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 receive got plenty fabric 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 hold off out for engaging ideas for revision lessons. Billy Adamson (@Billyads_47) shared this fantastic persuasion 'Maths Whispers!' inwards which pupils are given a fact or formula to communicate alongside their classmates, 'Chinese Whispers' style. Billy says that when his students were walking downwardly the corridor afterwards, they were excitedly talking almost what each disputation was initially as well as what it became. I dear this idea. It would function good inwards other subjects too. Check out Billy's resources on TES. Here's a variation I mightiness elbow grease for H5N1 degree revision: separate the course of written report into teams. The teams cast 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 example from S2:

All teams receive got the same message. The message is simultaneously passed along the lines inwards whispers. The in conclusion pupil inwards each describe writes the message on the board. The most accurate squad wins! Then shuffle the students as well as elbow grease some other message. My A degree revision cards receive got plenty of ideas for messages - definitions as well as formulae would function well.

2. Post-its. Mr Allan (@mrallanmaths) wrote this blog post almost his role of post-it notes inwards lessons. He displays questions on boards around his classroom. Students (in pairs or teams) function their agency around the room answering the questions on post-it notes. It's a quick as well as tardily agency of assessing agreement as well as finding misconceptions. It's also rattling engaging, fifty-fifty though the questions are exactly from a textbook. The persuasion 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 alongside you?' idea, shared past times @RemindHQ. It could hold upwards a overnice plenary activity in i lawsuit a week, or fifty-fifty at the halt of every lesson.

If yous desire to a greater extent than post-it banking concern notation teaching ideas thence banking concern fit out 'fractions weblog post this calendar week I discovered the blog Authentic Inquiry Maths which is total of expert ideas, similar T-charts for highlighting similarities as well as differences. Pupils role ICT to create their charts as well as yous larn a overnice mix of presentation styles, similar the example below.

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

Area occupation #2 - solvemymaths.com

Here's some other 'attractive' activity I spotted on Twitter this week. This i was shared past times Khan Academy (@khanacademy).  It's an engaging activity because it's visually striking, accessible as well as has a expert degree of challenge for pupils who've studied Pythagoras' Theorem. Shame I don't receive got the budget for coloring photocopying!

4. Starting a novel schoolhouse year. With solely 2 weeks left inwards the summertime holidays, I've started to run into weblog posts almost things to exercise inwards outset lessons of the schoolhouse year. I wrote a brace myself a few weeks agone - i on your outset lesson alongside Year 7 as well as i on kicking off Year 12.  Here's a few to a greater extent than I've spotted lately that are worth a read:

• This 'Deliberate Mistakes, Jo Boaler (@joboaler) talked this calendar week almost 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 as well as throw it at the board - exactly once, inwards a symbolic form of agency - non every fourth dimension they brand a mistake... Though I wonder if that would hold upwards worth trying too, to found a classroom civilisation of ‘everyone makes mistakes’ as well as to encourage risk-taking. Can yous imagine if your pupils threw all their mistakes at the board? It mightiness larn a flake messy. Fun though.
  
  Jo makes a give away of other useful suggestions inwards her article, such equally writing students' expert questions on posters around the room. She also talks almost the importance of valuing depth over speed. Many of my students brand it inwards secondary schoolhouse alongside the impression that it’s of import to exercise maths quickly. ‘Beat the clock’ type activities encourage this. What’s the rush?
  
  So, some helpful thoughts from Jo Boaler. Shame almost the negative article she wrote this calendar week almost maths teaching inwards the UK, but yay to the NCETM for defending us! It’s overnice to know individual has our backs.
  
  And finally...
  I'll destination off today's postal service alongside 3 recommended reads:
  
  • Interactive Bulletin Boards for Secondary School Mathematics
  • here). By the way, all my weekly Maths Gems posts volition hold upwards filed on this page, which yous tin access from the 'Extras' card on my blog. Thanks for reading.
    
    
    

Pythagoras' Theorem

Pythagoras' Theorem is ane of my favourite topics to teach. In my experience, students quite similar it too. At outset they may hold out intimidated past times the novel as well as seemingly complex mathematics. It's in all probability the outset fourth dimension they've seen words such equally theorem, proof as well as hypotenuse thus no wonder they're apprehensive. But they'll rapidly larn the hang of it.

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

I'm going to affect briefly on proofs at the terminate of this postal service but my master copy 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 commons caveat - there's absolutely loads of fantabulous Pythagoras resources online as well as hither I'm exactly showcasing a small-scale selection.

Interesting Questions
It's non ever necessary to strength a inquiry into a 'real world' context to larn inwards engaging. Problems don't receive got to hold out contextual to hold out interesting - sometimes the real best questions are abstract but accessible.

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

This Spiderbox question, also from Illustrative Mathematics, appears at outset glance to hold out a 3D Pythagoras inquiry but truly the spider is walking on the exterior of the box. Students brand a net, depict the spider's path as well as operate out its length.

amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out 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 most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly 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 exactly about other called 'amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out 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 most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly 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 travail 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 theme booklet' which covers the total theme from elementary exercise questions to work solving, using surds as well as 3D Pythagoras.

