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

Thursday, May 21, 2020

Factorising Harder Quadratics

My pupils panic at the sight of a quadratic alongside a leading coefficient greater than one.  I factorise these quadratics past times 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 real 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 commencement but paves the agency for a large publish 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 option - 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 past times Don Steward to run into his tap exceed method for finding factors as well as for lots of helpful practise questions.
Also worth a mention: when I commencement start didactics quadratic factorisation, I similar to role this well-designed sum-product worksheet from greatmathsteachingideas.com as a starter. It's proficient practise of an essential skill.


Monday, May 18, 2020

Large Foursquare Roots

In C1, the non-calculator Influenza A virus subtype H5N1 marking module, my pupils sometimes perish stuck solving quadratic equations that are difficult to factorise. This powerfulness live because the leading coefficient is greater than i (see my earlier post) or it may but live because the numbers inward the quadratic are large.  I commonly propose that they persevere amongst factorising, but if they convey to resort to using the quadratic formula in addition to thence they may require to foursquare origin a large foursquare number. Here's roughly uncomplicated ideas for how to create thence - inward this representative I'm finding the foursquare origin of 324, though these methods run every bit good for larger foursquare numbers.


Note that if the quadratic equation can't live factorised inward the commencement house in addition to thence nosotros tin either purpose the formula or consummate the foursquare to solve it, in addition to nosotros volition halt upwards amongst a surd inward our lastly answer.  My adjacent post service is all close didactics surds!


Tuesday, April 14, 2020

5 Maths Gems #4

Well the summertime holidays are good as well as really over. Many teachers, especially those who are relatively novel to teaching, volition pass this weekend making lists, planning lessons as well as experiencing that unsettling feeling of nervous excitement. If y'all create got fourth dimension to read this week's laid of maths gems, I promise they supply a petty calorie-free relief.

1. Maths lessons for maths teachers
I devote a lot of fourth dimension to thinking almost how to railroad train my teaching but pass far less fourth dimension edifice on my ain mathematical skills as well as knowledge. Whatever our background as well as nonetheless 'good' nosotros are at maths, there's ever to a greater extent than to learn. For example, I’ve never studied whatever mechanics inwards my life (I did Pure Maths Influenza A virus subtype H5N1 flat as well as a statistics degree) but SUVAT is on the novel GCSE syllabus as well as then I'd ameliorate uncovering 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 administration 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 as well as then I'd cheque the discriminant to confirm that this constituent has no existent roots. My side past times side pace 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 uncovering the vertex using this post written past times a pupil I flora out that inwards Republic of Lithuania 1st September is a 'celebration of cognition day'. Also, inwards the Lithuanian equivalent of our Year 13, they create got a '100 twenty-four lx minutes catamenia celebration' inwards which they create got a prom to commemorate that they create got solely 100 days left of school. The residuum of the post is to a greater extent than oftentimes than non almost clothing shopping for Lithuanian teenagers, as well as then non quite as well as then interesting... I'd similar to uncovering out to a greater extent than almost traditions inwards teaching around the world.

3. Plenaries, extensions, puzzles as well as loyalty cards
misstait.wordpress.com
This brilliant 'Finished? Try 1 of these...' display got me thinking almost the materials I ready 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 squeamish idea. Kerry is a scientific discipline instructor but this would operate as good inwards maths.

At the destination of my lessons I tend to become for extension activities rather than reflection tasks. In every lesson I give extension operate to the appropriate pupils at the appropriate time. My students know that I'm actually impressed if they create got a become at the extension cloth but at the same fourth dimension I emphasise that maths isn't a race. There's value inwards occasionally planning a relatively curt master copy exercise as well as an 'extension' that is accessible to all, non simply the brightest or the quickest. Most people relish beingness stretched. I desire all of my students to come upwards out of maths lessons feeling similar champions.

My extension operate is usually a challenging inquiry relating to the lesson theme but sometimes I purpose puzzles instead. For event at the destination of a Key Stage iii lesson on the monastic tell 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 relish this one), or perchance fifty-fifty something on Friedman numbers.
@edfromo
Here's a few to a greater extent than puzzles as well as extensions I've come upwards across this week. My schoolhouse has a lunchtime puzzle guild for Year 7s as well as then these volition come upwards inwards handy at that topographic point too, as well as I may prepare a weekly puzzle board as suggested past times Mr Duffy (@MrDuffyMaths).

