Off On A Tangent

At a recent Year xi Parents' Evening, I was guilty of hypocrisy. I reassured parents that their daughters would last really good prepared for their maths GCSE because we'd last doing one-half a term of revision lessons. Most parents nodded happily, but i dad challenged me. He asked why I didn't bring the chance to instruct his fille some calculus. Good point! I've written many times almost the importance of imparting mathematical noesis without focussing on exams (a 'no teaching to the test' philosophy), in addition to at that topographic point I was promising an extended catamenia of revision instead of mathematical enrichment.

I don't desire to instruct my students to travel past times exams. I desire to instruct them mathematics, in addition to I desire passing exams to last a welcome by-product of that. But what if some of my students neglect to come across their potential inwards their GCSE exams this summertime every bit a lawsuit of my determination to bring down revision time? It's a dilemma.

Bitesize enrichment
The solar daytime afterward Parents' Evening I'd planned a measure lesson on algebraic proof alongside my Year 11s (by 'standard' I hateful explanation, examples in addition to practice). At the root of the lesson, past times agency of introducing the topic of proof, I mentioned that many mathematicians pass their lives working on proofs. As I said it I was reminded of the BBC Horizon episode blog post almost teaching a lesson on Fermat.

It was alone 10 minutes of spontaneity inwards a lesson, but hence really worth it. My students went abode from schoolhouse having learnt something novel almost the world, in addition to that's what teaching is all about.

The success of this unplanned tangent gave me the confidence to root diverting from my lesson plans all over the place. In a Year 10 lesson on percentages I got carried away explaining how banks brand coin from involvement charge per unit of measurement spread. I know a lot almost finance from my previous career hence I felt confident talking almost this. But I acknowledge that my noesis of 'non-curricular' mathematics is limited. I possess got a pile of mathematical books that I'm desperate to read but never acquire time. Reading around your acre of report gives you lot the noesis in addition to confidence to acquire off on these interesting tangents. I must read more! If you're on Twitter in addition to hence do acquire involved in @MathsBookClub for encouragement in addition to inspiration.

How good read are you? Book recommendations from matheminutes.blogspot.co.uk.

Barriers to spontaneity

I don't deny that schemes of piece of occupation are necessary. For i thing, they ensure essential coverage of all the topics required for populace exams. In addition, synchronisation of teaching allows simultaneous assessment of whole twelvemonth groups, in addition to gives ambit for departmental collaboration. Schemes of piece of occupation are too a machinery for implementing a maths department's teaching strategy or philosophy. So they are 'a good thing' even though they may underpin a frustrating lack of freedom.

I was of late teaching 3D trigonometry to a top laid Year ix (very smart girls - many volition bring their GCSE inwards Year 10). I was going through the lawsuit below from CIMT. When nosotros got to business office (d) nosotros drew out the triangle inwards interrogation in addition to established that it was non-right angled. They haven't done the Sine in addition to Cosine Rules even hence so I said we'd skip it. I told them that they'd comprehend non-right angled triangles side past times side twelvemonth in addition to they accepted that without question. 

It's a fleck distressing isn't it? I was disappointed past times their lack of intellectual curiosity, but to a greater extent than disappointed alongside myself for telling them they'd possess got to facial expression a twelvemonth to complete solving the problem. Why didn't I but launch into teaching the Sine in addition to Cosine Rules? Firstly, because of fourth dimension pressure level - the class would possess got fallen behind their peers if we'd spent an extra calendar week or 2 on trigonometry, putting them at a disadvantage inwards their side past times side Year ix assessment (this would possess got upset them). Secondly, inconsistency of topic coverage would do problems for side past times side year's teachers. Thirdly, I hadn't idea inwards advance almost how I'd instruct non-right angled trigonometry. It takes a really confident in addition to experienced instructor to deliver a skillful lesson off the cuff. I demand at to the lowest degree 10 minutes thinking fourth dimension earlier I teach! So I left it at 'we'll do it side past times side year'. Most unsatisfactory.

