Showing posts with label Homework. Show all posts
Showing posts with label Homework. Show all posts

Thursday, October 24, 2019

5 Maths Gems #3

Well it's been an emotional twain of weeks. Influenza A virus subtype H5N1 plane in addition to GCSE results kept many of us upwards at black in addition to nosotros experienced the green feelings of joy, pride, relief in addition to sometimes disappointment. But nevertheless nosotros perish along to gear upwards for the novel schoolhouse twelvemonth in addition to intend nearly what we'll produce differently.

The hardest matter nearly writing these weekly posts is deciding which ideas to feature. I take away keep an increasingly long listing of unused fabric because fifty-fifty when Twitter's teachers are preoccupied alongside results, the incredible inventiveness in addition to spirit of collaboration remains. In this postal service I'll showcase only v of the real many ideas shared on Twitter this week.

1. Homework
Kathryn Forster (@DIRT_expert) shared a novel laid of homeworks that she has designed. Each homework consists of v sections: literacy, research, memory, skills in addition to stretch. These homeworks would live on followed upwards past times starter activities such equally spelling or retentiveness tests in addition to discussions nearly enquiry findings. Kathryn has real helpfully shared iv of her homeworks for us to borrow:
These are actually goodness ideas.

If you're thinking nearly trying out around unlike approaches to homework I recommend reading Cav's (Homework in addition to Retention and Take Away Homework.

 2. Influenza A virus subtype H5N1 Scavenger Hunt
Speaking of homework, the Mailbox (@TheMailbox) shared a 'scavenger hunt' which could live on adapted equally starting fourth dimension homework for Year seven or 8.  Alternatively yous could pick out a pile of newspapers in addition to magazines into i of your starting fourth dimension Year seven lessons so your pupils tin create a poster inward shape using this idea.

3. Oh for a room to telephone telephone my own...
There's nevertheless a lot of classroom display ideas going circular Twitter. One of my most retweeted retweets this calendar week was this 'Change your words' display:
It's of import to communicate these messages in addition to a display similar this is a goodness agency of doing so. The see originally came from Sarah Hagan's (@mathequalslove) post '2014-2015 Classroom Pics - My Most Colorful Room Yet!'. Sarah may good live on i of the most enthusiastic maths teachers inward the world! Her weblog is real popular, in addition to rightly so. Check out this lectern inward her room - yes, a lectern! Is this measure inward American classrooms? I must acquire one!

I saw lots of prissy display ideas inward Sarah's Homework in addition to Retention and Take Away Homework.

 2. Influenza A virus subtype H5N1 Scavenger Hunt
Speaking of homework, the Mailbox (@TheMailbox) shared a 'scavenger hunt' which could live on adapted equally starting fourth dimension homework for Year seven or 8.  Alternatively yous could pick out a pile of newspapers in addition to magazines into i of your starting fourth dimension Year seven lessons so your pupils tin create a poster inward shape using this idea.

3. Oh for a room to telephone telephone my own...
There's nevertheless a lot of classroom display ideas going circular Twitter. One of my most retweeted retweets this calendar week was this 'Change your words' display:
It's of import to communicate these messages in addition to a display similar this is a goodness agency of doing so. The see originally came from Sarah Hagan's (@mathequalslove) post 'post - similar the reckoner posters below - in addition to it made me long for my ain classroom. Whilst inward the baby-making phase of my life I'm having a brief piece equally a part-timer. It's a mixed blessing. One disadvantage is that I don't take away keep my ain classroom so I learn inward rooms all over the school. Between lessons I take away keep to squash downwards crowded corridors alongside my huge pocketbook of books in addition to equipment (this was a nightmare when I was heavily pregnant!). There are lots of other disadvantages to beingness part-time such equally missing of import information from unminuted meetings in addition to a total lack of career progression opportunities. Of class this is all outweighed past times the massive wages of getting to pass fourth dimension alongside my children, so I'm non complaining... (much).

Another display see I've seen this calendar week is this classroom rules poster, shared by @TeachThought inward this post. I intend pupils would appreciate these real clear in addition to reasonable messages.

On the land of written report of conduct management, I enjoyed David Didau's (@learningspy) post on schoolhouse routines.

If yous desire to brand your ain classroom posters so recitethis.com is dandy for creating pretty quotes in addition to notices - cheers to @mathminds for sharing the link.

