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

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 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

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 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

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 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**

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]]>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**

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]]>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.

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]]>The post Expanding Bracket Gap Fill: 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 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.

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

]]>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**

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

]]>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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]]>The post Daisy Christodoulou – Assessment, Multiple Choice Questions, 7 Myths about Education appeared first on Mr Barton Maths Blog.

]]>Daisy is a former English teacher and the current Head of Assessment at **Ark Schools**. She also has a new job for **No More Marking**, an online engine to help teachers with comparative judgement assessments. Daisy is the author of two books – **7 Myths about Education** and **Making Good Progress**. **7 Myths about Education** is quite simply one of the best books I have ever read, and along with Daniel Willingham’s **Why Don’t Students Like School** should be compulsory reading for all teachers. If that wasn’t enough, Daisy has been on University Challenge and is even famous enough to have her own Wikipedia page – something I can only dream of.

I must make it clear from the outset that Daisy is not a maths teacher, but please don’t hold that against her. We are an inclusive podcast, after all. And anyway, it turns our Daisy loves statistics

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

- The importance of planning examples ahead of planning explanations – this was something of a revelation to me
- If Bjork is right, and we cannot distinguish between learning and performance, does this mean formative assessment is fundamentally flawed?
- Speaking of fundamentally flawed – what is the big problem with the use of level/grade descriptors in assessment?
- What can and can’t we learn from student responses to multiple choice questions given in class?
- What advice does Daisy have for teachers creating internal assessments?
- Are QLAs of any use?
- What is Daisy’s take on the current confusion of GCSE Maths Grade Boundaries?
- Why does the concept of deliberate practice suggest an excessive use of past papers might not be a good idea?
- Then we delve into the fascinating area of Comparative Judgement, and how it might well be the future of assessment
- And to top it off, Daisy suggests two great research articles to read and an excellent set of Big 3 recommendations

If you enjoyed the **Dylan Wiliam episode**, then you are going to love this one. Daisy’s knowledge of assessment design is breathtaking, and there are tonnes of things that you can use to improve the way you assess your students on a day to day basis in the classroom, as well as those lovely end of term tests.

In the Takeaway section after the interview I discuss two points that I found particularly interesting – the importance of the examples we present to students, and the possible dangers of well designed questions actually causing misconceptions, taking a look at relevant research into these matters. So if that is of interest to you, make sure you stick around until the end.

Indeed, since the last episode, my Research Page has increased in size. There are now sections on Explicit Instruction, Cognitive Load Theory, Problem Solving, Memory, Testing, Revision, Formative Assessment, Improving Teaching and more, and each paper I reference has my own takeaway alongside it. You can find the page at **http://mrbartonmaths.com/teachers/research/** I really hope you find it both interesting and useful.

If you enjoy this podcast, please share it with your colleagues. This one in particular might provide a nice audial treat for your non maths colleagues, and is a nice complement to my **Dylan Wiliam interview**. And my usual plea – if you have time to give us a review on iTunes, then the egomaniac in me would be delighted.

On Twitter Daisy is **@diasychristo**

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

Her books are: **7 Myths about Education** and **Making Good Progress**

ARK Schools’ homepage is: **arkonline.org**

No More Marking can be found at: **nomoremarking.com**

Daisy recommended two excellent research papers:

1. Why Minimal Guidance During Instruction Does Not Work

2. Unskilled and unaware of it (The Dunning Kruger Effect)

You can find both these lovely papers, along with my thoughts on them, on my educational research page at: **http://mrbartonmaths.com/teachers/research/**

Daisy Christodoulou’s Big 3

1. **Dan Willingham Blog**

2. **Greg Asham’s Blog**

3. **A Comparison of Expected Difficulty, Actual Difficulty and Assessment of Problem Solving across GCSE Maths Sample Assessment Materials **

As ever, if you enjoy this podcast, please share it with your colleagues, and if you have time to give us a review on iTunes, then the egomaniac in me would be delighted.

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

Craig Barton

**mrbartonnmaths.com**

The post Daisy Christodoulou – Assessment, Multiple Choice Questions, 7 Myths about Education appeared first on Mr Barton Maths Blog.

]]>The post Perpendicular Lines: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a challenging question on perpendicular lines provided exclusively for my **Diagnostic Questions** website by OCR, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Discuss your students answers and explanations, their reasons for the incorrect answers, and their choice of alternative wrong answers
- Use our data analytics to see how the rest of the country performed on this question, and view alternative student explanations
- Set your students the entire quiz that this question comes from as a follow-up activity
- Direct your students to the Topic section on my website, where they will find videos, worksheets and extension material on this topic.