To some extent, schemes of piece of occupation bound our mightiness to acquire off on interesting mathematical tangents. But it could last worse. We could last forced to piece of occupation pre-written lesson plans, slides in addition to resources. I savour designing tailor-made lessons for my students. I similar having ambit to last creative in addition to I similar beingness able to divert from my programme during a lesson if I desire to. It's prissy to possess got this autonomy. Ideally our schemes of piece of occupation are flexible plenty to adapt these worthwhile diversions. If you're designing a system of piece of occupation for side past times side year, demeanor this inwards mind. Time for tangents is most welcome.

Enrichment

momath.org

I acknowledge to knowing real niggling virtually how schoolhouse finances work. Some schools possess got hundreds of iPads, others possess got leaking roofs. It's all a mystery to me. Due to budgetary constraints I've exclusively been on 1 maths schoolhouse trip inwards the final 5 years. This leads me to wonder how of import enrichment is, as well as what schools tin create when coin is tight.

Why enrichment?
When I was a teenager I did zippo inwards maths beyond what was needed to transcend my exams. Apart from a duo of maths competitions, my schoolhouse did non 'enrich' our mathematics education. I liked maths because I was proficient at it - maths lessons were my comfort zone. I enjoyed the satisfaction of solving problems but I had no involvement inwards mathematics exterior the classroom. I await that many of my electrical current students experience the same way.

Maths In Action

Influenza A virus subtype H5N1 duo of years agone I accompanied a grouping of xx Year 12 students to a hateful solar daytime of Maths inwards Action lectures. I saw amazing speakers including Simon Singh as well as Hannah Fry. I'm convinced that this trip made me a meliorate maths teacher. Not exclusively did I acquire loads of cool novel stuff to part amongst my students, I also gained a novel enthusiasm for mathematics. I'm certain at to the lowest degree some of my Year 12 students must possess got felt inspired too. Perhaps they went on to report maths at academy equally a result.

Education is all virtually making students to a greater extent than knowledgeable, so nosotros should part mathematics inwards all its glory - non only the content of the seek out syllabus. I've written virtually these ideas earlier inwards my ship service Off on a Tangent. We must give our students opportunities to appreciate the wonders of mathematics.

There are loads of brilliant places for mathematical schoolhouse trips. Bletchley Park is a wonderful example. The Mathematics Gallery at the Science Museum is due to conk the world's firstly mathematics gallery afterward a recent £5 1 1000 m donation, so volition no dubiety conk an outstanding finish for schoolhouse trips. The MathsWorldUK projection is also exciting. Maths Inspiration events are brilliant. Sometimes though it's non practical or affordable to possess got students out on trips. Bringing speakers into schoolhouse is a proficient alternative.

A thought of the novel Mathematics Gallery

In-School Speakers
Influenza A virus subtype H5N1 acre agone I asked Twitter virtually maths speakers as well as I was real grateful to have dozens of useful replies. I've listed a choice of speakers below. Costs are typically inwards the part £200 - £600.

Kjartan Poskitt

Kjartan Poskitt, author of Murderous Maths, comes highly recommended. Talks include 'Isaac Newton as well as his Falling Apple' as well as 'Mayhem amongst Maths as well as Music'. In his Murderous Maths sessions he performs a multifariousness of features from his Murderous Maths books including flexagons, magic squares, foreign pose out facts, knots, tricks, amazing pose out predictions as well as so on. Full details are available on his website.

Matt Parker (@standupmaths) runs Think Maths, a group of fantastic speakers who watch schools to perform maths talks as well as workshops for all ages as well as abilities. Topics gain from topology, pose out theory as well as probability to magic as well as maths inwards pop culture.

James Grime (@jamesgrime) travels extensively giving populace talks all over the world. Details of fees as well as workshops are available on his website. For instance 'The Enigma Project' is a presentation virtually the history as well as mathematics of codes as well as code breaking including a demonstration of an master WWII Enigma Machine, followed past times code breaking workshops. It's suitable for pupils of all ages as well as abilities from Key Stage ii to Key Stage 5.

Bletchley Park (@BletchleyParkGB) offers 'Enigma Outreach' inwards which they pick out a genuine, working Enigma machine to your school. Visits are built some the demonstration of this iconic slice of World War II history, as well as tin also include presentations on the history of Bletchley Park, interactive talks on codes as well as ciphers, as well as hands on codebreaking workshops. Full details as well as fees are available here.

