Linear Simultaneous Equations

Solving linear simultaneous equations is rather satisfying. In this postal service I advise unopen to techniques as well as resources for pedagogy this topic.

Equality as well as Lincoln
When I saw the cinema Lincoln I was struck yesteryear Abraham Lincoln’s reference to Euclid’s First Axiom ‘Things which are equal to the same affair are also equal to 1 another’. Influenza A virus subtype H5N1 well-made indicate inwards a tidings nigh racial equality, but also an interesting claw into a method for solving simultaneous equations such as

y = 4x + 6

y = 2x + 3

Both 4x + vi as well as 2x + three are equal to y, hence logically nosotros convey 4x + vi = 2x + three (this is essentially simply a exchange method). Why non demo this this blog gives a proficient explanation of Lincoln's point)

Elimination as well as 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils uncovering it real tardily to shout out back the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inwards the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inwards each equation is positive (‘same sign’), we subtract one equation from the other.

However, I noticed that when solving simultaneous equations such every 2nd -3x + 5y = 41; 2x + 5y = 56, unopen to pupils saw that the -3x as well as the 2x were different signs as well as incorrectly decided that this meant they should add the 2 equations. So it’s worth clarifying which signs nosotros are referring to inwards the ‘Same Sign Subtract’/’Different Sign Add’ approach.

Graphical Solutions
It’s as well as then of import for pupils empathise that whenever they solve linear simultaneous equations, they are inwards fact finding the indicate of intersection of 2 conduct lines. It’s essential to put a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) as well as decease them thinking nigh why at that spot are no solutions.  I similar to demo them this cute picture too.

Wordy Equations
This is 1 of my favourite simultaneous equation questions: “A zoo has several ostriches as well as several giraffes. In full they convey xxx eyes as well as 44 legs. How many ostriches as well as how many giraffes are inwards the zoo?”. Make certain yous discourage pupils from using the missive of the alphabet O for ostrich, because it looks similar a zero.

Resources
There's lots of resources online – here’s a few I’ve picked out:

• Don Steward’s Median blog has a huge arrive at of fantastic questions as well as activities.
• TeachitMaths has a slap-up ‘wordy question’ worksheet as well as clear slides on elimination as well as substitution.
• UEA has a worksheet on linear simultaneous equations amongst a overnice progression of questions.
• There is a useful worksheet on Solving Simultaneous Equations Graphically yesteryear Tristan Jones on TES. 
• This Geogebra worksheet yesteryear themathsteacher.com is a proficient practice inwards solving simultaneous equations graphically amongst ICT.
• Peter Bland and JustMaths both supply examination questions on this topic.
• MEI has a overnice extension activity. 

Linear Graphs

One of the topics that my pupils combat amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't function out how to respond a GCSE enquiry similar this:

Strangely, I learn this differently at GCSE as well as Influenza A virus subtype H5N1 level.  At GCSE my pupils write down

y = mx + c

as well as substitute values for y, k as well as x, as well as hence solve for c.  Whereas at Influenza A virus subtype H5N1 marking my pupils occupation the equation

y - y₁ = m(x - x₁)

Essentially the same method but a slightly dissimilar approach. Perhaps I should endure to a greater extent than consistent as well as innovate the 'A marking method' at GCSE. I'd similar to take away heed what other teachers do.

In this shipping service I’ll propose roughly ideas as well as resources for instruction linear graphs.

Key words

Let's kickoff amongst the basics. There's a lot of novel vocabulary inwards coordinate geometry, roughly of which pupils volition convey encountered at primary school. This is a overnice vocabulary cognition survey every bit suggested inwards my earlier post. 

Here's a overnice play tricks for remembering the words parallel as well as perpendicular (this could endure helpful for spellings - parallel is oft misspelt): 

as well as this activity is suitable for Year vi or 7. 

Introducing the shape y = mx + c
I'd unremarkably kickoff this theme inwards Year seven or 8 amongst plotting at nowadays occupation graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This theme provides an first-class chance for pupil investigation using Desmos. Use a worksheet to direct pupils through the lesson:

• Investigating Straight Lines amongst Desmos (by Tristan Jones on TES)
• Straight Line Graphs inwards Desmos (by me!)