All of this is free.

At our school we are using this once a week with our Year 11 classes. I really hope you and your students find it useful.

**Get extra help on Parallel and Perpendicular Lines**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Perpendicular Lines: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post TES Maths GCSE Revision Resources 2017 appeared first on Mr Barton Maths Blog.

]]>There’s nothing quite like the first set of exams of a new specification to really spice things up around this time of year! In this period of uncertainty, I hope that my **Inspect the Spec** blog series, exploring the key changes in different topic areas and offering top-quality resources to support your teaching, has been and continues to be of help.

So that students feel fully prepared for the unknown, I’ve also brought together this collection of engaging revision resources, complete with old favourites and brand-new ideas tailored to distinct areas of the new specification.

As ever, thanks must go to the generous and talented members of the Tes Maths community for sharing these top-notch lessons and activities, which are sure to keep pupils focused and on track until the minute they enter that exam hall.

Happy revising!

Craig Barton, TES Maths adviser

**Quick-mark question practice**

Make sure pupils develop confidence and fluency in a range of topic areas by using these straightforward sheets to practice getting those low-mark, easy-win questions right every time.**Problem-solving papers**

An interesting take on a traditional GCSE paper, these well-presented questions, covering the skills required for AO2 and AO3, come with three versions containing different levels of scaffolding.**Whole-class pub quiz lesson**

Increase levels of engagement through competition while ensuring students are exposed to exam-style questions with these presentations for foundation and higher classes.**Paired revision trail**

Previously featured as my Resource of the Week, this unusual activity gives students the incentive to combine forces with their partner to check one another’s workings are accurate.**Competitive revision races**

Designed for the legacy specifications but completely relevant to the new ones, these differentiated races require pupils to work together to solve a range of algebra and shape questions.

**Error intervals and truncation lesson**

Tackle the recapping of error intervals and rounding by truncation in one fell swoop with this complete lesson pack, including a presentation and worksheets with answers.**Introductory Venn diagram presentation**

Before getting bogged down in set notation and conditional probability, ensure that students can first create and interpret Venn diagrams in this well-structured lesson.**Frequency trees and systematic listing**

Packed with worked examples and differentiated practice activities, this presentation is the ideal starting point for refreshing pupils’ understanding of these two new topics.

**Finding gradients of and the area under curves**

Covering all of the basics and then a little bit more, this short unit is sure to bring your students up to scratch with these two particularly tricky additions to the new specification.**Capture-recapture lesson**

Also previously featured as my Resource of the Week, this comprehensive lesson is neatly rounded off by a codebreaker activity, which results in a classically corny joke.**Quadratic inequalities practice paper**

While good questions on new topics are often hard to come by, these specially created papers prove the exception to the rule with questions in an exam-style format.

The post TES Maths GCSE Revision Resources 2017 appeared first on Mr Barton Maths Blog.

]]>The post Lock Problems: 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 am a little bit obsessed with the Escape Rooms type puzzles that have swept the nation over the last couple of years. You know the ones – you must solve a puzzle to get a code, which unlocks a box, which leads to another puzzle, and so on. Indeed, I think I have dragged my wife and friends to most of them in the North West. Well, much to my companions’ delight, I can now bring the same level of nerdy excitement into the maths classroom. This collection of 11 Lock Problems, covering a whole host of topics such as ratio and probability, is simply amazing. The idea is relatively simple: students work their way through a series of questions, with each answer providing a key component of a code. A slick bit of algebraic substitution with their answers generates the final code, which they then take to the front of the class to try out on the combination lock to reveal a prize. Essentially, students are doing no more than working through a series of questions, but the fun setting leads to levels of engagement and determination that worksheets alone rarely induce.

**How can it be used?**

The author provides a really comprehensive series of instructions to follow, and whilst at first glance this may seem like a load of hassle to set up, it really isn’t. Snap up a cheap combination lock and a tin box, and you are away! In terms of support for students, I often use my Counter technique that I have discussed often on past ROTW selections (give each group a counter that they can exchange for one hint from me). And for extension, then students absolutely love creating their very own lock problem for other students (or teachers!) to solve. A fantastic bit of fun in the classroom that is also worthwhile and valuable.

Thanks so much for sharing

Craig Barton

**Download: Lock Problems
View the author’s other resources
**

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

]]>The post Dani Quinn – Part 1: Michaela School, Planning Lessons, Low Stakes Tests appeared first on Mr Barton Maths Blog.