Colin Beveridge (@icecolbeveridge) offers 'Games, Goats as well as Gold' which uses pop game shows to demonstrate that thinking clearly virtually probability isn’t only proficient for your exams, but has applications inwards the slightly-more-real but only equally arbitrary Earth of prime number fourth dimension TV. The workshop is aimed at vivid Year nine students, but tin hold upward adapted for most secondary schoolhouse groups. Details of this utter as well as others are available on Flying Colours Maths.

Colin Wright (@ColinTheMathmo) comes highly recommended. He offers a collection of talks as well as workshops that gain from ages xiii as well as onwards. One of his most pop talks, 'Juggling: Theory as well as Practice' is virtually the mathematics of juggling. Further data virtually his gain of talks is available on his website.

Colin Wright

Dr Matt Pritchard (@ScienceMagician) is an award-winning magician, comedian as well as creative communicator. He delivers talks inwards schools on both maths as well as scientific discipline topics. His maths talks include 'Magical Maths' as well as 'The Man Who Cannot Lose'. He also has a session aimed at D1 students - 'From Facebook Friends to Postman Pat'. Full details are available on his website.

Rob Eastaway (@robeastaway) is the writer of a pose out of mathematical books and the Director of Maths Inspiration, a national programme of interactive lecture shows. He offers a fantastic choice of in-school talks including 'What's the signal of maths?', 'When Maths Meets Psychology', 'Maths on the Back of an Envelope' as well as 'From Pepsi to Peace Deals'. Many of his talks are suitable for Sixth Form students. See his website for to a greater extent than information.

Ben Sparks (@SparksMaths) industrial plant part-time amongst the Further Maths Support Programme as a speaker, tutor as well as co-ordinator, as well as part-time equally a freelance maths enrichment speaker some the Great Britain – including with Maths Inspiration. His talks, including 'The Creation of Number' as well as 'Pretty Irrational' are listed on his website. 

Puzzle Days as well as Workshops
If you lot possess got a proficient prepare of resources so you lot may hold upward able to run puzzle workshops yourself (FunMaths Roadshow materials are exclusively £27). Alternatively, at that topographic point are companies who tin come upward to your schoolhouse to run workshops for you lot - hither are some examples:

The 7puzzle Company (@7puzzle) delivers fun as well as effective maths workshops inwards both principal as well as secondary schools all over the UK. The games played non exclusively challenge children’s pose out skills, but also human activeness equally a confidence-builder. They comprise strategy, logic, shape as well as space, retentiveness as well as visual aspects equally good equally helping children to focus on the social etiquette of communicating, listening, turn-taking, sharing as well as team-working acre participating inwards the activities. Further data virtually the 7puzzle experience is available here.

The 7puzzle experience

MMP Hands-On Maths Roadshow (@mathsroadshow). The NRICH Hands-On Maths Roadshow is a collection of hands-on mathematical puzzles, games as well as activities that tin hold upward brought to schools for a exceptional maths event. Roadshow activities are designed to promote creative approaches to mathematics as well as strategic thinking as well as to cause mathematical curiosity. The Roadshow tin hold upward tailored to suit diverse historic menses ranges, from Key Stage 1 to 4. The fee is £595 for a amount hateful solar daytime as well as £415 for a one-half hateful solar daytime - amount details are available here.

The Problem Solving Company (@problemsolveit) offers fun filled days of hands-on maths challenges to students from Early Years to KS3. Their maths puzzle days promote thinking, logical reasoning as well as mathematical agreement amongst an emphasis on teamwork as well as discussion. They also run Year 6/7 Transition Days as well as Sixth Form Team Building Days. Further data as well as prices are available here.

The Problem Solving Company

Happy Puzzle Company (@happypuzzle) also runs Puzzle Challenge Days for Schools - click here for details.

Maths competitions - local as well as national - are some other cracking source of enrichment, though they oftentimes involve exclusively a handful of high-attainers. It's worth offering opportunities to whole yr groups too.

