good at math: Vectors

Welcome to my 66^th update from the Blue Planet of Maths EduTwitter. This is where I part about of the latest ideas in addition to resources for teaching maths.

Nov is ever i of the hardest months for teachers. I'm drowning inwards workload at the instant in addition to I bet many of you lot are too. It's relentless. At times similar this I'm grateful for the Twitter community in addition to my lovely colleagues for their ongoing back upwards in addition to encouragement. I conception to write a weblog post service presently amongst about thoughts in addition to ideas on workload. In the meantime, hither are 5 slices of mathematical loveliness to cheer us up...

1. 3Blue1Brown
Thanks to ‏@johngreen for sharing YouTube channel 3Blue1Brown. I'll hold out using their Vectors video when I learn this theme inwards C4 afterwards this year.

If you lot learn logs in addition to then you lot powerfulness hold out interested inwards their video 'Triangle of Power'.

2. Classroom Display

Thanks to Clarissa Grandi (@c0mplexnumber) for sharing this beautiful classroom display 'The Faces Behind the Formulae' which she made for an Influenza A virus subtype H5N1 grade classroom.

I've added it to my displays page.

3. Pinpoint Learning

Last yr I featured Pinpoint Learning in Gems 45. It's a expert fourth dimension to advert this website i time to a greater extent than because most schools run mock GCSE exams inwards Nov or December. Pinpointlearning.co.uk provides students amongst personalised inquiry booklets based on bear witness results. There's a sample booklet here. You (or your students) only upload mock marks past times inquiry in addition to the website automatically produces private booklets featuring questions on the topics that students take away to run on. I'm told that students honey receiving their personalised booklets! I promise to endeavor it out amongst my Year 11s side past times side month.

Edexcel in addition to AQA mock QLA sheets are on the website in addition to you lot tin dismiss currently upload results for all iii mock papers for free during a i calendar month trial. If you lot subscribe during the lawsuit catamenia in addition to then you lot acquire an annual subscription for £300.

Follow @pinpntlearning for updates.

4. SMILE
I'm teaching an interesting Year vii course of written report this year. Having non taught Year vii for a seat out of years, I'm taking a fresh await at resources in addition to approaches. I lately rediscovered SMILE worksheets. Here are a twosome of examples:

Powers of Ten Flags

Coordinate Messages

Also, SMILE cards are available through STEM Learning - these are pretty one-time straightaway hence the character of the copies vary. I recall learning maths from SMILE cards when I was inwards Year 7. Thanks to Martin Colley for arranging the cards past times theme here.

5. Pythagoras amongst Blokus

I honey this halt displace video from ‏@JoelBSperanza.

If you lot desire to meet to a greater extent than of Joel's halt displace videos or honor out how to brand your own, cheque out his weblog post service Stop-Motion Education.

Update

La Salle accept announced about to a greater extent than dates for their conferences (including Wales in addition to Scotland for the starting fourth dimension time). I've added these to my conference listings and volition endeavor to attend equally many equally possible.

In illustration you lot missed it, my most recent post service was the tertiary inwards my serial '5 Websites You Should You Know'. It featured Jonathan Hall's websites MathsBot.com, Flashmaths.co.uk in addition to Formtimeideas.com.

I've also updated my recent post service most Corbettmaths.com. Since writing it I discovered how expert his textbook exercises are! I've institute them hence helpful for teaching Year vii this week.

Extract from CorbettMaths.com 'puzzle square. This i is for directed seat out practice.

Friday, October 11, 2019

Vectors For Enlargement

I'm going to produce a serial of brusque posts on approaches or methods that teachers powerfulness non lead maintain seen before. I'm really aware that at that spot volition hold upward many people who already purpose these approaches, simply I figure that non everyone volition lead maintain seen them thus they are worth sharing.

Today, vectors for enlargements. I start saw this on Twitter years agone simply I can't scream back who tweeted it (apologies!). Later I saw my old colleague Lizzie Stokes (@misstokesmaths) using this approach inward her teaching.

How I used to learn enlargement
I'll illustrate my previous method amongst a negative enlargement question:

I'd say my students to depict a business to whatever vertex from the centre of enlargement. Then I'd say them to count how many squares they've moved to larn to the start vertex. I e'er modelled this slow on the board. I showed the procedure of counting carefully ('count the corners, non the spaces!') because I uncovering they oft miscount.