]]>Dani is the Head of Maths at **Micheala Community School** – arguably the most discussed, scrutinised, controversial school in the county. It’s a school whose policies and practices divide opinion in both the teaching and political worlds. So, having read **Battle Hymn of the Tiger Teachers**, and seen Dani speak, and thoroughly enjoyed both experiences, I couldn’t wait to get her on the show.

Now, in a world first for the Mr Barton Maths Podcast, this interview will be split over two parts. Why, I hear you ask? Well, because it is so flipping long! I just had so many questions to ask Dani, and then loads of the things she spoke about prompted new questions. So, the part you about to listen to covers the planning and delivery of maths lessons in Michaela, going into minute detail about how each component works in practice and what the justification is, together with a discussion about Michaela’s homeworks and weekly tests. Dani and I – so long as this experience has not put her off – will then reconvene at some point in the future to discuss the practice of drilling, Michaela’s behaviour policy, wider issues in Maths teaching, her Big 3, advice for teachers, and probably a fair bit of other stuff as well.

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

- Why do maths teachers at Michaela not think in terms of planning lessons, but in planning topics?
- What do student topic booklets look like, and how do teachers use them to aid their planning?
- When might it be right to teach the “how” before the “why”?
- We go off on a bit of a tangent and discuss introducing linear equations, and why making it more difficult for the students in the initial stages might be a very good thing to do.
- How does Dani use the material of former podcast guests
**John Corbett**and**Will Emney**, together with Jo Boaler’s Number Talks? - One thing that struck me when reading the
**Tiger Teachers**book was the emphasis on a period of reading in each lesson – how exactly does this work in maths? - How are misconceptions addressed and resolved both before and during lessons?
- How does differentiation work?
- What does actual classwork look like?
- Why does Dani not bother with plenaries?
- Michaela students get maths homeworks every single night – what do these homeworks look like?
- Why don’t Michaela teachers mark books?
- A key component of the learning process at Michaela are the weekly tests. What do they look like, how are they marked, and how is the resulting information utilised?
- How does Dani use competition effectively, and why is controlling the narrative of this competition so important? And, if like me you have always shied away from publicly condemning students’ poor performance in front of other students, you will find this bit of particular interest – it has really got me thinking.
- Finally, we end Part 1 with Dani describing a bad lesson she taught, and what she learned from it. And please stick around for this one, as it is a classic with a very important message.

I am going to come right out and say it – I found this conversation fascinating. Dani was incredibly open and honest, and as a Head of Department she clearly and passionately believes wholeheartedly in what she is doing. You may not agree with a lot of what she has to say, but it is clear that each component of Michaela’s approach to teaching mathematics has been carefully thought through, so if nothing else it will give you plenty of food for thought.

Just before we get cracking, as I have discussed in the last few episodes, these interviews are really making me reflect on my teaching – scrutinising routines and practices that I have religiously followed for the last 12 years of my career without really giving them a second thought. Inspired by the likes of **Dylan Wiliam**, **Tom Bennett**, **Greg Ashman**, **Mark McCourt** and **Will Emney**, I have started to judge my approach to teaching under the microscope of educational based research. And it has been quite an eye opener. I have reviewed over 60 papers, from the fields of Explicit Instruction, Memory, Problem Solving, Fluency, Cognitive Load Theory, Formative Assessment and more, and for each paper I have provided a Takeaway where I describe the impact the paper has had on my teaching. You can find the page at: **mrbartonmaths.com/teachers/research/** I plan to add to it over the next few months, and indeed the rest of my career. I really hope you find it useful. And I’ll be discussing the **Retrieval Effect** in relation to Michaela’s weekly tests in the Takeaway at the end of the show, and it is something every teacher listening can put into practice.

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/**

As ever, if you enjoy this podcast, please share it with your colleagues. And seeing as we will have Dani back on the show, why not make a note of any questions you have, and tweet them to me at **@mrbartonmaths**. And if you have time to give us a review on iTunes, then the egomaniac in me would be delighted.

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

Craig Barton

**mrbartonnmaths.com**

The post Dani Quinn – Part 1: Michaela School, Planning Lessons, Low Stakes Tests appeared first on Mr Barton Maths Blog.

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

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

1st March: These BIDMAS Spiders are a nice way to spice up order of operations

2nd March: Really nice way to support students struggling with angles in parallel lines

3rd March: This magic square is a lovely way to practice expanding brackets and simplifying

4th March: This superb angle properties codebreaker covers all the basic angle facts

5th March: All the algebra practice your students could need with the eBook and solutions

6th March: Lots of different types of questions/activities to practice collecting like terms

7th March: Investigate prime and composite numbers via areas of rectangles

8th March: A superb lesson on listing combinations for the new maths GCSE

9th March: Another superb “spider” activity, this time on inequalities

10th March: Quick fire expanding double brackets quiz, complete with answers

11th March: A structured worksheet for calculating the surface area of a tin of beans!