Affordable enrichment
Don't forget that your nearest Maths Hub powerfulness run enrichment events. For instance the Surrey Plus Maths Hub runs Inspiration Days (featuring speakers such equally Matt Parker) that students tin attend for gratuitous - spaces are available on a get-go come, get-go served basis.

Look out for grant schemes equally good - your schoolhouse could have fiscal assistance to run maths enrichment events.

This ship service past times no agency represents an exhaustive listing of speakers as well as workshops. If you're looking for enrichment opportunities so you'll honor a plethora of providers inwards the STEM Directories. If you lot possess got whatever recommendations from personal experience so delight comment below.

5 Maths Gems #33

Hello too welcome to my 33^rd gems post. This is where I part 5 educational activity ideas I've seen on Twitter.

Well it's been fun educational activity inward this week's heatwave hasn't it?! I long for an air-conditioned classroom. Still, all this lovely sunshine serves equally a overnice reminder that the summertime holidays are but roughly the corner.

1. Pythagoras Pile Up
We've all seen the fantastic #mathsconf4 I was fortunate to bespeak heed a fantastic persuasion for educational activity Fractions, Decimals too Percentages from Number Resources page.

This calendar week @solvemymaths shared a actually overnice persuasion for educational activity estimator skills which comes from @Ms_Kmp's website mathssandpit.co.uk. Have a await at her post 'Calculators: The New Hope' to download the resource. And cheers to @solvemymaths for his novel '7 Days of Maths' series, which is good worth following.

4. Maths Videos
Thanks to @mhorley for sharing a link to the BBC's Kick Sum Maths videos - I've non seen these before. They powerfulness come upward inward handy to back upward the educational activity of a divulge of Key Stage 2/3 topics.

5. Self-Descriptive Numbers
Thanks to @LearningMaths for sharing this lovely activity 'Self-descriptive numbers'.

If yous await through the set of resources from which this activity comes too then you'll run into that there's enough of other corking materials inward at that spot too.

If yous similar these resources too then you'll honey cleavebooks.co.uk/trol which is total of first-class activities. For event I've long been a fan of the Vocabulary Exercises which would move good inward an information technology Room or amongst iPads.

Recommended Reading
Here's some links to banking concern agree out:

• Bruno Reddy (MEI Conference, Pret homework, #mathsconf4 and Favourite Problems. My final gems post - Gems 32 - was 1 of my most pop posts ever.

Finally, I desire to part a Don Steward activity that I constitute peculiarly effective this week. I was running an Influenza A virus subtype H5N1 marker induction session too decided to purpose the enquiry below equally a starter to brand a indicate almost algebra skills. The algebra hither should last straightforward for students who almost to embark on Influenza A virus subtype H5N1 level, but some students struggled to position the answer. I made the indicate that if yous desire to create Influenza A virus subtype H5N1 marker Maths too then this kind of algebra should come upward real naturally. Strong algebra skills - ie the powerfulness to create this activity effortlessly - should last embedded past times GCSE too are essential to every Influenza A virus subtype H5N1 marker mathematician.

5 Maths Gems #42

Hello in addition to welcome to my 42^nd gems post. This is where I part roughly of the best instruction ideas I've seen on Twitter.

1. Resources
To start, a few novel resources that yous mightiness non cause got seen.

Miss Norledge (@MissNorledge) drew inspiration from a Maths Feast problem to brand 3 coordinate geometry problems of her own. These lovely 'Triangle Regions' tasks are suitable for GCSE students or Year 12s.

The clever folks at MathsPad croak along to create fantabulous resources - this Always/Sometimes/Never True activity for Fractional Indices is excellent. The solutions render rattling helpful explanations too. I've added this to my resource library.

Here's roughly other corking novel resources from MathsPad - How many ways tin dismiss nosotros write 1 million? These are fantabulous activities for consolidating cognition of indices in addition to criterion form.

Check out mathspad.co.uk for to a greater extent than fantastic resources. And if you're on Twitter, Nicola (@MathsPadNicola) in addition to James (@MathsPadJames) are good worth following.