And if you're looking to render your classroom, Stephen Harris (@Stephen_H) shared a twain of awesome write-on tabular array designs: these ones are dandy for collaboration and tangram tables are perfect for a maths classroom.

And in conclusion on display ideas, Mr Allan (@mrallanmaths) shared his RAG123 display, Chris Smith (@aap03102) shared a motion-picture present of his 'Mathematician of the month' board, in addition to Mr Taylor (@taylorda01) adapted Spiked Math's Mathagasm comic so it's suitable for display. I'm going to steal all 3 ideas - if I always acquire my ain classroom.

4. Teaching ideas from #mathschat
Weekly maths chats accept identify on Twitter every Midweek at 8pm, organised by @BetterMaths. This calendar week nosotros discussed our favourite topics, tasks, resources in addition to investigations, so the goodness ideas were coming thick in addition to fast! I've got a long listing to form through.

There were lots of ideas nearly getting out of the classroom. Jon Treby (@JonTrebyAAN) suggested instruction loci exterior using buildings in addition to string. He too puts record on the flooring of the schoolhouse hall when he teaches angles inward parallel lines. Dawn (@mrsdenyer) has a schoolhouse treasure hunt for 3D trigonometry in addition to Martin Noon (@letsgetmathing) suggests using a clinometer to mensurate the summit of schoolhouse buildings in addition to trees.

There was too a lot of verbalize nearly popcorn! Dawn (@mrsdenyer) gets her students to blueprint a popcorn cone - an activity that involves sectors in addition to arcs, Pythagoras in addition to volume. If students tin function out the volume of their cone, they tin create total it alongside popcorn! Miss Ren (@ReynoldsBSGD) shared Dan Meyer's popcorn picker chore - 'all yous demand is A4 paper. I only stand upwards dorsum in addition to spotter the kids acquire stuck in!'.

5. Mistakes in addition to feedback
I've written a lot nearly learning from mistakes lately so this tweet was real relevant:

And here's a dandy see for marker from @ChrisHildrew.

So at that spot yous become - a pocket-sized option of ideas from a calendar week on Twitter. I promise that's helpful. If yous missed the previous ii Maths Gems posts, yous tin honor them here. I'll locomote out yous alongside a prissy inquiry for your students from Big Ideas Math.



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5 Maths Gems #4

Well the summertime holidays are good too genuinely over. Many teachers, specially those who are relatively novel to teaching, volition pass this weekend making lists, planning lessons too experiencing that unsettling feeling of nervous excitement. If yous stimulate got fourth dimension to read this week's laid of maths gems, I promise they furnish a piffling lite relief.

1. Maths lessons for maths teachers
I devote a lot of fourth dimension to thinking well-nigh how to railroad train my teaching but pass far less fourth dimension edifice on my ain mathematical skills too knowledge. Whatever our background too all the same 'good' nosotros are at maths, there's e'er to a greater extent than to learn. For example, I’ve never studied whatever mechanics inwards my life (I did Pure Maths H5N1 plane too a statistics degree) but SUVAT is on the novel GCSE syllabus too hence I'd improve discovery out what it is.

I experience that my cognition of secondary schoolhouse core mathematics is pretty audio but this calendar week Ed Southall (@edsouthall) inadvertently pointed me inwards the management of James Tanton's website (@jamestanton) and inside minutes I was learning novel things! Here's a few examples.

If asked to sketch the graph of y = x2 + 4x + 5, I'd realise that it can't live factorised too hence I'd banking concern tally the discriminant to confirm that this component subdivision has no existent roots. My side past times side footstep would live to consummate the foursquare to create upwards one's heed the vertex. I don't similar completing the square. I've never thought to discovery the vertex using this post written past times a pupil I works life out that inwards Republic of Lithuania 1st September is a 'celebration of cognition day'. Also, inwards the Lithuanian equivalent of our Year 13, they stimulate got a '100 twenty-four hours celebration' inwards which they stimulate got a prom to commemorate that they stimulate got exclusively 100 days left of school. The balance of the post is to a greater extent than oft than non well-nigh wearing clothing shopping for Lithuanian teenagers, too hence non quite too hence interesting... I'd similar to discovery out to a greater extent than well-nigh traditions inwards instruction around the world.