12th March: A lovely, practical bearings activity, complete with answers

13th March: I am loving these “spider” activities. His one is on expanding brackets

14th March: Really nice structured approach to factorising using difference of two squares

15th March: A wonderful 6 week Numeracy homework page to focus on many crucial skills

16th March: A fantastic, complete lesson on dividing by decimals

17th March: Lots of potential for interesting discussion with this ordering decimals lesson

18th March: Help students gain practice combining algebra and compound shapes

19th March: A remix of a classic activity on interpreting cumulative frequency & box plots

20th March: A fantastic look at some dodgy graphs to promote discussion on representing data

21st March: “Factor Bugs”, leading to primes numbers, square numbers, & even Venn Diagrams

22nd March: Practice key numeracy skills with this engaging collection of race games

23rd March: A superb set of relay activities for revising key algebra concepts

24th March: Uses exponential graphs to show how things can go viral on social media!

25th March: An outstanding 8 lesson series on fractions, decimals, percentages and ratio

26th March: A superb set of lessons on the basic of trigonometry, complete with answers

27th March: This mystery is ideal for open evenings, taster days, end of term, and more!

28th March: A simple dice game to add challenge and engagement to sharing in a ratio

29th March: This Topic Mat for Complex Numbers could easily be adapted for any topic

30th March: An ideal lesson on frequency tress and systematic listing for the new GCSE

31st March: Equations of quadratic graphs, simultaneous equations, and more! Lovely activity

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

]]>The post Scatter Diagrams: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a challenging question on scatter diagrams provided exclusively for my **Diagnostic Questions** website by AQA, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Discuss your students answers and explanations, their reasons for the incorrect answers, and their choice of alternative wrong answers
- Use our data analytics to see how the rest of the country performed on this question, and view alternative student explanations
- Set your students the entire quiz that this question comes from as a follow-up activity
- Direct your students to the Topic section on my website, where they will find videos, worksheets and extension material on this topic.

All of this is free.

At our school we are using this once a week with our Year 11 classes. I really hope you and your students find it useful.

**Get extra help on Scatter Diagrams**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Scatter Diagrams: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post Prime Factor Puzzle: 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 puzzle, and I love anything to do with prime factors. So, you can imagine my delight when those two things are combined together in this wonderful activity. Students are presented with a grid of numbers, each number being surrounded by four boxes. Students must fill those boxes with the prime factors of those numbers. But there is a twist! The completed grid must work for all the numbers that are in it. So, it is not enough for students simply to list the prime factors of a number, they must also consider the shared prime factors of the numbers around it. It gets quite tricky, quite quickly!

**How can it be used?**

For me this is an ideal example of something I feel incredibly passionate about: purposeful practice. Students have the opportunity to practice the key skill (prime factor decomposition), but in an interesting and engaging way. There is also the opportunity to discuss the properties of these numbers – for example, how can I tell if a number has 2 as one of its prime factors? More importantly, they also get to develop crucial skills such as problem solving, logical reasoning and deduction, all of which will serve them in good stead for whatever mathematical challenges come their way in the future. I think it is fair to say, I love this resource!

Thanks so much for sharing

Craig Barton

**Download: Prime Factor Decomposition Logic Puzzle
View the author’s other resources
**

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

]]>The post Inverse Proportion: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a challenging question on circle theorems provided exclusively for my **Diagnostic Questions** website by Edexcel, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Discuss your students answers and explanations, their reasons for the incorrect answers, and their choice of alternative wrong answers
- Use our data analytics to see how the rest of the country performed on this question, and view alternative student explanations
- Set your students the entire quiz that this question comes from as a follow-up activity
- Direct your students to the Topic section on my website, where they will find videos, worksheets and extension material on this topic.

All of this is free.

At our school we are using this once a week with our Year 11 classes. I really hope you and your students find it useful.

**Get extra help on Direct and Inverse Proportion**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Inverse Proportion: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post GCSE Revision Trail: 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?**

Well, there is no denying it. We are definitely hitting Revision Season. And this year, with the new more challenging GCSEs making their auspicious debut, there is little doubt that revision with be more fraught than ever. So, I am always on the lookout for a top-quality resource to spice up revision whilst keeping it engaging and useful. And for me, this resource fits the bill perfectly. It is a paired revision activity, covering a whole host of GCSE content, from solving equations to circle theorems. One student answers a question and then feeds the answer to the next student which is needed to answer their question, and the process continues. With each person in the pair relying on each other, this has the potential to spark positive discussions and promote peer-to-peer learning.