2. Enrichment for Sixth Form Mathematicians
Thanks to Graham Colman (@colmanweb) for sharing his listing of Maths Beyond the Curriculum activities. This listing is written for Year 12/13 - it would last especially useful for a pupil who intends to study maths at university. It could easily last adapted for other twelvemonth groups too. Here's an extract:

3. m4ths.com
Steve from m4ths.com teaches at Thomas Clarkson Academy inwards Wisbech. He has been sharing roughly bright novel resources recently. Here's a few examples.

His 'A flat page too.

4. Target Stickers
Target grades are an obsession inwards many schools. I'm non a fan. I tell my students to aim for hap grades regardless of what their target says. After all, targets are largely based on sweeping generalisations in addition to dodgy data.

Most teachers (myself included) are regularly required to study on progress against targets. I similar the sticker persuasion below from Charmayne Bailey (@MissBaileyMaths). The scale makes it actually clear to students where they stand, what their minimum target degree is, in addition to where they're heading.

5. GCSE Revision Ideas
I honey this persuasion from Mel (Some Things I've Tried inwards which I shared roughly novel instruction ideas I've been trying this term

In Case You Missed It... in which I shared roughly ideas in addition to resources that cause got been good received on Twitter

Five to Follow #ff in which I recommended 5 creative maths teachers to follow on Twitter.

I enjoyed participating inwards the bit Maths Journal Club chat - yous tin dismiss read a write-up of the intelligence here.

I used the fractions activity below alongside my Year 7s (I outset featured this activity inwards my post Thoughts on Teaching Fractions). I was quite taken aback yesteryear how revealing this chore was - it uncovered roughly serious misconceptions.

Ticket sales for my exciting Christmaths Party are going well.  There's solely 25 twenty-four hours tickets left in addition to then majority now! It's going to last a fantastic consequence - run into christmaths.weebly.com for details.

5 Maths Gems #45

Hello in addition to welcome to my 45^th gems post. This is where I portion v maths pedagogy ideas.

1. Circumference
Pi Development and Circle: Introducing Circumference. The latter features animations such every bit this:

in addition to a actually overnice laid of circumference questions.

2. Pinpoint Learning
Causing quite a stir on Twitter over the concluding ii weeks, @tom_quilter's novel website pinpointlearning.co.uk provides students with personalised enquiry booklets based on show results. It's perfect for later a mock exam. You merely upload students' marks in addition to the website automatically produces private booklets featuring enquiry on the topics that students demand to piece of job on. The website is gratis in addition to is ready for Edexcel papers, thence if you've lately done an Edexcel mock thence compass laissez passer it a go. I've seen many tweets from teachers who've already tried it in addition to speak rattling highly of it.

3. Five Minute Mock Analysis
When yous render mock exams to students yous powerfulness similar to piece of job this splendid Five Minute Mock Paper Analysis from @MathedUp. The file is editable thence yous tin customise it for your school.

4. C4 Integration
I'm pedagogy C4 integration to my Further Maths flat at the moment. We've exactly done Volumes of Revolution in addition to I enjoyed making piece of job of props to explicate the concept. Thanks to an stance from Chris Smith (@aap03102), I used paper decorations to demonstrate how a corporation is formed when a airplane is rotated to a greater extent than or less the x axis.

I used these alongside gifs such every bit those shown below.

I likewise enjoyed using constant characters for the commencement time. This is an stance from Gems 22. Students who forget the 'plus c' inwards their answers are asked to decorate a constant character. Hopefully this volition encourage them non to forget i time to a greater extent than in addition to volition brand an interesting display for the classroom wall. Here's a brace of examples of what my students came upwards with:

5. Snowflakes
These Star Wars snowflake designs are vivid in addition to fifty-fifty characteristic characters from the latest films.

Here's a video well-nigh how to crimp them:



If you're planning to compass some snowflake activities at schoolhouse inwards the concluding calendar week of term thence it's a corking chance to beak well-nigh fractals - read Gems 16 for to a greater extent than on this.

Snowflakes tin endure a combat tricky to brand thence yous powerfulness similar these real-life graphs.

Right, I convey mock marker to compass in addition to Christmas cards to write thence I improve acquire on. I'll move out yous with this overnice enquiry from @OCR_Maths - what fraction is unshaded?