These Pythagoras' Theorem Student Sheets (& notes) from Nuffield Foundation comprise adept work solving questions, equally 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 most Pret homeworks.

Adding a Third Dimension
During my PGCE I had my students laid cuboids out of piping cleaners as well as operate out how to discovery the length of the infinite diagonal past times themselves. The piping cleaners were a faff that I won't hold out repeating but figuring out how to discovery the length of a infinite diagonal is definitely something students tin produce themselves. Perhaps the easiest prop to role is your classroom. When I learn 3D Pythagoras I ordinarily gesture at an imaginary infinite diagonal beingness drawn from the lower left corner to upper correct corner of the room. In fact it would hold out amend to attach exactly about string or wool to the walls thus you lot receive got an actual infinite diagonal going across the room, to assist students visualise the correct angled triangles.

There's 2 approaches to pedagogy 3D Pythagoras. One is to receive got the pupils derive the formula for the infinite diagonal (eg d² =  x² + y² + z²) as well as and thus memorise it. This may hold out useful afterwards 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 depict the 2 correct angled triangles inwards question. I encourage them to overstep on 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 prissy 3D Pythagoras activity 'amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out 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 most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly 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 alongside your students. Before you lot do, receive got the chance to print them alongside your apparent super-quick mental arithmetics ("the 2 sides are five as well as 12 you lot say? Well the hypotenuse must hold out 13").

Activity 3.4 inwards this set of activities from the Mathematics Enhancement Programme is a brusque 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 recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out 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 most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly 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 individual to telephone phone the heavens a universe as well as the Blue Planet round. He also (allegedly) headed upwards a surreptitious cult of Pythagoreans who weren't allowed to consume 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 truly interesting as well as would brand a adept theme for inquiry or display work.

Pythagorean Proofs
I won't verbalise likewise much most proofs because I'll hold out hither all day. I must advert this vivid H2O demonstration video though.



If you lot desire your students to attempt exactly about proof activities, this line 'Proofs of the Pythagorean Theorem' from Mathematics Assessment Project is most comparison 3 unlike proofs.

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

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out 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 most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly 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 real pleasing to the eye.

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

I've similar a shot seat all my theme resources specials here so they are easier to browse.

5 Maths Gems #5

Twitter is a dissimilar identify similar a shot everyone's dorsum at school. During the 24-hour interval it's actually tranquillity because teachers are difficult at work, only inwards the eventide it comes hold upwards again. Despite beingness the kickoff calendar week of term, the Great Britain maths twitter chats (#mathscpdchat on Tuesdays as well as #mathschat on Wednesdays) were every bit busy every bit always - every bit park they gave me enough of inspiration.

This calendar week every bit good saw the provide of instructor blogs. I actually taste reading reflections of what teachers accept 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 transportation is (unintentionally) brought to you lot 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 virtually 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 real odd as well as master puzzles. I every bit good learnt a footling virtually topology - what a bizarre branch of mathematics. Here's an trial of a topological puzzle (students would demand to cite 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 peachy materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things virtually a broad arrive at of mathematical topics. He frequently features animations which you'll know I'm a fan of if you lot read my transportation virtually animations as well as simulations. For trial this is a real 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 splendid true or fake activity which students volition detect interesting as well as stretching.

I every bit good similar this action '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 take in of textbook redesign before, only it could hold upwards a actually adept mini-project at the halt of a topic. On blog post virtually 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 real odd as well as master puzzles. I every bit good learnt a footling virtually topology - what a bizarre branch of mathematics. Here's an trial of a topological puzzle (students would demand to cite 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 peachy materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things virtually a broad arrive at of mathematical topics. He frequently features animations which you'll know I'm a fan of if you lot read my transportation virtually Pythagoras' Theorem as well as added a topic specials page as well as thus you lot tin chop-chop detect similar posts. I every bit good had a rant virtually 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 every bit good added a brace to a greater extent than homeworks to the Pret homeworks page.

How adept are you lot at drawing lines of best fit? Test yourself here (thanks to @MARitchings) - fun for teachers as well as every bit good a useful lesson resource.

Finally - look, blog post virtually 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 real odd as well as master puzzles. I every bit good learnt a footling virtually topology - what a bizarre branch of mathematics. Here's an trial of a topological puzzle (students would demand to cite 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 peachy materials on primes this week.

Richard Green (@edfromo) is a mathematician who posts regularly on Google+. He writes actually interesting things virtually a broad arrive at of mathematical topics. He frequently features animations which you'll know I'm a fan of if you lot read my transportation virtually my final maths gems post.

5 Maths Gems #11

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

1. Quick Key
Last calendar week I wrote almost Plickers, which is an app y'all tin role inward the classoom for formative assessment - y'all need a device merely 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 selection homeworks or tests in addition to grade them inward seconds past times scanning the answer sheets ('Quick Tickets') with your phone.

Quick Key is the conception of American instructor Walter Duncan (@4_teachers). It "turns your cry upwardly into a scanner in addition to eliminates hand-grading of assessments, fifty-fifty for teachers working inward paper-based classrooms without a estimator or internet. Analytics in addition to information exports are easy, thence y'all tin focus on your students".

