher, currently teaching at Thornleigh Salesian College, Bolton, UK. Here are links to some of my work:**mrbartonnmaths.com**

The post Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables and Anxiety appeared first on Mr Barton Maths Blog.

]]>The post Finding Turning Points: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Often really good resources for teaching A Level maths are hard to find, largely because not as many teachers deliver the course. Hence, while you can find no end of top-quality lessons, activities and resources across TES for Key Stages 1 to 4, as soon as we hit that post-16 area, things get a little more barren. But there are gems out there, such as this delightful lesson on the nature of stationary points. It is a beautifully designed, detailed PowerPoint that gives a crystal clear explanation how to determine the nature of stationary points, together with several well-chosen worked examples. I particularly like the way common misconceptions or covered via a series of handy hints. For example, the fact that the graph can contain y-values lower than the minimum point, and a minimum followed by a maximum does not automatically guarantee that the graph is a cubic. These can often be overlooked and may lead to problems later on.

**How can it be used?**

As with all PowerPoint lessons on TES, I always advise adapting it to suit the needs of your students The slides are very detailed, and stripping them back may add clarity. There is also always a danger when having pre-written solutions to worked examples that you may wish to change things based on something a student says, and yet your hands are tied if all the steps of the example have been typed out and animated. But the detail in these slides could be used to your advantage by turning them into printed notes that could be given to students for revision, or to any student who may have missed the lesson. This is a wonderful resource to aid the planning of any lesson on the nature of stationary points.

Thanks so much for sharing

Craig Barton

Download: **Finding turning points with calculus**

View the **author’s other resources**

The post Finding Turning Points: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Tick-Trash-Improve – Standard Form: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Who doesn’t love a bit of Tick or Trash? For years it has been my go-to way of getting students to reflect on common errors in a bid to ensure they themselves do not make them. In my Pedagogy Place series, I discussed the research surrounding this approach to teaching (LINK TO SPOT THE MISTAKE). Here we have an upgrade to a classic. As well as being asked to either tick or trash an answer to a standard form question, there is now a third option – improve. This is for answers that are not entirely incorrect, but which could certainly be made better. This adds an extra degree of complexity to the activity, and could help ensure students’ understanding of the topic is even more secure.

**How can it be used?**

As I discussed in my Pedagogy Place article, activities like this are great for promoting a deeper understanding of a skill or concept, but should probably be left until students’ understanding of the basics is reasonably secure as there is a risk that they will not be in a position to distinguish between correct and incorrect approaches, and hence my in fact develop some misconceptions. As such, I like to use them at the end of a topic unit, maybe as part of a homework. Standard form lends itself particularly well to the tick, trash, improve approach as you can write answers that are mathematically equivalent, and yet not in standard form. However, the topic is by no means unique. Calculations involving fractions that have not been fully simplified, formulae that have not been fully rearranged, missing units, and indeed any question that has not been quite finished off would work just as well. Let’s hope this is just the beginning of tick, trash, improve!

Thanks so much for sharing

Craig Barton

Download: **Standard Form: Tick, Trash, Improve**

View the **author’s other resources**

The post Tick-Trash-Improve – Standard Form: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Kris Boulton – Part 2: Minimal guided instruction, Understanding, How before Why appeared first on Mr Barton Maths Blog.

]]>Since **I last spoke to Kris**, it is all change in his professional life as he has a brand new job. He is now the Director of Education at **UpLearn** – a project with the tagline: learning with certainty, powered by AI and neuroscience. Indeed, Kris is currently looking for teachers and tutors to work with him on this exciting venture, and you can find more details in **his blog post.**

**Kris’ first appearance on the show** caused a bit of a Twitter sensation, as he spoke at great length about how he planned a sequence of lessons on simultaneous equations. Indeed, “how do you plan a lesson?” was pretty much the only question I ask. Kris followed this up with a **wonderful series of blog posts** that I highly recommend checking out..

The danger with having a guest on twice is that the sequel never quite lives up to original. However, I am delighted to report that this is very much a case of Terminator 2 than Titanic 2.

So, in a wide-ranging discussion, we covered the following things, and more:

- Kris responds to two questions from Part 1 about his planning process – how can we make planning simple, and a classic from Dr Becky Allen who asks if Englemann is so great, why haven’t his methods taken off?
- Then we turn our attention to less teacher guided forms of instruction, and Kris addresses
**Andrew Blair’s question from last episode**about what Kris means by an “outcome” - Are less guided forms of instruction more motivating?
- Do they have any advantages at all over more explicit instructional approaches?
- Then we move onto performance, learning and understanding
- What does it mean to “understand” something in mathematics?
- How as teachers can we assess this understanding?
- When should we teacher the How before the Why – and indeed, should we ever teach the Why before the How?
- I pitt Sweller’s Cognitive Load Theory against Bjork’s Desirable Difficulties by asking i thinking should be easy or hard?
- And finally we turn to the issue of memory, and I ask if the approach to teaching Kris advocates runs the risk of not giving students enough time to forget, and hence benefit from Bjork’s New Theory of Disuse.

Scattered throughout this are Kris’ philosophical tangents about values, purpose, outcomes, expertise, scientific thinking, and much more besides. It is an absolute treat. I was cognitively knackered afterwards, and had to join my wife in watching an episode of Geordie Shore just to recover. And Kris has promised to return to the show to discuss such matters as schemes of work, variation theory, questioning, problem solving and teacher training. Some of Dan Carlin’s Hardcore History podcasts are 5 hours long – I reckon Kris and I can trop that, with some Hardcore Maths.

Speaking of podcasts, a quick shout-out to three new education ones that I have enjoyed listening to recently:

**Learning Scientists** – one of my favourite blogs for practical applications of education research now have their own show, and it is excellent.

**Michaela Community School** – hosted by Thomas Kendall, and featuring interviews with Michaela staff, including Joe Kirby on knowledge organisers. My advice to Tom would be to keep that trouble-maker Dani Quinn off the airwaves – we all know what happened after she appeared on this show.

**TES** - whose new Podagogy series not only features a good pun for a title, but also an impressive line-up of guests, including Daisy Christodoulou and Dylan Wiliam. I feel a bit like **Daisy** and **Dylan** have cheated on me by appearing on another podcast, but I will let them off.

Whilst these podcasts are great for my ears and brain, they are doing my iTunes ranking no favours whatsoever, so any help you can offer in terms of a review or spreading the words to your colleagues is highly appreciated.

On Twitter Kris is **@Kris_Boulton**

His excellent blog can be found at: **tothereal.wordpress.com**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Kris Boulton – Part 2: Minimal guided instruction, Understanding, How before Why appeared first on Mr Barton Maths Blog.

]]>The post 50 Maths Questions Ideas: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

This resource has been designed for primary maths lessons, but do not be fooled – this is something that could (and should!) be used in all maths classrooms across the land! This book includes ideas for questions that could be used in a maths lesson (or at any point in the school day) to inspire some mathematical thinking in your students. Each idea is followed by a more detailed explanation, and then examples to show how it could be used across several maths topics. There are classics in there, such as “True/False” and “Odd One Out”, but also some that I was not as familiar with. I am a now a particular fan of “Correct, Almost, No Chance”, and “What’s the same and what’s different?”, both of which are incredibly versatile, with the potential to promote deep thinking across multiple topics.

**How can it be used?**

Questions like these are ideal when reviewing topics, or for providing some extension material to students.Take “What’s the same and what’s different?”, for example. This could be used at the end of a unit on quadrilaterals, challenging the students to think about and discuss what is the same and what is different about a square, a rhombus and a rectangle. Similarly, following a unit on decimals, students could be presented with 3.45, 3 and 2.9 and asked the same question. I would also be tempted to print out these ideas and either stick them up around the room or have them close at hand when I need inspiration for a question during a lesson. Likewise, these are ideal to use when planning lessons to ensure your questions really get students thinking.

Thanks so much for sharing

Craig Barton

Download: **50 Maths Questions
**View the

The post 50 Maths Questions Ideas: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Clumsy Clive On Averages and Range: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Over the course of 2017, I have become more than a little obsessed with Clumsy Clive. It is such a wonderful idea for a series. In short, one of my all-time favourite TES authors, under the guise of a student called Clive, answers a series of questions, in this case on averages and range. The problem is, Clive is prone to making the odd mistake. It is the job of the students to cast their eyes over Clive’s work to see if they can spot, explain and correct the mistakes. The beauty is, the mistakes Clive makes have been carefully chosen to reflect common misconceptions in the topic, and hence completing this experience is a fantastic way to assess and help resolve any lingering misconceptions students may have.

**How can it be used?**

There is now a whole series of these covering a wide range of topics (click on the author’s name to visit his shop), and so you can bring Clive into many lessons if you choose. There is always the worry that presenting students with misconceptions may actually cause them to develop misconceptions that were not there in the first place. The evidence for that is limited at best, but it is probably fair to say that to fully benefit from this approach students must first know the correct procedure. So, my advice would be to either use these resources at the end of a topic unit as an effective way of assessing understanding, or use it as an introduction to a topic unit that you know students have studied in previous years as a means of assessing baseline knowledge. I love Clumsy Clive!