Once pupils are able to translate the values of k as well as c as well as hence they tin shipping away endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal as well as vertical lines.

My weblog shipping service 'All most gradient' features ideas as well as resources for instruction slope (the shipping service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets as well as activities).

Understanding parallel as well as perpendicular gradients

So here's the substitution data that pupils demand to understand:

(source)

If they know how to function out a slope every bit 'rise over run' (or equivalent) as well as hence pupils should endure able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this i from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

• Finding Equations of Parallel as well as Perpendicular Lines yesteryear Mathematics Assessment Project
• Perpendicular Lines Worksheet (by me!)
• AS marking Parallel as well as Perpendicular Lines  (suitable for GCSE extension)
• Perpendicular lines: equations yesteryear toticity.co.uk

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should convey the necessary skills as well as cognition to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for certain capable. Essentially it's simply the wording of the questions that throws them.

Here's roughly to a greater extent than recommended resources suitable for GCSE students:

• Foundation: Linear Graphs 'I Can' from Mathsbox
• Mathattack Linear Graphs homework sheet
• Topic checklist
• MathsPad Linear Graphs Problems
• Rich activities from Five Triangles
• Rich activities from Median Don Steward

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe as well as Lines.

Finally, e'er wondered which countries occupation y = mx + c annotation as well as which countries occupation something different? Check out this map.

Introducing Algebra

Building a venture conceptual agreement of algebra is absolutely fundamental. As alongside fractions, it's essential that nosotros acquire it correct because it underpins in addition to hence much of what follows. But, equally alongside fractions, pupils tin actually create do here.

Sometimes practiced educational activity resources inspire us when we're looking for ways to construction in addition to deliver our teaching. This post service contains around recommendations that may plough over you lot nutrient for sentiment when you’re planning your lessons.

Misconceptions
Before educational activity whatsoever topic for the start fourth dimension it's actually of import to intend close potential misconceptions. The best matter a pupil instructor or NQT tin do is inquire an experienced teacher. This algebra misconception summary is also helpful. 

The start fourth dimension I taught algebra, I used this true/false activity to discover whatsoever outstanding misconceptions inwards the concluding lesson of the sequence. As a newbie teacher, I was astounded yesteryear the mistakes pupils made, similar putting both of these cards inwards the 'true' column:

This activity provided a practiced chance to own got private discussions alongside pupils in addition to attention them brand sense of it all. So it’s useful both equally a learning sense in addition to for formative assessment.

I'm non stalking him, promise
I've featured resources from Don Steward inwards almost every spider web log post service I've written. I brand no apologies for this. His website is amazing. Here's a few highlights from his algebra collection:

• Lengthy expressions is a squeamish means to acquire pupils used to forming expressions containing letters in addition to numbers.
• Expression pyramids are an engaging means to practise simplifying in addition to this activity is a perfect extension.
• In Steps, pupils own got to create upward one's hear what pace has been taken to acquire from 1 appear to the adjacent (see below).
• Six expressions is a rich activity for pupils who've been taught how to expand unmarried brackets.
• Three sets of first-class activities attention students explore concepts relating to simplifying in addition to equivalence: 'equivalence', 'same in addition to transformed' and 'equivalent things'.

Steps - Median Don Steward

There's lots to a greater extent than on Median Don Steward - expect nether the labels algebra, simplifying, expressions in addition to substitution.

Fawn Nguyen’s Noah’s Ark
This is a lovely activity which gets pupils used to the sentiment of representing values alongside letters (or pictures inwards this case).

Noah's Ark yesteryear Fawn Nguyen

Visual representations
'I'm thinking of a number' questions are a practiced means to acquire started alongside solving equations. MathsPad had a squeamish card sort that makes the link betwixt words in addition to algebra. MathsPad also features a worksheet that uses visual representations to cook an agreement of how to solve equations. The same approach is taken to rearranging formulae - this lesson plan features their make of associated resources.

