Matrix Multiplication

When I teach matrix multiplication I discovery that pupils tin rate the axe top away a fleck lost inward their calculations.  I constitute a fantastic novel method on this blog.

Let's tell nosotros accept matrix A together with matrix B.  We desire to calculate AB.  Write downwardly the 2 matrices side-by-side.  Then move matrix Influenza A virus subtype H5N1 down. Now write your answer inward the infinite at the bottom right.  I intend the side past times side measuring is self-explanatory from the film below, merely read the master copy blog post for a amount explanation.

I honey this method - it's together with thence unproblematic to retrieve together with at in 1 trial most impossible to top away lost when multiplying matrices.

And - on the dependent area of matrices - this made me chuckle:

Maths Painting Demo Quiz

Spiked Math has roughly fantabulous Maths Movie Quizzes.  I chose these ones to entertain my Year 13s at Christmas.  Great fun for Maths teachers too!

Venn Activities

This post service is nigh using Venn Diagrams equally a didactics tool, rather than didactics the concept of Venn Diagrams themselves.  To quote the splendid Johnny Griffiths, 'The Venn Diagram amongst iii bubbles is the maths teacher's friend! ... To move able to fill upward inward an eight-region diagram shows a actually deep agreement of the distinctions that a practiced pupil has to move able to make, spell the weaker pupil finds beingness faced amongst a moving-picture exhibit such equally this much less threatening than a page of exercises'.

Before nosotros foremost using Venn activities inward Maths lessons, let's mean value nigh whether pupils are familiar amongst how Venn Diagrams work. I acknowledge to beingness a flake clueless nigh just what children written report at master copy school. The primary here), only I straight off prefer the simpler method described in linear equations activity. It helped consolidate their noesis of linear graphs in addition to allowed me to banking concern check their understanding.

Johnny Griffith's splendid RISPs (Rich Starting Points for H5N1 Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) in addition to Risp 4 (periodic functions).  In the instructor notes for Risp 10 Johnny shares his views on the usefulness of Venns.

A Venn action for Solving Quadratics past times Factorising past times aka nka on TES. 

A GCSE extension action on quadratic graphs from MEI.

I haven't tried this all the same only Don Steward also gives us this lovely here), only I straight off prefer the simpler method described in number activity.

Interactive Venns

Venns piece of occupation good on the Interactive Whiteboard - here's roughly examples.

• Nrich has roughly interactive Venn diagrams on types of number.
• MathsPad has roughly lovely Venn activities (most ask a subscription). I've successfully used this Factors, Primes in addition to Multiples Activity with my Year 8s.   
• Teachitmaths.co.uk has interactive Venn activities - for instance for shapes and prime factors, or y'all tin create your ain (subscription required).

Other Uses

• When I innovate complex numbers inward FP1 nosotros create a Venn Diagram during degree news nigh types of numbers (real, rational, integers etc) in addition to their Greek symbol notation.  The NCETM has a similar Venn action inward this resource sheet.
• Up until lately I used Venn Diagrams to learn Highest Common Factor in addition to Lowest Common Multiple (method explained here), only I straight off prefer the simpler method described in this post.
• Quadrilaterals tin move classified using a Venn Diagram similar this one.  We tin in addition to hence answer questions such as 'Is every foursquare a rectangle? Is every rhomb a square?' A 'family tree' also plant well.

In determination - Venns are everywhere! But inward secondary Maths they are alone formally taught to those studying iGCSE (set theory) in addition to Statistics 1 at H5N1 flat (probability). I'm pleased to run across that Venn Diagram methods inward probability are on the new Maths GCSE Syllabus so volition move to a greater extent than widely studied inward future. But inward add-on to beingness taught equally a topic inward their ain right, Venn Diagrams are a versatile didactics tool amongst numerous applications inward the classroom. And they bring the added bonus of beingness created past times a British Mathematican! Well done Mr Venn.

