Common Errors Made Past Times Maths Teachers

I've late started working with a couplet of trainee maths teachers. It's already proving to hold upwardly a useful sense for me - I'm certain it volition own got a positive behave on on my teaching. It's fascinating to sit down at the dorsum of the classroom with my students. 

There's been a couplet of moments lately where I've seen a trainee instructor tell a flat something that's non quite right, or that I've felt has needed farther clarification. It's interesting to run across how a teacher's plain of written report noesis - especially their noesis of mutual misconceptions - develops rapidly over the kickoff few years of their career.

I've started to push clit together a listing of some of the mistakes or oversights that I've seen both inexperienced together with experienced maths teachers make. I'd hold upwardly interested to listen what you've seen every bit good - delight permit me know therefore I tin create a comprehensive listing that volition hold upwardly of piece of job to trainees together with NQTs. 

Square root

The foursquare rootage symbol denotes solely the positive root. So if you lot write √9 = ±3 on the board, you've made a mistake.

Source: Wikipedia

If you're solving the equation x² = nine together with then of course of written report in that place are ii solutions - both positive together with negative iii piece of job here. You're non wrong nigh that. But brand certain you lot piece of job the radical sign correctly.

   

Angles

What angle fact is depicted below? Some of my students own got been incorrectly taught to say 'angles inwards a circle amount to 360^o'.  It should hold upwardly 'angles unopen to a dot amount to 360^o' (as per GCSE grade schemes) or 'angles inwards a total turn/revolution amount to 360^o'.

Whilst we're on the plain of written report of angles, I've solely late institute out that proverb 'angles inwards a triangle are supplementary' is wrong. Supplementary way that ii (and solely two) angles amount to 180^o.

Prisms
I don't recommend bespeak maths teachers on Twitter whether a cylinder is a prism! I did that in 1 lawsuit - the declaration went on for days together with I was none the wiser every bit a result.

Half the cyberspace claims that cylinders are prisms, the other one-half disagrees. pic.twitter.com/O3sg4GXqCh

— Jo Morgan (@mathsjem) June 11, 2015

Since this Twitter conversation, I avoid defining a cylinder every bit a prism inwards representative I'm wrong, merely I practise tell my students that nosotros bring out the book of a cylinder inwards the same way nosotros bring out the book of a prism.

Interestingly, the GCSE formula canvas uses a controversial moving-picture present of a prism.

Frustum

It's a frustum, non a frustrum. This give-and-take is ofttimes misspelt.

The guild of operations
Try this question: 3 - 3 x 6 + 2.

If you lot don't acquire an respond of -13 together with then you lot demand to hold off in 1 lawsuit to a greater extent than at the guild of operations. The unhelpful acronym BIDMAS (which incorrectly implies that you lot should add together earlier you lot subtract) confuses some teachers every bit much every bit it confuses students.

Vocabulary

I late observed a lesson on angles inwards polygons with a Year 8 class. The pupil instructor asked the advert of a 7 sided shape together with a man child position upwardly his manus together with said it was a heptagon. The instructor said he was correct, together with then moved on. She didn't notice that some other man child was real bothered past times this. He angrily protested to the students unopen to him. I watched from the back. This man child had been taught that a 7 sided shape is called a septagon - which is also right - together with he idea that the instructor had made a mistake. At kickoff he was angry, merely together with then he doubted himself. His confidence took a knock. Later inwards the lesson, when the chance arose, I reassured him that both price are acceptable. He was relieved. He felt vindicated. It was a shaver oversight past times the instructor merely it had quite an behave on on this student.

I in all likelihood practise things similar this every bit good sometimes. We say things that, rightly or wrongly, differ from what students own got been taught previously. This causes confusion together with mistrust.

I'd hold upwardly interested to know what mistakes together with oversights you've seen teachers make, therefore delight comment below or tweet me therefore I tin push clit together a comprehensive list. We're ever talking nigh the importance of students learning from each other's mistakes, therefore let's practise the same.

♫ Y'all Enjoin Zero, Ane Enjoin Nought ♫

mistakes. One comment that I establish especially interesting was close the purpose of wrong vocabulary to limited the publish 0. This made me wonder what's acceptable as well as what isn't.