Thanks so much for sharing

Craig Barton

Download: **Clumsy Clive On Averages and Range
**View the

The post Clumsy Clive On Averages and Range: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Teach for Understanding Bigger Picture: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

I dread to think how many department meetings I have say through over the course of the last 13 years, and likewise what proportion of that time has been spent doing painful admin – filling out forms, checking dates, writing predictions, etc. Bringing meaningful, effective CPD into such meetings can be a tricky business, but this lovely resource offers one possibility. It is called “Teaching for Understanding”, and its stated aim is to encourage discussion amongst maths teachers about how to teach for understanding instead of tricks. A variety of topics are presented, including fractions, indices and negative numbers, and teachers are challenged to write down:

1. The method – the basic approach

2. The understanding – why does the method work?

3. The bigger picture – how and where does this topic fit in the real world application?

**How can it be used?**

I am a great believer in the power of habit. Too many times I have seen a good teaching idea, hammered it to death for a couple of weeks, and then never returned to it. Students only really see the benefit once something become habitual. I believe the same is also true for something like this resource. Use it once in a departmental meeting, and you are unlikely to see much long-term benefit.; However, make this a regular part of meetings – it should only take around 10 minutes to fill-in and discuss once colleagues are used to how it works – and the benefits could be significant. It is an opportunity for colleagues of all experiences and backgrounds to share their knowledge, expertise and opinions in a positive, structured way,. And it is fascinating to see the different approaches.I highly recommend giving it a try.

Thanks so much for sharing

Craig Barton

Download: **Teach for Understanding Bigger Picture (Maths CPD)**

View the **author’s other resources**

The post Teach for Understanding Bigger Picture: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Andrew Blair – prequel: Inquiries and being a Head of Department appeared first on Mr Barton Maths Blog.

]]>**Last episode** I interviewed Andrew about running inquiries. There has been a fantastic reaction to the interview, and I am pleased to see that it has given other people plenty to think about, and not just myself. Indeed, I am not sure my head has quite finished spinning. If all goes to plan, next episode I will be recording Part 2 of my interview with **Kris Boutlon**, and I want to discuss directly the points Andrew made about outcomes, fluency and purpose.

So, in preparation for that, I thought it would be a good idea to release my first interview with Andrew Blair, that I recorded back in 2014 when I used to host the TES Maths Podcast. Here Andrew describes in detail a far more open-ended, less structured inquiry than the one he talked about last episode. It is fascinating to listen to how you plan and deliver a lesson that – quite literally – could go in any direction, and that direction is determined 100% by the students themselves. As a bonus, Andrew also shares his invaluable experiences and advice on being a head of department.

I hope you agree with me that this is a superb listen. No takeaway this time, so I won’t see you on the other side, but I will see you soon, and I hope you enjoy the journey back to 2014 – a time when I could sleep at night, unconsumed as I was with concerns about working memory, cognitive load and desirable difficulties. It was also a time when I used to record in a professional studio, had different intro music, an alluring female voice to introduce me, and considered interviews over an hour rather excessive. How times have changed. Enjoy.

On Twitter, Andrew is: **@inquirymaths**

Andrew’s Inquiry Maths website can be found at: **inquirymaths.org**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Andrew Blair – prequel: Inquiries and being a Head of Department appeared first on Mr Barton Maths Blog.

]]>The post Times Tables Mastery: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Pedagogy Place, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

There is little doubt that the ability to fluently recall times table facts is a huge advantage across many areas of the mathematics students need to learn at school, from fractions to ratio, equations to angle facts. However, once students are able to recall times tables, the next step is to enable them to flexibly use these relationships in a variety of contexts. That is where this wonderful collection of resources comes into play. For exam times table there are three sets of 10 questions. These questions do not simply ask things such as “what is 4 x 8?” Instead they probe students deeper with a variety of word problems, challenges to convince why something works, and links to decimals. If students can do these, then mastery of times tables is in sight.

**How can it be used?**

With three sets of questions for each times table there are plenty of questions to keep students occupied. Using a couple of these sheets each week with a key stage 3 class, especially at the start of the year, might be a good idea. However, I have two quick points to make. The first is that these sheets are only really effective if students are fluent in the basics of times tables. If students are having to use up valuable working memory capacity trying to calculate, for example, what 4 x 7 is, then the challenge of applying this to solve a word problem or a related question involving a decimal is likely to be too much. Secondly, once students have been through one cycle of these sheets, there is a fantastic opportunity to interleave. Simply copying a question from each of the times tables and creating a super sheet is a great way to push students on to the next level, calling upon all their times table knowledge at once.

Thanks so much for sharing

Craig Barton

Download: **Times Table Mastery**.

View the **author’s other resources**

The post Times Tables Mastery: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Andrew Blair: Inquiry Maths appeared first on Mr Barton Maths Blog.

]]>Andrew is the Head of Maths at Haverstock School, in Camden Inner-London, and the creator of **inquirymaths.org**.

Now, in recent episodes this podcast has featured guests who favour an explicit instruction approach to teaching – most notably my interviews with **Greg Ashman** and **Kris Boulton**. Speaking to these guests, together with the reading of educational research I have been doing over the last 12 months, has led to me moving rather rapidly along this path myself, favouring teacher-led instruction ahead of the rich tasks and investigations I so passionately believed in for most of my career.

This was why I was so keen to have Andrew on the show. I have known Andrew for many years, he is someone I admire and respect greatly. Indeed I interviewed him about inquiries and being a head of maths back in 2013 when I used to do my TES Maths podcast – a time where I considered a 1 hour interview a little on the excessive side. I will release this old interview as a special podcast in the next few weeks, as listening back to it in preparation for this show may me realise it is still very much worth a listen. Andrew’s **Inquiry Maths website** is a gold mine of ideas, complete with teacher guidance, examples of students work, and supporting resources for those wishing to try out inquiries. But there is no doubt that this approach to teaching and learning is the polar opposite to that favoured by many of the traditionalists. As the homepage of the Inquiry Maths website explains:

*Inquiry Maths is a model of teaching that encourages students to regulate their own activity while exploring a mathematical statement (called a prompt). Inquiries can involve a class on diverse paths of exploration or in listening to a teacher’s explanation. In Inquiry Maths, students take responsibility for directing the lesson with the teacher acting as the arbiter of legitimate mathematical activity.*

So, in a wide-ranging interview, we covered the following and more:

- Andrew describes in great detail how he plans and delivers a sequence of five structured inquiry lessons to a Year 7 class
- We discuss why inquiry lessons sometimes go wrong
- We look at the popular debate between explicit instruction and more minimally guided forms of instruction, and why Andrew feels it is not right to lump things like discovery learning and inquiries together
- Andrew answers a guest question from fellow podcast guest Kris Boulton about explicit instruction and problem solving – and I have promised Andrew he can have one for Kris in return
- I ask what are the major advantages of inquiries?
- Why does Andrew feel key skills and procedures can be taught within an inquiry, and how does this work practically?
- What type of classes do inquiries work best with?
- Should teachers in their first few years of teaching try to run inquiries?
- Are there a generic set of inquiry skills that can be taught within the domain of mathematics?
- And what does Andrew wish he knew when he first started teaching that he knows now?

I know I say this every time, but honestly, this is an absolute cracker. If – like me – you have been convinced by the arguments of **Greg Ashman** and **Kris Boulton** in recent episodes, I promise you this interview will give you food for thought. I had to go on a long walk after it – followed by a long lie down, followed by a pint of Guinness – to try and organise the thoughts whizzing around in my head. I will share what I have come up with so far in my Takeaway at the end of the interview.

The usual desperate plea to give me a rating and a quick review on iTunes if you have a spare minute, and thank you so much for those of you who have, and the incredibly kind words you have written.

On Twitter, Andrew is: **@inquirymaths**

Andrew’s Inquiry Maths website can be found at: **inquirymaths.org**

Andrew’s **post on discovery learning**

Andrew’s **post on fluency**

Andrew Blair’s Big 3 (with one extra!)

1. **Bruce Ferrington – Authentic Inquiry Maths**

2. **Graham Henshaw – Enquiry-Based Maths**

3. **Simon Gregg – Following Learning**

4. **Amanda Klahn – Doing Maths**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Andrew Blair: Inquiry Maths appeared first on Mr Barton Maths Blog.

]]>The post Distance, Speed & Time – Find Someone Who: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**What is it?**

A classic start of year activity might be to play a game of “Find Someone Who…”. Challenging your students to find someone who has an older brother, or a birthday in August is a good way to encourage them to talk to their fellow classmates, forming the bonds that may prove vital for the challenges ahead. That is all well and good, but how about something even better – a mathematical version of Find Someone Who? Yes, instead of attempting to unearth generic information, students instead are asked to track someone down who can write 30 minutes as a decimal or (my personal favourite) can calculate the distance travelled (to 3 s.f.) when travelling for 8 hours 10 minutes at a speed of 55 km/h. That is the kind of person I would want to know better.

**How can it be used?**

This wonderful resource is ideal for the start of the year, especially if students have been moved into different classes. However, it could be used all year round as a way of revising key concepts in a productive, cooperative manner. Better still, why limit ourselves to the study of speed, distance and time? A similar format could be used with any topic, and with any age of student. All you need are a nice selection of questions. Of course, careful consideration will need to be given to behaviour management to ensure things do not get out of hand, but there is a great deal of potential here.