Teaching Amongst Desmos

I discovered Desmos terminal yr through @ColleenYoung's fantastic weblog Mathematics, Learning in addition to Web 2.0. It chop-chop became my favourite slice of 'teachnology'. Before Desmos I occasionally used Omnigraph or Autograph, but I at nowadays utilization Desmos regularly because it's but so tardily to use. It actually couldn't travel simpler. As it's web-based, I encourage my pupils (particularly at Influenza A virus subtype H5N1 level) to utilization Desmos at domicile to back upward their studies, for trial to depository fiscal establishment gibe graph sketches.

Desmos on the Interactive Whiteboard
When instruction exponential functions to Year 12, I used Desmos on my IWB to present the graphs of functions such every bit y = 2^x in addition to y = 3^x. We discussed our expectations for graphs such every bit y = 2^-x in addition to used Desmos to check.  When nosotros plotted y = (-2)^x nosotros got an interesting trial - which had me stumped for a infinitesimal - tin you lot explicate it?

Desmos is specially helpful for demonstrating concepts inwards Further Maths (such every bit the directrix in addition to focus of a parabola) - there's unopen to expert examples in this blog.

Desmos inwards the information technology Room

My schoolhouse doesn’t ain tablets in addition to information technology rooms are rarely available, in addition to hence my pupils don't oftentimes acquire the conduct a opportunity to utilization applied scientific discipline during their Maths lessons. But I was in addition to hence non bad to part Desmos alongside my Year ix class, I made a big endeavor to acquire organised. I produced this worksheet for them to utilization inwards an information technology room, alongside the aim of introducing dissimilar types of graph (quadratic, cubic, reciprocal) in addition to uncomplicated transformations. After a real brusk demonstration of Desmos, the degree spent ii whole lessons working independently. I was pleased alongside their progress in addition to I promise that they'll hollo upward Desmos in addition to proceed to utilization it every bit a learning tool both at domicile in addition to at school.

I loaded my worksheet onto TES today - along alongside a graph transformation activity that I utilization at Key Stage iv - in addition to it got me thinking well-nigh whether whatsoever other resources are available for instruction alongside Desmos.  I establish a few examples on TES, such as Investigating at in i trial lines alongside Desmos past times Tristan Jones and Using Desmos to learn Coordinate Geometry (KS3) past times phildate. I facial expression that the make of instruction resources available volition grow every bit increasing numbers of teachers respect in addition to encompass this fantastic tool.  

Resource Library: Complex Numbers

Resources Anonymous, I admitted I convey a serious resources addiction. Based on the popularity of that post, I intend I mightiness brand this spider web log primarily a resources library. So yous tin come upwardly hither to hold off for resources as well as ideas when you're planning lessons. Would that endure helpful? I similar to endure helpful. I suppose that's why I became a teacher.

Today I'm focusing on complex numbers. Although non widely studied inwards United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland secondary schools (only yesteryear Further Maths students), there's sure no shortage of didactics resources online - here's around highlights:

• First, my locomote yesteryear honor - Complex Number Operations Teaching & Learning Plans from the Project Maths Development Team. This is packed amount of lesson ideas as well as in that place are tonnes of vivid pupil activities inwards the appendices. I'm excited to origin using these. There's equally good a PowerPoint version.
• I highly recommend the activities provided yesteryear the Further Maths Support Network/MEI (school login required). Here's an example of their topic notes. Their attain of resources equally good includes worksheets, activities as well as assessments.  
• SRWhitehouse on TES produces fantabulous Influenza A virus subtype H5N1 score resources, including a choice on complex numbers. I specially similar this introductory exercise.
• Illustrative Mathematics gives us 7 fantabulous activities: 
• Venn activities, this resource sheet is nearly classifying types of numbers.  There's a related activeness on page 32 of Complex Number Operations Teaching & Learning Plans.  



Finally, fun for teachers as well as students alike - here's a nice Complex Adding Maze and Nrich has a Complex Countdown game! Enjoy.

What topic would yous similar me to characteristic next? Please tweet me your requests!

Animations Together With Simulations

Last night's #mathschat discussion close images gave me in addition to therefore many practiced teaching ideas, I woke upward at 2am to write a list! One affair that came upward was animations. I dear a practiced animation that demonstrates a concept beautifully, in addition to therefore here's a few examples.