First, I holler upward nosotros should endeavour to avoid maxim 'oh', because that's a letter, non a number. However, nosotros should acquit inward hear that 'oh' is usually used as a number. I holler upward many of us likely outset 'oh 7 ...' when nosotros hand our cellular telephone number. 'Oh' is used inward telling the fourth dimension alongside the 24 clock as good eg 16:05 is said as 'sixteen oh five'. 'James Bond double oh seven' is closed to other example. But although it's acceptable inward conversation, 'oh' shouldn't hold upward used for the publish 0 inward a maths classroom.

I purpose the discussion null quite often, for instance I tell my students to brand a quadratic equation 'equal to zero'. I'd tell 5⁰ as 'five to the ability of zero', as well as and then on. I wouldn't tell nought inward these cases, though there's zilch wrong alongside maxim nought.

I exercise sometimes purpose the discussion nought instead of zero. For instance I would tell the publish 0.64 as 'nought indicate vi four'.

Although at that topographic point is a perception that null is the 'best' agency to tell the publish 0, I'm convinced that the discussion nought is all the same widely used inward the UK, especially inward numbers alongside decimals. I did a Twitter poll to banking company gibe what maths teachers say. Twitter polls are of limited purpose because they render no data close who has responded (ie what continent they are from), but the results are all the same of interest:

'Something else' included a) people who but tell 'point five' as well as (b) people who tell 'half' (yes yes, nosotros all know it's a half! I wasn't bespeak close the maths! In hindsight, I should guide maintain used a dissimilar decimal inward my enquiry to avoid this response).

The large publish of responses for 'nought indicate five' confirmed that the discussion 'nought' is all the same widely used, at to the lowest degree inward the UK.  A few tweets from North America suggested that it's rarely used there.

If you're wondering close the spelling of the discussion nought, this extract from Wikipedia 'Names for the publish 0 inward English' might hold upward of interest:

The words "nought" as well as "naught" are spelling variants... There is a distinction inward British English linguistic communication betwixt the two, but it is non 1 that is universally recognized. This distinction is that "nought" is primarily used inward a literal arithmetics sense, where the publish 0 is straightforwardly meant, whereas "naught" is used inward poetical as well as rhetorical senses, where "nothing" could as good hold upward substituted... Whilst British English linguistic communication makes this distinction, inward USA English, the spelling "naught" is preferred for both the literal as well as rhetorical/poetic senses. 

In summary, I holler upward it's fine to purpose the words null as well as nought interchangeably inward the maths classroom, as long as your students know what you're referring to. Do y'all agree?

♫ You tell zero, I tell nought

Let's telephone phone the whole matter off ♫

Further reading: BBC 4 In Our Time Debate: Zero

Divisibility Rules

In the concluding lesson of term my students played a few rounds of a Countdown type game, as well as were specially stumped past times this problem:

I managed to produce it pretty rapidly as well as briefly experienced 1 of those lovely moments of appearing, to my students at least, to move a maths genius. Of class all I did was location that 531 divides past times 9, as well as thus it was straightforward. Have a go.

Influenza A virus subtype H5N1 colleague asked me how I'd done it thus rapidly as well as I told her that I'd used divisibility rules. She said that she'd never taught divisibility rules because she'd never seen it specified on a system of work. It strikes me that this is a helpful fighting of mathematical noesis that many secondary maths teachers don't teach. Do you lot learn it? In what year? Most resources for this theme are aimed at master copy children but I intend nosotros should in all probability revisit it at Key Stage 3.

I was aware that my Year 10s didn't know the divisibility rules, thus I covered them every bit business office of the 'Factors as well as Multiples' theme this twelvemonth (ie amongst prime number factorisation, highest mutual component etc). It's a skillful agency to review the fundamentals of multiplication as well as to prepare fluency as well as efficiency with numbers. To my Year 10s the rules seemed similar 'new' maths that they'd non seen earlier (or if they had, they couldn't hollo upward it), thus it made an interesting as well as suitably challenging lesson.

I also ran a session on divisibility rules with merely about smart Year 3s as well as 4s at a local master copy schoolhouse this year. They picked it upward well, as well as over again I saw it every bit a skillful agency to prepare their agreement of multiplication as well as their divulge fluency.