My initial thoughts were that although this app could last real 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 gibe students' methods, which limits opportunities for useful feedback. But for straightforward cognition checks, to inform me how much my students know, it would function real well.

But thence I read this post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely 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 render scaffolding for selected students. I mean value my boss would last 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) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last 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 break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward my reflection stickers. Students stick a 'Not withal yeti' or 'I got it' sticker inward their mass to permit y'all know whether they've understood the work.

Speaking of stickers, Adil Jaffer (@adil_3) shared his fantastic feedback stickers thence y'all don't possess got to buy the farm on 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 come across this actually improving the character of students' function - many of my students would honey the chance to print their parents. If y'all role iDoceo thence it's slowly to accept a motion painting on your iPad in addition to electronic mail it to a parent.

Did y'all come across these practise books, tweeted by @dandesignthink? The boxes at the bottom of the pages incorporate a checklist (accuracy, spelling, grammar), telephone commutation words, farther questions, telephone commutation points, what went well, in addition to feedback. An 'Exercise mass 2.0' costs 50p - amount details are available here. There's also a maths version - Maths mass 2.0 is every bit awesome. I wishing I had a budget to pass because I'm desperate to guild 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 possess got to confine myself from putting hashtags inward text messages to my hubby ('what do y'all desire for dinner tonight? #pleasesaytakeaway'). It's overnice to come across that I'm non lonely - Cathy Yenca (post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely 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 render scaffolding for selected students. I mean value my boss would last 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) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last 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 break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward 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 gibe out a big arrive at of clock break ideas that could also last used on break lines.

And finally...
Algebraic long partition is fun when y'all know how to do it, merely it tin last a flake tricky to learn to Year 12. It's overnice to know in that place are option methods. I've factorised polynomials past times inspection earlier merely non using a grid as suggested by post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely 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 render scaffolding for selected students. I mean value my boss would last 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) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last 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 break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward my The Art of Collaboration', it's ever neat to listen when these ideas larn far into classrooms. Have a neat half-term interruption 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 habitation on motherhood leave. My babe keeps me busy during the day, but my evenings are blissfully gratis from mark together with lesson planning thence I create got a rare chance to reverberate on my teaching together with assemble 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 travel inwards Jan I'll create got 100 maths teaching gems inwards my toolkit - it volition last difficult to know where to start! 

1. Two Truths together with a Lie

Two Truths together with a Lie is traditionally an icebreaker game - person tells y'all 3 facts almost themselves together with y'all jurist which ane is the lie. For event my blood brother powerfulness tell y'all that he was in ane lawsuit bitten yesteryear a donkey, he was in ane lawsuit bitten yesteryear a serpent together with he was in ane lawsuit bitten yesteryear a monkey. Bizarrely, exclusively ane of those statements is a lie. So let's accept this game together with 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 about other word for shape' when inwards fact I should last to a greater extent than specific - a polygon is a 2D figure amongst at to the lowest degree 3 conduct sides together with angles (the word derives from the Greek 'many-angled'), thence a circle is non a polygon.

The ii truths almost quadrilaterals ('a foursquare is a rectangle' together with 'a rectangle is a parallelogram') volition also prompt interesting discussions almost definitions. The quadrilateral identify unit of measurement tree powerfulness attention clarify things. The Euler diagram below is also helpful. 

Quadrilaterals (source: Wikipedia)

Here's a duet to a greater extent than examples of mathematical 'Two Truths together with a Lie' activities:

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

xkcd.com

2. Wikipedia and visualisation

From 1 to 1,000,000' from Gems 7 almost Estimation 180). Show your students the dotty pictures thence they larn a skillful feel of the magnitude of numbers. 

The paradigm higher upward reminds me of the 'If the World Were a Village of 100 People' visuals I talked almost inwards Gems 1 - this is a nice agency of conceptualising information that powerfulness attention 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 frequently reluctant to test a dissimilar approach if their get-go test at answering a enquiry is a dead end. Show this video at schoolhouse to encourage your students to last creative inwards their mathematical thinking. 

4. Communicating Reasoning
Continuing the theme of encouraging students to test 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 terminal calendar week that I was peculiarly proud of. I dearest my gems posts together with my resources library, but it's my topic specials that I intend people volition detect the most helpful. I similar to intend that novel or late qualified teachers volition actually produce goodness from these posts when planning to learn a theme for the get-go time. 

If y'all similar my weblog together with then delight vote for it inwards the Great Britain Blog Awards (click hither to vote). There are over fifty blogs inwards the freelance teaching category together with exclusively 10 volition become through to the side yesteryear side stage. My weblog is tiny compared to the super-successful, well-established blogs I'm upward against. I've exclusively been writing it since Apr but I've done a lot inwards that fourth dimension - I pose my ticker together with soul into it, thence if y'all detect it useful together with then your vote would last really much appreciated.

Finally, produce y'all receive Chris Smith's (@aap03102)  weekly newsletter?  If y'all don't already subscribe together with then email him forthwith to larn 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 first-class puzzle below, which I'm looking forrad to giving my students when I provide to travel inwards January.