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

The animation below shows how the outside angles of a polygon amount to 360^o. Sometimes it's meliorate to purpose an animation that y'all tin sack suspension in addition to speak through though, in addition to therefore I prefer this animation for outside angles of a polygon. Absorb Learning is an fantabulous website for animations.

Another instance of an animation y'all tin sack suspension during teaching is this 'bisecting an angle' tool. It comes alongside both a clear teaching canvass for students in addition to associated proofs. There are similar pages for every possible construction! As I mentioned inwards a previous post, I loathe teaching constructions, in addition to therefore I honour this real helpful.

Here's some other maths gif. This 1 is for demonstrating the properties of parabolas, every bit taught inwards Further Maths. This tin sack also locomote demonstrated nicely using Desmos.

I also desire to get upward PhET simulations. I don't instruct mechanics exactly I'm told that PhET has lots of bully interactive simulations for demonstrating concepts. 'Balancing Act' is a practiced example. They also convey simulations for Key Stage iii topics such every bit fractions - run across the full maths alternative here. The simulations tin sack locomote downloaded in addition to run from your schoolhouse network. 

Balancing Act - PhET

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

If y'all know of whatever other practiced animations or interactive tools, delight comment below or tweet me.

5 Maths Gems #83

Welcome to my 83^rd gems post. This is where I portion or together with thus of the latest news, ideas together with resources for maths teachers. Many of us are on one-half term this week, which is a bully relief every bit usual. Time to select handgrip of upward on or together with thus sleep, pass or together with thus fourth dimension amongst my children, together with learn on move past times of my growing to make list. If you lot haven't had much fourth dimension for Twitter lately, this post features or together with thus things that you lot mightiness possess got missed.

1. Find Me... Problems
Mr Hill (Find Me.. Problems. There are xxx tasks together with thus far, roofing a broad attain of topics. These are tardily to usage together with tardily to adapt.

2. Algebra Starter Pack
Ed Southall (@solvemymaths) shared a bully fix of 'introduction to algebra' lesson activities on TES.

3. H5N1 Level Questions together with Assessment
I offset mentioned Gems 79. I've forthwith explored it inwards to a greater extent than special together with possess got realised that it's a actually useful website for teachers of the novel H5N1 level. Register for gratuitous together with you lot tin dismiss access a large alternative of good written questions for both the novel together with former H5N1 degree specifications.

Each enquiry comes amongst rattling detailed worked solutions. I've been using the questions every bit examples inwards shape but they tin dismiss also live assigned online to students. For free, you lot tin dismiss fix iii online worksheets per shape - this is virtually iii hours of piece of work for each student. By upgrading, you lot unlock all the other content.

In related news, Edexcel's novel mock papers were due to live published inwards belatedly Jan but possess got been delayed. Given that my schoolhouse has Year 12 mocks withdraw later half-term, this meant I ended upward making my ain assessment. It took hours to brand together with I drew questions from a issue of sources - I am happy to e-mail it to anyone else inwards the same position! Just allow me know if you lot demand it.

Note also that CRASHMaths of late published a large fix of new H5N1 degree practise papers. My students are using these to revise for their upcoming mocks.

Finally, whilst I'm on the discipline of H5N1 level, you lot mightiness live interested inwards the outcome of this Twitter poll regarding educational activity fourth dimension for Further Maths.

4. Primary 'Topics inwards Depth'
I possess got previously blogged virtually the importance of discipline specific CPD. I scream back that maths teachers demand CPD that focuses on misconceptions, approaches, methods together with activities for private topics. I started designing CPD similar this concluding twelvemonth together with although I'm even together with thus working on it, my progress has been rattling boring because my workload is together with thus heavy this twelvemonth together with these things possess got a long fourth dimension to produce.  Thankfully I possess got a wonderful collaborator called Nikki Martin (@nikki_nzmartin), who I met at an ATM/MA lawsuit concluding summer. She has been busy producing Topics inwards Depth packs for Year half-dozen together with Year two topics, together with piloting them inwards the principal schools she supports. She has rattling generously shared her piece of work on my Topics inwards Depth page.