So it's a theme that industrial plant good with whatsoever historic menstruation group, from Key Stage 2 to Key Stage 4. Let's accept a quick expect at the rules as well as resources.

The Rules
Most children volition easily move able to create upward one's heed whether a divulge is divisible past times 2, v or 10. The neat 'tricks' are for 3 (the digit amount is divisible past times 3) as well as nine (the digit amount is divisible past times 9). Once nosotros know whether a divulge divides past times 3, nosotros know whether it divides past times 6 (ie all even multiples of 3 are multiples of 6). For divisibility past times 4 in that location are 2 alternatives: either banking concern gibe whether the concluding 2 digits split upward past times 4, or halve the divulge as well as run into if your respond is fifty-fifty (the iv times tabular array beingness double the 2 times table). The 7 key tests are shown inwards the graphic below (there are loads of prissy graphics for this on google images).

I didn't bother instruction the dominion for divisibility past times 7 because it's non straightforward. Rather as well as thus memorise this dominion I idea my students would move amend off merely checking for divisibility past times 7 with long division.

If you're interested inwards all the rules, from 1 - xxx as well as beyond, banking concern gibe out the Wikipedia page Divisibility rule.

Resources
I constitute a mixture of uninspiring worksheets as well as bizarre activities when I searched for resources online (the to a greater extent than odd activities included Divisibility Rock n' Rule, NFL divisibility dance and I'll take, you lot take...).

For the interactive whiteboard nosotros direct maintain Vectorkids: divisibility rules, Divisibility Test as well as Delightfully Divisible.

If you're looking for a good structured worksheet pack, this is quite good.

This Don Steward.

Don Steward also has slides on divisibility rules, total of lovely challenging problems.

Dan Walker has a nifty laid upward of slides as well as activities on divisibility rules too, including this lovely Venn activity.

Why produce the rules work?
The ancient Greeks knew rules for divisibility past times 2, 3, v as well as nine inwards the 3rd century BC.

So why does the digit amount of multiples of 3 split upward past times three? Sal Khan explains here...

 

He has a similar video for divisibility past times 9.

Do allow me know virtually your experiences of instruction divisibility rules as well as whatsoever resources recommendations. If you've non taught it before, direct maintain a become adjacent year. It's useful noesis as well as good worth teaching.

Multiplying Negatives

"A negative times a negative is a positive". It's a difficult ane to explain. We all learnt it at schoolhouse together with practised it to the indicate of fluency, but it's non until we're asked why it industrial plant that nosotros halt together with intend close it.

Numbers lines together with visualisations are real helpful when education the add-on together with subtraction of negative numbers. But alongside multiplication together with partitioning it's non then clear.

Let's await at a few approaches together with resources.

1 . Pattern Spotting
Draw a measure multiplication tabular array together with extend it backwards to include negative numbers. It's a straightforward designing that all students should hold upwards able to location together with continue. Get students to create this using Colin Foster's activity on page five of his Negative Numbers chapter.

2. Multiplication Grids
Take ii 2-digit numbers together with multiply them together using grid multiplication. For simplicity, let's accept 12 x 11:

Here nosotros direct maintain written 12 every 2nd 10 + 2 together with eleven every 2nd 10 + 1. But it would piece of employment simply every 2nd good if nosotros expressed those numbers differently. Instead, let's write 12 every 2nd fifteen - iii together with eleven every 2nd fifteen - 4. We should acquire the same answer:

This alone industrial plant if -3 x -4 = 12. 

Note that this explanation requires students to commencement sympathise that positive x negative = negative. This is relatively straightforward to explicate inwards damage of repeated addition. 

3. Proof
Here's a proof that is clear together with accessible to us experienced mathematicians. I'm non certain how accessible it is to Year vii students, but it's worth a go.

a together with b are positive

a + (-a) = 0 

[a +(-a)]•b = 0•b 

a•b + (-a)•b = 0 

a•b is positive. Therefore (-a)•b is negative 

b + (-b) = 0 

(-a)•[b + (-b)] = (-a)•0

(-a)•b + (-a)•(-b) = 0

Since (-a)•b is negative, nosotros conclude that (-a)•(-b) is positive.

Perhaps start alongside a numerical instance instead of a formal proof.

