5 Maths Gems #2

Last calendar week I promised I'd write a weekly postal service summarising the novel teaching ideas I'd seen on Twitter. Afterwards I worried whether I'd direct maintain plenty cloth to write about, but this calendar week I wasn't disappointed. Plenty of ideas were shared - here's v of them.

1. Revision Whispers. As I've said before, I'm ever on the await out for engaging ideas for revision lessons. Billy Adamson (@Billyads_47) shared this fantastic sentiment 'Maths Whispers!' inwards which pupils are given a fact or formula to communicate amongst their classmates, 'Chinese Whispers' style. Billy says that when his students were walking downwards the corridor afterwards, they were excitedly talking most what each disceptation was initially too what it became. I dearest this idea. It would operate good inwards other subjects too. Check out Billy's resources on TES. Here's a variation I powerfulness endeavor for Influenza A virus subtype H5N1 plane revision: carve upwards the degree into teams. The teams shape lines from the dorsum of the classroom upwards to the board. The pupils at the dorsum are given a message to read. Here's an representative from S2:

All teams direct maintain the same message. The message is simultaneously passed along the lines inwards whispers. The finally pupil inwards each describe writes the message on the board. The most accurate squad wins! Then shuffle the students too endeavor some other message. My A plane revision cards direct maintain plenty of ideas for messages - definitions too formulae would operate well.

2. Post-its. Mr Allan (@mrallanmaths) wrote this blog post most his purpose of post-it notes inwards lessons. He displays questions on boards around his classroom. Students (in pairs or teams) operate their agency around the room answering the questions on post-it notes. It's a quick too tardily agency of assessing agreement too finding misconceptions. It's also really engaging, fifty-fifty though the questions are precisely from a textbook. The sentiment originated from a tweet past times Chris McGrane (@ChrisMcGrane84) back inwards January. Shelley Smith (@saxsmith27) successfully tried it out this week.

Speaking of post-it notes, I similar this 'What stuck amongst you?' idea, shared past times @RemindHQ. It could endure a prissy plenary activity ane time a week, or fifty-fifty at the terminate of every lesson.

If you lot desire to a greater extent than post-it banknote teaching ideas too then banking concern jibe out 'fractions weblog post this calendar week I discovered the blog Authentic Inquiry Maths which is total of skillful ideas, similar T-charts for highlighting similarities too differences. Pupils purpose ICT to create their charts too you lot larn a prissy mix of presentation styles, similar the representative below.

Ed Southall's (@edsouthall) tricky maths problems on his website solvemymaths.com are also actually visually appealing too I await forrad to using them to challenge too extend my students adjacent year.

Area employment #2 - solvemymaths.com

Here's some other 'attractive' activity I spotted on Twitter this week. This ane was shared past times Khan Academy (@khanacademy).  It's an engaging activity because it's visually striking, accessible too has a skillful plane of challenge for pupils who've studied Pythagoras' Theorem. Shame I don't direct maintain the budget for colour photocopying!

4. Starting a novel schoolhouse year. With exclusively ii weeks left inwards the summertime holidays, I've started to meet weblog posts most things to practise inwards starting fourth dimension lessons of the schoolhouse year. I wrote a pair myself a few weeks agone - ane on your starting fourth dimension lesson amongst Year 7 too ane on kicking off Year 12.  Here's a few to a greater extent than I've spotted late that are worth a read:

• This 'Deliberate Mistakes, Jo Boaler (@joboaler) talked this calendar week most the value of mistakes inwards ‘Setting upwards Positive Norms inwards Maths Class'. In this document, she suggests that nosotros brand a habit of inviting pupils to the board to portion their conceptual mistakes. She also suggests that pupils crumple a slice of newspaper too throw it at the board - precisely once, inwards a symbolic form of agency - non every fourth dimension they brand a mistake... Though I wonder if that would endure worth trying too, to works life a classroom civilization of ‘everyone makes mistakes’ too to encourage risk-taking. Can you lot imagine if your pupils threw all their mistakes at the board? It powerfulness larn a chip messy. Fun though.
  