**How can it be used?**

The activity is really well structured and should run as the author describes it. As is always the case with activities like these, it is often the classroom dynamic and the mood of the students that can make or break a task. It is also important to ensure that one student in the pair does not dominate and do all the work. With that in mind I would be tempted to impose a restriction that students cannot show their questions to each other. They can describe them, and ask for help, but no direct sharing of questions. That way you should get the best of both worlds – each student will do a decent amount of work, whilst at the same time benefiting from positive discussions with their partner.

Thanks so much for sharing

Craig Barton

**Download: GCSE Revision Trail
View the author’s other resources
**

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

]]>The post Equation of a Circle: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a challenging question on circle theorems provided exclusively for my **Diagnostic Questions** website by OCR, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

**Get extra help on Other Types of Graphs**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Equation of a Circle: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post Capture-Recapture Sampling: 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?**

If you are following the Edexcel new maths GCSE, then you may well have noticed the introduction of a delightful addition to the wonderful world of Sampling – the Capture-Recapture method. Something that until now had been confined to Biology classrooms has now happily found its way onto the maths syllabus. The problem is, of course, whenever anything new comes along, there tends to be a relative scarcity of good resources to help teach it. Fortunately, this resource will help take care of many of your Capture-Recapture needs. It consists of a PowerPoint with some really well presented worked examples, followed by a codebreaker activity complete with the obligatory corny joke!

**How can it be used?**

The resource itself is pretty straight-forward: there are worked examples and questions for the students to try. However, there is plenty of opportunity to discuss the logic of the Capture-Recapture technique, its merits and limitations, and the necessary assumptions that make it a valid process. Likewise, you always have the option of challenging your students to make up their own questions, or (and this is my favourite) do a live demonstration of the technique in class using a bag of coloured counters. Maths in action!

Thanks so much for sharing

Craig Barton

**Download: Capture-Recapture
View the author’s other resources
**

The post Capture-Recapture Sampling: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Circle Theorems: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a challenging question on circle theorems provided exclusively for my **Diagnostic Questions** website by AQA, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

**Get extra help on Circle Theorems**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Circle Theorems: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

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

]]>If you haven’t already started, it’s highly likely you’ll be getting down to some serious revision for the upcoming exams in the next few weeks. In anticipation of that, we’ve brought together a collection of lesson ideas designed to help you to consolidate understanding and extend thinking in a variety of topic areas.

As usual, we’ve got the generous and talented members of the TES Maths community to thank for these imaginative ideas. So take a look and be inspired to try something different with your classes.

Craig Barton, TES Maths adviser

**Exploring frequency trees**

Including supporting teacher notes, this engaging presentation not only neatly introduces the topic, but also contains exam-style questions that are ideal for promoting discussion in the classroom.

**Arrangements and permutations lesson**

Covering the new requirement to teach systematic listing strategies, this one-off lesson culminates in a stimulating codebreaker activity to get pupils practising the relevant skills.

*Adventure Time*-themed ratio practice

Liven up your ratio lessons with these captivating practice questions, which pupils must solve in order to save Princess Bubblegum from the evil Ice King.

**Proportion spider activity sheets**

Designed specifically to encourage discussion, these unique worksheets cover all aspects of direct and inverse proportion. The more challenging sheets even involve some surds practice, too.

**Good graph, bad graph?**

Exploring an often overlooked part of the topic, this interesting lesson tasks students to examine a range of graphs from a variety of contexts in order to start a discussion about misleading representation.

**Interpreting cumulative frequency diagrams**

This adaptation of a classic activity nicely links cumulative frequency with box plots, while retaining an emphasis on comparing and interpreting the data.

**Social media plot**

With almost all students on some form of social media, this investigation is sure to interest your class. Handily, it’ll also get them using their estimating skills to predict and describe the spread of information.

**The maths of a fretboard**

Get learners thinking about how geometric sequences can be used to calculate distances on a guitar fretboard with this thought-provoking lesson, including questions to promote positive discussion.