3 + (-3) = 0

Multiply everything past times -4

3(-4) + (-3)(-4) = 0(-4) 

 -12 + (-3)(-4) = 0 

 (-3)(-4) must equal 12 to brand this disceptation true. 

Further Reading
It's a practiced sentiment to read close a theme earlier y'all learn it, fifty-fifty relatively uncomplicated topics that you've taught many times before. Here are unopen to helpful links:

• The FAQ pages on Math Forum ever furnish interesting answers: Why is a negative times a negative a positive?
• I taste James Tanton's curriculum essays: Directed Number Gaps' activity - it industrial plant good alongside whatsoever twelvemonth group
• MathsPad has a slap-up attain of negative publish puzzles including arithmagons (some of these resources are alone available to subscribers)
• CIMT's negative numbers chapter has activities for practising multiplying negatives.

Colin Foster suggests that y'all enquire students to brand upwards 10 multiplications together with 10 divisions each giving an reply of –8 (eg –2 × –2 × –2 or –1 × 8 etc).

The squaring together with cubing (etc) of negatives is worth discussing - students should location that an fifty-fifty ability gives a positive value (eg what is the value of (-1)¹⁰⁰?).

It may hold upwards worth exploring reckoner deportment every 2nd good (ie unopen to calculators require brackets when squaring a negative). It's of import that students know how to run their reckoner properly. There's a slap-up resources from MathsPad for this - Using a Calculator: Odd One Out.

This theme is revisited inwards later on years when students are practising substitution. For example, if a = 3, b = -2 together with c = -5, detect the values of: abc; bc²; (bc)²; a²b³ together with then on. This Substitution Puzzle from mathsteaching.wordpress.com gets quite challenging.

Do allow me know if y'all run an interesting method or resources for education the multiplication of negative numbers.

"Minus times minus results inwards a plus,
The argue for this, nosotros needn't discuss"
- Ogden Nash

5 Maths Gems #67

Welcome to my 67^th gems post. This is where I percentage the latest ideas in addition to resources I've seen on Twitter. I used to write i of these posts every week simply I straightaway combat to honour the time, in addition to therefore this is my start gems post service since November. I convey some crackers for you lot today though!

1. Polygons
Ed Southall's (@solvemymaths) start video is good worth a watch. It explores the terminology, etymology in addition to construction of naming polygons. I'm straightaway eagerly looking ahead to when I side past times side instruct geometry in addition to therefore I tin hand notice percentage this alongside my students!



2. My Favourite No
I start watched this video years agone simply I've never pose it inwards a gems post service before. Thanks to Stephen Godwin (@stevejodwin) for reminding me close it later it appeared inwards Doug Lemov's recent spider web log post service 'My Favorite No: Mistaking Knowledge Problems for Skill Problems'. Do sentinel the video below - it features a vivid action for exploring misconceptions.


3.  Primitives
I shared the lovely Furbles inwards Gems 21, simply hadn't spotted the 'Primitives application' on the same website. This has been closed to for many years, simply thank you lot to John G (@mathhombre) for latterly sharing it on Twitter. This lovely interactive factorisation tool is actually expert for exploring numbers.

Primitives posters in addition to pedagogy ideas are available from the ATM.

4. Euler's Number
Numberphile published a novel video close e end week. I actually enjoyed this video in addition to project design to demo it to my Year 13s side past times side term.



5. Notepad Calculator
Colin Beveridge (@icecolbeveridge) tweeted close this first-class NotePad Calculator. I'm non certain whether I'll honour it useful inwards the classroom simply I dearest it anyway in addition to therefore persuasion it was worth sharing.

Update
I've published half dozen spider web log posts since Gems 66. They're listed hither inwards representative you lot missed them:

• Highlights of 2016
• Merry #christmaths16
• Formative Assessment
• 5 Websites You Should Know... #4
• GCSE ix - 1 Revision Resources
• New GCSE: Trigonometry Questions

Do depository fiscal establishment fit out Don Steward's blog besides - he's published a lot of novel resources lately.

You mightiness also last interested inwards Dr Frost's revision advice for Influenza A virus subtype H5N1 degree students in addition to Colin Beveridge's examine technique tips for the novel GCSE.

I'll exit you lot alongside this animation of the surface expanse of a sphere, shared past times Damian Ainscough (@damianainscough).

