Angles Facts

I've e'er taught angles inwards parallel lines equally Fs, Cs too Zs, but I late discovered that pupils prefer to think of Fs, Us too Ns, which operate inwards precisely the same agency but may live on easier to retrieve because they acre the give-and-take FUN.

(image from greatmathsteachingideas.com)

Of course of written report there's yet the challenge of remembering the to a greater extent than formal descriptions that they volition remove to purpose inwards their GCSE examination (for event they are required to purpose the term 'corresponding angle' inwards their answers, instead of F-angle).  I advise that they think of 'FC' (football lodge - equally inwards Tottenham Hotspur FC) for F angles = corresponding angles.  I likewise advise they could retrieve that Z angles = alternate angles yesteryear thinking of the showtime too final letters of the alphabet. But this doesn't operate if I alter Z to N!  I'll bring to think of something else (or fifty-fifty better, learn them to come upwardly up amongst something).

Resources

There are loads of skillful resources for pedagogy this topic. Here are a few examples:

• I beloved the 'Spot the Angle' action from mathspad.co.uk. This website likewise has a cracking interactive Parallel Lines Tool.
• Teachitmaths.co.uk has a cracking angle carte du jour form activity and useful revision cards.
• Mark Horley has made a Basic Angle Properties activity.
• Missbrookesmaths.com has a prissy angles inwards parallel lines tick or trash activity.
• There are a position out of angle chases here - cheers to @MathedUp.
• Greatmathsteachingideas.com has a position out of lovely worksheets, activities too applets including Angles inwards Parallel Lines Colouring Fun and First Letter Prompts which gets pupils thinking virtually the language of their angle fact answers.
• This comprehensive booklet 'Introducing Angles' yesteryear Gareth Evans is helpful. 

There are loads to a greater extent than resources for this theme inwards my shape resources library. 

More Angle Facts

On a related note, here's only about tips for pedagogy to a greater extent than basic angle facts:

• greatmathsteachingideas.com)

Of course of written report there's yet the challenge of remembering the to a greater extent than formal descriptions that they volition remove to purpose inwards their GCSE examination (for event they are required to purpose the term 'corresponding angle' inwards their answers, instead of F-angle).  I advise that they think of 'FC' (football lodge - equally inwards Tottenham Hotspur FC) for F angles = corresponding angles.  I likewise advise they could retrieve that Z angles = alternate angles yesteryear thinking of the showtime too final letters of the alphabet. But this doesn't operate if I alter Z to N!  I'll bring to think of something else (or fifty-fifty better, learn them to come upwardly up amongst something).

Resources

There are loads of skillful resources for pedagogy this topic. Here are a few examples:

• I beloved the 'Spot the Angle' action from mathspad.co.uk. This website likewise has a cracking interactive Parallel Lines Tool.
• Teachitmaths.co.uk has a cracking angle carte du jour form activity and useful revision cards.
• Mark Horley has made a Basic Angle Properties activity.
• Missbrookesmaths.com has a prissy angles inwards parallel lines tick or trash activity.
• There are a position out of angle chases here - cheers to @MathedUp.
• Greatmathsteachingideas.com has a position out of lovely worksheets, activities too applets including Angles inwards Parallel Lines Colouring Fun and First Letter Prompts which gets pupils thinking virtually the language of their angle fact answers.
• This comprehensive booklet 'Introducing Angles' yesteryear Gareth Evans is helpful. 

There are loads to a greater extent than resources for this theme inwards my mathsisfun.com has a yoke to a greater extent than ideas - I similar their proposition that the C of the give-and-take complementary stands for 'corner' (ie a correct angle) too the southward inwards supplementary stands for 'straight' (ie 180 degrees on a at nowadays line).

Interestingly, the give-and-take complementary comes from Latin completum (meaning completed) because the correct angle is sentiment of equally a consummate angle.

Ideas For Education Circle Theorems

There was no inquiry nearly whether circle theorems should earn their house on the novel mathematics curriculum. They are the perfect representative of a theme that is good placed inward secondary schoolhouse mathematics. In teaching this topic, nosotros receive got the pleasance of exploring a prepare of theorems - a pocket-size alternative of the many fascinating properties of circles - thence teaching students how to apply their novel mathematical noesis to solve geometrical problems.

Background
Imagine designing a mathematics GCSE from scratch. What topics would yous include? There's a lot of mathematics to select from. You exclusively receive got to glance at an quondam textbook or O score newspaper to come across that the topics studied at secondary schoolhouse receive got changed considerably over the final century. Have circle theorems ever featured on the United Kingdom of Great Britain together with Northern Ireland of Britain together with Northern Republic of Ireland curriculum?