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

]]>The post Low Stakes Assessments: 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?**

One of my current obsessions is the importance of low stakes assessments. There is little doubt that one of the best ways to test how much students understand about a topic is… well, to give them a test! But, the vast majority of students do not like being tested, and us teachers simply do not have the time to mark each of these tests. This is where quick-fire low-stakes assessments come into play. Give them to students at the end of a topic, they complete them in class, mark them themselves, reflect on what areas they need to work on, and everybody benefits. And this collection is a perfect way to get started. 18 number and algebra topics for GCSE are included, each with their very own lovely, ten minute assessment, covering all the key skills for that particular topic.

**How can it be used?**

I see these being used in two, complementary ways. Firstly, it seems sensible to use them immediately at the end of a topic. This will give you and – more importantly – the students themselves an idea of what they know and what they do not know. But then, I would be tempted to issue the same assessment around 3 weeks later. This will then allow you both to see how much has really stuck, and how deep the level of understanding is. As soon as tests like these become part of your regular routine, and students realise that the inherent usefulness of them, the stress and time-consuming costs of doing and marking tests disappear, and only the benefits remain.

Thanks so much for sharing

Craig Barton

Download: **Low Stakes Assessments
**View the

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

]]>The post Percentage Increase: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a lovely little question on percentage increase provided exclusively for my **Diagnostic Questions** website by Edexcel, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

**Get extra help on Percentage Increase and Decrease**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Percentage Increase: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post Greg Ashman – Cognitive Load Theory and Direct Instruction vs Inquiry Based Learning appeared first on Mr Barton Maths Blog.

]]>Greg is a maths and science teacher, originally from the UK but now based in sunny Australia. He is a prolific and influential blogger and is also working towards his PhD in Cognitive Load Theory, something which Dylan Wiliam recently tweeted was “the single most important thing for teachers to know”.

Now, if you enjoyed the educational research aspects of my interview with **Dylan Wiliam**, and the memory related discussion I had with **Will Emeny**, then you are going to love this. We dig deep into Cognitive Load Theory and in particular its implications for Direct or Explicit Instruction versus inquiry or discovery based learning in the classroom. And I will say from the outset – and discuss more in my Takeaway at the end of the show – reading Greg’s work and the research he cites has really changed the way I approach my own teaching 12 years into my career.

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

- How does Greg plan series of lessons, and what would a typical lesson look like?
- Why is Greg such a big fan of joint planning within his department with an emphasis on refinement, and how do new ideas break through in this model?
- Why does Greg believe behaviour management is not something you are born with, but something that can be learned like any other skill
- And then we dive deep into Cognitive Load Theory, where Greg gives a lovely summary of the theory, looking at the role of working and long-term memory, the process of chunking and the dangers of means-end problems.
- We then look at some key Cognitive Load Theory “effects” including The Worked Example Effect, the Redundancy Effect and the Expertise Reversal Effect, each time asking what are the implications for the classroom. The Redundancy Effect in particular has huge consequences for how we present information to students.
- I then quiz Greg about implications for exam preparation, especially how to help students answer those tricky 5 mark questions that call upon a lot of different skills
- Surely if students discover something they will remember it better? Not according to Greg, and he has an anecdote about beer to try to convince me!
- What about the role of puzzles, real life maths, and the story structure of 3 Act Math lessons?
- Finally Greg has some excellent book recommendations, and a wonderful Big 3 selection.

If, like me, you are interested in educational research, no matter how much you have looked into it, I really believe you will find this discussion of great interest. I have tried as much as possible to tease out the practical implications for the classroom – and that is the great advantage of having Greg as a guest. He is a working maths teacher who can put the ideas he reads into practice every single day.

On Twitter Greg is **@greg_ashman**

His excellent blog can be found at: **gregashman.wordpress.com
**Greg’s ebook, “Ouroboros”, is available to purchase

Links to the research that Greg mentions, as well as all the research cited by my previouis guests, can be found **here**

The books Greg recommends, along with those recommended by my other guests, can be found **here**

Greg Ashman’s Big 3

1. **American Educator**

2. **Education Echo Chamber **

3. **Research Ed **

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

Craig Barton

**mrbartonnmaths.com**

The post Greg Ashman – Cognitive Load Theory and Direct Instruction vs Inquiry Based Learning appeared first on Mr Barton Maths Blog.

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

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

1st February: A fantastic interactive teaching aid for all aspects of bearings

2nd February: “Make the Totals” is a simple, engaging activity to practise addition and multiplication

3rd February: An absolutely superb non-calculator GCSE revision activity

4th February: A fantastic “tick or trash” activity on adding and subtracting fractions

5th February: A wonderful, rich data lesson about population size and the Olympics

6th February: A superb introduction to Venn Diagrams, using a clear, visual method

7th February: Frosty is back, this time with complete coverage of Indices for GCSE

8th February: A lovely GCSE Starter activity, covering a wide range of topics

9th February: Can you use Estimation to work out how much water the Great Pyramid can hold?