3. Plenaries, extensions, puzzles too loyalty cards
misstait.wordpress.com
This brilliant 'Finished? Try 1 of these...' display got me thinking well-nigh the materials I create for my early on finishers. The creator of this display, Kerry Tait (@misstait_85), wrote a blog post describing the review tasks contained within, which are intended to encourage students to reverberate on their learning. This is a actually prissy idea. Kerry is a scientific discipline instructor but this would piece of work as good inwards maths.

At the goal of my lessons I tend to become for extension activities rather than reflection tasks. In every lesson I give extension piece of work to the appropriate pupils at the appropriate time. My students know that I'm actually impressed if they stimulate got a become at the extension fabric but at the same fourth dimension I emphasise that maths isn't a race. There's value inwards occasionally planning a relatively brusk principal exercise too an 'extension' that is accessible to all, non only the brightest or the quickest. Most people savour beingness stretched. I desire all of my students to come upwards out of maths lessons feeling similar champions.

My extension piece of work is usually a challenging query relating to the lesson topic but sometimes I run puzzles instead. For instance at the goal of a Key Stage iii lesson on the monastic enjoin of operations I give students the classic four fours puzzle. For fifty-fifty an greater challenge there's this sixes puzzle shared by Chris Smith (@aap03102) (I recall my 6th formers would savour this one), or mayhap fifty-fifty something on Friedman numbers.
@edfromo
Here's a few to a greater extent than puzzles too extensions I've come upwards across this week. My schoolhouse has a lunchtime puzzle monastic enjoin for Year 7s too hence these volition come upwards inwards handy at that spot too, too I may gear upwards a weekly puzzle board as suggested past times Mr Duffy (@MrDuffyMaths).

For the 'Finished? Try 1 of these...' display, the creator says that she powerfulness pattern a checklist too prize organization to encourage students to run the total arrive at of reflective tools. This proffer reminded me of a duo of other ideas I saw on Twitter this week. In @CorbettMaths' post well-nigh how to run his 5-a-day questions, he suggests that students lay their completed questions inwards a ballot box too a fortnightly prize describe takes place. He also shared @MissKMcD's loyalty bill of fare ideas which she's explained inwards this weblog post 'Learning amongst Loyalty Cards'.
misskmcd.wordpress.com
4. Everyday lessons
My weblog is well-nigh sharing creative ideas too engaging resources. But my lessons aren't all-singing all-dancing. If yous were to notice most of my lessons you'd run across a pretty measure format of: starter, explanation, discussion, practice, extension. I create create opportunities for students to create investigations too exciting activities but non inwards every unmarried lesson. As yous tin tell past times the championship of my blog, it's actually of import to me that I pick engaging resources. Sometimes that only agency a good designed worksheet. Harry Webb's (@websofsubstance) post well-nigh maths lessons too priorities is good worth a read, specially for NQTs who volition shortly live drowning inwards lesson plans. In my NQT twelvemonth each lesson took me a duo of hours to plan. Four years on, my lessons stimulate got around thirty - 45 minutes to plan, which is soundless totally unsustainable too inefficient but I acquire a chip quicker every year. Being able to acquire proficient resources from my weblog should increase my planning speed as I won't stimulate got to create too hence much hunting for resources.

Harry's post also gave me a novel idea. H5N1 box on the board for students to write downwards the homework questions they works life difficult - such a uncomplicated thought but much improve than how I create it at the moment, which usually involves lots of students talking at me at once!

5. Bits too pieces
Here's a pocket-size choice of the other ideas I saw on Twitter this week:
  • I honey this 'things to create when you're stuck' poster from The Maths Magpie (@TheMathsMagpie).
thegriddle.net
I works life out this calendar week that my term 'maths gems' is totally unoriginal - here's a prissy 'assortment of mathematical marvels' which are also called maths gems. Speaking of nicely designed websites, create stimulate got a await at Mathigon, shared this calendar week past times Chris Watts (@watchri01) - stunning, isn't it?

So that's it for this week. My topic resources posts volition render shortly too I'll also piece of work on a this post written past times a pupil I works life out that inwards Republic of Lithuania 1st September is a 'celebration of cognition day'. Also, inwards the Lithuanian equivalent of our Year 13, they stimulate got a '100 twenty-four hours celebration' inwards which they stimulate got a prom to commemorate that they stimulate got exclusively 100 days left of school. The balance of the post is to a greater extent than oft than non well-nigh wearing clothing shopping for Lithuanian teenagers, too hence non quite too hence interesting... I'd similar to discovery out to a greater extent than well-nigh traditions inwards instruction around the world.