MathsPad

More ideas

• These slides from newmrsc (@_z_0_e) on TES are actually practiced for a start expect at algebra.
• For substitution, I similar this code breaker from Teachit Maths (and this minute code breaker, which involves harder expressions). Substitution scenarios is squeamish too.
• algebra resources library. Do comment below or tweet me if you lot own got whatsoever to a greater extent than resources or ideas to add.

Image: crotchetycomics.blogspot.com

5 Maths Gems #11

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

1. Quick Key
Last calendar week I wrote close Plickers, which is an app y'all tin role inwards the classoom for formative assessment - y'all ask a device only your students don't. Today I'm suggesting roughly other app that y'all tin role for assessment - Quick Key. With this app y'all tin laid multiple alternative homeworks or tests as well as grade them inwards seconds past times scanning the respond sheets ('Quick Tickets') with your phone.

Quick Key is the excogitation of American instructor Walter Duncan (@4_teachers). It "turns your band into a scanner as well as eliminates hand-grading of assessments, fifty-fifty for teachers working inwards paper-based classrooms without a calculator or internet. Analytics as well as information exports are easy, thus y'all tin focus on your students".

My initial thoughts were that although this app could live on rattling useful (less fourth dimension spent marking = to a greater extent than fourth dimension spent planning character lessons), it won't allow me to banking concern friction match students' methods, which limits opportunities for useful feedback. But for straightforward cognition checks, to inform me how much my students know, it would operate rattling well.

But as well as then I read this post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my reflection stickers. Students stick a 'Not nonetheless yeti' or 'I got it' sticker inwards their majority to allow y'all know whether they've understood the work.

Speaking of stickers, Adil Jaffer (@adil_3) shared his fantastic feedback stickers thus y'all don't own got to proceed writing the same affair all the fourth dimension when you're marking.

One of the post pop tweets I saw this calendar week was from @MathedUp who shared his fantastic 'request a selfie' idea. I tin encounter this actually improving the character of students' operate - many of my students would honey the chance to print their parents. If y'all role iDoceo as well as then it's slow to own got a movie on your iPad as well as e-mail it to a parent.

Did y'all encounter these practice books, tweeted by @dandesignthink? The boxes at the bottom of the pages incorporate a checklist (accuracy, spelling, grammar), cardinal words, farther questions, cardinal points, what went well, as well as feedback. An 'Exercise majority 2.0' costs 50p - amount details are available here. There's also a maths version - Maths majority 2.0 is as awesome. I wishing I had a budget to pass because I'm desperate to gild these!

The to a greater extent than I role Twitter, the to a greater extent than inclined I am to hashtag everything I write (or say!). I own got to bound myself from putting hashtags inwards text messages to my hubby ('what do y'all desire for dinner tonight? #pleasesaytakeaway'). It's prissy to encounter that I'm non lone - Cathy Yenca (post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my Open Evening post where y'all concur a 'design a maths clock' competition. The clock pictures below are all taken from sbcrafts.net where y'all tin banking concern friction match out a big attain of clock let on ideas that could also live on used on let on lines.

And finally...
Algebraic long segmentation is fun when y'all know how to do it, only it tin live on a chip tricky to learn to Year 12. It's prissy to know at that spot are alternative methods. I've factorised polynomials past times inspection earlier only non using a grid as suggested by post close it. Find the Factors is designed by @IvaSallay who says it's an fantabulous agency for children as well as adults to review multiplication facts, role logic, as well as strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers own got been removed. The grid tin live on completed using logic as well as cognition of factors - inwards the event below y'all could foremost past times completing the 2 circled cells. The puzzles come upward inwards varying levels of difficulty, as explained here. Find the Factors has already been rattling pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted close chalk pens. I've written close writing on desks, windows as well as walls before, only these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or supply scaffolding for selected students. I intend my boss would live on happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inwards i post, only he's a legend thus I'll allow it... In the same agency the maths clock inwards my kitchen makes a nifty talking betoken for guests to my house, his alternative let on line should live on displayed inwards Influenza A virus subtype H5N1 grade classrooms - students (and teachers!) volition live on intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the let on business upward as well as give it to your Year 13s thus they tin kind it into order. They may non live on familiar with roughly of the annotation only it's a skillful chance for interesting discussions (I flora out how to read ternary to sympathise Ed's alternative for let on 5. I'd also non seen flooring as well as ceiling annotation before).