5. Shape Transformations 

Every calendar month I learn an update of novel resources from MathsPad together with it's e'er total of bully stuff. Some of it is freely available, including a few of these interactive tools together with worksheets for transformations. The tracing newspaper overlays piece of work actually good here, enabling the instructor to demonstrate spell pupils consummate the matching questions.

Update 

In my last post I shared a fix of former textbook exercises that possess got been typed upward for usage inwards lessons. There's or together with thus bully questions inwards these exercises together with thus make cheque them out.

Last calendar week my weblog had its iii millionth visit. Thank you lot to everyone who visits regularly - I'm together with thus glad people respect it useful. I actually appreciate all the support. 

Last calendar week I also got a novel job! In September I'll live joining the Harris Federation, supporting maths teachers inwards a issue of Harris schools. I'll also live getting involved inwards their Maths Hub work. I'm actually deplorable to move out behind my lovely schoolhouse that has been together with thus skillful to me, together with my colleagues together with students who I'll actually miss, but excited virtually this side past times side stride inwards my career together with all the opportunities it volition bring. Huge cheers to Colin, Bruno, Craig, Ed together with Tom for all their advice on this large decision.

It's exclusively 4 weeks until the Kettering conference forthwith - I promise to run into lots of you lot at the Fri nighttime drinks. If I don't select handgrip of you lot at the drinks, make come upward together with nation howdy at the conference - I'll live on the MA stand upward when I'm non inwards workshops. The line up of workshops is fantastic together with thus I'm actually looking forwards to it.

There are or together with thus other pair of novel events coming upward that are forthwith opened upward for bookings:

• Stuart Price is hosting his tertiary annual 'conferences page.
  
  Finally, every bit business office of my operate every bit the Chair of the MA's Publicity together with Media Committee, I've made a alternative of splendid MA magazine articles available for free. If you lot bask these articles, I promise this encourages you lot to join the MA.
  
  • Can I but motility the decimal point? by Colin Foster (Mathematics inwards School, September 2017). 
  • Mathematical argument, linguistic communication together with proof (AS together with H5N1 Level 2017) past times Elizabeth Glaister together with Paul Glaister (Mathematics inwards School, September 2017).
  • William Oughtred by Jenny Ramsden (Mathematics inwards School, Nov 2017).
  • Models of Multiplication: unlock the ability by Kuchemann together with Hodgen (Primary Mathematics, Summer 2017).
  • Will my numbers add together upward correctly if I circular them? by David Hopkins (The Mathematical Gazette, Volume 100).
  
  I'll move out you lot amongst this factorisation puzzle, shared past times @YohakuPuzzle. Fill inwards cells to learn the products inwards each row/column.
  
  

  
  

  
  
  
  
  
  
  

Matrix Multiplication

When I teach matrix multiplication I discovery that pupils tin rate the axe top away a fleck lost inward their calculations.  I constitute a fantastic novel method on this blog.

Let's tell nosotros accept matrix A together with matrix B.  We desire to calculate AB.  Write downwardly the 2 matrices side-by-side.  Then move matrix Influenza A virus subtype H5N1 down. Now write your answer inward the infinite at the bottom right.  I intend the side past times side measuring is self-explanatory from the film below, merely read the master copy blog post for a amount explanation.

I honey this method - it's together with thence unproblematic to retrieve together with at in 1 trial most impossible to top away lost when multiplying matrices.

And - on the dependent area of matrices - this made me chuckle:

Maths Painting Demo Quiz

Spiked Math has roughly fantabulous Maths Movie Quizzes.  I chose these ones to entertain my Year 13s at Christmas.  Great fun for Maths teachers too!

Venn Activities

This post service is nigh using Venn Diagrams equally a didactics tool, rather than didactics the concept of Venn Diagrams themselves.  To quote the splendid Johnny Griffiths, 'The Venn Diagram amongst iii bubbles is the maths teacher's friend! ... To move able to fill upward inward an eight-region diagram shows a actually deep agreement of the distinctions that a practiced pupil has to move able to make, spell the weaker pupil finds beingness faced amongst a moving-picture exhibit such equally this much less threatening than a page of exercises'.