3. Plenaries, extensions, puzzles too loyalty cards
misstait.wordpress.com
This brilliant 'Finished? Try 1 of these...' display got me thinking well-nigh the materials I create for my early on finishers. The creator of this display, Kerry Tait (@misstait_85), wrote a blog post describing the review tasks contained within, which are intended to encourage students to reverberate on their learning. This is a actually prissy idea. Kerry is a scientific discipline instructor but this would piece of work as good inwards maths.

At the goal of my lessons I tend to become for extension activities rather than reflection tasks. In every lesson I give extension piece of work to the appropriate pupils at the appropriate time. My students know that I'm actually impressed if they stimulate got a become at the extension fabric but at the same fourth dimension I emphasise that maths isn't a race. There's value inwards occasionally planning a relatively brusk principal exercise too an 'extension' that is accessible to all, non only the brightest or the quickest. Most people savour beingness stretched. I desire all of my students to come upwards out of maths lessons feeling similar champions.

My extension piece of work is usually a challenging query relating to the lesson topic but sometimes I run puzzles instead. For instance at the goal of a Key Stage iii lesson on the monastic enjoin of operations I give students the classic four fours puzzle. For fifty-fifty an greater challenge there's this sixes puzzle shared by Chris Smith (@aap03102) (I recall my 6th formers would savour this one), or mayhap fifty-fifty something on Friedman numbers.
@edfromo
Here's a few to a greater extent than puzzles too extensions I've come upwards across this week. My schoolhouse has a lunchtime puzzle monastic enjoin for Year 7s too hence these volition come upwards inwards handy at that spot too, too I may gear upwards a weekly puzzle board as suggested past times Mr Duffy (@MrDuffyMaths).

For the 'Finished? Try 1 of these...' display, the creator says that she powerfulness pattern a checklist too prize organization to encourage students to run the total arrive at of reflective tools. This proffer reminded me of a duo of other ideas I saw on Twitter this week. In @CorbettMaths' post well-nigh how to run his 5-a-day questions, he suggests that students lay their completed questions inwards a ballot box too a fortnightly prize describe takes place. He also shared @MissKMcD's loyalty bill of fare ideas which she's explained inwards this weblog post 'Learning amongst Loyalty Cards'.
misskmcd.wordpress.com
4. Everyday lessons
My weblog is well-nigh sharing creative ideas too engaging resources. But my lessons aren't all-singing all-dancing. If yous were to notice most of my lessons you'd run across a pretty measure format of: starter, explanation, discussion, practice, extension. I create create opportunities for students to create investigations too exciting activities but non inwards every unmarried lesson. As yous tin tell past times the championship of my blog, it's actually of import to me that I pick engaging resources. Sometimes that only agency a good designed worksheet. Harry Webb's (@websofsubstance) post well-nigh maths lessons too priorities is good worth a read, specially for NQTs who volition shortly live drowning inwards lesson plans. In my NQT twelvemonth each lesson took me a duo of hours to plan. Four years on, my lessons stimulate got around thirty - 45 minutes to plan, which is soundless totally unsustainable too inefficient but I acquire a chip quicker every year. Being able to acquire proficient resources from my weblog should increase my planning speed as I won't stimulate got to create too hence much hunting for resources.

Harry's post also gave me a novel idea. H5N1 box on the board for students to write downwards the homework questions they works life difficult - such a uncomplicated thought but much improve than how I create it at the moment, which usually involves lots of students talking at me at once!