5 Maths Gems #48

Hello as well as welcome to my 48^th gems post. This is where I percentage instruction ideas as well as resources I've seen on Twitter.

1. UKMT inward the Classroom
H5N1 few people get got asked how they tin contain UKMT maths challenge questions inward their teaching. I've seen 3 resources that mightiness live on helpful here:

• Thanks to Lisa Chalmers ‏(@MsChalmersMaths) for telling me almost this resource from Dan Walker on TES. He has taken problems from Junior as well as Intermediate Maths Challenges as well as organised them past times topic inward a PowerPoint, alongside solutions.

• I've written earlier almost the first-class website DrFrostMaths.com. The resources hither are designed for high attainers as well as many of the worksheets depict questions from maths challenges as well as olympiads.
• I mentioned inward Gems 4 that Mathster has an online UKMT Maths Challenge Quiz. 

2. 'Grade 9' Paper
Thanks to Steve of m4ths.com for pulling together a set of questions that are aimed at the strongest mathematicians sitting the novel GCSE. There's approximately lovely questions here.

3. Teaching Ideas
I spotted 2 overnice instruction ideas on Twitter. The showtime thought is from Clare Hill (@chilledmaths). For instruction or revising calculus, she suggests the following:

Students accept a slice of newspaper alongside facial expression written at the top. The showtime soul integrates the expression, folds over the top as well as passes it to the side past times side student, who differentiates the facial expression that they see. They thus crimp over the top as well as go past times it to the side past times side educatee who integrates the expression, as well as thus on... At the terminate the newspaper is unfolded and, if all went well, the facial expression at the top should gibe the facial expression at the bottom.

The minute thought - shown inward the tweet below - was shared past times Liz Gibbs (@Liz_Gibbs). This would function at both primary as well as secondary bird for exploring plans, elevations as well as nets.

Which 3D shape did I press into the clay? Which shapes were non pressed into the clay? How create yous know? pic.twitter.com/Vq0vyY452b

— Liz Gibbs (@Liz__Gibbs) February 3, 2016

4. Fact of the Day
I was emailed past times Ann Rush (@MissARush) with a GCSE revision thought that they've used at their schoolhouse for several years.

Their 'Maths Fact of the Day' tin live on used inward a seat out of ways inward the run-up to GCSE exams:

• Print the fact of the solar daytime give to each student
• Laminate large versions as well as display inward classrooms
• Display the fact of the solar daytime inward a prominent expanse inward the maths corridor
• Refer to the fact as well as previous facts inward lesson starters/plenaries
• Ask shape tutors to percentage at shape time.

My schoolhouse does a 'Word of the Week' that is displayed all over the schoolhouse - this mightiness function for 'Maths Fact of the Day' too.

5. Feedback Sheets

Grant's (@AccessMaths) novel thought has been actually popular. If you're non on Twitter thus yous mightiness get got missed this. He has designed excellent 9 - 1 Feedback Sheets for a large seat out of topics. The collection continues to grow. Grant completes a feedback canvass for each educatee afterwards they've done an assessment. They thus response to his feedback and, alongside access to a assist sheet, consummate the questions provided. Read Grant's recent blog posts for all the details.

Update

If yous banking concern check out my late revamped blog archive you'll watch that Jan was a busy blogging calendar month for me. Did yous grab these posts?

• The Joy of Planning
• Handwriting
• New GCSE: Pythagoras Questions
• Classroom Photos - #mathscpdchat
• Five things yous mightiness non know almost the novel GCSE content #2
• Worries

I also took business office inward a podcast alongside Craig Barton which yous tin psyche to here, as well as I announced a Don Steward event at my school, which has similar a shot sold out (100 tickets went real quickly).

I'm looking frontwards to aid and/or presenting at xi events this year, the showtime of which is #mathsconf6 inward Peterborough on fifth March. If yous haven't got a ticket yet, yous tin learn i at mathsconf.com. Watch this infinite for information almost the pre-conference drinks on Fri 4th.

Don Steward late sent me all his PowerPoints on a retention stick - best acquaint ever! - as well as I've been enjoying looking through them. I'll learn out yous alongside his lovely activity Circle Remainders: