Animations In Addition To Simulations

Last night's #mathschat discussion nigh images gave me as well as hence many skillful teaching ideas, I woke upwardly at 2am to write a list! One affair that came upwardly was animations. I dearest a skillful animation that demonstrates a concept beautifully, as well as hence here's a few examples.

blog post) and judging past times the release of retweets, I gauge others similar it equally much equally I do. There's to a greater extent than gifs similar this here. 

The animation below shows how the outside angles of a polygon amount to 360^o. Sometimes it's improve to purpose an animation that yous tin intermission as well as speak through though, as well as hence I prefer this animation for outside angles of a polygon. Absorb Learning is an fantabulous website for animations.

Another instance of an animation yous tin intermission during teaching is this 'bisecting an angle' tool. It comes amongst both a clear pedagogy canvass for students as well as associated proofs. There are similar pages for every possible construction! As I mentioned inwards a previous post, I loathe teaching constructions, as well as hence I uncovering this really helpful.

Here's some other maths gif. This i is for demonstrating the properties of parabolas, equally taught inwards Further Maths. This tin also move demonstrated nicely using Desmos.

I also desire to cite PhET simulations. I don't instruct mechanics simply I'm told that PhET has lots of smashing interactive simulations for demonstrating concepts. 'Balancing Act' is a skillful example. They also accept simulations for Key Stage iii topics such equally fractions - run into the full maths alternative here. The simulations tin move downloaded as well as run from your schoolhouse network. 

Balancing Act - PhET

Aren't nosotros lucky to accept such fantabulous applied scientific discipline to heighten our teaching?

If yous know of whatever other skillful animations or interactive tools, delight comment below or tweet me.

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 #6

introducing calculus, a post nearly starters together with teaching inequalities together with a calendar of maths educational activity conferences. I've also added novel bits together with pieces to my resource libraries together with homeworks page. I've withal flora fourth dimension for Twitter - here's this week's highlights.

1. Geogebra

For those of us who are likewise busy or non techy plenty to make clever things alongside Geogebra, in that location are really helpful people who make it for us. I've mentioned Mathimation before. Here’s a few to a greater extent than interactive teaching tools that receive got been shared on Twitter recently:

• Custom Cuboid by @the_chalkface allows you lot to highlight specific cuboid faces - this is a helpful tool when teaching the surface surface area together with book of cuboids. 
• @TheMathsTeach gives us interactive circle theorems for students to explore. Each Geogebra worksheet has uncomplicated instructions together with questions - students tape their findings on the Student Conjecture Sheet.
• Parts of a Circle by @Mr_Mathematics is great for exploring circle vocabulary.

2. Two Superb Resources

I encounter a hell of a lot of skillful maths resources inwards my resource-addled life, but every right away together with and then I encounter ane that is absolutely superb. This calendar week was groovy because I discovered 2 such resources.

Ben Tanner (A level, my students flora them really useful for testing each other both inwards flat together with at home.

Extract from GCSE revision cards - tannermaths.co.uk

Chris Smith (@aap03102) produces a vivid weekly newsletter total of fantastic maths teaching ideas - if you lot don't already subscribe together with then email him right away to learn on the mailing list. This calendar week he tweeted nearly his relay races because they passed 100,000 downloads on TES. I can't believe that I, the resourceaholic, receive got never seen these before.

I've used revision relays alongside my classes earlier together with they've ever worked really well, therefore I'll definitely live using these release puzzle races. There are 10 relays hither including ane for Halloween, ane for Christmas together with ane for Easter. That's terminate of term sorted then.

Extract from Halloween Relay Race - Chris Smith on TES

The 100,000 downloads got me thinking nearly how many maths teachers in that location are inwards the UK. First I started thinking nearly how many schools in that location are together with how many maths teachers per school, but together with then I thought it mightiness live easier to outset from how many teenagers in that location are inwards the UK. This reminded me of a undertaking interview I ane time had. Now here's a story for your students if they ever inquire when they'll demand maths.

During my lastly twelvemonth at academy I had an interview for a graduate undertaking equally a administration consultant at PwC. I'd already done a summertime internship at KPMG therefore was feeling fairly confident. The pick solar daytime started alongside a maths examine much similar this one. After the examine I had dejeuner inwards a conference room alongside the other candidates. An administrator came inwards after dejeuner to denote who had failed the maths examine (the unsuccessful candidates had to learn out at that indicate - an awkward 2d for all). I survived the cutting together with proceeded to a bizarre undertaking interview.

The interviewer asked me how many planes were inwards the heaven at that moment. He wanted an actual number, non merely a method. Once I'd had a learn (starting point: how many airports inwards the world) he together with then asked me to reply ane time to a greater extent than using a dissimilar method, therefore I did (starting point: world's population). He together with then asked for some other method. We went through the same procedure for 'how many babies were born inwards the Britain yesterday?'. I intend I did a reasonably skillful undertaking of answering these questions - us mathematicians are skillful at lateral thinking. The lastly interrogation inwards the interview was nearly how I would mensurate the peak of a edifice using merely a barometer. I gave a few sensible answers but he kept asking for more. He stopped when I gave an utterly ridiculous reply which I won't acknowledge to hither (if you're coming the conference inwards 2 weeks, inquire me then). Moral of the story - maths together with occupation solving skills learn you lot far. You never know what you'll live asked inwards a undertaking interview. And don't live the somebody sent dwelling identify at lunch.

3. Two Superb Websites
@dazmck shared the website 'That Quiz' which allows you lot to laid complimentary online tests together with homeworks inwards a broad gain of topics from Key Stage three to H5N1 level. It alone takes a infinitesimal to brand a examine together with e-mail the URL to your students. They learn instant feedback on their answers (either throughout the quiz or at the end). They also learn an chance to right their mistakes. There are a release of settings but it's ridiculously tardily to use.

thatquiz.org menu

If you lot register (which takes roughly 5 seconds) you lot tin also collect your students' scores online. Here's an instance of a box plot examine question:

Example interrogation from thatquiz.org

This website is therefore incredibly helpful together with tardily to use, it reminds me of some other groovy website - Form Time Ideas. This is past times far the best tutor fourth dimension resources I've seen. It's beautifully designed together with tardily to use. The content is location on together with it changes every day. Websites that salve fourth dimension are a god-send for busy teachers.

formtimeideas.com

4. Words to Avoid
Twitter had me inwards stitches this week. @taylorda1 tweeted nearly something he'd said inwards a lesson that his students had flora amusing. Most teachers receive got made slips similar this - they tin stimulate a lot of disruption!

The conversation that followed this tweet was really funny. For the sake of novel or trainee teachers, here's a listing of things to avoid maxim inwards maths lessons:

• In probability, don't toss a money together with learn a head. In a room total of teenagers, far amend to flip a money together with learn a tail.
• Avoid examples involving 'balls inwards a bag'. 'Discs inwards a bag' tin live merely equally problematic if non said clearly. Try counters instead.
• Also inwards probability, live careful how you lot country 'the or rule'.
• When writing on the board make non shorten the give-and-take cumulative. Cum freq is probable to stimulate a stir.
• Don't brand c proportional to k (c∝k).
• Careful what you lot country (and how you lot gesture) when talking nearly enlargements, top heavy fractions together with going downwardly the release line.
• Be prepared for giggles if an reply is 69.
• Avoid having refer to 'the d' or maxim 4q ('4q too!').
• We can't avoid f(x) but live prepared for 'f off' silliness. Avoid f(u).
• When writing page numbers on the board, beware of p155.
• Don't country cos. Say cosine. Cos Omac is an insult together with for sure non suitable for a maths lesson if whatever of your students speak Arabic!

Thanks to all the tweeters who contributed to this list.

It plant both ways. I had to stifle my young giggles when I attended a Year 13's verbalize on the dangers of fracking.

There's to a greater extent than 'dirty mathematics' here.

5. Calligrams
@edsouthall tweeted some of these Minimal Math Concepts.

I beloved these together with was really pleased to discovery that you lot tin purchase them equally a sheet or framed impress - some other affair for my christmas list! I've added this to my mathsy gifts page.

@tessmaths shared her lovely thought for a flat activity on Maths Calligrams. A calligram is a phrase or give-and-take inwards which the text is arranged inwards a agency that creates a visual image. The epitome created past times the words expresses visually what the give-and-take says. This could live incorporated into a main or secondary maths lesson - give students a listing of maths vocabulary together with inquire them to create pictures to assist agreement together with recall.

Maths Calligram by @JonTrebyAAN

I promise you've flora some of these ideas helpful. I'm taking requests for futurity resources posts therefore if there's a detail theme you'd similar me to feature, delight email or tweet me.

5 Maths Gems #7

Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Maths Gems 4? That was skillful too).

Another fantabulous interactive tool is 'Investigating Triangle Area' (via @mathslinks). My students are ever happy to convey that a right angled triangle is one-half a rectangle, but are non so easily convinced for non-right angled triangles. The tool illustrates the fact past times allowing students to rearrange triangles into rectangles (click on subdivide as well as and then rotate as well as interpret the travel past times sections).

2. Estimation

Examples from estimation180.com

I've seen a lot of American teachers tweet close Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Every Math Teacher inwards the World Should Do This...Right Now!' by @nathankraft1 (shared amongst me past times @DianeMaths) y'all tin come across students working on whiteboards unopen to the classroom (I wishing my classroom was this big!).

Nathan enthusiastically says, 'When students are working on the whiteboards, I tin come across everything happening at once. It's similar I'm looking at the freaking Matrix. With a quick glance, I tin come across which students got it, which students are making fry mistakes, as well as which students lead maintain no sentiment what's going on. I tin chop-chop position errors for students. I tin inquire a stronger educatee to tending a struggling one. Once a educatee has the right answer, I yell, "Great! Erase it! Next problem!"'. His enthusiasm has rubbed off on me. I desire to sweat it! And earlier y'all disregard this sentiment because y'all don't lead maintain a room total of whiteboards, ship inwards involve heed that whatsoever vertical surface will produce - sweat writing on windows or using Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards related post summarises the benefits of 'Vertical Non-Permanent Surfaces':

• Improves visibility.
• Allows for transfer of cognition unopen to the room.
• Non-Permanent removes fearfulness of writing.
• Formative assessment past times instructor at all times.
• Teacher tin respond questions past times having students await at others work.

Influenza A virus subtype H5N1 related sentiment comes from Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Improving students' collaboration using acrylic sheets'. Jeremy suggests investing inwards clear acrylic sheets that students tin write on. Diagrams, pictures, axes etc tin last pose underneath. Read his send service for to a greater extent than on this, it actually is a bright idea.

Next week
A lot of my readers volition last at La Salle Education's maths conference side past times side week. I’m actually looking forrad to it. Please come upward as well as tell how-do-you-do if y'all topographic point me. Bear inwards involve heed that I lead maintain a iii calendar month onetime babe who rarely sleeps, so if y'all come across me doze off at whatsoever betoken as well as then simply laissez passer on me a nudge.

I however promise to write a maths gems send service side past times side week, it volition last a twenty-four hours slow but hopefully total of ideas shared at the conference.

By the way, if y'all didn't grab my final send service 'Common practise of successful departments' as well as 'What I learnt today' - both are good worth a read, especially for teachers of Influenza A virus subtype H5N1 degree maths.

Influenza A virus subtype H5N1 lot of the inspiration behind today's maths gems has come upward from teachers' blogs - I'm incredibly grateful to those who convey the fourth dimension to portion their ideas as well as experiences for the produce goodness of others.

1. Interactive Areas
Computer-based tools lead maintain made it easier to explicate some mathematical concepts as well as generate interesting questions. It's fantastic when applied scientific discipline enhances as well as enriches mathematics education.

I late tweeted this colourful instance which shows that nosotros tin cutting a circle into sectors as well as rearrange them to create upward one's involve heed the expanse (taken from @edfromo's Google+ post). @fmaths42 replied amongst this bright applet which illustrates the same matter inwards real clear interactive steps. Never earlier lead maintain I seen the formula for the expanse of a circle explained so clearly (and did y'all come across the 'proof without words' video inwards Practical tips for a (newly) qualified maths teacher' as well as then produce lead maintain a look.  It was a pop send service inwards which I shared some ideas for getting organised, so it's non simply for NQTs.