10th February: A lovely use of the New York Subway to study graph theory

11th February: This “Gradients and Distance” Game is quirky, challenging and engaging

12th February: Uses skills such as volume and properties of circles in an engaging, real world context

13th February: A fun activity to practice finding the midpoint between two coordinates

14th February: “Fairground Probability” makes use of sample space diagrams and tree diagrams

15th February: A really nice puzzle involving ordering negative numbers

16th February: A complete, really well structured lesson on standard form

17th February: A top-quality, complete lesson on ratio and scale drawing

18th February: A complete lesson on the basics of laws of indices, complete with lots of activities

19th February: Students must match up sketches, factorised form & the minimum point of quadratics

20th February: I adore this prime factor decomposition logical problem

21st February: A lovely activity to practice very basic multiplication

22nd February: A really useful collection of tricky straight li9ne graphs questions for the new GCSE

23rd February: This football pitches activity is ideal for scale drawings, perimeter & converting units

24th February: A simple, but effective codebreaker on adding and subtracting negative numbers

25th February: A superb GCSE intervention pack on sequences, functions and graphs

26th February: A complete lesson on Iteration for the new maths GCSE

27th February: A superb lesson and worksheet for introducing prime numbers

28th February: This varied collection of 11 Lock Problems is simply superb

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

]]>The post Handling Data Intervention Pack: 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 often worry about the effectiveness of so-called Intervention in the build up to GCSE. This usually comprises of taking students out of tutor time, or even other subjects, to work in small groups or one-to-one with a teacher or teaching assistant. This is fine, and there is no doubt that any extra help can only be of benefit, but how do we know how effective the intervention has been? This is where this lovely resource, specially on Representing Data, comes into play. Not only does it provide material to use in the intervention session itself (no more frantically searching through textbooks or past papers fro appropriate questions), but also an objective way to measure how successful the intervention has been.

**How can it be used?**

There are three parts to this resource, but I am going to make a case for a fourth!

1. There is a pre-test, which is ideal for deciding which students would benefit for the topic-specific intervention. This could be given as a quick in-class assessment, and even marked by the students themselves.

2. Then there is the Intervention Booklet, rammed full of top-quality questions perfectly aligned to the new Maths GCSE. This could be used in the intervention sessions themselves, or taken by the student to complete at home.

3. Finally, there is the post-test to see how much progress the student has made as a result of the intervention. This is a simple, but effective model.

4. My only addition would be a second post-test to be given to the student around three weeks later. This would then enable you as a teacher to see which concepts have truly stuck, as opposed to simply dangling in the student’s short-term memory immediately following the intervention sessions. Such a test could easily be created by manipulating the numbers in the existing post test.

Thanks so much for sharing

Craig Barton

**Download GCSE Intervention Pack
View the author’s other resources
**

The post Handling Data Intervention Pack: TES Maths Resource of the Week appeared first on Mr Barton Maths Blog.

]]>The post Fraction Application Problem: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a lovely contextual question on fractions provided exclusively for my **Diagnostic Questions** website by OCR, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

**Get extra help on Multiplying and Dividing Fractions**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Fraction Application Problem: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The post Growing Patterns: 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 long been an advocate of exploring sequences through geometric patterns, as opposed to just relying on numerical or algebraic representations. Looking at how shapes grow can help students gain a deeper understanding of the underlying rule of a sequence, enabling them to make predictions and generalisations in a way that merely looking at an nth term algebraic rule does not allow. As such, I am a huge fan of the website Visiaul Patterns (http://www.visualpatterns.org/), which contains more patterns that you could ever need. But this amazing resource takes it to a whole new level. For each pattern students are presented with a geometric representation, an nth term, a table of numbers and a graph. Having filled out as much information as they can, they are then challenged to look where the numbers in the nth term formula appear in each of the representations. It is this linking together of different areas of mathematics, spotting connections and beginning to understand why these connections exist, that will give students the depth of understanding they need.

**How can it be used?**

The activity is fully resourced and really well structured. The author suggests running it as a group activity with each member of the group being given a different pattern to work on, before sharing their finding and seeking help where needed from the rest of the group. This seems like an excellent structure to me. As I often say, I would be tempted to have Desmos on hand. In my experience there are not many students who make the link between straight lines graphs and sequences, and this activity really has the potential to solidify that connection, and the ability to instantly generate graphs will come in useful. Finally, there is always the option of giving students a blank card and asking them to create their own patterns, or giving them just one piece of information (the graph, for example), and asking them, to fill in the rest of the card. Excellent stuff!