Stuart also suggests that students pattern their ain let on lines. I honey this thought - it would operate with students of whatever age, from principal schoolhouse to university. It's like to an activity I suggested inwards my The Art of Collaboration', it's e'er nifty to take heed when these ideas larn far into classrooms. Have a nifty half-term intermission everyone!

5 Maths Gems #13

In my gems posts I portion approximately 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 inward which students brand 'Flying Numbers' to hang from the ceiling inward the classroom or corridor. It industrial plant similar this: they select a discover together with brand that discover from forest inward Design & Technology (drill a hole at the overstep for hanging). They pigment their discover hence purpose fine markers or chalk pens to decorate it alongside facts almost that number. This is a lovely chance for students to purpose the cyberspace to explore discover properties together with discovery 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 almost teaching a binary lesson).

Alice inward FractalLand is a stunning animated slideshow. Show it to your degree together with explore sequences, fractals, the golden ratio together with more. The text at the bottom explains each concept real clearly. I love this! This is precisely the variety of affair I was referring to inward my post service 'A house for gimmicks?' when I said that nosotros should brand fourth dimension to enrich our students' teaching alongside interesting mathematics that is non on the GCSE syllabus.

The Primary and Secondary Treasure Hunts are real good designed. Full instructions are included together with at that topographic point are questions on areas of mathematics such equally cryptography, primes together with probability. The questions are rather challenging for the intended historic menses groups - if I was organising an inter-school maths challenger hence I mightiness purpose these questions.

The video collection is due to grow - an exciting prospect if this 2 infinitesimal wordless video exploring triangles is a gustation of things to come. 

3. Imbalance Problems
If you're non familiar alongside Don Steward's resources hence halt reading this post service straightaway together with depository fiscal establishment friction match out his mobiles', hence 'mobile inequalities' together with finally 'mobile moments'.

In mobiles, the activities foremost alongside discover problems that learn progressively harder, hence motion on to algebraic balancing problems. Here's a numerical instance which tin displace live solved alongside arithmetics together with logic (fill inward the missing weights hence that everything balances correctly). 

There are lots of variations, such equally this 1 where the weights must add together upward to the discover inward the triangle (this is a straightforward example):

The algebraic problems educate skills inward writing algebraically together with simplifying expressions. In the work below, students accept to consummate the missing weights to brand the combined hanging weight equal to 8n.

These are swell problems. Check out all 3 posts to run across how Mr Steward developed the idea. It's equally 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 post service almost circle theorems which volition live cook soon. Also, later seeing approximately swell Halloween together with Guy Fawkes maths resources, I've started to collate a 'seasonal resources' page. I've seen hence many skillful Christmas resources, it's difficult to select the best simply I'm getting there.

So at that topographic point you lot go, my 13th gems post. It wasn't scary at all.

Image source: guernseydonkey.com

5 Maths Gems #15

Welcome to my 15th weekly gems post - this is where I characteristic roughly of the best teaching ideas I've seen on Twitter each week.

1. Slice The Pie

Paul Rehmet (@prehmet) has built an interactive tool to help students ready numerical fluency. It's a uncomplicated fraction game - Slice The Pie - which helps students railroad train an intuitive sense of the relative sizes of numbers. It's non compatible alongside mobiles yet but would piece of work on your interactive whiteboard. I honey this. Have a play alongside it, I think you'll honey it too. And follow Paul on Twitter because there's to a greater extent than to come upward from him.

2. Remembering Inequalities

In my post almost Ideas from Shanghai I shared this visualisation which helps students squall upward which inequality sign is which.

All students demand to exercise is visualise numbers equally blocks - the wider terminate of the inequality symbol fits over the bigger stack of blocks. So if x > 2, nosotros know x must hold out a number bigger than 2. 