5. Bits too pieces
Here's a pocket-size choice of the other ideas I saw on Twitter this week:
  • I honey this 'things to create when you're stuck' poster from The Maths Magpie (@TheMathsMagpie).
  • I discovered a website for maths animations - mathimation.co.uk. New stuff is beingness added all the fourth dimension too hence follow @mathimation for updates.
  • Anna Hester (@TypeAMathLand) shared an infographic syllabus - I borrowed her thought too made a 'brief guide to AS plane maths' infographic for my Year 12s. It was fun too straight off I'm looking for other things to infograph!
  • I actually enjoyed JemmaPDuck's (@JemmaPDuck) blog post well-nigh her commencement twenty-four hours back, lots of teaching ideas here.
  • There's far likewise much shape filling inwards our lives, but here's some forms I read well-nigh via Twitter this calendar week that may live useful for conduct management. These powerfulness non appeal to everyone, but are worth a look.
  • Mr Taylor (@taylorda01) has been making some amazing video problems - this one is specially terrifying too hence students volition honey it.
  • Mr Collins (@mrprcollins) created these incredible last gems post. Using her template, I created a Pythagoras homework too recall to brand some more. I'd honey to part a big arrive at of Pret homeworks too hence delight e-mail me resourceaholic@gmail.com if yous brand 1 that you're happy to share.
    Pythagoras Pret Homework

    Those of yous going dorsum to schoolhouse side past times side week, proficient luck! I'd actually appreciate it if you'd hollo resourceaholic.com to your colleagues.  I'll acquire out yous amongst a prissy maths occupation for your Key Stage iii students - this 1 was shared past times F chiliad Jones (@FMJonesMaths).



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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
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.




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5 Maths Gems #9

Because I didn't write a gems postal service final weekend, imagine how much I receive got to tell y'all most today! Quick - let's acquire started...

1. Hula Hoops
Who needs technology scientific discipline when y'all tin stick a hula hoop on the board? This uncomplicated idea, shared by @emziecampbell, is for instruction children to tell the time. It would function good for other circle-based topics too. Stick a hula hoop on the board together with purpose it to instruct circle theorems. Stick 2 or 3 on the board to brand a Venn diagram. Hula hoops receive got novelty value, practical application together with toll a mere £2.
2. Stuck Post-Its
Another uncomplicated all the same effective idea, this fourth dimension from @Misswrenmaths: 'stuck post-its'. Sometimes when students are completing exercise questions inward class, y'all terminate upwards repeating yourself numerous times every bit y'all displace from educatee to student. Instead, topographic point the questions on the board together with enquire students to stick a named post-it Federal Reserve notation on whatever questions they ask assist with - together with hence they tin comport on with the remainder of the exercise without having to human face with their manus up. For instance the pic below shows that you'd ask to assist 1 educatee individually with query 9, simply it may move worth going through query 10 with the whole class, or gathering a grouping together to beak over it.

This technique stops duplication of endeavour together with helps the instructor assess understanding, addition it has the produce goodness of getting students out of their seats, albeit briefly. Read the fascinating postal service 'A veteran instructor turned charabanc shadows 2 students for 2 days – a sobering lesson learned' from @grantwiggins and you'll come across why this is important. Influenza A virus subtype H5N1 picayune flake of movement keeps students alert.

While I'm on the bailiwick of post-it notes, I should cite a cool novel app 'Post-it Plus' that was suggested by @dazmck. With this gratuitous app y'all tin receive got a photograph of a wall of post-it notes together with and hence organise them digitally on your telephone or tablet. Amazing.

3. Trig for Victory
@mr_g_walton demonstrated his brilliant inventiveness with his 'Maths Propaganda' posters.

Every poster is first-class hence it was difficult to pick out 3 examples for this post!

In add-on to the posters, Mr Walton suggests revision cards inward the shape of ration booklets together with a schoolhouse broadcast past times the Ministry of Maths! Fantastic ideas. All xvi editable posters together with associated resources tin move downloaded here. Credit also to @El_Timbre for inspiring the 'Trig for Victory' poster.

4. Parabolic Multiplication
qedcat.com
If y'all were at the recent Maths Conference inward Kettering together with hence y'all may receive got been interested inward Johnny Ball's parabolic multiplication. This involves drawing a trouble from 1 betoken on the graph of y = x2 to another. Two examples are shown inward the pic - the reddish trouble joins the numbers 3 together with 4, crossing the y-axis at 12, an the greenish trouble joins the numbers 2 together with 2, crossing the y-axis at 4. It's a bizarre multiplication method.

Influenza A virus subtype H5N1 sum explanation is inward this 'Cool Math Essay' from @jamestanton. The algebra is accessible together with satisfying. Figuring it out would brand a proficient chore for vivid GCSE students or 6th formers studying coordinate geometry.