Then I circled the scale component subdivision in addition to said that because the scale component subdivision is negative two, to uncovering the icon they lead maintain to double the distance from the centre of enlargement. But because it's negative, they lead maintain to larn inward the opposite direction from the centre. So inward this case, nosotros started past times going 2 units right and i unit of measurement upward thus straight off nosotros lead maintain to go four units left and 2 units down. I emphasised that we're going the opposite direction because it's a negative enlargement. We thus produce the same matter for each of the other vertices inward turn. At the end, all the corresponding vertices should hold upward joined amongst direct lines going through the centre of enlargement. If not, you've miscounted!

I'd demo around other illustration amongst a dissimilar scale factor, thus larn them to exercise a lot of these on printed worksheets. It was commonly a relatively tranquillity lesson every bit they all had to produce a lot of counting! I'd larn circular berating them for using pen when I'd told them to purpose pencil 10 K times.

In hindsight I realise that this method could hold upward better. It plant fine for super smart students (most things do!), simply others struggled amongst it. One employment is that you lot lead maintain to concur lots of details inward your caput piece you lot move though the question. Another employment is that the method is dissimilar to the method for positive enlargement - there's an extra matter to remember.

How I straight off learn enlargement
They start past times labelling each vertex amongst a missive of the alphabet in addition to thus finding the vector that takes them from the centre of enlargement to each vertex. They are already fluent inward using vectors from our come about translation thus this should hold upward straightforward.

They write downwards the vectors rather than trying to concur the information inward their caput similar they did before. Then all they lead maintain to produce is multiply each of their vectors past times the scale factor, in addition to this gives them the vector for each of the vertices of the image. So they know just where to depict the icon - it's all calculated in addition to recorded earlier they start drawing.

I've used 'Year 11' vector musical note inward the film inward a higher house for clarity, though it's non essential at this stage.

This method is identical regardless of whether nosotros are enlarging amongst a positive or negative integer or a fraction. So all of a abrupt negative enlargements are no harder than positive enlargements (assuming students know how to multiply negatives). H5N1 clear in addition to consistent method all circular - I don't know why I didn't e'er produce it similar this.

Any others?
I promise that was helpful if you'd non seen it before!

I've blogged a break of times earlier almost choice methods for diverse topics (see my posts tagged 'methods'). If at that spot are whatever approaches or methods that you lot purpose that you lot mean value other teachers powerfulness non use, I'd dearest to listen them! Please comment below or electronic mail me or tweet me.

5 Maths Gems #110

Welcome to my 110^th gems post. This is where I part some of the latest news, ideas together with resources for maths teachers.

1. TES Author
When nosotros did the latest circular of TES Maths Panel reviews, my swain panelist Damian Watson discovered the wonderful costless resources of TES writer cparkinson3. This author's PowerPoints are actually good designed - they are slick together with professional person amongst neatly animated worked examples addition exercises amongst solutions.

For instance cheque out the ii lessons on volume of prisms - i for Foundation tier together with i for Higher tier.

This resources on curve sketching is excellent.

I actually similar the bar modelling lesson too.

Check out the full collection. I've added them all to my resource libraries.

2. Vectors inward Transformations
There's been some updates to BossMaths including changes to their Geogebra applets. The rotations applet instantly lets you lot exhibit together with shroud tracing paper. You tin move also move vectors equally an choice to using tracing paper. I similar this thought - I honour using tracing newspaper a chip unsatisfactory thus I volition endeavor vectors adjacent fourth dimension I instruct this.

The here.

3. SATs Support
I know this is a chip belatedly for Year half-dozen teachers because SATs are adjacent week, but these resources mightiness live on helpful to teachers of other twelvemonth groups, together with to Year half-dozen teachers adjacent year.

Mr Morgs (@_mrmorgs) shared a PowerPoint explaining the linguistic communication used inward the KS2 Maths SATs. This follows on from his detailed analysis of bear witness language. This is actually interesting together with comes amongst lots of advice for teachers. I promise that i twenty-four hours individual does a similarly detailed analysis of the linguistic communication used inward GCSE maths exams.