Thanks so much for sharing

Craig Barton

Download: **Distance, Speed & Time – Find Someone Who…**

View the **author’s other resources**

The post Distance, Speed & Time – Find Someone Who: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post TES Maths Back to School appeared first on Mr Barton Maths Blog.

]]>Happy new school year! September is back and so are your students, all of whom seem to have forgotten every ounce of mathematical knowledge they once had.

So, get the new term off to a flying start with this selection engaging, mathematically sound and, dare I say, even fun exercises, designed to make the return to school as painless as possible. And for even more inspiration, why not visit the GCSE maths hub, jam-packed with resources that have been hand-selected by the Tes Maths panel?

As always, a big thank you must go to the generous and incredibly talented members of the Tes Maths community, whose resources make time fly and provide invaluable support for teachers all year around. It’ll be Christmas before you know it!

Craig Barton, Tes Maths Adviser

**Back-to-school activities**

Ease younger learners into KS3 with this cross-curricular icebreaker, in which they’ll get to know their peers through estimating, measuring and recording each other’s heights.**Mathematical name cards**

Warm up your new students’ brains with collection of easily adaptable questions. Once completed, they also double up as handy name cards.**Maths rich task**

Ideal as an introductory lesson for Year 7s, this activity can be accessed by all abilities and includes an extra challenge for more-able learners.**Connecting times tables game**

Develop pupils’ multiplication skills and encourage a healthy dose of competition with this twist on a classic game.

**Problem-solving cards**

Expose students to non-routine problems and encourage them to communicate their methodology with this collection of challenging questions.**Puzzle sheets**

Suitable for the first few lessons, these challenges are ideal for helping pupils to think more deeply and work productively with their peers.**Question of the day**

Introduce the new GCSE specification and challenge learners to answer one non-routine problem a day with this comprehensive pack.**Lock problems**

Covering a wide range of topics, this themed activity adds a fun twist to testing understanding as learners solve a series of questions.

**Algebra skills sheets**

As learners make the jump from GCSE to A-level, ensure basic algebra and number skills are up to scratch with this range of questions, complete with solutions.**Year 12 skills evaluation**

Test prerequisite A-level skills and identify pupils who are in need of more support with this introductory assessment.**Core 1 algebra introduction**

Recap your Year 12s’ understanding of algebra and set the tone for learning in the year ahead with this match-up activity.**Indices tasks**

Test students’ understanding of indices at a higher level and identify any common misconceptions they may have with this collection of exercises.

The post TES Maths Back to School appeared first on Mr Barton Maths Blog.

]]>The post Primary School Teacher Rachel Webster: How your Year 7s have been taught maths appeared first on Mr Barton Maths Blog.

]]>Rachel is a former primary school teacher who is taking on the role of a Primary Maths Specialist with the White Rose Maths Hub from September.

The reason I wanted to interview Rachel is that for many years I do not feel I have been teaching each new crop of Year 7s as well as I could have done. Dylan Wiliam has said one of the most important things for a teacher to know is where their learners are at, and I have made the mistake of pretty much assuming these Year 7s know very little about maths. I have introduced concepts such as fractions, factors, ratio and algebra as if they have never seen them before. Perhaps just as importantly, I wasn’t sure exactly what these Year 7s would be expecting maths lessons to be like based on their prior experiences. Just in case any other teachers out there want to know a bit more about the mathematical background of their Year 7s, I thought it would be worthwhile having an experienced primary teacher such as Rachel on the show, and thank goodness I did, as it proved to be a cracker!

In a wide-ranging interview, we covered the following and more:

- Rachel takes us through the planning and delivery of a Year 6 lesson on percentages, explaining the format and content of the lesson – and I learn all about steps to success!
- We look at how Rachel differentiates
- I ask how has maths teaching at primary school changed over the last few years?
- We discuss the content and difficulty of the work students will have covered in Year 6
- We look at Year 6 students’ experiences solving problems
- Are Year 6 students used to explicit instruction?
- Why is mindset so important?
- What kind of homeworks would students be set?
- If it was up to Rachel, what would the first few lessons of Year 7 maths look like, and what advice does she have for Year 7 teachers?
- What are the best transition practices she has seen?
- And then a big one that I almost forgot – the role of manipulatives and equipment. What are students used to using?

If you have Year 7s at all this year, or if you have any influence over your school’s transition policy, then hopefully this will prove an invaluable listen. I know it will change how I approach my teaching, and I will reflect on that during my takeaway at the end of the interview.

The books Rachel recommends, along with the book recommendations of all my previous guests, can be found at **mrbartonmaths.com/teachers/books**

My research page, summarising my takeaways to over 100 papers can be found at **mrbartonmaths.com/teachers/research**

Rachel Webster’s Big 3

1. **NRICH**

2. **TES** for the **White Rose Maths Hub Schemes of Work**

3. **YouCubed**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Primary School Teacher Rachel Webster: How your Year 7s have been taught maths appeared first on Mr Barton Maths Blog.

]]>The post Chief Examiner Trevor Senior: How GCSE Maths exams are written appeared first on Mr Barton Maths Blog.

]]>Trevor is AQA’s Chief Examiner for the Maths GCSE.

As those of you teaching maths in the UK in the last couple of years will have experienced, there has been a tremendous amount of uncertainty, anxiety and expectation surrounding the new maths GCSE. It’s kind of been like awaiting the new series of Game of Thrones, only with slightly fewer dragons but possibly slightly more violent twists. Now, two years on, we have finally had the first set of students through and – at the time of recording – are awaiting the inaugural set of results. So, I thought it would be interesting to talk to one of the people behind the creation of the exams, and so it proved it be.

In a wide-ranging interview, we covered the following and more:

- How did the papers for the 2017 maths GCSE get written, from start to finish?
- How many people are involved?
- did the fact that it was a new specification change this process?
- What was the hardest part?
- How are the order of the questions decided?
- What role do multiple choice questions play?
- What makes a good and what makes a bad question?
- What are the considerations when writing contextual questions?
- What are some of Trevor’s favourite questions he’s ever written?
- How does the marking process happen?
- What makes a question particularly difficult to mark?
- When in the whole process, as a Chief Examiner, is Trevor at his most nervous?
- How are grade boundaries set?
- If Trevor could change the maths GCSE, what would he do?

If you teach GCSE maths now, or are planning to in the future, or if you have any interest whatsoever about how questions and exams are written, then I think you will like this one. Trevor is a knowledgeable, experienced, and an all-round superb guest. The episode is a nice companion piece to **my interview with Daisy Christodoulou** where we focussed in depth on assessment, and indeed I will discuss more about that in my Takeaway at the end of the interview.

The usual desperate plea that if you enjoy these interviews, and you have a spare minute, then please give the podcast a rating and a quick review on iTunes if. It really does make a difference and mean a lot, and thank you so much to those of you who already have. A new podcast seems to have entered the education chart this week – the Sexplanationas Podcast. I am not sure my three hour discussions of lesson planning, misconceptions and the subtleties of assessment objectives, will appeal to their audience, so I will need to rely on my own. Thanks you so much continuing to listen.

Trevor Senior’s Big 3

1. **Graphpapermaker.com**

2. **All about maths**

3. **How grades are awarded**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Chief Examiner Trevor Senior: How GCSE Maths exams are written appeared first on Mr Barton Maths Blog.

]]>The post Nick Rose: Mindset, Misconceptions, Differentiation appeared first on Mr Barton Maths Blog.

]]>Nick is a former science teacher who now works as a researcher for **TeachFirst** . He runs the excellent **Evidence into Practice** blog, and is the co-author of one of my favourite education books: **What every teacher needs to know about Psychology**, which he wrote with David Didau. Nick is particularly interested in applying psychology to teaching, and as a former A Level Psychologist myself (although I chose it more because there were only 3 lads on the course and 15 girls), and someone who is fascinated in how students think and behave, I was particularly interested in talking to him.

In a wide-ranging interview we covered the following, and more::

- How did Nick’s scientific background and study of paranormal activity affect the early days of his teaching career when confronted by things such as Brain Gym and Learning Styles?
- How did Nick plan not just a sequence of lesson, but an entire course?
- What did Nick learn from a lesson on half-lives that did not go to plan?
- Then we dive into some of Nick’s favourite areas of research, beginning with something I could happily talk about all day – misconceptions
- Is creating cognitive conflict an effective way to overcome misconceptions, and indeed can we ever truly overcome them?
- Should we only teach correct procedures, or should we expose students directly to misconceptions as part of the learning process?
- Then we move onto differentiation, looking at the many meanings of the term and some of the associated difficulties in building it into our teaching
- Next up is the concept of a growth mindset – is there any scientific validity in it, and crucially what can we do as classroom teachers to promote a positive way of thinking in our students?
- We touch upon motivation, and why success is an important factor for learning. I will discuss more on this during my Takeaway after the end of the interview.
- Finally, Nick reflects on some of his favourite pieces of research before selecting three cracking websites for us to check out

You know what I am going to say here – I think this is another must-listen. Nick drops little piece of gold dust throughout the interview. Mindset and psychology in general are topics that we have only touched upon in previous episodes, and it was both fascinating and enlightening to delve deep into them with an expert such as Nick. Along with my interviews with **Daisy Christodoulou**, **Tom Bennett**, **Dylan Wiliam** and the **Bjorks**, it could well be another one to share with you non-maths colleagues.

The usual mention of my research page. I have linked to and provided my own practical takeaways to over 100 papers that have changed my approach to teaching, and I will be adding the ones Nick discusses in this interview. You can find the page at **mrbartonmaths.com/teachers/research/**. And the usual plea, that if you enjoy what you hear, then please give the podcast a quick rating or review on iTunes. I have peaked at number 12 in the global Education chart, and am currently working on a petition to get all “learning language” podcasts banned so I can sneak into the top 10. Who needs languages anyway?…

On Twitter Nick is **@Nick_J_Rose**

His excellent blog can be found at: **evidenceintopractice.wordpress.com**

His phenomenal book is **What every teacher needs to know about Psychology**

Nick Rose’s Big 3

1. **American Educator**

2. **Dan Willingham blog**

3. **ResearchEd**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Nick Rose: Mindset, Misconceptions, Differentiation appeared first on Mr Barton Maths Blog.

]]>The post TES Maths Resource of the Day: July 2017 appeared first on Mr Barton Maths Blog.

]]>Here are my July selections. Just click on the resource description to download it.

And of course, all the resources selected are completely free. You just need to register on the TES website to download them. And as ever, a huge thank you to all the teachers who share resources. You make TES what it is

1st July: An interactive differentiated worksheet generator for expanding brackets

2nd July: A lovely set of PowerPoints on how to read and write bearings

3rd July: A nice way to visualise the famous grains of rice on a chessboard

4th July: A colourful clear way of working with fractions that make a whole

5th July: A collection of questions for regular practice on changing the subject

6th July: I love the OCR check in tests – this is on polygon properties

7th July: A Help Sheet and consolidation questions on constructions

8th July: A lovely set of questions on angles in polygons – not your usual ones!

9th July: A great exploration into the equation of a circle for GCSE

10th July: “Find someone who” is a lovely way to consolidate speed, distance, time

11th July: One for us Stats teachers: visualise confidence intervals on Excel

12th July: Ever wanted a formula for solving cubic equations? Here you go

13th July: A nice crossword puzzle on order of operations

14th July: A fun starter activity that is ideal for revising number properties

15th July: It’s amazing the range of questions you can ask on the 4 times table!

16th July: Shadows are made from a 3D shape. What is the 3D shape?

17th July: A short investigation into a puzzling percentages problem

18th July: A lovely collection of misleading graphs to provoke discussion

19th July: Assess students’ rounding skills all in one go!

20th July: Fraction picture, problem, calculation, solution match-up activity

21st July: A comprehensive Pythagoras revision activity

22nd July: A game of Snap with a negative numbers twist!

23rd July: Coordinate geometry and Pythagoras are needed for this aviation problem

24th July: My favourite spider activity now covers basic calculus!

25th July: A structured investigation into graphical transformations

26th July: A comprehensive lesson on place value

27th July: Use bar modelling for fractions of an amount

28th July: A gentle introduction to solving equations, complete with answers

29th July: A great review of area and circumference with plenty of variety in the Qs

30th July: A really nice expression match-up activity

31st July: A graphical way to see the purpose of expanding & factorising quadratics

The post TES Maths Resource of the Day: July 2017 appeared first on Mr Barton Maths Blog.

]]>The post Ed Southall – Part 2: Maths Puzzles and Lessons from Japan appeared first on Mr Barton Maths Blog.

]]>Ed is the course leader for the Maths Secondary PGCE at Huddersfield University, a maths tutor, and now a best-selling author, with his debut book **Yes, but why? Teaching for understanding in mathematics** currently Sage’s highest-selling book of the year. It’s an absolutely brilliant read, no matter how experienced a teacher you are, and surely it’s a matter of time before some Hollywood big-shot acquires the film rights.

Now, long time listeners of the podcast may remember **Ed’s first appearance on the show**, which was an absolute cracker. So, when I heard that Ed had been to Japan as part of the **IMPULS Lesson Study Project** to investigate how maths is taught in the Far East, I had to invite him back on, and flipping heck am I glad I did.

We had a fantastic conversation that covered the following things, and more:

- Why does Ed feel puzzles are so important, both for teachers and students, and what makes a good puzzle?
- What were Ed’s expectations before going to Japan?
- Then Ed describes in fascinating detail a lesson on sequences, comparing and contrasting it with how he might have approach the topic with his students in the UK
- How does planning take place in Japan?
- What does the scheme of work look like?
- How about the culture?
- Then the big one really: how will Ed’s experience in Japan change his own practice?
- And then, just as we are getting on so well and the interview is coming to an end, I decide to ruin it all by suggesting that there is a danger in asking for students’ thoughts and ideas when initially presenting a concept. Ed politely disagrees.

Ed is a pleasure to talk to, and whether I chat to him at a maths conference or over Skype for a podcast, I always come away more knowledgeable and with plenty to think about. I feel I understand the differences in approaches between Japan and the UK far more now, and crucially what we may want and not want to use in our own practices.I’ll even forgive him for not agreeing with me at the end.

The usual plea that if you enjoy this podcast, please give it a quick review and rating on iTunes. It really does make a difference to the podcast’s ranking, and thus to my ego. And please help spread the word about this podcast to your colleague. Many of you are using them as CPD on the move, whether it’s in the car on your way to work, doing the washing up, or as Jonathan Hall tweeted recently – providing a soundtrack at a barbeque. Who needs Ed Sheeran?

On Twitter Ed is **@solvemymaths**

His excellent blog can be found at: **solvemymaths.com**

His outstanding book is **Yes, but why? Teaching for understanding in mathematics**

Ed Southall’s Big 3

1. **Geogebra** and associated **materials **

2. **Mathforum.org**

3. **Mathschallenge.net**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Ed Southall – Part 2: Maths Puzzles and Lessons from Japan appeared first on Mr Barton Maths Blog.

]]>The post Maths Drills: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**What is it?**

Earlier this year I had the pleasure of attending a workshop called “Drill and Thrill” delivered by Dani Quinn, the Head of Maths at Michaela Community School. Since then, I have become a little obsessed with drilling. I had previously assumed it to be a case of hammering students with a load of the same questions, essentially drilling them into submission. But now I realise the key is the in the intelligent design of the questions – ensuring there is sufficient variety so that students do not develop an incomplete set of automated procedures that could lead to them being tripped up later on. Fortunately, Hin Tail from Michaela has shared this Drill Generator which shows exactly what such drills look like and how they are constructed. This particular one concerns multiplying and dividing by powers of 10 and is aimed at Year 7s, and you can generate different questions by pressing Shift-F9.

**How can it be used?**

Dani has provided an excellent overview of when drills should and should not be used in **a blog post** (based on her session and this resource in particular, and I would strongly advise readsing that before embarking upon some drilling with your students. Like many of the resources I feature on Resource of the Week, they key to success is consistency. Doing a drill once in a blue moon is not likely to have any long-lasting effect, and neither is drilling regularly for two weeks and then forgetting about it. Once or twice a week, every week, at the start of a lesson, can have a massive benefit on the fluency, competency and confidence of your students, and really stand them in good stead for all the mathematical topics that rely on a strong sense of number.

Thanks so much for sharing

Craig Barton

Download: **Maths Drills Generator
**View the

The post Maths Drills: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Kris Boulton – Part 1: Planning Lessons, Engelmann and Differentiation appeared first on Mr Barton Maths Blog.

]]>Kris is a maths teacher and the former second in department at King Solomon Academy, where he worked alongside fellow podcast guest **Bruno Reddy**, achieving incredible GCSE results in challenging circumstances. Kris now works for **TeachFirst**, where he is Associate Director of Participant Development, recruiting and training nearly 200 new teacher educators for the PGDE programme.

Kris’ blog **“… to the real”** is an absolute must read for all teachers, covering a wide range of issues, including how aspects of cognitive science, memory, philosophy, and even business principles can be applied to education.

If any of you have had the pleasure of speaking to Kris, and you have listened to one of my podcasts before, then you will not be at all surprised that Barton + Boulton does not equal Brevity. Indeed, Kris and I agreed to talk for two hours, and I had a list of questions to get through, covering areas such as questioning, schemes of work, variation theory, problem solving, and more. However, in the end I only really managed to ask one question: “how does Kris plan a lesson?”. But his answer is fascinating.

So, in covering that question we dived into issues such as:

- Why is planning a lesson the wrong way to approach planning?
- How and why does Kris break a topic – in this case simultaneous equations – into individual concepts?
- How has Kris been influenced by the work of Siegfried Engelmann?
- Can you teach the way Kris describes without the supporting behaviour and school ethos?
- How do you differentiate in a model of direct instruction, and indeed does differentiation matter?
- How do you interleave throughout a sequence of lessons, and what happens if students get stuck on a given concept?
- How can you tell that you have taught a successful sequence of lessons?
- What has Kris learned from lessons that did go wrong, and yet why as he unable to break that cycle for much of his first year of teaching?

As ever, I am ridiculously, biased, but this is pure gold. Kris is a thinker – “cerebral”, as previous podcast guest, **Will Emeny** described him. If any of you have been lucky enough to attend one of his workshops, or even just follow him on **Twitter**, you will have seen that for yourself. Kris has an ability to dissect issues, question assumptions, and convey complex ideas in ways that even someone like me can understand. There are few people in education that I have learned more from, and this interview is no exception.