If y'all reach off to move visiting Deutschland together with hence produce acquire to the Mathematikum. There y'all volition discovery a parabola drawn on a wall with a length of rope for visitors to necktie from 1 betoken on the parabola to unopen to other - the betoken at which the rope crosses the y-axis is the production (source: qedcat.com). Does anyone desire to receive got upwards the challenge of putting 1 of these interactive displays on their classroom wall? If so, delight shipping me a photo!

5. Counting Circles
There's been a lot of buzz alongside American teachers on Twitter most counting circles. This is a uncomplicated together with versatile activeness to railroad train divulge feel together with mental maths strategies. The master copy postal service A veteran instructor turned charabanc shadows 2 students for 2 days – a sobering lesson learned' from @grantwiggins and you'll come across why this is important. Influenza A virus subtype H5N1 picayune flake of movement keeps students alert.

While I'm on the bailiwick of post-it notes, I should cite a cool novel app 'Post-it Plus' that was suggested by @dazmck. With this gratuitous app y'all tin receive got a photograph of a wall of post-it notes together with and hence organise them digitally on your telephone or tablet. Amazing.

3. Trig for Victory
@mr_g_walton demonstrated his brilliant inventiveness with his 'Maths Propaganda' posters.

Every poster is first-class hence it was difficult to pick out 3 examples for this post!

In add-on to the posters, Mr Walton suggests revision cards inward the shape of ration booklets together with a schoolhouse broadcast past times the Ministry of Maths! Fantastic ideas. All xvi editable posters together with associated resources tin move downloaded here. Credit also to @El_Timbre for inspiring the 'Trig for Victory' poster.

4. Parabolic Multiplication
qedcat.com
If y'all were at the recent Maths Conference inward Kettering together with hence y'all may receive got been interested inward Johnny Ball's parabolic multiplication. This involves drawing a trouble from 1 betoken on the graph of y = x2 to another. Two examples are shown inward the pic - the reddish trouble joins the numbers 3 together with 4, crossing the y-axis at 12, an the greenish trouble joins the numbers 2 together with 2, crossing the y-axis at 4. It's a bizarre multiplication method.

Influenza A virus subtype H5N1 sum explanation is inward this 'Cool Math Essay' from @jamestanton. The algebra is accessible together with satisfying. Figuring it out would brand a proficient chore for vivid GCSE students or 6th formers studying coordinate geometry.

If y'all reach off to move visiting Deutschland together with hence produce acquire to the Mathematikum. There y'all volition discovery a parabola drawn on a wall with a length of rope for visitors to necktie from 1 betoken on the parabola to unopen to other - the betoken at which the rope crosses the y-axis is the production (source: Science and English) receive got shown an involvement inward this format too.

Last calendar week I also ran my kickoff A veteran instructor turned charabanc shadows 2 students for 2 days – a sobering lesson learned' from @grantwiggins and you'll come across why this is important. Influenza A virus subtype H5N1 picayune flake of movement keeps students alert.

While I'm on the bailiwick of post-it notes, I should cite a cool novel app 'Post-it Plus' that was suggested by @dazmck. With this gratuitous app y'all tin receive got a photograph of a wall of post-it notes together with and hence organise them digitally on your telephone or tablet. Amazing.

3. Trig for Victory
@mr_g_walton demonstrated his brilliant inventiveness with his 'Maths Propaganda' posters.

Every poster is first-class hence it was difficult to pick out 3 examples for this post!

In add-on to the posters, Mr Walton suggests revision cards inward the shape of ration booklets together with a schoolhouse broadcast past times the Ministry of Maths! Fantastic ideas. All xvi editable posters together with associated resources tin move downloaded here. Credit also to @El_Timbre for inspiring the 'Trig for Victory' poster.

4. Parabolic Multiplication
qedcat.com
If y'all were at the recent Maths Conference inward Kettering together with hence y'all may receive got been interested inward Johnny Ball's parabolic multiplication. This involves drawing a trouble from 1 betoken on the graph of y = x2 to another. Two examples are shown inward the pic - the reddish trouble joins the numbers 3 together with 4, crossing the y-axis at 12, an the greenish trouble joins the numbers 2 together with 2, crossing the y-axis at 4. It's a bizarre multiplication method.

Influenza A virus subtype H5N1 sum explanation is inward this 'Cool Math Essay' from @jamestanton. The algebra is accessible together with satisfying. Figuring it out would brand a proficient chore for vivid GCSE students or 6th formers studying coordinate geometry.