Greg Chantler (@gregchantler) set all Key Stage 2 SATs arithmetics questions together inward a PowerPoint together with split upward them yesteryear curriculum year. Each query comes amongst word prompts.

4. Defend Yourself
Amie Albrecht (@nomad_penguin) shared a novel thought for an activity. Students are assigned to a representation or method together with bring to endeavor to explicate why it's best. I recollect this would prompt rich word together with thinking.

5. Shifting Times Tables
This action from Miss Konstantine (@GiftedBA) provides a actually clear representation of linear sequences equally 'shifting times tables'.

Here nosotros tin move run into the 4 times tabular array (4n) highlighted inward the outset row, together with thus nosotros run into that the times tabular array has been shifted downward yesteryear i inward the mo row, pregnant the nth term of the sequence is 4n - 1. I dearest the visualisation here. Check out Miss Konstantine's regularly updated blog for lots of corking maths activities together with resources.

Update
My weblog has been receiving tape issue of visitors inward the final twosome of weeks. I estimate a lot of people are using my GCSE revision resources page and my late published post on Foundation revision resources.

I've late uploaded ii sets of revision mats to TES. I made these at piece of job when I realised it's hard to honour suitable resources for students who are working at a Grade 1 or 2. Most GCSE resources are inaccessible to them, together with this tin move effect inward disengagement together with sometimes bad behaviour. So I made A3 revision mats that are to a greater extent than accessible, together with spell I was doing that I made similar resources for other classes. So in that place are 4 levels of difficulty. You tin move download these resources here:

I also made some Foundation workouts which are especially 'print budget friendly'.

GCSE exams are but circular the corner now. Don't forget that final twelvemonth I made breakfast revision resources for all 3 exams. These tin move live on used either on the morning time of the exams or inward the lessons leading upward to them.

Last calendar week I published yesteryear 5th Annual Gem Awards. Do cheque it out if you lot missed it thus you lot tin move run into all the best gems of the year.

Congratulations to Emma McCrea on the publication of her novel majority 'Making Every Maths Lesson Count'. This is an first-class majority for maths teachers.

Here are another things you lot mightiness bring missed:

In 2017 I published a post on approaches to answering AQA GCSE ratio questions. It's i of my nearly pop posts amongst over 20,000 reads. I've instantly made a lesson to accompany this post.
Adam Boxer (@adamboxer1) shared a post on observing proficient teaching which includes an 'expert teaching observation form'. I contributed to this post yesteryear testing the shape out inward a maths lesson.
Richard Tock (@TickTockMaths) published a issue of novel lessons including some on indices which depict a lot of ideas from my Topics inward Depth CPD. Check them out on his blog.
One of my Year 11s was flummoxed yesteryear rotational symmetry final calendar week thus I used the FlashMaths rotational symmetry tool to exhibit him how it works. This has been roughly for a real long fourth dimension thus I was surprised that a lot of teachers on Twitter hadn't seen it before.

Don't forget that in that place are a issue of events inward the summertime term that are instantly opened upward for booking (see my events listings here). I volition live on presenting at researchED Rugby 2019, the Complete Mathematics Conference, the MEI Conference and the Kent together with Medway Secondary Maths Conference. Speaking of events, I also bring something a chip dissimilar to denote before long - lookout this space.

I'll move out you lot amongst this video on why null is the naughtiest together with nearly of import issue from BBC Ideas.

Why null is the naughtiest together with nearly of import number

via @bbcideas pic.twitter.com/pRJ0M6uEdC
— BBC Teach (@BBC_Teach) 2 May 2019

Thursday, September 5, 2019

5 Maths Gems #29

Hello too welcome to my 29^th Maths Gems. This is where I portion 5 instruction ideas too resources I've seen on Twitter.

