Showing posts with label Quadratics. Show all posts
Showing posts with label Quadratics. Show all posts

Friday, October 25, 2019

Factorising Harder Quadratics

My pupils panic at the sight of a quadratic alongside a leading coefficient greater than one.  I factorise these quadratics yesteryear inspection (the 'guess as well as test' method) but my pupils aren't satisfied alongside this proposition - they desire a to a greater extent than structured approach.

Influenza A virus subtype H5N1 normally taught method inwards the Great Britain involves splitting the middle term inwards 2 (sometimes called the 'Grouping Method'). This is explained really clearly here (thanks to SRWhitehouse for this resource). Teachitmaths.co.uk has a PowerPoint explaining this method. It's worth watching James Tanton's video 'Splitting the Middle Term' too. He's non a fan!
'Grouping'. Source: Flat World Education
An alternative, which seems slow at get-go but paves the agency for a large reveal of misconceptions, is the 'slide as well as divide' method. The method, as well as its associated problems, are nicely described inwards Nix the Tricks.
Nix the Tricks offers an interesting choice - I've provided 2 examples hither but it's worth reading the majority for the total explanation.
It's also worth looking at this post yesteryear Don Steward to run across his tap live yesteryear method for finding factors as well as for lots of helpful exercise questions.
Also worth a mention: when I get-go start instruction quadratic factorisation, I similar to purpose this well-designed sum-product worksheet from greatmathsteachingideas.com as a starter. It's skillful exercise of an essential skill.


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Large Foursquare Roots

In C1, the non-calculator H5N1 degree module, my pupils sometimes conk stuck solving quadratic equations that are difficult to factorise. This mightiness live on because the leading coefficient is greater than i (see my earlier post) or it may only live on because the numbers inwards the quadratic are large.  I usually propose that they persevere amongst factorising, but if they accept to resort to using the quadratic formula together with thence they may need to foursquare origin a large foursquare number. Here's only about elementary ideas for how to produce thence - inwards this example I'm finding the foursquare origin of 324, though these methods travel as good for larger foursquare numbers.


Note that if the quadratic equation can't live on factorised inwards the outset house together with thence nosotros tin either role the formula or consummate the foursquare to solve it, together with nosotros volition destination upwardly amongst a surd inwards our finally answer.  My side past times side post service is all most didactics surds!


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Thursday, October 24, 2019

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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5 Maths Gems #19

Hello in addition to welcome to my 19th gems post. This is where I part approximately of the best didactics ideas I've seen on Twitter each week. Most of my gems convey come upwards from across the Atlantic today.

1. Polygraph
There's been a lot of buzz almost Desmos' novel Polygraph activities. They're mathematical versions of Guess Who, designed to 'foster the pleasance in addition to the ability of words without the drudgery of the lists'. There are currently 4 Polygraph activities:

Let's expect at Polygraph: Parabolas. Students move inwards pairs (a picker in addition to a guesser) on split upwards tablets, phones or computers. The picker selects a graph from a ready of parabolas. The guesser sees the same ready of parabolas - their trace is to position which graph the picker has chosen past times cry for a serial of yes/no questions. For instance they mightiness inquire almost the seat out of roots or the place of the vertex or y-intercept. The guesser types their questions in addition to the picker responds alongside yes, no, or don't know. The guesser keeps cry for questions until they are able to position the chosen graph.
Students in addition to then convey the chance to analyse in addition to refine their questioning, in addition to y'all convey a flat discussion to formalise the mathematical vocabulary.

As alongside Desmos' awesome Gems 13, it's incredibly quick in addition to slow to larn started. I'm going to survive didactics quadratics to Year 10 before long in addition to can't hold back to purpose the Parabolas activity. And I computer program to purpose the Linear Graphs version alongside my Year 9s too.
Extract from Polygraph: Lines
2. Point, Point, Gradient
Tina Cardone (@crstn85) shared this lovely activity 'Point, Point, Slope' past times Michael Fenton (@mjfenton). It's a unproblematic precisely effective lesson stance inwards which students convey to purpose whatsoever digit from 2 to ix to create 2 points - y'all could rank them post-its or seat out tiles to shuffle around. You furnish criteria, such every bit 'create 2 points which create upwards one's heed a trace alongside the greatest possible gradient'. Read the amount post for to a greater extent than ideas. There's loads y'all could create alongside this activity, for instance y'all could inquire your students to use half dozen unlike digits (from 0 - 9) to create iii points which prevarication on the same line. It's a expert agency to railroad train agreement of linear graphs in addition to I cry back it would move good at both GCSE in addition to AS level.