I will be back at the end of the interview to share what I think is an important point about Direct or Explicit instruction, and Kris has promised to return, so I can work my way down the list of other questions I want to ask him. At this rate we should be done in around 87 hours, with the Boulton Box Set ready for some binge listening in time for Christmas 2026.

If you haven’t checked it out already, you may enjoy the research section of my website, which contains links and my takeaways to over 100 papers that have changed my approach to teaching. You can find the page at **mrbartonmaths.com/teachers/research/**. And the usual plea, that if you enjoy what you hear to give the podcast a quick rating or review on iTunes. I’m getting closer and closer to the Top 10 in the Education Chart. There’s just some obscure, low-budget affairs such as TED Talks, Tony Robbins and the London School of Economics standing in my way.

On Twitter Kris is **@Kris_Boulton**

His excellent blog can be found at: **tothereal.wordpress.com**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Kris Boulton – Part 1: Planning Lessons, Engelmann and Differentiation appeared first on Mr Barton Maths Blog.

]]>The post Averages and Range Spiders: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

For me, 2017 has been the year of the spider! I have already featured a spider activity as one of my previous Resource of the Week selections, but when I saw the quality of this resource, I could not resist choosing one again. This particular spider tackles the topic of averages and range in an incredibly challenging, engaging and ultimately useful way. Given a set of 5 numbers, one of which is missing, students must choose a correct number to match a series of conditions related to average and range, such as making the median 4, or the range 6. This gets them thinking about averages in reverse, and can lead to a deeper understanding of a topic that is often in danger of being dominated by abstract, easily forgotten rules.

**How can it be used?**

If students are not comfortable with the basics, then an activity like this may well tip them over the edge! So, I would advise covering or recapping the concepts of mean, median, mode and range first. Then, when you feel students are ready for the challenge, it is time to unleash the spider! This activity lends itself well to paired work, providing plenty of opportunity for discussion, especially on those occasions when there might be more than one correct answer. The third spider even introduces two missing numbers, which significantly ups the challenge. Fortunately, answers are provided. Finally, there is always the opportunity to ask students to create their own spiders, maybe with constraints that they cannot have the same answer more than once, to really test their understanding.

Thanks so much for sharing

Craig Barton

Download: **Average and Range Spiders**

View the **author’s other resources**

The post Averages and Range Spiders: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post TES End of Term Activities appeared first on Mr Barton Maths Blog.

]]>Now that the exams are done and your reports have been submitted, the countdown to the summer break is officially on! And what better way to end the year than with a few fun lessons, designed to keep pupils learning right up until the final bell rings?

As always, a big thank you must go to the Tes Maths community, which is entirely responsible for this creative collection of mathematical challenges and games. I look forward to seeing even more innovative ideas in the new academic year. Happy holidays to you all!

Craig Barton, Tes Maths adviser

**Whole-class pub quizzes**

Encourage healthy competition between pupils as they group together to answer quick-fire questions, complete memory challenges and solve dingbats as part of these multi-round quizzes.**Fun review quiz for KS3**

Revise essential topics with a variety of questions and timed challenges spread over five rounds. The answers are even included, making awarding the winner that much easier.*Pointless*-themed activity

Merge maths with a classic teatime game show to stimulate interesting discussions among your students using this interactive presentation, covering a number of key topics.**Maths murder mystery**

Get pupils deciphering five clues to reveal a single culprit from 32 suspects in this murderous activity, which recaps knowledge of 2D shapes, angles and coordinates.

**Modern art maths**

Practise converting fractions, decimals and percentages by encouraging pupils to create works of art using a classic 10×10 number grid as part of this well-structured activity.**Curves of pursuit slides**

Promote an interest in geometry while recapping key compass and ruler skills in this fascinating lesson, which sees learners creating beautiful, display-worthy shapes.**Maths relay races**

Pit pairs of students against each other to see who will be the first to complete a series of number puzzles, ideal for both KS3 and KS4 classes.**Ever-popular pirate game**

This pirate-themed strategy game is a firm favourite in many classrooms. And now, why not maximise your time on the high seas using this handy game grid generator?

The post TES End of Term Activities appeared first on Mr Barton Maths Blog.

]]>The post Sequences Visualiser: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

This is a superb resource to help students relate the nth term form of a sequence to the actual sequence itself. It consists of an Excel file, where the user can adjust the nth term rule and see the sequence magically appear on a 10 x 10 number grid. The advantage of displaying the terms of the sequence in this form, as opposed to simply listing them, is that it is easier to spot patterns and hence form a better understanding of the role each of the variables in the nth term representation of the sequence plays.

**How can it be used?**

This wonderful resource could be used two ways. Firstly, as a way to introduce nth term rule via pattern-spotting – with the teacher systematically changing the variables in the formula, the students observing the effect on the grid, and then discussing and predicting what role each variable plays. Secondly, it could be used to facilitate a deeper understanding and further investigation into linear sequences. On this latter point, the author provides some excellent suggestions for questions to ask.

Can you tell me a sequence that:

i, only uses multiples of 3

ii, includes as many prime numbers as possible,

iii, only makes numbers appear in columns

iv, makes only 6 numbers appear

v, makes only numbers under 40 appear

vi, shows all the numbers that are 3 less than a multiple of 7…

Thanks so much for sharing

Craig Barton

Download: **Linear Sequence Visualiser**

View the **author’s other resources**

The post Sequences Visualiser: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post TES Maths ROTD: June 2017 appeared first on Mr Barton Maths Blog.

]]>Here are my June selections. Just click on the resource description to download it.

And of course, all the resources selected are completely free. You just need to register on the TES website to download them. And as ever, a huge thank you to all the teachers who share resources. You make TES what it is

1st June: Quiz students on key GCSE formulae with this Catchphrase activity

2nd June: Loads and loads of manipulating algebraic expressions practice

3rd June: Clear step-by-step guide to dividing using the bus-stop method

4th June: Another amazing spider activity, this time on Rounding

5th June: These gradient and area graphs lessons are phenomenal

6th June: Lovely worksheets and [problem cards for addition and subtraction

7th June: Differentiated questions on probability tree diagrams

8th June: Problems & activities for multiplying & dividing by 10, 100 etc

9th June: All the Excel generated worksheets you could ever need!

10th June: A superb selection of Key Stage 4 starters, complete with answers

11th June: A great 16 question angle properties relay race

12th June: Practice equations of straight lines with this aircraft hanger mini project

13th June: Pre and post assessments on a range of statistics topics

14th June: Some nice probability problem solving questions with And or OR

15th June: A quick True-False activity for multiplying with algebraic terms

16th June: A simple, but effective activity on converting hrs & mins to decimals

17th June: A fun theme-park activity on writing formulae

18th June: A superb mystery on roots, factors and links to cubic graphs

19th June: “A Dozen Questions” is a nice format for a homework or low-stakes quiz

20th June: “The Little Book of Circle Theorems” is a fun, foldable revision tool

21st June: A simple, but effective fraction sorting activity that leads to ordering

22nd June: A fantastic lesson on all aspects of pie charts, complete with animations

23rd June: “Related Calculations” challenges students’ knowledge of decimal operations

24th June: A great set of coordinates problem solving activities

25th June: Nice choice of questions on algebraic area and perimeter

26th June: A really nice lesson to introduce algebraic fractions

27th June: A lovely quiz that you might want to bank for the end of term

28th June: Want 50 factorising quadratic questions with answers? Here you go

29th June: A nice set of quick number puzzles that would make ideal starters

30th June: A nice introduction to vectors using chess pieces

The post TES Maths ROTD: June 2017 appeared first on Mr Barton Maths Blog.

]]>The post Robert and Elizabeth Bjork – Memory, Forgetting, Testing, Desirable Difficulties appeared first on Mr Barton Maths Blog.

]]>Robert Bjork is Distinguished Research Professor in the Department of Psychology at the University of California, Los Angeles. Robert’s research focuses on human learning and memory and on the implications of the science of learning for instruction and training. Elizabeth Bjork is Professor of Psychology and Senior Vice Chair in the Psychology Department also at the University of California. Elizabeth’s main area of research has been the study of human memory, in particular, the role that inhibitory processes – such as those underlying goal-directed forgetting and memory updating – play in creating an adaptive human memory system. As well as countless prestigious honours they have received across their distinguished careers, they now have a new one: the first married couple on the Mr Barton Maths Podcast.

I thought my life had peaked when I interviewed **Dylan Wiliam**, but it has risen to a whole new level when I got to interview not one, but two of my heroes. Along with Dylan and Dan Willingham, Robert and Elizabeth Bjork have had a profound effect on my career, making me realise – among other things – that forgetting is beneficial, learning and performance are different, and learning should be desirably difficult. A huge thank you to **Will Emeny** for playing match-maker and helping this interview take place. I owe you, Will, big time.

In a wide ranging conversation we covered the following things and more:

- What misconceptions do you find people have about how memory works?
- What is the relationship between learning and performance? Can it really be inverse?
- Should learning be desirably difficult in the initial skill acquisition phase, and how does this fit in with Cognitive Load Theory?
- The most requested question on Twitter: Is there an optimal spacing schedule? And stay tuned for my Takeaway at the end of the podcast for more on this.
- What is worse – too short a spacing interval so students have not had time to forget, or too long so students have completely forgotten?
- Do the benefits of interleaving suggest deliberate practice (breaking down of skills, immediate feedback) is not an effective form of instruction?
- After decades of work in the field of memory, what is the piece of research that has surprised them the most – and it has significant implications for how we develop our students to become problem solvers.
- And to top it off, Robert has a selection of book and website recommendations, all of which are linked to in the show notes.

In the Takeaway section after the interview I delve deeper into a few points I have been thinking lots about since the conversation. I look again as Assessment for Learning, including the use of Exit Tickets, and I feel I am finally at a place where I am happy with its role in lessons. I look at a way to calculate an optimal spacing schedule. I discuss the aforementioned implication of how memory works for the development of problem solving. And finally, I touch upon the role of motivation in learning with respect to desirable difficulties and the concept of a pre-test. It’s a big fat tasty Takeaway this time! So, if that is of interest, please stick around at the end.

I have written up my Takeaways to many of the concepts and research papers we discuss in the interview, along with hundreds of others, on my research page. You can find it at **mrbartonmaths.com/teachers/research/** I really hope you find it both interesting and useful.

Finally, If you enjoy this podcast, please share it with your colleagues. This one in particular might be of interest to your less mathematically inclined workmates. You can assure them that (for once) all references to numbers and algebra are kept to an absolute minimum. And my usual plea – if you have time to give us a review on iTunes, then the egomaniac in me would be delighted.

The Bjork Learning and Forgetting Lab, which contains lots of incredible research papers, can be found at **bjorklab.psych.ucla.edu**

To excellent blog post on spacing that I discuss in the takeaway is by Damian Benney and can be found **here **

The Bjork’s Big 3

1. Book: **Make it Stick: The Science of Successful Learning**

2. Book: **How We Learn: Throw out the rule book and unlock your brain’s potential**

3. Website: **Lasting Learning **

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

The post Robert and Elizabeth Bjork – Memory, Forgetting, Testing, Desirable Difficulties appeared first on Mr Barton Maths Blog.

]]>The post Gradients and Distances Game: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>To see all of the work I do for TES Maths, including Resource of the Week, **Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Picture the scene. You have just your class how to work out the gradient and distance between two points, they have practiced the basics, and now you are on the lookout for something different. If only there was a way to ensure they continued to get that valuable practice, but in a slightly more engaging context that may just lead to them developing other skills along the way. Well, fear not! Your prayers have been answered. This is a lovely, original strategy game, where two students play against each other, plotting points on a coordinate grid and working out the gradient and distance. The twist is that once a particular gradient or distance has been used, it cannot be used again!

**How can it be used?**

This is an ideal activity to use either straight after gradients and distance have been taught, or as a way of revising the skills. You also have the added bonus that it helps to develop the skill of completing the gradient/distance calculation on a grid by imagining the appropriate right-angled triangle. As with any game like this, you are faced with the problem of checking students’ answers. With so many different possibilities for game structures, how on earth are you going to check if students are making mistakes or not? Well, that is the beauty of competition – the opposing player has every opportunity to check the player’s answers. Any disputes could be settled by you, or better still be another student. If you are feeling particularly brave, a good question to ask might be: “what is the longest game two people could play before one person cannot move?”. I would love to say I have worked that one out myself, but I would by lying. I just love the simplicity of this game, and yet it does absolutely everything I could want.

Thanks so much for sharing

Craig Barton

Download: **Gradients and Distances Game**

View the **author’s other resources**

The post Gradients and Distances Game: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Place Value and Number Properties: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

I love this simple, engaging activity that helps students practice their key numeracy skills. It consists of a bright, colourful Excel file that is able to generate a random 4 digit number, and a worksheet. But that is all you need! Once the number has been generated, students are then challenged to write down things like: the biggest number, the smallest odd number, the smallest three digit number, the number closest to 3000, and to use each digit once to make the biggest total _ _ + _ _. Think of all the key numeracy skills students are practising here. And there is potential for even more, as we will see shortly!

**How can it be used?**

We have started using this once a week with our lower Year 7 and Year 8 classes, and it has been a huge success. We have printed out loads of copied if the worksheet so they are to hand in classrooms whenever they are needed, and then no preparation is needed at all. I use this at the start of a lesson, give the students around five minutes to complete, and then talk through the answers. There is always at least of couple of controversial questions that cause some discussion. So, this resource is excellent as it stands, but I think it could be made even better by the addition of a few extra questions to accompany the selection of numbers. How about asking some/all of the following:

What is the largest factor of 3?

What is the largest 2 digit prime number?

What is the smallest multiple of 12?

What is the biggest total _ _ – _ _?

What is the biggest total _ x _ _ _?

The beauty is that every number-based topic you study probably lends itself to even more questions, so this really is the activity that keeps on giving

Thanks so much for sharing

Craig Barton

**Download: Place Value and Number Properties
View the author’s other resources
**

The post Place Value and Number Properties: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Fractions Mastery Lesson: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

The term “Mastery” gets banded around a lot these days. I think we need to be clear that there are series of lessons that are used with a complete mastery approach, but the idea that you can dip into mastery for one off lessons is – in my opinion, anyway – a bit of a misnomer. However, this is undoubtedly an excellent lesson on the four operations of fractions, that with adaptation could be used by anyone. There is a starter that covers concepts that the students may have encountered earlier in the year, including factorising and rearranging equations. And then we move onto my favourite part – the selection of questions. Take the slide on additional and subtraction of fractions. Sure, we have standard questions involving proper fractions, but then we have improper fractions, three fractions, algebraic numerators and algebraic denominators. This is one of the key components of mastery – when introducing a new skill (adding and subtracting fractions) take the opportunity to revisit previous topics (conversion, simplifying expressions, expanding brackets, etc). All of this is rounded off with a classic problem from NRICH and an exit ticket that can be used to review progress.

**How can it be used?**

The reason I put that warning at the start was that if students are not used to this kind of approach, trouble may be brewing! If students have not encountered, or are not comfortable with, the additional concepts that are woven into this study of fractions, then they will not be able to answer the questions and as a teacher you will have a difficult decision to make – do you teach them the topic there and then and risk derailing the main purpose of the lesson, or do you just move on and leave your students confused? It is a tricky one. That is why lessons such as these need to be used carefully. May advice – even if you are following a mastery curriculum – is that you go through the questions and edit them as necessary to ensure they are suitable for your class. That way you will end up with all the benefits of this wonderful resource – the lovely structure, the range of questions complete with answers – but with none of the potential pitfalls. Alternatively, this lesson may be used as a revision resource for a Year 10/11 class who have finished the curriculum and are preparing for an exam. The fact that several concepts are all rolled into one makes it particularly suitable for this.

Thanks so much for sharing

Craig Barton

Download: **Fractions Mastery Lesson**

View the **author’s other resources**

The post Fractions Mastery Lesson: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post TES Maths Newsletter: June 2017 appeared first on Mr Barton Maths Blog.

]]>With the summer holidays in sight, what better time to review the crucial skills that students have learnt throughout the year? To make this as easy as possible, I’ve pulled together a selection of some of my favourite, top-rated resources to support learners as they revisit their old friends: algebra, probability and the four operations.

Once again, a big thank you must go to the kind and generous Tes Maths community, whose resources continue to help make teaching and learning mathematics endlessly engaging.

Craig Barton, Tes Maths adviser

**Addition and subtraction activity**

Encourage younger students to nuture a deeper understanding of the process and meaning of adding and subtracting with this selection of problem-solving cards.**Bus stop division presentation**

Introduce learners to the bus stop method of division using this interactive presentation, complete with starters, clear examples and differentiated consolidation questions.**Long multiplication worksheets**

Develop pupils’ understanding of multiplication using these scaffolded worksheets, jam-packed with non-routine questions covering a variety of methods.

**Algebraic expressions booklet**

Including a wide range of ready-to-use practice questions, this versatile resource explores a number of key algebraic skills and comes complete with answers.**Manipulating algebraic expressions**

Covering 11 topics, this collection of thought-provoking tasks allows more-able students to start spotting useful patterns as they progress.**Algebraic magic square**

Use this simple idea to get pupils simplifying algebraic expressions by expanding linear brackets, collecting like terms and using logical reasoning.

**Bottle-flipping exercise**

Cover the abstract concept of experimental probability with this innovative activity, in which learners investigate fractions, decimals and percentages.**Venn diagrams presentation**

Help older students to identify and shade the key regions of a Venn Diagram, including unions and intersections, with this clear set of animations.**Tree diagram problems**

Challenge pupils to delve a little deeper into probability and tree diagrams by working through this selection of extension questions.

The post TES Maths Newsletter: June 2017 appeared first on Mr Barton Maths Blog.

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]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

I am a huge fan of novel, engaging ways to test familiar and crucial mathematical skills. Take expanding and factorising single brackets. Students probably encounter this topics for the first time in Year 7, and yet the vast majority will still need practice into Year 11. This variation on a traditional worksheet is a superb way to ensure get that all-important practice, but with the added bonus of a bit more challenge and hopefully some extra engagement. Basically, there are 18 questions, ranging from expanding a single bracket right up to expanding and then simplifying via subtraction. Each question has been completed, but… and here is the twist.. there are gaps to be filled in! Now, this may not sound like much, but successfully filling in these gaps requires students to demonstrate their full range of skills when it comes to expanding, factorising and simplifying algebraic expressions.