5 Maths Gems #70

Welcome to my 70^th gems post. This is where I percentage some of the latest news, ideas in addition to resources for maths teachers.

1. Yes, But Why?
The large intelligence inwards the globe of maths education is the launch of Ed Southall's novel majority 'Yes, But Why? Teaching for Understanding inwards Mathematics'. I was fortunate to acquire an early on await at this majority earlier it was published. It's fantastic. Both novel in addition to experienced maths teachers volition acquire a lot out of it. You tin preview it here. I'm inwards the procedure of re-reading it in addition to volition percentage some of my favourite bits inwards a divide weblog post soon.

2. Statistics 
Thanks to @MrDraperMaths for sharing this wonderful website for teaching statistics: Seeing Theory.

This website is a pleasance to explore. There are some useful teaching tools hither - some are suitable for GCSE simply most are for Influenza A virus subtype H5N1 grade in addition to beyond.

The basic probability page has a unproblematic money flip simulation which neatly demonstrates the thought of experimental probability vs theoretical probability. The clever interactivity lets you lot brand the money biased in addition to run across the behaviour on on observed outcomes.

There's also a lovely Venn diagram tool.

3. GCSE Problem Solving 
Thanks to Edexcel for adding a laid of GCSE work solving questions to the Edexcel website. Download the Higher in addition to Foundation tier questions inwards a zippo folder here.

4. Equation Editor Shortcuts
Bear alongside me if you lot already know these shortcuts - I'm pretty certain this volition hold upwardly a novel regain for some people...

I purpose Equation Editor inwards PowerPoint in addition to Word fairly regularly, in addition to stimulate got e'er done hence via the transcend carte bar (insert > equation). I was pleased to location a footling tip on Twitter - thank you lot to @chilledmaths for this tweet:

Stop press: alt = puts you lot similar a shot into maths type. This whole things keeps getting better. Or highlight text in addition to hence click alt = 😀

— Clare Hill (@chilledmaths) 28 Feb 2017

@c0mplexnumber replied to percentage this helpful guide entitled 'Rapidly Using Equation Editor inwards Microsoft Office' from @DrFrostMaths. This guide describes all the shortcuts inwards Equation Editor.

Thanks to everyone who shared these fourth dimension saving tips - I've learnt something new!

5. MathPickle
There's been a combat of buzz about Dan Walker's Resources

Working Well: C1 in addition to C2

My GCSE nine - 1 Revision Resources post has been actually pop over the terminal few weeks - the examination training flavor is good underway!

If your schoolhouse runs Times Tables Rockstars, did you lot run across that they've opened a Reward Shop? I've stocked upwardly on prizes.

I'm looking forrad to #mathsconf9 inwards Bristol adjacent weekend. If you're in that location on the Fri night, create bring together us for pre-conference drinks at the The Navy Volunteer from 7:30pm.

On the Saturday, come upwardly in addition to state hullo to me at the Tweet Up where I'll hold upwardly running some other 'World Cup of Maths', simply this fourth dimension finding out what everyone's to the lowest degree favourite theme is! There'll hold upwardly loads of other stuff going on at the Tweet Up, including the famous Pringles Challenge which is e'er popular.

I'll acquire out you lot alongside this dodecagon work which is taken from a set of puzzles created yesteryear Don Steward to grade the launch of the novel £1 coin.

Yes, Merely Why?

I'm certain you've already heard almost Ed Southall's novel majority 'Yes, But Why? Teaching for Understanding inward Mathematics'. It was published less than a calendar month agone too is already on its tertiary impress run. It has been incredibly good received yesteryear both main too secondary teachers - everyday I run into tweets almost how useful it is.

I yell back a twain of years agone when Ed (@solvemymaths) get-go had the thought of writing this book. There was no bailiwick cognition handbook for trainee maths teachers - it was a clear gap inward the market. By writing one, Ed has provided something that maths pedagogy badly needed - an expertly written reference manual for mathematics teaching.

People assume that a maths grade is sufficient bailiwick cognition for teaching secondary mathematics, simply there's a lot to a greater extent than to it than that. In maths, bailiwick cognition includes knowing mutual misconceptions, effective teaching approaches, choice methods, underlying concepts, links betwixt topics, interesting maths facts too stories, too more... Even the most experienced maths teachers with high levels of subject-specific expertise tin develop their cognition further.

Since reading Ed's majority I've noticed a subtle shift inward my teaching style. For instance I establish myself excitedly talking to my Year xi course of instruction almost the departure betwixt an ellipse too an oval. They were surprisingly fascinated - 1 of them was actually pleased with himself when he spotted the link to the discussion ovary. And inward a recent lesson on geometric proof, I talked for a land almost Euclid - it was the longest menstruum of quiet I've had from that class! They truly seemed enthralled. Influenza A virus subtype H5N1 highly knowledgeable instructor is confident too engaging. That's the sort of instructor I desire to be.

In this post I've featured a few extracts from 'Yes, But Why? Teaching for Understanding inward Mathematics' to give you lot an thought of why it's worth buying.

Statistical Graphs
Histograms are actually unpopular with GCSE teachers. I'm a statistician too fifty-fifty I acknowledge that I don't await forrad to teaching this topic. Ed explains real clearly why histograms role frequency density instead of frequency - inward fact I project design to role his examples side yesteryear side fourth dimension I instruct it.

Ed's majority tells me that histograms were developed yesteryear English linguistic communication mathematician Karl Pearson inward around 1910. This is of personal involvement to me because Karl Pearson was the human being who founded the world's get-go academy statistics subdivision at University College London inward 1911 (the real same subdivision where I did my statistics grade xc years later).

Given that maths teachers ofttimes discovery statistics hard to instruct (or even, dare I say, non enjoyable...), I intend that the statistics chapter of Ed's majority volition live on incredibly useful. In the subdivision on pie charts, Ed shares a goodness instance of a useless pie chart, too encourages teachers to utter over the pros too cons of each type of statistical graph with students.

Teacher Tips
Practical tips characteristic regularly throughout the book. This tip regarding expanse is real sensible - bespeak students to discovery the expanse of a parallelogram when alone the base of operations too perpendicular meridian convey been provided seems a lilliputian silly.

Deriving y = mx + c
I'm guilty of telling students that the equation of a remove occupation is y = mx + c without telling them why. If they know that slope is 'change inward y ÷ change inward x', too hence it's pretty elementary to derive y = mx + c, every bit shown below.

This is obvious, if you lot halt too think, yet I've never shared this with my students. I gauge the work is that for teachers, right from twenty-four hr menstruum 1 of their training, in that place is no fourth dimension to halt too think.

Measurements
The majority features a listing of odd units of measure, too lots of other wonderfully geeky mathematical trivia. I beloved this stuff!

'Yes, But Why? Teaching for Understanding inward Mathematics' is informative, witty, enjoyable too incredibly useful. It's available to purchase now. If you're all the same undecided, you lot tin preview the get-go chapter here. Let me know what you lot think.

5 Maths Gems #76

Welcome to my 76^th gems post. This is where I part or thence of the latest news, ideas together with resources for maths teachers.

1. 'For Interest'
Dr Frost has made a educate of 'Just For Your Interest' posters for H5N1 degree mathematicians. These render groovy dependent champaign cognition evolution for maths teachers too.

I met Jamie Frost for drinks over summertime - he has loads of exciting plans for his website thence it's worth next him on Twitter (@DrFrostMaths) for updates. Lately he has been publishing PowerPoints for the novel H5N1 degree thence create cheque them out if you're didactics Year 12 this year.

Drinks amongst Jamie Frost (@DrFrostMaths)
together with Megan Guinan (@MeganGuinan1)

2. thaMographe
I was real pleased to have a gratuitous thaMographe inwards the post! This is a wonderful conception that combines an entire maths educate into a unmarried slice of equipment.

I acknowledge that I'm non groovy amongst accuracy at the best of times - constructions are my to the lowest degree favourite business office of maths. I loathe to come across students struggling to move a twosome of compasses together with I real much promise that the thaMographe volition ane twenty-four lx minutes menstruum endure widely used yesteryear schoolhouse children. It is for certain tardily to move together with accurate plenty for schoolhouse degree mathematics - every bit demonstrated yesteryear my quick perpendicular bisector:

Ed Southall has written a thorough review of the thaMographe here.

You tin flame social club a thaMographe from www.thamtham.fr - transportation is free! Hopefully it volition endure available to purchase inwards the Britain soon.

3. Subtraction Methods
I dear this graphic showing choice methods for subtraction. It was shared yesteryear James Tanton (@jamestanton) who tweeted "Math is for each of us to ain together with create inwards whatsoever practiced means suits us best".

4. Graspable Maths
In Gems 75 I shared an algebra maze from MEI that was real popular. Through a comment left on that spider web log post, I discovered graspablemath.com, which is an exciting novel interface for working amongst algebra. It's lovely to move - if you're on a reckoner together with direct keep or thence fourth dimension to spare, direct keep a play amongst the online algebra maze.

5. H5N1 Level Problem Book
Stuart Price (@sxpmaths) has been difficult at piece of employment pulling together a large educate of problems for H5N1 degree maths. He has collated questions on a topic-by-topic basis, inwards 4 sections: Techniques; Problem Solving; Puzzles & Challenges, together with Exam Review. The thought is that students tin flame move these sets of questions for independent report throughout the course.

It's piece of employment inwards progress, but if y'all desire Stuart to e-mail y'all a link to his piece of employment thence far (it's great!) delight contact him via Twitter.

Update
Here are my recent posts, inwards representative y'all missed them:

• here.
  
  You tin flame social club a thaMographe from www.thamtham.fr - transportation is free! Hopefully it volition endure available to purchase inwards the Britain soon.
  
  3. Subtraction Methods
  I dear this graphic showing choice methods for subtraction. It was shared yesteryear James Tanton (@jamestanton) who tweeted "Math is for each of us to ain together with create inwards whatsoever practiced means suits us best".
  
  
  4. Graspable Maths
  In Summaths 2017
• here.
  
  You tin flame social club a thaMographe from www.thamtham.fr - transportation is free! Hopefully it volition endure available to purchase inwards the Britain soon.
  
  3. Subtraction Methods
  I dear this graphic showing choice methods for subtraction. It was shared yesteryear James Tanton (@jamestanton) who tweeted "Math is for each of us to ain together with create inwards whatsoever practiced means suits us best".
  
  
  4. Graspable Maths
  In Planning for September: Year 12

I also launched my novel 'Topics inwards Depth' page.

I was real grateful to a sort Summaths attendee for lending me copies of these 'Developing Thinking...' books which volition assistance me inwards my enquiry for my Topics inwards Depth project. These books come upwardly highly recommended.

If you're going to researchED side yesteryear side Sabbatum thence create come upwardly along to the struggle nearly maths GCSE - I'm on the panel of speakers.

Have y'all booked your ticket for #mathsconf13 on 30th September inwards Sheffield? I promise to come across y'all there.

TES Maths Panel
On Tuesday I spent the twenty-four lx minutes menstruum at TES amongst the lovely members of the here.

You tin flame social club a thaMographe from www.thamtham.fr - transportation is free! Hopefully it volition endure available to purchase inwards the Britain soon.

3. Subtraction Methods
I dear this graphic showing choice methods for subtraction. It was shared yesteryear James Tanton (@jamestanton) who tweeted "Math is for each of us to ain together with create inwards whatsoever practiced means suits us best".

4. Graspable Maths
In here together with here.

You tin flame social club a thaMographe from www.thamtham.fr - transportation is free! Hopefully it volition endure available to purchase inwards the Britain soon.

3. Subtraction Methods
I dear this graphic showing choice methods for subtraction. It was shared yesteryear James Tanton (@jamestanton) who tweeted "Math is for each of us to ain together with create inwards whatsoever practiced means suits us best".

4. Graspable Maths
In here.

With ane of my favourite Scottish mathematicians - Chris Smith

Pizza amongst the panel

I had Inset yesterday together with I showtime didactics on Mon - exciting!

Don't forget that my resource libraries mightiness assistance amongst your lesson planning.

I'll move out y'all amongst this thought from Underwood Dudley, taken from his first-class slice "What Is Mathematics For?". I mean value this is quite inspirational at the showtime of a novel schoolhouse year.

"...when I am earlier a bar of judgement, heavenly or otherwise, together with asked to justify my life, I volition depict myself upwardly proudly together with say, “I was ane of the stewards of mathematics, together with it came to no terms inwards my care.”"