Michael's spider web log is amount of fantabulous ideas. For instance in Two Fractions students house digits in addition to operators inwards the boxes below to brand an facial expression alongside the greatest possible value.
This reminds me of the Blanks activities I featured inwards Gems 17, which y'all tin rank the axe read to a greater extent than almost inwards Sarah Aldous' post Gems 13 I talked almost making your students 'Number Experts'. I shared 2 websites that are useful for finding out properties of numbers (numbergossip.com in addition to numdic.com). Both websites are fantabulous - for example, numbergossip.com tells me that 28 is a perfect, composite, happy number, and numdic.com (which wins the prize for funniest URL) gives me the binary in addition to Roman Numeral representations of 28. I've immediately discovered a novel website - the Number Property Calculator - which I similar because of the agency it gives data almost the important of the seat out properties. Here's a small extract from what comes upwards when I search for 28:
I flora this website when I was browsing through sometime posts on Math Munch. Math Munch is a 'Weekly Digest of the Mathematical Internet'. It's packed amount of fantastic resources in addition to ideas thus it's definitely worth subscribing to have weekly e-mail updates, in addition to y'all tin rank the axe follow them on Twitter also (@MathMunch).

5. Drawing Euclid
Andy Shaw (@Squidworm74) pointed me inwards the direction of these lovely Euclid videos on YouTube past times Shoo Rayner (@shoorayner). They are fantastic videos in addition to I can't hold back to part them alongside my Year vii students. Check out the amount playlist here. Here's an instance almost unlike types of triangles:



That's it for this week. I promise you've flora approximately inspiration inwards this post. I'll move out y'all alongside this bright video past times the always awesome Vi Hart - The Gauss Christmath Special. Thanks to Chris Smith (@app03102) for sharing this.




Have a wonderful Christmas!


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5 Maths Gems #20

Hello. I'm pleased to introduce my 20th gems post today - a milestone! Twitter has been repose this calendar week because Christmas took our minds off travel for a span of days, but I've nevertheless got around nifty ideas for you. The Christmas holidays are curt in addition to busy therefore it won't live on long earlier you're dorsum to planning lessons - I promise this post gives you lot around inspiration for the Spring term.

1. Factorising Quadratics
You know questions like this:
In Question 1 above, you lot tin give notice run across that the travel past times left jail cellular telephone has to incorporate a iii because it's a element of both iii in addition to 6. The residual of the cells tin give notice live on completed speedily 1 time 1 mutual element has been established. This is a unproblematic instance but Don develops the questions to choke increasingly difficult, around having multiple solutions. 

The adjacent prepare of activities extend the same sentiment to algebra, starting amongst this:
There's lots of these to consummate - first-class practise of factorising linear expressions.

The adjacent phase of this exercise is factorising quadratics.
Conveniently I'm currently planning a Year 10 lesson on factorising quadratics. I desire my students to create a lot of practise therefore volition definitely live on using this activity. The questions construct upward to a suitably challenging degree of difficulty, ending amongst this one:
I desire to encourage my students to factorise 'harder' quadratics (ie a > 1) past times inspection. This is my preferred method (ie 'guess in addition to test') but my students ever need that I instruct them a to a greater extent than structured approach (eg 'the Grouping Method') which frustrates me. Their insistence on next an algorithm suggests a lack of confidence. I intend the inquiry inward a higher house turns factorising quadratics into a form of logic problem. Tackling this inquiry without an algorithm powerfulness aid my students educate the confidence to factorise harder quadratics past times inspection.

One final sentiment for a lesson on factorising quadratics - I similar the occupation below from openmiddle.com. There are a publish of possible solutions therefore you lot could challenge students to discovery a dissimilar solution to the someone adjacent to them. 

2. Angle Sense amongst the Interactive Whiteboard
I've been planning a Year vii lesson on angles inward which I'd similar my students to approximate angle sizes. If you lot were asked to to pull an angle of 210o freehand, how would you lot create it? I'd intend of it equally a guide business addition a 3rd of a right-angle. If you lot choose proportional reasoning skills therefore it's pretty slowly to brand an educated guess. An angle estimation activity would travel perfectly good without applied scientific discipline (read out a serial of angle sizes in addition to enquire your students to pull their freehand estimates on paper. They therefore depository fiscal establishment jibe their estimates using a protractor - around other useful skill). But if you lot desire a similar activity for the interactive whiteboard therefore you lot powerfulness similar this fun here. Some of these angle games are quite funny - Banana Hunt in special made me chuckle.
If you lot similar these interactive whiteboard games therefore you'll discovery loads at Sheppard Software. It's amusing that there's an Absolute Value Number Balls game - this concept isn't covered until Year thirteen inward the United Kingdom of Great Britain in addition to Northern Ireland but I bet my students would honey to play this game - 5 minutes lite relief inward a C3 lesson!
FlashMaths.co.uk is around other nifty website for interactive whiteboard activities. Flash Maths was created past times Jonathan Hall (@studymaths) who brings us a plethora of fantastic tools on StudyMaths.co.uk. If you lot haven't seen it before, depository fiscal establishment jibe out MathsBot.com which is his unproblematic (but brilliant) worksheet generator.

3. Big Questions
Billy Adamson (@Billyads_47) shared a fantastic prepare of mathematical thinking prompts 'The Big Questions'. Here's a few examples: 


Lovely opened upward questions from Billy to generate intelligence in addition to educate understanding. There's around to a greater extent than expert examples of opened upward questions here:



4. Trigonometric Problem Solving
Our Year 13s' occupation solving skills are tested when they're asked to simplify expressions involving trigonometric identities inward C3 (like the example below).
I discovery that my students acquire frustrated when they can't topographic point a 'way in' guide away. They surrender quickly. There's genuinely a pretty criterion prepare of starting points, equally described on www.intmath.com (@intmath). 

I combat to aid my students experience confident inward tackling these problems, therefore I genuinely similar this activity from @mjfenton. Here's an extract:
The sentiment is that nosotros offset amongst a lot of construction in addition to gradually give fewer hints until students are able to solve the problems themselves. The steps powerfulness appear logical to us, but we're experienced occupation solvers. 

It's a expert sentiment for maths teachers to attempt to solve unfamiliar problems every at 1 time in addition to therefore (like the instance below from ‏@dannytybrown) to remind ourselves that mathematical occupation solving oftentimes requires patience, inventiveness in addition to multiple attempts. We all experience frustration inward occupation solving, merely similar our students do, but nosotros know that the satisfaction of eventually finding the solution is good worth it.

5. Dividing amongst Decimals
I've mentioned earlier that I honey MathsPad's resources - enough of them are complimentary in addition to the residual come upward at a terms of alone £3 per month. Whether your schoolhouse subscribes or not, it's worth registering for electronic mail updates inward companionship to proceed rail of all the novel resources. This month, the interactive resources on Decimal Calculations caught my eye. It ever surprises me how many students volition happily nation that forty divided past times ½ equals 20. Activities similar the 1 shown below volition aid tackle this misconception in addition to encourage students to intend earlier they answer.

That's it for this week. I'll travel out you lot amongst a video from 1977 - 'Congruent Triangles' past times Bruce in addition to Katharine Cornwell (another precious rock found on @MathMunch). Happy New Year!

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Polygraph Rocks

Gems 19.

My Year 10s are really smart girls as well as we've been working on quadratics for a duet of weeks - it's been a fleck 'death past times algebra' to live on honest. We've practised factorising, solving, using the formula, sketching as well as completing the square. Today I got them inward an information technology room as well as nosotros had a larn at Polygraph: Parabolas. It was superb.

One of the huge advantages of this lesson is that it requires absolutely cipher preparation. Once you've registered amongst Desmos, simply log inward as well as start the activity. Your students larn to student.desmos.com and locomote inward a code as well as their name, therefore off they go. You don't actually demand to hand whatever instructions because Desmos does it all for you.

The bulk of the lesson is similar a game of 'Guess Who' but for parabolas. Each educatee chooses a parabola from a choice as well as Desmos randomly pairs them upwardly amongst some other student. Their partner therefore has to type yes/no questions to figure out which parabola they've chosen.

Behind the scenes the instructor is able to monitor all the conversations. The interface is fantastic. 

Here's some examples of the questions asked past times my students today:
These examples were from quite early on inward the lesson. Throughout the lesson I occasionally picked out actually skilful questions as well as shared them amongst the whole class. At ane betoken I wrote 6 words on the board as well as encouraged students to outset using those words inward their questions:
  • Roots
  • Quadrant
  • Intercept
  • Vertex
  • Origin
  • Symmetry
I was actually impressed past times how speedily their mathematical linguistic communication developed. They started using the novel words (roots, vertex as well as quadrant) fluently. It was a pleasance to watch. Even when they got a fleck silly, they were using sophisticated terminology:

The lesson includes other tasks which give away misconceptions, similar the query below.
Overall it was a fantastic lesson. I actually saw my students' mathematical vocabulary develop. I too saw progress inward their agreement of quadratic graphs. The lesson was slow to project design as well as utterly engaging. 

At the goal I allow them play or therefore amongst Polygraph: Hexagons for ten minutes. Wow, they actually don't convey a clue how to depict polygons! We'll tackle that some other 24-hour interval though.

Well done Desmos, Polygraph rocks. 



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Dreaming Close Maths

I've alone been dorsum at function 3 weeks together with I've already started to dream nigh maths again. And non inwards a expert way. I score a laid of homeworks together with dream nigh the answers - they swim around my caput all nighttime long, tormenting me. Perhaps I shouldn't score inwards the evenings.

I also prevarication awake at nighttime thinking nigh lessons that didn't acquire well. I know, I know - don't dwell on them - afterwards all, I acquire from my mistakes together with they brand me a ameliorate teacher.

Today I desire to focus on the expert lessons. This post service is nigh 3 things that went good this week. As good every bit beingness therapeutic for me, hopefully there'll also endure some ideas hither to inspire you.

1. Angles
At the terminate of a sequence of lessons on angles amongst Year seven I gave out this vocabulary check. I told my students to examine to fill upwards it inwards without referring to their notes. I was pleased that some high lineament function was submitted:
It turned out to endure a genuinely worthwhile exercise for revealing misconceptions. The most mutual misconception was that co-interior angles are equal. There were also a lot of sketches missing the right parallel business notation:
Just forgetting the arrows or unaware the lines must endure parallel?
Influenza A virus subtype H5N1 few to a greater extent than surprising misconceptions came upwards too:
Worrying misunderstanding of the Definition of parallel
Confusion over vertically contrary angles
Normally I'd avoid an activity that doesn't genuinely involve solving maths problems, only I recollect I'll purpose this 1 in 1 trial again because it was thus revealing.

I took a commencement await at my Year 7's books this weekend. Some were a big mess thus I require to produce to a greater extent than function on improving their presentation. I recollect it's genuinely of import to constitute expert working practices inwards Year 7. The painting exhibit below shows 1 of the best books inwards the class. This is why I desire to purpose iVisualiser inwards my classroom - I desire to exhibit this student's mass to the degree every bit an illustration of how classwork should await (margins, sketches inwards pencil, clear workings, underlined answers etc).

2. Problems
At the terminate of a sequence of lessons I oftentimes brand an A3 canvas of problems relating to that topic. The questions come upwards from a multifariousness of sources including Median Don Steward together with Brilliant.org, together with sometimes I include 1 or 2 yesteryear GCSE questions. My students function inwards pairs answering the questions inwards whatever monastic state - sometimes this is for a whole lesson, sometimes one-half a lesson. The illustration below is 1 I used inwards a Year 10 quadratics lesson, afterwards they'd completed a bill of fare sorting activity.
The radius work (bottom left) originated from Chris Smith's newsletter together with I've mentioned it inwards a span of spider web log posts before. I told my Year 10s I'd endure real impressed if anyone managed to solve it. The adjacent lesson, 2 girls brought me the right solution together with talked me through their method. I honey it when students produce maths 'voluntarily' inwards their ain time, together with I honey it when they surprise me yesteryear figuring out the solution to a challenging problem.
Solving the radius problem
I gave the same work to my Year 9s. Influenza A virus subtype H5N1 few girls came upwards the solution 36 - although it was incorrect, their thinking was interesting. They correctly argued that the circle must endure inwards a foursquare - they thought that the overstep must endure a multiple of nine together with the side must endure a multiple of 8, thus the sides of the foursquare must endure a multiple of both nine together with 8 (ie 72). I similar their reasoning together with they explained it well, only there's no ground why the sides of the foursquare receive got to endure a multiple of 8 together with 9. Actually the radius is 29, thus the foursquare has sides of length 58.

I've been doing a lot of problem-based lessons this yr (using upwards my school's stocks of A3 paper!) together with I've been real impressed yesteryear my students' efforts thus far. They seem to relish these lessons, thus I'll proceed doing them every instantly together with then.
Lovely work for a surds work solving lesson
3. #LikeAGirl
This isn't maths, only it does receive got a link to maths thus deport amongst me.

I've taken on a Year eleven tutor grouping this term. They're lovely girls, if a lilliputian loud at times. I receive got 3 twenty infinitesimal afternoon registration slots to fill upwards each week. This calendar week I showed them the vivid #thisgirlcan video, only they didn't seem especially inspired. I recollect it has to a greater extent than of an deport on on women my historic menses than teenage girls. The Head of PE thus recommended the #likeagirl video together with this 1 got a ameliorate reaction. If you lot haven't seen it, produce receive got a look.


It struck me that this video has parallels amongst gender issues inwards maths together with science. I function at a girls' schoolhouse where these gender issues are non-existent. We receive got over 200 6th shape students taking maths - it's the most pop dependent area inwards the schoolhouse - together with at that spot is absolutely no perception of it beingness a 'male' subject. I acknowledge that at that spot are some disadvantages of single-sex education, only this liberty from the influence of gender stereotypes is 1 of the clearest advantages I've seen. If I was to tell my students that maths together with scientific discipline are male-dominated, they'd endure surprised together with perplexed. But inwards many schools (and inwards social club inwards general), doing maths 'like a girl' is considered an insult, similar throwing similar a daughter or running similar a girl.

The video genuinely got me thinking nigh the maths gender debate thus I'm going to position 'discovering this video' downwardly every bit my 3rd success of the week.

The rest
Please don't recollect that every lesson I learn goes well... far from it! Many lessons aren't worth commenting on, together with some could genuinely endure classified every bit disastrous... I tried Plickers for the commencement fourth dimension amongst Year seven on Friday. At the final infinitesimal my iPad app randomly froze thus I had to purpose my iPhone instead. Scanning the room took far likewise long. In fact, it was painfully slow. We gave upwards afterwards 4 questions, which was a shame because I'd spent a land setting it all up. I even thus genuinely similar the thought though, together with my students seemed to similar it too. So if I tin acquire it working in 1 trial again on my iPad, I'll definitely examine in 1 trial again some other day.

Speaking of trying novel technology, I've gear upwards a multiple selection examination for my Year 10s on Mon which I intend to score using Quick Key. I'll write nigh how it goes adjacent week.

Polygraph was the absolute highlight of the calendar week for me only I haven't featured it hither because I wrote a split post about it (as shortly every bit I got habitation from schoolhouse on Wednesday, because I was thus excited!).

That's it from me. I promise there's been some helpful ideas inwards this post. I recollect all teachers would honour it genuinely worthwhile to reverberate on a few things that went good each week. If you lot desire to slumber soundly, don't dwell on the bad stuff, only pat yourself on the dorsum for the expert stuff. And don't score afterwards 9pm!


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