Before nosotros foremost using Venn activities inward Maths lessons, let's mean value nigh whether pupils are familiar amongst how Venn Diagrams work. I acknowledge to beingness a flake clueless nigh just what children written report at master copy school. The primary here), only I straight off prefer the simpler method described in linear equations activity. It helped consolidate their noesis of linear graphs in addition to allowed me to banking concern check their understanding.

Johnny Griffith's splendid RISPs (Rich Starting Points for H5N1 Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) in addition to Risp 4 (periodic functions).  In the instructor notes for Risp 10 Johnny shares his views on the usefulness of Venns.

A Venn action for Solving Quadratics past times Factorising past times aka nka on TES. 

A GCSE extension action on quadratic graphs from MEI.

I haven't tried this all the same only Don Steward also gives us this lovely here), only I straight off prefer the simpler method described in number activity.

Interactive Venns

Venns piece of occupation good on the Interactive Whiteboard - here's roughly examples.

• Nrich has roughly interactive Venn diagrams on types of number.
• MathsPad has roughly lovely Venn activities (most ask a subscription). I've successfully used this Factors, Primes in addition to Multiples Activity with my Year 8s.   
• Teachitmaths.co.uk has interactive Venn activities - for instance for shapes and prime factors, or y'all tin create your ain (subscription required).

Other Uses

• When I innovate complex numbers inward FP1 nosotros create a Venn Diagram during degree news nigh types of numbers (real, rational, integers etc) in addition to their Greek symbol notation.  The NCETM has a similar Venn action inward this resource sheet.
• Up until lately I used Venn Diagrams to learn Highest Common Factor in addition to Lowest Common Multiple (method explained here), only I straight off prefer the simpler method described in this post.
• Quadrilaterals tin move classified using a Venn Diagram similar this one.  We tin in addition to hence answer questions such as 'Is every foursquare a rectangle? Is every rhomb a square?' A 'family tree' also plant well.

In determination - Venns are everywhere! But inward secondary Maths they are alone formally taught to those studying iGCSE (set theory) in addition to Statistics 1 at H5N1 flat (probability). I'm pleased to run across that Venn Diagram methods inward probability are on the new Maths GCSE Syllabus so volition move to a greater extent than widely studied inward future. But inward add-on to beingness taught equally a topic inward their ain right, Venn Diagrams are a versatile didactics tool amongst numerous applications inward the classroom. And they bring the added bonus of beingness created past times a British Mathematican! Well done Mr Venn.

Teaching Amongst Desmos

I discovered Desmos terminal yr through @ColleenYoung's fantastic weblog Mathematics, Learning in addition to Web 2.0. It chop-chop became my favourite slice of 'teachnology'. Before Desmos I occasionally used Omnigraph or Autograph, but I at nowadays utilization Desmos regularly because it's but so tardily to use. It actually couldn't travel simpler. As it's web-based, I encourage my pupils (particularly at Influenza A virus subtype H5N1 level) to utilization Desmos at domicile to back upward their studies, for trial to depository fiscal establishment gibe graph sketches.

Desmos on the Interactive Whiteboard
When instruction exponential functions to Year 12, I used Desmos on my IWB to present the graphs of functions such every bit y = 2^x in addition to y = 3^x. We discussed our expectations for graphs such every bit y = 2^-x in addition to used Desmos to check.  When nosotros plotted y = (-2)^x nosotros got an interesting trial - which had me stumped for a infinitesimal - tin you lot explicate it?

Desmos is specially helpful for demonstrating concepts inwards Further Maths (such every bit the directrix in addition to focus of a parabola) - there's unopen to expert examples in this blog.