Chris Smith (@aap03102) pointed out that this doesn't piece of work for negative numbers. 

I'm sure as shooting our friends inward Shanghai own got a solution for this but that data hasn't filtered through to us, thence let's come upward up alongside our ain alternative that industrial plant for both positive in addition to negative numbers. We simply demand a agency for students to squall upward which symbol is which.

I'm actually grateful to all the lovely creative tweeters who offered ideas - my favourite was this calligram from Chris. 

So if x < - 8, nosotros run into the < symbol in addition to think of the missive of the alphabet L, thence nosotros know x is less than -8.

Eventually students volition automatically know the important of the symbols on sight, without having to visualise blocks or words.

These methods are far ameliorate than thinking of crocodiles - this tin give notice confuse students, equally described inward Nix the Tricks (extract below).

3. Squares in addition to Cubes
I'm enjoying La Salle Education's (@LaSalleEd) novel 'Problem of the Day' series.  You tin give notice search the collection yesteryear historic current or topic. The instance below (Square Boxes) is a dainty logic occupation consolidating noesis of foursquare numbers.

If you're teaching foursquare numbers, yous mightiness also similar this 'Square in addition to Cube Numbers Puzzle' from MathsPad...

... in addition to this lovely square in addition to cube numbers display from Clarissa Grandi (@c0mplexnumber).

4. Mathsticks
I late discovered the brilliant Mathsticks website which is created yesteryear John Duffty (@johnduffty). I registered in addition to explored - it's by in addition to large primary materials but roughly of the ideas mightiness hold out helpful at Key Stage 3. Here's a twosome of examples:

This Parallel & Perpendicular Slope. Once you've taught students almost the gradients of parallel in addition to perpendicular lines, larn them inward a reckoner room (or larn the iPads out, if yous own got them) in addition to give them this worksheet, which I think volition hold out real slowly for them to follow independently. They are given sure as shooting lines which they plot (in Desmos, though I suppose this could hold out done yesteryear hand) in addition to and thence they add together the right parallel or perpendicular lines to brand the required shape. It's a actually dainty activity which volition assistance yous banking enterprise check their agreement of this topic.

Extract from Desmos Graph Challenge

Here's my response to the 2nd query inward the extract above.

To extend this task, yous could own got students confine the domains of the functions, equally I've done below. If yous exercise this, it's of import that they figure out how to calculate the coordinates of the vertices.

If you're teaching parallel in addition to perpendicular lines in addition to thence also banking enterprise check out my post linear graphs for to a greater extent than ideas in addition to resources.

A asking for misconceptions
When I project design lessons, I uncovering it helpful to travail to predict the misconceptions that mightiness come upward up. Sometimes I'm surprised yesteryear the mistakes that students make, which are ofttimes the number of my explanations non beingness clear enough. Knowledge of mutual misconceptions comes alongside sense but I think it would exercise goodness novel maths teachers if they could consult a website to run into examples of the kind of things students larn wrong. 

A not-so-common misconception from i of Chris Smith's students

American instructor Michael Pershan (@mpershan) has a bright website Math Mistakes where he compiles, analyses in addition to discusses the mathematical errors that students make. I desire to prepare something similar for the United Kingdom of Great Britain in addition to Northern Ireland (because our curricula in addition to vocabulary are thence different), but I won't own got fourth dimension to exercise the fantabulous analysis that Michael does. Instead it would simply hold out a collection of misconceptions, tagged yesteryear topic. But I notwithstanding think it mightiness hold out useful.

So I own got a asking - could yous kickoff taking photos of misconceptions inward your students' piece of work in addition to emailing or tweeting them to me? Once I've got a small-scale choice I'll kickoff a website in addition to I hope, similar my Pret homework website, it volition grow chop-chop in addition to seek to hold out a helpful resource. Thank yous inward advance!

That's it for today. Please don't forget to vote for me! :), I'll move out yous alongside this cute 'Math nosotros know drama', shared yesteryear @FascinatingVids.