1. Nix the Tricks Videos
I've long been a fan of the majority Nix the Tricks - I intend it should live compulsory reading for all trainee maths teachers. I'm excited to come across that Owen Tabbert (@OTmath) is making a serial of Nix the Tricks videos for teachers. I intend these videos are going to live incredibly useful - non exclusively for non-specialists too anyone preparing to learn maths for the start time, but too for experienced teachers reflecting on how they explicate mathematical concepts. There's exclusively 2 videos thus far, but to a greater extent than to come. This video almost the concept of 'borrowing' inwards subtraction is excellent:

2. #AlmostMondayMaths
I like @OxfordEdMaths' novel tweeting initiative. Every Lord's Day at 7.15pm they tweet a maths enquiry for teachers to role inwards the calendar week ahead, using the hashtag #AlmostMondayMaths. Here's a duet of examples of what they've shared thus far:

#AlmostMondayMaths - rounding

#AlmostMondayMaths - algebra

3. Radians too Quadrants
Thanks to Meg Craig (Unit Circle too Radians' from Math Teacher Mambo (@MTMambo) which is almost instruction radians using cut-out pieces representing diverse angles (π/4, π/3, π/6 etc).

When I learn Year 12 students to role a quadrant when solving trigonometric equations, they (just about!) sympathise where to depict angles inwards degrees but uncovering it actually difficult to travel inwards radians. I've previously written almost helping students to understand radians, but I've non seen this lovely template approach before.

4. Problems from MathsPad
MathsPad is ane of my favourite resources websites. I'm actually pleased that James (@MathsPadJames) and Nicola (@MathsPadNicola) from MathsPad are directly on Twitter because they're sum of adept ideas. Do cheque out the problems too weblog posts that James tweets, similar this cuboid problem:

The website MathsPad has lots of complimentary resources too the balance are available for a small-scale subscription charge. All of their resources are excellent.

5. Grange Maths Camp

I'm rattling impressed past times the dedication of Chris Smith (@aap03102) too his colleagues who gave upwardly a weekend to run a maths army camp for their Sixth Form students. I'm too impressed that thus many students attended - I can't fifty-fifty larn my students to attend a thirty infinitesimal lunchtime revision session! If you lot haven't nevertheless read Chris' report of the sense thus create conduct maintain a hold off - it's inspiring stuff. It sounds similar Chris' students volition live rattling good prepared for their upcoming exams.

Update

I conduct maintain ane to a greater extent than calendar week alongside my Year 11s too 12s earlier they start Study Leave. In my concluding Year eleven maths lesson this Fri I innovation to role this bright 'last year.

I'm a Year eleven shape tutor thus there's a lot going on this calendar week (including enough of cake eating!). Next calendar week I'll live making certain that the members of my tutor grouping larn to their GCSE exams on time. After one-half term I start my novel chore at Glyn School inwards Epsom (only iii weeks to become - it's been a long hold off since I was offered the chore inwards December!).

If you lot learn GCSE classes thus I recommend you lot read '#mathsconf2015 inwards Birmingham.

Although I've been adding lots of novel resources to my libraries, I've non written many novel weblog posts lately. That's because I've been actually busy both at schoolhouse too at home. It was my youngest daughter's Christening on Lord's Day thus I had to create a lot of organising. Now that's done I'll conduct maintain fourth dimension to write some posts - create allow me know if there's whatsoever specific topics you'd similar me to write about. Last fourth dimension I asked for postal service suggestions, I ended upwardly writing iii challenging posts - algebra, fractions too calculus. I'm cook for some other challenge!

Saturday, March 9, 2019

5 Maths Gems #66

2. Classroom Display

Thanks to Clarissa Grandi (@c0mplexnumber) for sharing this beautiful classroom display 'The Faces Behind the Formulae' which she made for an Influenza A virus subtype H5N1 grade classroom.

I've added it to my displays page.

3. Pinpoint Learning

Powers of Ten Flags

Coordinate Messages

5. Pythagoras amongst Blokus

I honey this halt displace video from ‏@JoelBSperanza.

If you lot desire to meet to a greater extent than of Joel's halt displace videos or honor out how to brand your own, cheque out his weblog post service Stop-Motion Education.

Update

Extract from CorbettMaths.com 'puzzle square. This i is for directed seat out practice.

good at math

Thursday, October 24, 2019

5 Maths Gems #29

Saturday, October 12, 2019

5 Maths Gems #66

Friday, October 11, 2019

Vectors For Enlargement

5 Maths Gems #110

Thursday, September 5, 2019

5 Maths Gems #29

Saturday, March 9, 2019

5 Maths Gems #66