For the 'Finished? Try 1 of these...' display, the creator says that she mightiness blueprint a checklist as well as prize organisation to encourage students to purpose the total attain of reflective tools. This proposition reminded me of a dyad of other ideas I saw on Twitter this week. In @CorbettMaths' post almost how to purpose his 5-a-day questions, he suggests that students set their completed questions inwards a ballot box as well as a fortnightly prize depict takes place. He also shared @MissKMcD's loyalty carte du jour ideas which she's explained inwards this weblog post 'Learning amongst Loyalty Cards'.
misskmcd.wordpress.com
4. Everyday lessons
My weblog is almost sharing creative ideas as well as engaging resources. But my lessons aren't all-singing all-dancing. If y'all were to uncovering 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 as well as exciting activities but non inwards every unmarried lesson. As y'all tin tell past times the championship of my blog, it's actually of import to me that I pick engaging resources. Sometimes that simply agency a good designed worksheet. Harry Webb's (@websofsubstancepost almost maths lessons as well as priorities is good worth a read, especially for NQTs who volition presently live drowning inwards lesson plans. In my NQT twelvemonth each lesson took me a dyad of hours to plan. Four years on, my lessons accept around xxx - 45 minutes to plan, which is soundless totally unsustainable as well as inefficient but I acquire a flake quicker every year. Being able to acquire skilful resources from my weblog should increase my planning speed as I won't create got to create as well as then much hunting for resources.

Harry's post also gave me a novel idea. Influenza A virus subtype H5N1 box on the board for students to write downward the homework questions they flora difficult - such a uncomplicated thought but much ameliorate than how I create it at the moment, which unremarkably involves lots of students talking at me at once!

5. Bits as well as pieces
Here's a modest option of the other ideas I saw on Twitter this week:
  • I dearest this 'things to create when you're stuck' poster from The Maths Magpie (@TheMathsMagpie).
thegriddle.net
I flora out this calendar week that my term 'maths gems' is totally unoriginal - here's a squeamish 'assortment of mathematical marvels' which are also called maths gems. Speaking of nicely designed websites, create accept a hold off at Mathigon, shared this calendar week past times Chris Watts (@watchri01) - stunning, isn't it?

So that's it for this week. My theme resources posts volition render presently as well as I'll also operate on a this post written past times a pupil I flora out that inwards Republic of Lithuania 1st September is a 'celebration of cognition day'. Also, inwards the Lithuanian equivalent of our Year 13, they create got a '100 twenty-four lx minutes catamenia celebration' inwards which they create got a prom to commemorate that they create got solely 100 days left of school. The residuum of the post is to a greater extent than oftentimes than non almost clothing shopping for Lithuanian teenagers, as well as then non quite as well as then interesting... I'd similar to uncovering out to a greater extent than almost traditions inwards teaching around the world.

3. Plenaries, extensions, puzzles as well as loyalty cards
misstait.wordpress.com
This brilliant 'Finished? Try 1 of these...' display got me thinking almost the materials I ready 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 squeamish idea. Kerry is a scientific discipline instructor but this would operate as good inwards maths.

At the destination of my lessons I tend to become for extension activities rather than reflection tasks. In every lesson I give extension operate to the appropriate pupils at the appropriate time. My students know that I'm actually impressed if they create got a become at the extension cloth but at the same fourth dimension I emphasise that maths isn't a race. There's value inwards occasionally planning a relatively curt master copy exercise as well as an 'extension' that is accessible to all, non simply the brightest or the quickest. Most people relish beingness stretched. I desire all of my students to come upwards out of maths lessons feeling similar champions.

My extension operate is usually a challenging inquiry relating to the lesson theme but sometimes I purpose puzzles instead. For event at the destination of a Key Stage iii lesson on the monastic tell 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 relish this one), or perchance fifty-fifty something on Friedman numbers.
@edfromo
Here's a few to a greater extent than puzzles as well as extensions I've come upwards across this week. My schoolhouse has a lunchtime puzzle guild for Year 7s as well as then these volition come upwards inwards handy at that topographic point too, as well as I may prepare a weekly puzzle board as suggested past times Mr Duffy (@MrDuffyMaths).