Looking dorsum at the 1957 O score Syllabus, nosotros receive got the following:

Extract from 1957 O score maths syllabus

Most of this looks really familiar, although the theorem 'if 2 circles touch, the indicate of contact is on the business of the centres' is non covered anymore. Note that the term 'cyclic quadrilateral' isn't used, but instead 'angles inward contrary segments are supplementary'.

In the 1957 O score exam there were many questions relating to circle theorems, including a seat out of proofs. The inquiry below is perchance the easiest, together with is similar inward mode to the questions seen on electrical flow GCSE papers. Our students mightiness relish having a become at questions similar this - the maths that their grandparents did at school.

1957 O score question

There was also a inquiry inward the 1957 newspaper relating to the Power of a Point Theorem, which at in ane lawsuit features inward iGCSE (specifically the Intersecting Chords Theorem) but non GCSE.

Interestingly the wording (but non the substance) of the circle theorems content on the 1974 O score Syllabus differs notably from the 1957 Syllabus. Again, circle theorems characteristic heavily inward the Geometry department of the 1974 O score exam. In the inquiry below, our electrical flow GCSE students would live able to do purpose a, but non purpose b.

1974 O score question

Over the next forty years, circle theorems content was reduced (in business amongst a gradual displace to include more topics inward secondary mathematics, but less depth). The 1984 O level (an splendid seek - similar to today's higher GCSE but to a greater extent than challenging) contained exclusively 2 circle theorem questions. Here's ane of them:

1984 O score question

The electrical flow GCSE specifications are really specific nearly which theorems are included (most of circle theorems on the 1957 Syllabus receive got stood the seek of time). The extract below is from the 2012 Edexcel GCSE specification.

Extract from Edexcel GCSE 2012 Mathematics Influenza A virus subtype H5N1 specification

The novel Edexcel GCSE maths specification (effective from 2015) is far less specific, only stating:

Thankfully the new AQA specification is less vague, confirming the continuation of the existing content.

The novel OCR specification contains a similar score of detail.

Source: Wikipedia

So it's long been accepted that circle theorems are worth including inward secondary mathematics education. Although there's been a pocket-size reduction inward the attain of theorems covered over the final lx years, the bulk receive got survived. Circle theorems may receive got petty straight application inward 'real life', but that doesn't matter. Mathematicians relish applying circle theorems to solve interesting geometrical problems. The trickier problems tin actually seek our logical thinking skills together with are especially satisfying. I'm pleased that circle theorems are hither to stay. So let's expect at a few teaching ideas.

Influenza A virus subtype H5N1 skillful house to start when teaching circle theorems is a recap of angle facts relating to triangles together with parallel lines. Most teachers thence acquire their students doing some exploration into angles inward circles. Once each theorem is established, students should do a lot of practice, starting amongst uncomplicated cases thence moving onto to a greater extent than complex questions involving to a greater extent than than ane theorem. We ask to expect at proofs along the way too.

Vocabulary

Paper plate vocab from Mr Collins

There's a lot of novel vocabulary inward this topic. First nosotros receive got the parts of a circle - your students could explore these using this blog post from Mr Collins.

This is also a skillful chance to verbalize about etymology - tangent originates from the Latin tangere 'to touch' and arc originally referred to the sun's apparent motility inward the sky. Segment (think oranges) and sector (think pie charts) are both from the Latin secare 'to cut'. Diameter is from the Greek dia- "across, through" and metron "a measure".

As good every bit the parts of a circle, nosotros also receive got novel words inward the descriptions of the theorems. For example vocabulary I brand some suggestions for activities to back upwards students when yous innovate novel cardinal words, such every bit vocabulary noesis surveys together with literacy walls.

'Name the line'
vocabulary exercise

Investigations
It's squeamish to give students the chance to investigate the angles inward a circle using ICT, geoboards (virtual or real), worksheet investigations or paper folding.  I honey this serial of Geogebra worksheets from The Maths Teacher. Students tin play around amongst the angles on enshroud thence respond the questions provided. In Folding Circles: Exploring Circle Theorems through Paper Folding from the NCTM, students manipulate newspaper circles to explore circle theorems (scroll downwardly to theorems 3 together with iv inward the instructions). I also similar these 2 uncomplicated paper-based demonstrations: angle at the centre and angles inward the same segment.

Extract from Folding Circles (NCTM)

Another persuasion for investigating angles inward circles involves hula hoops - this originates from the invitee post this post by Kelly Achtymichuk (source of the pictures below) together with Mr Collins' post 'Circle Theorems & Hula Hoops!!' to come across how other teachers receive got adapted the idea.

Cyclic Quadrilaterals

I'm non going to become into item nearly each theorem but I do desire to call cyclic quadrilaterals. The give-and-take cyclic is from the Greek kuklos which agency 'circle' or 'wheel'. A cyclic quadrilateral is a quadrilateral whose vertices all prevarication on a unmarried circle (ie the vertices are concyclic).