Desmos inwards the information technology Room

My schoolhouse doesn’t ain tablets in addition to information technology rooms are rarely available, in addition to hence my pupils don't oftentimes acquire the conduct a opportunity to utilization applied scientific discipline during their Maths lessons. But I was in addition to hence non bad to part Desmos alongside my Year ix class, I made a big endeavor to acquire organised. I produced this worksheet for them to utilization inwards an information technology room, alongside the aim of introducing dissimilar types of graph (quadratic, cubic, reciprocal) in addition to uncomplicated transformations. After a real brusk demonstration of Desmos, the degree spent ii whole lessons working independently. I was pleased alongside their progress in addition to I promise that they'll hollo upward Desmos in addition to proceed to utilization it every bit a learning tool both at domicile in addition to at school.

I loaded my worksheet onto TES today - along alongside a graph transformation activity that I utilization at Key Stage iv - in addition to it got me thinking well-nigh whether whatsoever other resources are available for instruction alongside Desmos.  I establish a few examples on TES, such as Investigating at in i trial lines alongside Desmos past times Tristan Jones and Using Desmos to learn Coordinate Geometry (KS3) past times phildate. I facial expression that the make of instruction resources available volition grow every bit increasing numbers of teachers respect in addition to encompass this fantastic tool.  

Resource Library: Complex Numbers

Resources Anonymous, I admitted I convey a serious resources addiction. Based on the popularity of that post, I intend I mightiness brand this spider web log primarily a resources library. So yous tin come upwardly hither to hold off for resources as well as ideas when you're planning lessons. Would that endure helpful? I similar to endure helpful. I suppose that's why I became a teacher.

Today I'm focusing on complex numbers. Although non widely studied inwards United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland secondary schools (only yesteryear Further Maths students), there's sure no shortage of didactics resources online - here's around highlights:

• First, my locomote yesteryear honor - Complex Number Operations Teaching & Learning Plans from the Project Maths Development Team. This is packed amount of lesson ideas as well as in that place are tonnes of vivid pupil activities inwards the appendices. I'm excited to origin using these. There's equally good a PowerPoint version.
• I highly recommend the activities provided yesteryear the Further Maths Support Network/MEI (school login required). Here's an example of their topic notes. Their attain of resources equally good includes worksheets, activities as well as assessments.  
• SRWhitehouse on TES produces fantabulous Influenza A virus subtype H5N1 score resources, including a choice on complex numbers. I specially similar this introductory exercise.
• Illustrative Mathematics gives us 7 fantabulous activities: 
• Venn activities, this resource sheet is nearly classifying types of numbers.  There's a related activeness on page 32 of Complex Number Operations Teaching & Learning Plans.  



Finally, fun for teachers as well as students alike - here's a nice Complex Adding Maze and Nrich has a Complex Countdown game! Enjoy.

What topic would yous similar me to characteristic next? Please tweet me your requests!

Animations Together With Simulations

Last night's #mathschat discussion close images gave me in addition to therefore many practiced teaching ideas, I woke upward at 2am to write a list! One affair that came upward was animations. I dear a practiced animation that demonstrates a concept beautifully, in addition to therefore here's a few examples.

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

The animation below shows how the outside angles of a polygon amount to 360^o. Sometimes it's meliorate to purpose an animation that y'all tin sack suspension in addition to speak through though, in addition to therefore I prefer this animation for outside angles of a polygon. Absorb Learning is an fantabulous website for animations.

Another instance of an animation y'all tin sack suspension during teaching is this 'bisecting an angle' tool. It comes alongside both a clear teaching canvass for students in addition to associated proofs. There are similar pages for every possible construction! As I mentioned inwards a previous post, I loathe teaching constructions, in addition to therefore I honour this real helpful.

Here's some other maths gif. This 1 is for demonstrating the properties of parabolas, every bit taught inwards Further Maths. This tin sack also locomote demonstrated nicely using Desmos.

I also desire to get upward PhET simulations. I don't instruct mechanics exactly I'm told that PhET has lots of bully interactive simulations for demonstrating concepts. 'Balancing Act' is a practiced example. They also convey simulations for Key Stage iii topics such every bit fractions - run across the full maths alternative here. The simulations tin sack locomote downloaded in addition to run from your schoolhouse network. 

Balancing Act - PhET

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

If y'all know of whatever other practiced animations or interactive tools, delight comment below or tweet me.