For the 'Finished? Try 1 of these...' display, the creator says that she mightiness blueprint a checklist as well as prize organisation to encourage students to purpose the total attain of reflective tools. This proposition reminded me of a dyad of other ideas I saw on Twitter this week. In @CorbettMaths' post almost how to purpose his 5-a-day questions, he suggests that students set their completed questions inwards a ballot box as well as a fortnightly prize depict takes place. He also shared @MissKMcD's loyalty carte du jour ideas which she's explained inwards this weblog post 'Learning amongst Loyalty Cards'.
misskmcd.wordpress.com
4. Everyday lessons
My weblog is almost sharing creative ideas as well as engaging resources. But my lessons aren't all-singing all-dancing. If y'all were to uncovering 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 as well as exciting activities but non inwards every unmarried lesson. As y'all tin tell past times the championship of my blog, it's actually of import to me that I pick engaging resources. Sometimes that simply agency a good designed worksheet. Harry Webb's (@websofsubstancepost almost maths lessons as well as priorities is good worth a read, especially for NQTs who volition presently live drowning inwards lesson plans. In my NQT twelvemonth each lesson took me a dyad of hours to plan. Four years on, my lessons accept around xxx - 45 minutes to plan, which is soundless totally unsustainable as well as inefficient but I acquire a flake quicker every year. Being able to acquire skilful resources from my weblog should increase my planning speed as I won't create got to create as well as then much hunting for resources.

Harry's post also gave me a novel idea. Influenza A virus subtype H5N1 box on the board for students to write downward the homework questions they flora difficult - such a uncomplicated thought but much ameliorate than how I create it at the moment, which unremarkably involves lots of students talking at me at once!

5. Bits as well as pieces
Here's a modest option of the other ideas I saw on Twitter this week:
  • I dearest this 'things to create when you're stuck' poster from The Maths Magpie (@TheMathsMagpie).

Sunday, January 26, 2020

5 Maths Gems #19

Hello in addition to welcome to my 19th gems post. This is where I percentage but about of the best education ideas I've seen on Twitter each week. Most of my gems accept come upward 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 operate inwards pairs (a picker in addition to a guesser) on split tablets, phones or computers. The picker selects a graph from a prepare of parabolas. The guesser sees the same prepare of parabolas - their employment is to position which graph the picker has chosen past times quest a serial of yes/no questions. For instance they mightiness inquire almost the release of roots or the place of the vertex or y-intercept. The guesser types their questions in addition to the picker responds amongst yes, no, or don't know. The guesser keeps quest questions until they are able to position the chosen graph.
Students hence accept the chance to analyse in addition to refine their questioning, in addition to yous accept a degree discussion to formalise the mathematical vocabulary.

As amongst Desmos' awesome Gems 13, it's incredibly quick in addition to slow to larn started. I'm going to endure education quadratics to Year 10 presently in addition to can't hold off to purpose the Parabolas activity. And I programme to purpose the Linear Graphs version amongst 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 elementary but effective lesson view inwards which students accept to purpose whatsoever digit from 2 to nine to create 2 points - yous could laissez passer them post-its or release tiles to shuffle around. You furnish criteria, such equally 'create 2 points which create upward one's heed a draw amongst the greatest possible gradient'. Read the amount post for to a greater extent than ideas. There's loads yous could create amongst this activity, for instance yous could inquire your students to use 6 unlike digits (from 0 - 9) to create 3 points which prevarication on the same line. It's a expert means to educate agreement of linear graphs in addition to I recall it would operate good at both GCSE in addition to AS level.

Michael's spider web log is amount of splendid ideas. For instance in Two Fractions students house digits in addition to operators inwards the boxes below to brand an facial expression amongst the greatest possible value.
This reminds me of the Blanks activities I featured inwards Gems 17, which yous tin laissez passer notice 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 splendid - 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 right away discovered a novel website - the Number Property Calculator - which I similar because of the means it gives data almost the important of the release properties. Here's a small extract from what comes upward when I search for 28:
I constitute this website when I was browsing through onetime 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 hence it's definitely worth subscribing to have weekly e-mail updates, in addition to yous tin laissez passer notice follow them on Twitter likewise (@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 off to percentage them amongst 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 constitute but about inspiration inwards this post. I'll travel out yous amongst 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!


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 operate for a duet of days, but I've even therefore got around corking ideas for you. The Christmas holidays are brusk in addition to busy therefore it won't live on long earlier you're dorsum to planning lessons - I promise this post gives y'all around inspiration for the Spring term.

1. Factorising Quadratics
You know questions like this:
In Question 1 above, y'all tin come across that the move past times left jail mobile telephone has to comprise a three because it's a constituent of both three in addition to 6. The residue of the cells tin live on completed speedily i time i mutual constituent has been established. This is a uncomplicated instance but Don develops the questions to acquire increasingly difficult, around having multiple solutions. 