All triangles receive got a circumcircle but non all quadrilaterals do. Ask your students to sketch an representative of a quadrilateral amongst circumcircle (eg a square) together with ane without (eg a rhombus).

I similar the inquiry below (from this CIMT exercise) to develop understanding of the give-and-take concyclic.

Question from CIMT

Proof

Students should receive got a become at working the proofs out themselves. But they're non accustomed to proof, thence they'll in all likelihood ask some direction. For example, when they're proving that the angle inward a semicircle is a right-angle, yous could exhibit them the pace pictured together with inquire 'how would yous acquire to this step?' And where would yous become from here?'.

I also actually similar this activity from rhemsley on TES which makes the proofs to a greater extent than accessible yesteryear starting amongst numbers earlier generalising.

The NCETM also gives us this proof worksheet where students create total inward the missing words.

Tangent proofs are non currently on the GCSE syllabus but if yous desire to evidence the tangent theorems amongst your class, scout James Tanton's video Tangent Theorems for Circles together with the Pythagorean Theorem beforehand - the explanations are really clear.

If yous desire circle theorems together with proofs on your classroom wall thence these posters from danbar1000 on TES are great.

Resources
If you're planning a sequence of lessons on circle theorems thence you'll detect enough of useful worksheets together with activities listed inward my shape resources library. 

In my final gems post I mentioned the costless app Angles? - Let's solve figures problems! by Gakko Net Inc. If your students receive got access to iPads inward lessons thence this is a bright app for practice. It starts off amongst triangles together with parallel lines but yous tin skip ahead to circle theorems.

Particularly complex circle theorem questions, or 'busy' diagrams (like the inquiry below), could live enlarged on A3 newspaper - this would live a skillful chance to job the acrylic sheets suggested inward Jeremy Denton's post 'Improving students' collaboration using acrylic sheets'.

Source: CIMT

Memorising the theorems

Circle theorems are ane of those topics that require think every bit good every bit understanding. If students acquire by to spot the solution to a job thence I encourage them to become through a checklist of circle theorems inward their head, annotating the diagram where they can. Often students missy the 'angles inward the same segment are equal' steps because they aren't ever every bit obvious every bit others (as inward the representative shown below).

Enough practise of using circle theorems mightiness live sufficient to memorise them, but in this post Don Steward suggests that at that spot mightiness live do goodness inward chanting the theorems. I've non tried this yet but dorsum inward chief schoolhouse I learnt my times tables yesteryear chanting - it seemed to operate well. He suggests that the instructor taps on a diagram together with the cast telephone phone out the theorem (see his post for associated resources).

Chanting exercise from Don Steward

Off on a tangent
I desire to cease amongst a twain of curt non-syllabus ideas that would live squeamish to expect at amongst your students if yous receive got time.

Have yous ever looked at a regular This post nearly Thales Theorem describes how the presenter of children's TV programme Art Attack demonstrated how to detect the centre of a circle. If it featured on Art Attack thence why non do it inward a maths lesson? There is a squeamish interactive demonstration of the method here including printable instructions.

If you're teaching circle theorems for the start fourth dimension or yous precisely wanted some fresh ideas, I promise this post has been helpful. Please percentage your ideas together with favourite resources inward the comments below, or through Twitter. 

This was a rather long post thence if yous made it this far together with it's nonetheless Nov 2014, delight vote for me inward the United Kingdom of Great Britain together with Northern Ireland of Britain together with Northern Republic of Ireland Blog Awards! Thank you.

All O score cloth inward this post was taken from Cambridge Assessment.

5 Maths Gems #14

Welcome to my 14th weekly gems post - this is where I characteristic 5 of the best teaching ideas I've seen on Twitter each week.

You may or may non know that I've been writing these posts spell I've been at habitation on motherhood leave. My babe keeps me busy during the day, but my evenings are blissfully gratis from mark together with lesson planning thence I create got a rare chance to reverberate on my teaching together with assemble novel ideas. It's a shame that all teachers can't accept a mini-sabbatical every 5 years to produce the same. When I become dorsum to travel inwards Jan I'll create got 100 maths teaching gems inwards my toolkit - it volition last difficult to know where to start! 

1. Two Truths together with a Lie

Two Truths together with a Lie is traditionally an icebreaker game - person tells y'all 3 facts almost themselves together with y'all jurist which ane is the lie. For event my blood brother powerfulness tell y'all that he was in ane lawsuit bitten yesteryear a donkey, he was in ane lawsuit bitten yesteryear a serpent together with he was in ane lawsuit bitten yesteryear a monkey. Bizarrely, exclusively ane of those statements is a lie. So let's accept this game together with plow it into an action that prompts mathematical discussion.