**How can it be used?**

If students are not comfortable with the basics, then an activity like this may well tip them over the edge! So, I would advise starting with a few worked examples, together with similar questions for students to complete. Once you are happy that the core elements are in place, then you can unleash them on this beauty. Another advantage of an activity like this is that it is easy for the students to check if they have got a question correct – simply tell them to cover up the answer, and work through the now completed question like they would in any other circumstance and see if they arrive at the answer. I am such a fan of this format that it has got me wondering just how many other topics it could be applied to. Operations with fractions immediately springs to mind, but I am sure there are more

Thanks so much for sharing

Craig Barton

**Download: Expanding Bracket Gap Fill
View the author’s other resources
**

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]]>The post TES Maths Resource of the Day: May 2017 appeared first on Mr Barton Maths Blog.

]]>Here are my May selections. Just click on the resource description to download it.

And of course, all the resources selected are completely free. You just need to register on the TES website to download them. And as ever, a huge thank you to all the teachers who share resources. You make TES what it is

1st May: An excellent lesson on Venn Diagrams, ideal for GCSE revision

2nd May: These average and range spiders are amazing

3rd May: A stunningly good circle theorems codebreaker

4th May: If you’ve not seen Going for Gold GCSE Problem Solving, you’re in for a treat

5th May: A wonderful collection of addition & subtraction, standard and worded problems

6th May: A superb lesson on sketching cubics and quadratics – perfect GCSE revision

7th May: This tool for visualising nth term sequences is absolutely ideal

8th May: An amazing lesson on surds, right up to Grade 9 and beyond!

9th May: One for A Level teachers Laws of Logs Codebreakers!

10th May: Students are given various 3D shapes and must come up with questions to answer

11th May: There’s not much good GCSE stuff around for tangents to graphs – until now!

12th May: It’s Spider Time! Here we look at linear graphs. I love these!

13th May: Turn the annoying craze of bottle flipping into an experimental probability activity

14th May: A couple of challenging angle problems to get your students thinking

15th May: A differentiated set of worksheets on factors, multiples and primes

16th May: A fantastic lesson on the equation of a circle for the new GCSE

17th May: A well designed worksheet on simplifying expressions, with answers

18th May: A lovely set of questions on similarity in 2D shapes

19th May: Let’s play “Independence, Dependence, Mutually Exclusive or Not?”

20th May: A superb introduction lesson to Venn Diagrams and sorting

21st May: Mathonopoly is a simply superb GCSE Maths revision activity

22nd May: A lovely selection of worksheets and activities on long multiplication

23rd May: A great set of questions on circumference and area

24th May: These Explosions are ideal for practising the basics of solving linear inequalities

25th May: “Teach for Understanding” is excellent for departmental meetings

26th May: An outstanding Proportion Spider for top-quality, engaging practice

27th May: A complete lesson on error intervals and truncation

28th May: A superb lesson introducing the balancing method for solving equations

29th May: A lovely set of questions on ratio & proportion within the context of a theme park

30th May: A superb lesson on drawing and comparing bar charts

31st May: Practice solving quadratic equations with this lovely codebreaker

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]]>The post Diminishing Fractions Diagrams: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Fractions are a minefield of misconceptions. Despite the fact that students technically encounter equivalent fractions for the first time in Year 2, many still enter Year 11 with some serious holes in their understanding of fractions. Hence, any activity that can help students develop a deeper understanding, perhaps by presenting fractions in a different way, is going to be a Godsend for me. Step forward Diminishing Fraction Areas. This is a wonderful collection of fraction diagrams, accompanied by a series of questions. These include things like “what fraction of the whole shape is the red square?”, right the way up to “what is two thirds of a half?”. The supporting diagrams help illuminate potentially abstract concepts and should provoke plenty of discussion amongst your students.

**How can it be used?**

In my opinion, there is no point taking on an activity like this until students’ basic understanding of equivalent fractions and fractions of a shape is reasonably secure. You cannot teach the basics of fractions through this activity, but you can use it to help students make connections and deepen their understanding. Personally, I would have the students working in paris on one sheet at a time. The collection of questions is well structured in that it increases in difficulty as you go through it, so starting everyone off on the first square challenge seems sensible. Students will undoubtedly need support, and periodically stopping the class to discuss strategies and assumptions may be a good way to go. But even if students run into difficulties, I would advise you persist with this wonderful resource, because the concepts involved are crucial, not only for students’ understanding of fractions, but they also transcend into topics such as area, geometrical properties of shapes, ratio and more.

Thanks so much for sharing

Craig Barton

**Download: Diminishing Fraction Diagrams
View the author’s other resources
**

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]]>The post Fairground Probability Games: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

I have discussed before how much I adore probability, and yet it continues to be a topic that many students find tough to grasp. I believe that is due to the abstract nature of the topics. Probabilities of 0.34 and ⅖ may mean very little to students, and hence they have no way of judging the validity of their answers or forming the deep structures needed to fully understand the topic. Therefore, any resource that can make probability a little more concrete is always going to go down a storm with me. And this is exactly what Fairground Probability does. Students are presented with 8 classic fairground games and asked to work out the percentage of winning each one. Along the way they cover sample spaces and tree diagrams, as well as looking at dependent and independent events. It is pretty much the entirety of GCSE probability all wrapped up into one lovely activity.

**How can it be used?**

Such an activity lends itself particularly well to students working in small groups. You could give them all 8 games out at once, or set this up as a carousel activity whereby students get to spend 5 minutes analysing each game before moving on. To aid the move from abstract to concrete it would be great to provide students with some physical materials, such as dice and spinners so they could try out the games to get a sense of their answers match up in practice. Finally, alongside the lovely extension material provided there is also the opportunity to have students produce their own fairground game and work out its probability. Or – and this is a classic – can they design a game that has a given probability of being won?

Thanks so much for sharing

Craig Barton

**Download: Fairground Probability
View the author’s other resources
**

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]]>The post The pitfall of inquiry based learning – My interview on the Bedley Bros Podcast appeared first on Mr Barton Maths Blog.

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]]>The post Dani Quinn – Part 2: Michaela School, Behaviour, Drills, Culture appeared first on Mr Barton Maths Blog.

]]>This is Part 2 of my interview with Dani Quinn, the Head of Maths at **Michaela Community School** (Part 1 can be found **here**). Before we go any further, I feel I must clear a few things up. Firstly, I do not receive money or gifts or products or anything like that for having particular guest on the show, as has been claimed by some – although if representatives from Adidas, Apple, or Caribbean Cruises would like to be interviewed, then those rules could easily be changed. Likewise, I am not under any pressure whatsoever from anyone to have particular guests on the show. I choose who I find interesting and who I hope my listeners will find interesting. Secondly, if you disagree with what I say, or what my guests say, then that is absolutely fine. In fact, I encourage it. If you choose to air your disagreements on Twitter, copying in the likes of Ofsted, Nick Gibb, the NSPCC, the DfE and The Christian Society, then that is also fine. It is your right, after all. But if you make personal insults towards my guests who have given up hours of their free time, or tell me (as two people did) to “go to hell”, then I am unlikely to engage in debate with you. Whenever I say “I will see you on the other side” just before I introduce each guest, I didn’t quite expect the other side to be interpreted as the fiery gates of the underworld. I do these podcasts because they make me think about my own practice, learn things, strive to get better, and because I get to enjoy conversations with some of my heroes. If you want to debate, then brilliant, just try not to be a *?!* about it.

Anyway, onto the show. Now this interview is essentially split up into three sections.

Section 1 wasn’t really supposed to be a section at all – more of a quick way to introduce Part 2. But it led us into some unexpected and fascinating territory.

– I asked Dani what it is like to be head of maths in arguably the most scrutinised school in the country

– Why does she feel internal scrutiny more than external scrutiny, and why is this a good thing?

– Why are staff at Michaela so honest in their evaluations of each other both in and out of lessons – I found this bit fascinating, and I am sure the haters will have a field day with this one!

– How do Dani – and Michaela staff as a whole – react to something so public, like “angle-gate”?

Section 2 is the big one – behaviour at Michaela

– What is the philosophy underpinning the behaviour policy at Michaela?

– How does the system of merits and demerits work?

– On the spot we invent the game “Merit, De-merit, Nothing or Impossible at Michaela” (I need to work a little on the title before I sell this to And and Dec for millions) to see how common student behaviours would be dealt with at Michaela

– How does the policy of “no exceptions” or “no excuses” work when faced with students with particularly difficult circumstances?

– How do students who join the school mid-year cope with such a shift in culture and practice?

Section 3 returns to the topic of teaching mathematics,

– How do drills in maths lessons work at Michaela?

– How does Dani prevent students valuing speed ahead of accuracy?

– How does Dani decide which “tricks” or shortcuts are acceptable to be used in Drills, and which are not?

– We dig deeper into teaching the how before the why – something that I am fascinated about at the moment

– And then – after getting on so well over two podcasts and 6 hours of conversation – it all falls apart when Dani and I clash on the use of mistakes and misconceptions during explicit instruction. Should students be confronted with common incorrect procedures in a bid to convince them why they are wrong, or does this do them more harm than good? You’ll have to stick around to the end to find out.

You know what I am going to say here – I think this is a fascinating conversation. Whether you agree or not with what Dani says, and the philosophies and practices at Michaela as a whole, two things remain unequivocally true. Firstly, you cannot fault Dani’s enthusiasm, passion and dedication to what she believes in. Secondly, I guarantee it will make you think.

On Twitter Dani is **@danicquinn**

Her excellent blog can be found at: **missquinnmaths.wordpress.com/**

My educational research page can be found at: **mrbartonmaths.com/teachers/research/**

Dani Quinn’s Big 3

1. **Median Maths Blog**

2. **UKMT Past Papers**

3. **David Rayner Textbooks**

Dani’s Book recommendations:

**Seven Myths About Education
**

You can find all the books my podcast guests have recommended here: **mrbartonmaths.com/teachers/books/**

If you enjoy this podcast, please share it with your colleagues, leave a review on iTunes if you have time, and feel free to give me a shout on Twitter where I am **@mrbartonmaths**

Thanks so much for listening, and I really hope you enjoy the show!

Craig Barton

**mrbartonnmaths.com**

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]]>The post Last Minute Revision Resources – GCSE and A Level appeared first on Mr Barton Maths Blog.

]]>With examinations fast approaching, revision is now firmly on the brain. To help your students feel prepared for any question, I’ve pulled together this collection of classroom-ready resources, ideal for recapping key topics on the new GCSE and A-level specifications.

As always, a big thank you must go to the ever-talented Tes Maths community for contributing their imaginative and engaging ideas. With these activities, notes and worksheets, pupils are sure to feel secure in their mathematical ability as they turn over that exam paper for the first time.

**Multiple-choice quizzes**

Designed for those taking the higher exam, this collection of multiple-choice quizzes covers 13 key skills and provides an engaging way for students to ensure that their knowledge is secure.**Handy revision mats**

Take the stress out of revision with these mats, which are comprised of multi-mark questions covering a wide range skills, from solving linear equations to interpreting distance-time graphs.**Topic-based revision clocks**

Revision clocks are back! Focusing on tricky four-mark questions and complete with a mark scheme, this very timely resource offers a unique format for revising six different topic areas.**Maths revision race**

This revision tool, consisting of 15 foundation-level questions, encourages a bit of healthy competition and is particularly helpful in helping pupils to identify gaps in their knowledge.**Beat the clock game**

Suitable for both foundation and higher classes, this simple activity is ideal for getting students to practise answering straightforward questions quickly and effectively within an allotted time.

For even more revision inspiration, look back at our **dedicated GCSE revision collection**, including both general and tier-specific lesson ideas.

**C1 revision notes**

Designed for the Edexcel specification but applicable to most boards, these hand-written, student-friendly revision notes provide a visually attractive way of recapping key learning points.**Revision relay game**

Get learners flying through exam-style questions related to the C2 module with this highly engaging relay structure, which comes complete with detailed teacher instructions.**More revision races**

Covering a number of different modules, these races offer ample opportunity for students to check their understanding of a range of topic areas in a competitive classroom environment.**General assessments**

Realistic, exam-style practice is crucial and these comprehensive assessment sheets provide exactly that. They can be used in class or at home and are perfect for revision across the boards.**Homework packs**

Jam-packed with exam questions, these workbooks are ideal for recapping specific topics outside of the classroom. There are even separate answer booklets to help make marking simple.

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]]>The post Algebra Relay Races: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

I love a relay race. Okay, it can become a little bit on the hectic side, but in my experience this is more than made up for by the fact that students seem to get through considerably more work than they would in a normal lesson. There is something about the increased levels of engagement and focus that such competition brings. And this relay activity is particularly impressive given that it covers most of the key algebra skills that students will need for their GCSEs. Throughout the 10 rounds we cover expanding brackets, factorising, substitution, solving linear equations and identifying expressions, equations and formula. The choice and progression through the questions is outstanding. Best of all the answers are also provided, saving us busy teachers a good amount of precious minutes.

**How can it be used?**

This activity is perfect for GCSE revision, but also more than suitable for younger year groups. The rounds increase in difficulty, so there is no problem chopping off a few of the later rounds if they prove too challenging. The author provides some really nice suggestions and variations for running this activity, and I can do little better than to share their thoughts:

Depending on ability I give different guidance. For top groups I say how many are incorrect but do not identify which ones and for lower ability I point out the questions they need to work on.

Makes for a very fun and competitive lesson. Feel free to make up your own rules to direct the game. I use time outs for cheating (or running!) and give a merit to the pair who has completed the most rounds. For some groups I create an accuracy prize as well so it’s not all about speed.

Thanks so much for sharing

Craig Barton

**Download: Algebra Relay Races
View the author’s other resources
**

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]]>The post Expanding Brackets Spiders: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

Despite being a little bit of an arachnophobe, I have been very pleased to see a growing number of these “spider” activities appearing on TES. They are simply ideal for getting students to practise key skills in an engaging way, whilst at the same time allowing them to spot patterns and make connections. This particular one on brackets is a prime example. Students are challenged to complete spiders that start with the basics of expanding double brackets, right through to factorising tricky quadratics. They do this by filling out the missing boxes in the brackets spider. As with all good resources, students get through a large amount of important work without necessarily realising it.

**How can it be used?**

This set of sheets provides ideal practice following the introduction of brackets, or as part of a revision exercise. Students can work together, or on their own, and can be challenged to identify which squares they found the trickiest to complete and discuss why that might be the case. Best of all (and I love it when this is the case) the answers are provided, which makes maring a breeze. The author has also kindly provided a template, which could be used by the teacher to create their own examples, but better still give this to the students. If they can both complete and create spiders, then we can be pretty sure that they understanding is secure.

Thanks so much for sharing

Craig Barton

Download: **Expanding Bracket Spiders**

View the **author’s other resources**

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]]>The post TES Maths ROTD: April 2017 appeared first on Mr Barton Maths Blog.

]]>Here are my April selections. Just click on the resource description to download it.

1st April: A lovely problem-solving question on perimeter, ideal for Years 5 to 9

2nd April: A set of differentiated worksheets on working with algebraic indices

3rd April: Practise percentage increase/decrease via Supermarket Sweep!

4th April: 3 ideal trigonometry codebreakers on SOHCAHTOA and Sine/Cosine rules

5th April: A well structured & resourced lesson on the basics of place value

6th April: I could do with these myself – a series of lessons on Financial Maths

7th April: An excellent end of topic fractions summary quiz on PowerPoint with answers!

8th April: A superb lesson on expanding single brackets

9th April: Resources to cover the basics of negative numbers, then a problem solving twist!

10th April: A lovely lesson on associative and distributive laws

11th April: A lovely set of activities on classifying regular and irregular polygons

12th April: Thoughts and Crosses returns with Volume of a Frustum!

13th April: The complete guide to Box Plots using the TI Inspire calculator

14th April: A delightful BIDMAS activity involving adding brackets

15th April: A differentiated set of worksheets on solving simultaneous equations

16th April: Worksheets from the basics of linear equations to worded questions

17th April: Complete lesson on completing the square, including turning points

18th April: A superb, challenging lesson on all aspects of fractions, complete with answers

19th April: These algebraic expression spiders are a thing of beauty

20th April: Lovely activity to help students develop the vocab to describe sequences

21st April: An ideal, scaffolded worksheet on calculating surface area of prisms

22nd April: I love this rearranging formula match-up activity

23rd April: An epic collection of starter questions on completing the square

24th April: A superb set of challenging ratio questions ideal for the new GCSE

25th April: This Capture-Recapture lesson is perfect for the new Edexcel Higher GCSE

26th April: A fantastic Venn Diagram lesson, suitable for GCSE or A Level students

27th April: A great resource for building confidence in unstructured trigonometry questions

28th April: This might well be my favourite expanding brackets activity ever

29th April: A really clear lesson on division of fractions by a whole number

30th April: A really engaging lesson idea for working with scale and bearings

The post TES Maths ROTD: April 2017 appeared first on Mr Barton Maths Blog.

]]>The post Numeracy Races: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>**Inspect the Spec**, Maths Newsletters and Topic Collections, please visit the **TES Maths Blog here**

**What is it?**

There is little doubt (at least in my mind anyway!) that developing student’s fluency in mental calculations is absolutely crucial for their mathematical development. If students are using valuable working memory capacity dealing with times tables or simple subtractions then they have little chance of success when it comes to more complex problems. Hence, any resource that allows students to practise these key skills, but in an engaging way, is always going to go down a storm with me. And that is exactly what this collection of wonderful numeracy races do. It is such a simple idea – students must complete the circuit around the track as quickly as possible, answering questions on each of the four operations or rounding. The benefits of this could be immense!

**How can it be used?**

I think the key to something like this is consistency. If such activities are used a couple of times and then forgotten about, they tend to have very little impact. However, if this becomes a regular part of your daily or weekly routine, then both you and your students will see the long term benefits. Personally I would give this printed sheet out at the start of each lesson, or maybe do this every Monday and have other forms of key numeracy practice on the remaining days of the week. My only plea to the author (and I know I am being very cheeky here!) is to use their Excel wizardry to enable the answers to automatically generate. Then we might well have one of the best resources I have ever seen.

Thanks so much for sharing

Craig Barton

Download: **Numeracy Races**

View the **author’s other resources**

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