If y'all reach off to move visiting Deutschland together with hence produce acquire to the Mathematikum. There y'all volition discovery a parabola drawn on a wall with a length of rope for visitors to necktie from 1 betoken on the parabola to unopen to other - the betoken at which the rope crosses the y-axis is the production (source: Bridging the Gap to Influenza A virus subtype H5N1 level' featured inward this week's edition of Academies Week (thanks to @oldandrewuk) - I subscribe to this newspaper hence was rattling excited when it arrived inward the post.

I also featured inward the 'Behind the Mathematician' serial from @WorkEdgeChaos - writing that postal service was a slap-up chance for me to reverberate on my instruction together with mean value most what motivates me together with what I discovery challenging.

I desire to terminate today's postal service past times encouraging y'all to majority a ticket for @LaSalleEd's next National Maths Teacher Conference, which is on Sat 14th March 2015 inward Birmingham. Click here to majority your gratuitous ticket - I'll come across y'all there.


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5 Maths Gems #13

In my gems posts I portion roughly of the best teaching ideas I've seen on Twitter each week. This is my 13th gems post. I promise you're non triskaidekaphobic.

1. Flying Numbers
At Julia Smith's (@tessmaths) creativity workshop at the lastly maths conference, she shared an activeness inwards which students brand 'Flying Numbers' to hang from the ceiling inwards the classroom or corridor. It industrial plant similar this: they direct a release in addition to brand that release from forest inwards Design & Technology (drill a hole at the overstep for hanging). They pigment their release in addition to then role fine markers or chalk pens to decorate it amongst facts virtually that number. This is a lovely chance for students to role the cyberspace to explore release properties in addition to detect out all sorts of wonderful mathematical things that are non on the curriculum. The examples below were made at the maths conference - it was a actually enjoyable exercise.
Ed Southall (post virtually teaching a binary lesson).

Alice inwards FractalLand is a stunning animated slideshow. Show it to your shape in addition to explore sequences, fractals, the golden ratio in addition to more. The text at the bottom explains each concept really clearly. I love this! This is just the kind of affair I was referring to inwards my postal service 'A house for gimmicks?' when I said that nosotros should brand fourth dimension to enrich our students' instruction amongst interesting mathematics that is non on the GCSE syllabus.
  • The Primary and Secondary Treasure Hunts are really good designed. Full instructions are included in addition to in that place are questions on areas of mathematics such every bit cryptography, primes in addition to probability. The questions are rather challenging for the intended historic catamenia groups - if I was organising an inter-school maths contender in addition to then I mightiness role these questions.
  • The video collection is due to grow - an exciting prospect if this 2 infinitesimal wordless video exploring triangles is a gustatory modality of things to come. 

    • 3. Imbalance Problems
    If you're non familiar amongst Don Steward's resources in addition to then halt reading this postal service straight off in addition to banking concern lucifer out his mobiles', in addition to then 'mobile inequalities' in addition to finally 'mobile moments'.

    In mobiles, the activities kickoff amongst release problems that larn progressively harder, in addition to then motion on to algebraic balancing problems. Here's a numerical instance which tin live solved amongst arithmetics in addition to logic (fill inwards the missing weights thence that everything balances correctly). 
    There are lots of variations, such every bit this 1 where the weights must add together upwardly to the release inwards the triangle (this is a straightforward example):
    The algebraic problems railroad train skills inwards writing algebraically in addition to simplifying expressions. In the occupation below, students accept to consummate the missing weights to brand the combined hanging weight equal to 8n.
    These are dandy problems. Check out all 3 posts to run into how Mr Steward developed the idea. It's every bit good worth reading Paul Salomon's (last week's gems post has paid off - both Debbie Hart ‏(@Debbie_Hart_UK) and Jane Appleton (‏@JaneAppleton24) accept tried it.

    I've been busy writing a postal service virtually circle theorems which volition live attain soon. Also, later seeing roughly dandy Halloween in addition to Guy Fawkes maths resources, I've started to collate a 'seasonal resources' page. I've seen thence many adept Christmas resources, it's difficult to direct the best only I'm getting there.

    So in that place yous go, my 13th gems post. It wasn't scary at all.

    Image source: guernseydonkey.com



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