  Jo makes a position out of other useful suggestions inwards her article, such equally writing students' skillful questions on posters around the room. She also talks most the importance of valuing depth over speed. Many of my students larn inwards in secondary schoolhouse amongst the impression that it’s of import to practise maths quickly. ‘Beat the clock’ type activities encourage this. What’s the rush?
  
  So, some helpful thoughts from Jo Boaler. Shame most the negative article she wrote this calendar week most maths teaching inwards the UK, but yay to the NCETM for defending us! It’s prissy to know somebody has our backs.
  
  And finally...
  I'll destination off today's postal service amongst 3 recommended reads:
  
  • Interactive Bulletin Boards for Secondary School Mathematics
  • here). By the way, all my weekly Maths Gems posts volition endure filed on this page, which you lot tin give the axe access from the 'Extras' bill of fare on my blog. Thanks for reading.
    
    
    

Pythagoras' Theorem

Pythagoras' Theorem is 1 of my favourite topics to teach. In my experience, students quite similar it too. At outset they may endure intimidated past times the novel as well as seemingly complex mathematics. It's in all likelihood the outset fourth dimension they've seen words such every bit theorem, proof as well as hypotenuse hence no wonder they're apprehensive. But they'll apace larn the hang of it.

When H5N1 score students receive got to uncovering the distance betwixt 2 points or verify that a triangle is right-angled, their outset thought should endure Pythagoras. By Year 12, Pythagoras' Theorem should endure a staple inwards their mathematical toolkit, along amongst other skills such every bit arithmetic, fractions, simplifying algebra, using index laws as well as factorising quadratics. In my thought these things are the breadstuff as well as butter of secondary schoolhouse higher mathematics.

I'm going to behave upon briefly on proofs at the halt of this postal service but my primary focus is on interesting Pythagoras questions as well as resources for Key Stage 3 as well as 4. Before nosotros start, I should number my green caveat - there's absolutely loads of first-class Pythagoras resources online as well as hither I'm exactly showcasing a pocket-sized selection.

Interesting Questions
It's non e'er necessary to strength a interrogation into a 'real world' context to larn inwards engaging. Problems don't receive got to endure contextual to endure interesting - sometimes the really best questions are abstract but accessible.

In this example from illustrativemathematics.org, students receive got to function out whether the shaded triangle is right-angled.

This Spiderbox question, also from Illustrative Mathematics, appears at outset glance to endure a 3D Pythagoras interrogation but genuinely the spider is walking on the exterior of the box. Students brand a net, describe the spider's path as well as function out its length.

amusing post from Math Jokes four Mathy Folks.

I also remember it's worthwhile spending a few minutes discussing the important of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a lawsuit that has been proven to endure true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory virtually who committed the murder') as well as inwards scientific discipline (such every bit Einstein's theory of relativity). In everyday linguistic communication it has a important similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory merely attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this two diagonals' as well as around other called 'amusing post from Math Jokes four Mathy Folks.

I also remember it's worthwhile spending a few minutes discussing the important of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a lawsuit that has been proven to endure true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory virtually who committed the murder') as well as inwards scientific discipline (such every bit Einstein's theory of relativity). In everyday linguistic communication it has a important similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory merely attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this kite areas'.

Helpful Worksheets

horacek.com.au

This 'Investigating the sides of right-angled triangles' worksheet from Teachit Maths is a straightforward activity inwards which students sweat to 'discover' Pythagoras' Theorem past times drawing right-angled triangles as well as investigating the human relationship betwixt the lengths of their sides. Teachit Maths also provides a 'Pythagoras' Theorem - consummate topic booklet' which covers the total topic from uncomplicated exercise questions to occupation solving, using surds as well as 3D Pythagoras.

These Pythagoras' Theorem Student Sheets (& notes) from Nuffield Foundation comprise proficient occupation solving questions, every bit does Pythagoras Problems from The Chalk Face.

I've written a Pythagoras Pret homework - run across this page for to a greater extent than data virtually Pret homeworks.

Adding a Third Dimension
During my PGCE I had my students educate cuboids out of pipage cleaners as well as function out how to uncovering the length of the infinite diagonal past times themselves. The pipage cleaners were a faff that I won't endure repeating but figuring out how to uncovering the length of a infinite diagonal is definitely something students tin reach the axe produce themselves. Perhaps the easiest prop to role is your classroom. When I learn 3D Pythagoras I commonly gesture at an imaginary infinite diagonal beingness drawn from the lower left corner to upper correct corner of the room. In fact it would endure meliorate to attach around string or wool to the walls hence y'all receive got an actual infinite diagonal going across the room, to assist students visualise the correct angled triangles.

There's 2 approaches to didactics 3D Pythagoras. One is to receive got the pupils derive the formula for the infinite diagonal (eg d² =  x² + y² + z²) as well as hence memorise it. This may endure useful later on on, for instance when they report vectors inwards C4, but it's non helpful when they come upwards to 3D trigonometry. My preferred approach for 3D problems is that they position as well as separately describe the 2 correct angled triangles inwards question. I encourage them to proceed their workings inwards surd cast for accuracy.

Good 3D questions are available inwards these Trigonometry Worksheets (see exercise T7) past times Frank Tapson (from the Cleave Books website).

Also, here's a dainty 3D Pythagoras activity 'amusing post from Math Jokes four Mathy Folks.

I also remember it's worthwhile spending a few minutes discussing the important of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a lawsuit that has been proven to endure true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory virtually who committed the murder') as well as inwards scientific discipline (such every bit Einstein's theory of relativity). In everyday linguistic communication it has a important similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory merely attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this Cuboid Diagonal' from Don Steward.

Triples
Pythagorean Triples are fun to explore amongst your students. Before y'all do, accept the chance to print them amongst your apparent super-quick mental arithmetics ("the 2 sides are five as well as 12 y'all say? Well the hypotenuse must endure 13").

Activity 3.4 inwards this set of activities from the Mathematics Enhancement Programme is a brusk as well as accessible investigation into Pythagorean Triples. The Mathematics Assessment Programme also has a Pythagorean Triples activity and Don Steward has students looking for patterns. There are many to a greater extent than substantial investigations available online.

Vocabulary

amusing post from Math Jokes four Mathy Folks.

I also remember it's worthwhile spending a few minutes discussing the important of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a lawsuit that has been proven to endure true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory virtually who committed the murder') as well as inwards scientific discipline (such every bit Einstein's theory of relativity). In everyday linguistic communication it has a important similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory merely attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this here.

Pythagoras of Samos
Apparently Pythagoras was the outset mortal to telephone outcry upwards the heavens a universe as well as the the world round. He also (allegedly) headed upwards a hugger-mugger cult of Pythagoreans who weren't allowed to swallow beans. Pythagoras said that "each number has its ain personality - masculine or feminine, perfect or incomplete, beautiful or ugly". The mysterious story of Pythagoras of Samos is genuinely interesting as well as would brand a proficient topic for enquiry or display work.

Pythagorean Proofs
I won't verbalise besides much virtually proofs because I'll endure hither all day. I must advert this bright H2O demonstration video though.



If y'all desire your students to essay around proof activities, this chore 'Proofs of the Pythagorean Theorem' from Mathematics Assessment Project is virtually comparison 3 dissimilar proofs.

Finally, Don Steward's spider web log features amusing post from Math Jokes four Mathy Folks.

I also remember it's worthwhile spending a few minutes discussing the important of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a lawsuit that has been proven to endure true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory virtually who committed the murder') as well as inwards scientific discipline (such every bit Einstein's theory of relativity). In everyday linguistic communication it has a important similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory merely attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this Herve Lehning's posters of Pythagoras past times agency of dissections which are really pleasing to the eye.

I promise this has been helpful if you're planning Pythagoras lessons. Please comment if y'all receive got whatsoever ideas to add.

I've at in 1 lawsuit seat all my topic resources specials here so they are easier to browse.

5 Maths Gems #5

Twitter is a unlike identify straightaway everyone's dorsum at school. During the solar daytime it's actually tranquillity because teachers are difficult at work, merely inwards the eve it comes live on again. Despite existence the outset calendar week of term, the United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland maths twitter chats (#mathscpdchat on Tuesdays as well as #mathschat on Wednesdays) were equally busy equally e'er - equally park they gave me enough of inspiration.

This calendar week likewise saw the supply of instructor blogs. I actually bask reading reflections of what teachers convey been trying inwards their lessons, what went good as well as what didn't. These blogs are a fantastic source of ideas.

This 5th weekly gems shipping is (unintentionally) brought to yous past times the missive of the alphabet P. It features patterns, puzzles, primes, projects, plenaries as well as posters.

1. Patterns as well as Puzzles

Fawn Nguyen's (blog post close a successful lesson inwards which her students were actually engaged inwards exploring these sequences.

Sticking amongst visual maths, Denise Gaskins (@letsplaymath) shared a puzzle from the website 1001 Visual Puzzles. I explored this site as well as constitute that it's full of rattling odd as well as master copy puzzles. I likewise learnt a piddling close topology - what a bizarre branch of mathematics. Here's an event of a topological puzzle (students would demand to advert to a map of South America for this):

2. Primes

Primes are actually interesting, aren't they? I've seen to a greater extent than or less slap-up materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things close a broad gain of mathematical topics. He frequently features animations which you'll know I'm a fan of if yous read my shipping close animations as well as simulations. For event this is a rattling clear explanation of Mersenne primes as well as perfect numbers.

If you're thinking of doing something on primes amongst your students, @the_chalkface shared this first-class true or fake activity which students volition detect interesting as well as stretching.

I likewise similar this activeness 'Further Factor Properties' from @TeachitMaths, mainly because it involves sexy primes as well as I'm a chip young similar that.

4. Projects

I've never sentiment of textbook redesign before, merely it could live on a actually skilful mini-project at the destination of a topic. On blog post close a successful lesson inwards which her students were actually engaged inwards exploring these sequences.

Sticking amongst visual maths, Denise Gaskins (@letsplaymath) shared a puzzle from the website 1001 Visual Puzzles. I explored this site as well as constitute that it's full of rattling odd as well as master copy puzzles. I likewise learnt a piddling close topology - what a bizarre branch of mathematics. Here's an event of a topological puzzle (students would demand to advert to a map of South America for this):

2. Primes

Primes are actually interesting, aren't they? I've seen to a greater extent than or less slap-up materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things close a broad gain of mathematical topics. He frequently features animations which you'll know I'm a fan of if yous read my shipping close Pythagoras' Theorem as well as added a topic specials page as well as thence yous tin rapidly detect similar posts. I likewise had a rant close student targets inwards which I questioned whether they are effective or fifty-fifty necessary. After Ed Southall (@edsouthall) shared these awesome wall decals, I updated my mathsy gifts page. I've likewise added a duo to a greater extent than homeworks to the Pret homeworks page.

How skilful are yous at drawing lines of best fit? Test yourself here (thanks to @MARitchings) - fun for teachers as well as likewise a useful lesson resource.

Finally - look, blog post close a successful lesson inwards which her students were actually engaged inwards exploring these sequences.

Sticking amongst visual maths, Denise Gaskins (@letsplaymath) shared a puzzle from the website 1001 Visual Puzzles. I explored this site as well as constitute that it's full of rattling odd as well as master copy puzzles. I likewise learnt a piddling close topology - what a bizarre branch of mathematics. Here's an event of a topological puzzle (students would demand to advert to a map of South America for this):

2. Primes

Primes are actually interesting, aren't they? I've seen to a greater extent than or less slap-up materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things close a broad gain of mathematical topics. He frequently features animations which you'll know I'm a fan of if yous read my shipping close my end maths gems post.

5 Maths Gems #11

I've got roughly vivid gems for y'all this week. As commons Twitter has been on transcend form.

1. Quick Key
Last calendar week I wrote close Plickers, which is an app y'all tin role inwards the classoom for formative assessment - y'all ask a device only your students don't. Today I'm suggesting roughly other app that y'all tin role for assessment - Quick Key. With this app y'all tin laid multiple alternative homeworks or tests as well as grade them inwards seconds past times scanning the respond sheets ('Quick Tickets') with your phone.

Quick Key is the excogitation of American instructor Walter Duncan (@4_teachers). It "turns your band into a scanner as well as eliminates hand-grading of assessments, fifty-fifty for teachers working inwards paper-based classrooms without a calculator or internet. Analytics as well as information exports are easy, thus y'all tin focus on your students".

My initial thoughts were that although this app could live on rattling useful (less fourth dimension spent marking = to a greater extent than fourth dimension spent planning character lessons), it won't allow me to banking concern friction match students' methods, which limits opportunities for useful feedback. But for straightforward cognition checks, to inform me how much my students know, it would operate rattling well.

But as well as then I read this post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my reflection stickers. Students stick a 'Not nonetheless yeti' or 'I got it' sticker inwards their majority to allow y'all know whether they've understood the work.

Speaking of stickers, Adil Jaffer (@adil_3) shared his fantastic feedback stickers thus y'all don't own got to proceed writing the same affair all the fourth dimension when you're marking.

One of the post pop tweets I saw this calendar week was from @MathedUp who shared his fantastic 'request a selfie' idea. I tin encounter this actually improving the character of students' operate - many of my students would honey the chance to print their parents. If y'all role iDoceo as well as then it's slow to own got a movie on your iPad as well as e-mail it to a parent.

Did y'all encounter these practice books, tweeted by @dandesignthink? The boxes at the bottom of the pages incorporate a checklist (accuracy, spelling, grammar), cardinal words, farther questions, cardinal points, what went well, as well as feedback. An 'Exercise majority 2.0' costs 50p - amount details are available here. There's also a maths version - Maths majority 2.0 is as awesome. I wishing I had a budget to pass because I'm desperate to gild these!

The to a greater extent than I role Twitter, the to a greater extent than inclined I am to hashtag everything I write (or say!). I own got to bound myself from putting hashtags inwards text messages to my hubby ('what do y'all desire for dinner tonight? #pleasesaytakeaway'). It's prissy to encounter that I'm non lone - Cathy Yenca (post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my Open Evening post where y'all concur a 'design a maths clock' competition. The clock pictures below are all taken from sbcrafts.net where y'all tin banking concern friction match out a big attain of clock let on ideas that could also live on used on let on lines.

And finally...
Algebraic long segmentation is fun when y'all know how to do it, only it tin live on a chip tricky to learn to Year 12. It's prissy to know at that spot are alternative methods. I've factorised polynomials past times inspection earlier only non using a grid as suggested by post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my The Art of Collaboration', it's e'er nifty to take heed when these ideas larn far into classrooms. Have a nifty half-term intermission everyone!

5 Maths Gems #14

Welcome to my 14th weekly gems post - this is where I characteristic 5 of the best teaching ideas I've seen on Twitter each week.

You may or may non know that I've been writing these posts spell I've been at domicile on motherhood leave. My babe keeps me busy during the day, but my evenings are blissfully costless from marker too lesson planning hence I induce got a rare chance to reverberate on my teaching too get together novel ideas. It's a shame that all teachers can't accept a mini-sabbatical every 5 years to produce the same. When I become dorsum to function inwards Jan I'll induce got 100 maths teaching gems inwards my toolkit - it volition live on difficult to know where to start! 

1. Two Truths too a Lie

Two Truths too a Lie is traditionally an icebreaker game - somebody tells y'all 3 facts near themselves too y'all guess which 1 is the lie. For instance my blood brother mightiness tell y'all that he was 1 time bitten yesteryear a donkey, he was 1 time bitten yesteryear a serpent too he was 1 time bitten yesteryear a monkey. Bizarrely, solely 1 of those statements is a lie. So let's accept this game too plow it into an action that prompts mathematical discussion.

This thought came from a tweet yesteryear @TCM_at_NCTM:

Polygons (source: mathsisfun.com)

This tweet made me realise that I'm guilty of lazily telling my students that polygon is 'just approximately other word for shape' when inwards fact I should live on to a greater extent than specific - a polygon is a 2D figure amongst at to the lowest degree 3 at 1 time sides too angles (the word derives from the Greek 'many-angled'), hence a circle is non a polygon.

The ii truths near quadrilaterals ('a foursquare is a rectangle' too 'a rectangle is a parallelogram') volition also prompt interesting discussions near definitions. The quadrilateral solid unit of measurement tree mightiness assistance clarify things. The Euler diagram below is also helpful. 

Quadrilaterals (source: Wikipedia)

Here's a span to a greater extent than examples of mathematical 'Two Truths too a Lie' activities:

Influenza A virus subtype H5N1 related idea, Maths Lies (where the instructor tells 1 deliberate prevarication per lesson - run across my first gems post) is even hence 1 of my favourite teaching ideas ever.

xkcd.com

2. Wikipedia and visualisation

From 1 to 1,000,000' from Gems 7 near Estimation 180). Show your students the dotty pictures hence they learn a practiced feel of the magnitude of numbers. 

The epitome to a higher identify reminds me of the 'If the World Were a Village of 100 People' visuals I talked near inwards Gems 1 - this is a nice means of conceptualising information that mightiness assistance students sympathise percentages.

3. Creative Mathematicians

Thanks to @gareth_metcalfe for sharing this bright video 'What is a mathematical proof?'. The video explains why mathematicians pass most of their fourth dimension trying things that don't work. Students are oft reluctant to examine a dissimilar approach if their outset examine at answering a inquiry is a dead end. Show this video at schoolhouse to encourage your students to live on creative inwards their mathematical thinking. 

4. Communicating Reasoning
Continuing the theme of encouraging students to examine diverse approaches to solving problems, bright NQT blogger gems post (unlucky 13) was my most pop post ever, amongst almost 2,000 views inwards a week. I also wrote a post on circle theorems final calendar week that I was peculiarly proud of. I beloved my gems posts too my resources library, but it's my topic specials that I mean value people volition discovery the most helpful. I similar to mean value that novel or latterly qualified teachers volition actually produce goodness from these posts when planning to learn a theme for the outset time. 

If y'all similar my weblog hence delight vote for it inwards the Great Britain Blog Awards (click hither to vote). There are over fifty blogs inwards the freelance educational activity category too solely 10 volition become through to the side yesteryear side stage. My weblog is tiny compared to the super-successful, well-established blogs I'm upwardly against. I've solely been writing it since Apr but I've done a lot inwards that fourth dimension - I set my pump too soul into it, hence if y'all discovery it useful hence your vote would live on real much appreciated.

Finally, produce y'all receive Chris Smith's (@aap03102)  weekly newsletter?  If y'all don't already subscribe hence email him at nowadays to learn on the mailing list. This calendar week he featured Pret homeworks which y'all should accept a await at if y'all haven't seen them before. Chris also featured the fantabulous puzzle below, which I'm looking frontward to giving my students when I provide to function inwards January.