The adjacent ready of activities extend the same see to algebra, starting alongside this:
There's lots of these to consummate - first-class exercise 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 exercise therefore volition definitely live on using this activity. The questions construct upwards to a suitably challenging marking of difficulty, ending alongside 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 mean value the enquiry higher upwards turns factorising quadratics into a sort of logic problem. Tackling this enquiry without an algorithm mightiness aid my students prepare the confidence to factorise harder quadratics past times inspection.

One final see for a lesson on factorising quadratics - I similar the work below from openmiddle.com. There are a unwrap of possible solutions therefore y'all could challenge students to discovery a dissimilar solution to the someone adjacent to them. 

2. Angle Sense alongside the Interactive Whiteboard
I've been planning a Year vii lesson on angles inwards which I'd similar my students to approximate angle sizes. If y'all were asked to to clitoris an angle of 210o freehand, how would y'all create it? I'd mean value of it every bit a direct delineate of piece of work addition a 3rd of a right-angle. If y'all choose proportional reasoning skills in addition to therefore it's pretty slow to brand an educated guess. An angle estimation activity would operate perfectly good without technology (read out a serial of angle sizes in addition to inquire your students to clitoris their freehand estimates on paper. They in addition to therefore banking firm represent their estimates using a protractor - around other useful skill). But if y'all desire a similar activity for the interactive whiteboard in addition to therefore y'all mightiness similar this fun here. Some of these angle games are quite funny - Banana Hunt in exceptional made me chuckle.
If y'all similar these interactive whiteboard games in addition to 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 inwards the U.K. but I bet my students would beloved to play this game - 5 minutes lite relief inwards a C3 lesson!
FlashMaths.co.uk is around other corking 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 y'all haven't seen it before, banking firm represent out MathsBot.com which is his uncomplicated (but brilliant) worksheet generator.

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


Lovely opened upwards questions from Billy to generate give-and-take in addition to prepare understanding. There's around to a greater extent than adept examples of opened upwards questions here:



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

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

It's a adept see for maths teachers to seek to solve unfamiliar problems every instantly in addition to and therefore (like the instance below from ‏@dannytybrown) to remind ourselves that mathematical work solving oftentimes requires patience, inventiveness in addition to multiple attempts. We all experience frustration inwards work solving, only similar our students do, but nosotros know that the satisfaction of eventually finding the solution is good worth it.

5. Dividing alongside Decimals
I've mentioned earlier that I beloved MathsPad's resources - enough of them are costless in addition to the residue come upwards at a toll of exclusively £3 per month. Whether your schoolhouse subscribes or not, it's worth registering for e-mail updates inwards lodge to continue runway 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 tell that xl divided past times ½ equals 20. Activities similar the i shown below volition aid tackle this misconception in addition to encourage students to mean value earlier they answer.

That's it for this week. I'll exit y'all alongside a video from 1977 - 'Congruent Triangles' past times Bruce in addition to Katharine Cornwell (another jewel found on @MathMunch). Happy New Year!

Polygraph Rocks

Gems 19.

My Year 10s are real smart girls as well as we've been working on quadratics for a yoke of weeks - it's been a flake 'death past times algebra' to survive honest. We've practised factorising, solving, using the formula, sketching as well as completing the square. Today I got them inwards 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 zero preparation. Once you've registered amongst Desmos, only log inwards as well as start the activity. Your students larn to student.desmos.com and larn into a code as well as their name, thence off they go. You don't actually demand to laissez passer on 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 alternative as well as Desmos randomly pairs them upwards amongst some other student. Their partner thence 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 inwards the lesson. Throughout the lesson I occasionally picked out actually skillful questions as well as shared them amongst the whole class. At ane signal I wrote vi words on the board as well as encouraged students to commencement using those words inwards 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 flake silly, they were using sophisticated terminology:

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

At the halt I allow them play only about amongst Polygraph: Hexagons for x minutes. Wow, they actually don't accept a clue how to depict polygons! We'll tackle that some other twenty-four threescore minutes menses though.

Well done Desmos, Polygraph rocks. 



Dreaming Close Maths

I've exclusively been dorsum at piece of work iii weeks as well as I've already started to dream near maths again. And non inwards a adept way. I grade a laid of homeworks as well as dream near the answers - they swim around my caput all nighttime long, tormenting me. Perhaps I shouldn't grade inwards the evenings.

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

Today I desire to focus on the adept lessons. This post is near iii things that went good this week. As good every bit beingness therapeutic for me, hopefully there'll also hold upwards some ideas hither to inspire you.

1. Angles
At the terminate of a sequence of lessons on angles amongst Year vii 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 character piece of work was submitted:
It turned out to hold upwards 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 delineate of piece of work notation:
Just forgetting the arrows or unaware the lines must hold upwards 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 reverse angles
Normally I'd avoid an activity that doesn't genuinely involve solving maths problems, exactly I shout out back I'll locomote this i over again because it was hence revealing.

I took a outset await at my Year 7's books this weekend. Some were a big mess hence I demand to produce to a greater extent than piece of work on improving their presentation. I shout out back it's genuinely of import to found adept working practices inwards Year 7. The moving painting below shows i of the best books inwards the class. This is why I desire to locomote iVisualiser inwards my classroom - I desire to demonstrate this student's majority to the aeroplane every bit an example 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 sail of problems relating to that topic. The questions come upwards from a diversity of sources including Median Don Steward as well as Brilliant.org, as well as sometimes I include i or 2 past times GCSE questions. My students piece of work inwards pairs answering the questions inwards whatever monastic state - sometimes this is for a whole lesson, sometimes one-half a lesson. The example below is i I used inwards a Year 10 quadratics lesson, later on they'd completed a carte sorting activity.
The radius employment (bottom left) originated from Chris Smith's newsletter as well as I've mentioned it inwards a duo of weblog posts before. I told my Year 10s I'd hold upwards really impressed if anyone managed to solve it. The adjacent lesson, 2 girls brought me the right solution as well as talked me through their method. I beloved it when students produce maths 'voluntarily' inwards their ain time, as well as I beloved it when they surprise me past times figuring out the solution to a challenging problem.
Solving the radius problem
I gave the same employment 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 hold upwards inwards a foursquare - they thought that the overstep must hold upwards a multiple of ix as well as the side must hold upwards a multiple of 8, hence the sides of the foursquare must hold upwards a multiple of both ix as well as 8 (ie 72). I similar their reasoning as well as they explained it well, exactly there's no ground why the sides of the foursquare receive got to hold upwards a multiple of 8 as well as 9. Actually the radius is 29, hence the foursquare has sides of length 58.

I've been doing a lot of problem-based lessons this twelvemonth (using upwards my school's stocks of A3 paper!) as well as I've been really impressed past times my students' efforts hence far. They seem to bask these lessons, hence I'll snuff it on doing them every directly as well as then.
Lovely employment for a surds employment solving lesson
3. #LikeAGirl
This isn't maths, exactly it does receive got a link to maths hence behaviour amongst me.

I've taken on a Year xi tutor grouping this term. They're lovely girls, if a piffling loud at times. I receive got iii twenty infinitesimal afternoon registration slots to fill upwards each week. This calendar week I showed them the vivid #thisgirlcan video, exactly they didn't seem peculiarly inspired. I shout out back it has to a greater extent than of an behaviour on on women my historic menstruation than teenage girls. The Head of PE hence recommended the #likeagirl video as well as this i 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 as well as science. I piece of work 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 land inwards the schoolhouse - as well as in that place is absolutely no perception of it beingness a 'male' subject. I acknowledge that in that place are some disadvantages of single-sex education, exactly this liberty from the influence of gender stereotypes is i of the clearest advantages I've seen. If I was to tell my students that maths as well as scientific discipline are male-dominated, they'd hold upwards surprised as well as perplexed. But inwards many schools (and inwards guild 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 near the maths gender debate hence I'm going to set 'discovering this video' downwards every bit my tertiary success of the week.

The rest
Please don't shout out back that every lesson I learn goes well... far from it! Many lessons aren't worth commenting on, as well as some could genuinely hold upwards classified every bit disastrous... I tried Plickers for the outset fourth dimension amongst Year vii on Friday. At the final infinitesimal my iPad app randomly froze hence I had to locomote my iPhone instead. Scanning the room took far every bit good long. In fact, it was painfully slow. We gave upwards later on iv questions, which was a shame because I'd spent a piece setting it all up. I yet genuinely similar the thought though, as well as my students seemed to similar it too. So if I tin acquire it working over again on my iPad, I'll definitely examine over again some other day.

Speaking of trying novel technology, I've ready a multiple selection examination for my Year 10s on Mon which I shout out back to grade using Quick Key. I'll write near how it goes adjacent week.

Polygraph was the absolute highlight of the calendar week for me exactly I haven't featured it hither because I wrote a carve upwards post about it (as before long every bit I got habitation from schoolhouse on Wednesday, because I was hence excited!).

That's it from me. I promise there's been some helpful ideas inwards this post. I shout out back all teachers would detect 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, exactly pat yourself on the dorsum for the adept stuff. And don't grade later on 9pm!