Thanks so much for sharing

Craig Barton

**Download Representing Growing Patterns**

** **

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

]]>The post Interpreting Grouped Data: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a lovely question on Interpreting Grouped Data, provided exclusively for my **Diagnostic Questions** website by AQA, but suitable no matter which awarding body you are following.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

**Get extra help on Grouped Data**

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Interpreting Grouped Data: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

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

]]>It may be the calm before exam season, but that’s no reason to rest on your laurels. It’s hard enough keeping students motivated at the best of times, not least when they’re now well established into the routines of the new term. Luckily, help is at hand.

Once again, the generous and talented members of the TES Maths community have come up with the goods, creating and sharing unique lesson resources to help you to revitalise old topics and discover interesting ways to teach new ones. Why not take a look for yourself?

Craig Barton, TES Maths adviser

**New GCSE specification**

**Venn diagrams introduction**

Introduce classes to Venn diagrams and the accompanying set notation with this simple lesson, which makes the topic less abstract through the use of pictures.**Iteration practice questions**

Complete with an engaging starter, a step-by-step presentation and a tricky worksheet, this lesson is ideal for helping pupils get to grips with the fundamentals of this new GCSE topic.

Factors and primes

**Prime factor decomposition puzzle**

Combining the best elements of a logic puzzle with the revision of finding prime factors, this unique task is a great way of adding richness and challenge while practising a key skill.**Finding factors hints poster**

Help pupils to speed up the process of finding factors of large numbers by displaying this top tips poster in your classroom. Or, for a more regular reminder, why not get them to stick a copy in their books?

Negative numbers

**Directed numbers worksheet**

Use this problem-solving task to get learners adding and subtracting directed numbers in the context of weather, including a handy visual in the form of a bar chart.**Negative numbers codebreaker**

Recap key principles about the addition and subtraction of negative numbers with this simple but effective codebreaker activity, useful as a starter for more-able classes.

Advanced coordinate geometry

**Facial expressions presentation**

Test pupils’ knowledge of the basics shapes of a variety of functions, including reciprocal, circles and cubics, by matching them up to faces in this engaging activity.**Exponential growth and decay**

With links to real-life applications and dynamic graphing software, this well-structured lesson neatly introduces the concept to older students.

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

]]>The post Surds for GCSE: 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 struggle to remember quite what my life was like in those dark days before I discovered Dr Frost’s amazing lessons.I spent many hours scrabbling around looking for a way to introduce the topic, well presented worked examples, slides of questions, and tricky challenges. Now, when I start my planning for any topic, for first port of call is always to grab one of his PowerPoints. As you will see from this example on Surds, they contain everything you could possible need. There is an overview of where surds fit into to the whole spectrum of numbers, then there are clear notes on the laws of surds, followed by examples for the students to try. This is then followed up whole slides of exercises and GCSE exam questions, each complete with “bro tips” and a beautiful green box than can be clicked on when you and your students are ready to reveal working out and the answers. Finally, there is the dreaded skull and crossbones – a sure sign that a question will stretch even your most able of students

**How can it be used?**

I have one piece of advice for using Dr Frost’s lessons – never use them without first checking them very carefully. I had the pleasure of interviewing **Dr Frost for my podcast**, and the achievement of his pupils is quite staggering. Hence, he has a need to challenge them as much as he can in his TES resources. The result of this can mean that a Dr Frost Year 7 lesson contains questions that your average Year 11 would struggle with, and which have been known to drive more than one of my Year 9s to tears! So, like any resource on TES, check it over, take the parts that you need and are suitable for your class, build it into your own lesson, and then you are good to go.

Thanks so much for sharing

Craig Barton

**Download GCSE Surds
View the author’s other resources
**

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

]]>The post Composite Functions: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

]]>The latest edition of my **GCSE Maths Question of the Week** series is a lovely Composite Functions question provided exclusively for my **Diagnostic Questions** website by Edexcel.

Here is one suggestion for using this resource:

- Print out the worksheet for use as a starter in lessons, or a homework.
- Set your students the entire quiz that this question comes from as a follow-up activity

All of this is free.

Try the **Question online**

View the **Question Data and Explanations**

Try the **Quiz ****online**

View the **Quiz Data**

For all the questions in this series, please visit my **GCSE Maths Question of the Week **page.

The post Composite Functions: GCSE Maths Question of the Week appeared first on Mr Barton Maths Blog.

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