This thought came from a tweet yesteryear @TCM_at_NCTM:

Polygons (source: mathsisfun.com)

This tweet made me realise that I'm guilty of lazily telling my students that polygon is 'just about other word for shape' when inwards fact I should last to a greater extent than specific - a polygon is a 2D figure amongst at to the lowest degree 3 conduct sides together with angles (the word derives from the Greek 'many-angled'), thence a circle is non a polygon.

The ii truths almost quadrilaterals ('a foursquare is a rectangle' together with 'a rectangle is a parallelogram') volition also prompt interesting discussions almost definitions. The quadrilateral identify unit of measurement tree powerfulness attention clarify things. The Euler diagram below is also helpful. 

Quadrilaterals (source: Wikipedia)

Here's a duet to a greater extent than examples of mathematical 'Two Truths together with a Lie' activities:

Influenza A virus subtype H5N1 related idea, Maths Lies (where the instructor tells ane deliberate prevarication per lesson - encounter my first gems post) is nonetheless ane of my favourite teaching ideas ever.

xkcd.com

2. Wikipedia and visualisation

From 1 to 1,000,000' from Gems 7 almost Estimation 180). Show your students the dotty pictures thence they larn a skillful feel of the magnitude of numbers. 

The paradigm higher upward reminds me of the 'If the World Were a Village of 100 People' visuals I talked almost inwards Gems 1 - this is a nice agency of conceptualising information that powerfulness attention students sympathise percentages.

3. Creative Mathematicians

Thanks to @gareth_metcalfe for sharing this bright video 'What is a mathematical proof?'. The video explains why mathematicians pass most of their fourth dimension trying things that don't work. Students are frequently reluctant to test a dissimilar approach if their get-go test at answering a enquiry is a dead end. Show this video at schoolhouse to encourage your students to last creative inwards their mathematical thinking. 

4. Communicating Reasoning
Continuing the theme of encouraging students to test diverse approaches to solving problems, bright NQT blogger gems post (unlucky 13) was my most pop post ever, amongst almost 2,000 views inwards a week. I also wrote a post on circle theorems terminal calendar week that I was peculiarly proud of. I dearest my gems posts together with my resources library, but it's my topic specials that I intend people volition detect the most helpful. I similar to intend that novel or late qualified teachers volition actually produce goodness from these posts when planning to learn a theme for the get-go time. 

If y'all similar my weblog together with then delight vote for it inwards the Great Britain Blog Awards (click hither to vote). There are over fifty blogs inwards the freelance teaching category together with exclusively 10 volition become through to the side yesteryear side stage. My weblog is tiny compared to the super-successful, well-established blogs I'm upward against. I've exclusively been writing it since Apr but I've done a lot inwards that fourth dimension - I pose my ticker together with soul into it, thence if y'all detect it useful together with then your vote would last really much appreciated.

Finally, produce y'all receive Chris Smith's (@aap03102)  weekly newsletter?  If y'all don't already subscribe together with then email him forthwith to larn on the mailing list. This calendar week he featured Pret homeworks which y'all should accept a await at if y'all haven't seen them before. Chris also featured the first-class puzzle below, which I'm looking forrad to giving my students when I provide to travel inwards January.

A Calendar Week Inwards The Classroom

My start calendar week dorsum at run has been challenging to tell the least. Eight novel classes, a novel Year eleven tutor group, over 200 names to learn, changes to schoolhouse policies together with practices, novel plant nursery routines for my toddler together with baby... the listing goes on. I also celebrated a Fibonacci birthday this week, therefore I’ve been actually busy both at run together with at home. I know it volition acquire easier when I acquire dorsum into the swing of things.

I received my timetable yesteryear electronic mail during the Christmas holidays therefore at that topographic point was no chance for a handover with the previous teacher. This calendar week I've been busy trying to figure out what topics to learn and, for my examine classes, how I'm going to lucifer everything inward earlier study locomote out commences inward May. I'm out of my comfort zone without detailed plans! I solely run 3 days a calendar week but this yr I'm teaching viii unlike classes nether a undertaking part organisation (double the release of classes I had final year!). I'll accept to survive real mindful of the sense of my students, who all accept at to the lowest degree 2 maths teachers right away - switching betwixt teachers together with topics tin sack survive hard for them.

Job sharing has its challenges but at that topographic point are simply about advantages, the head i beingness that I right away accept my ain classroom (most part-timers are schoolhouse nomads). I dear non having to motion from room to room all the fourth dimension - it actually does brand my days less stressful.

When I left run to accept a babe I was Key Stage 5 Coordinator, a role that I loved. I don't accept a TLR anymore therefore am focusing all my efforts on teaching. Since starting to write this weblog together with entering the Twittersphere I've acquire a much to a greater extent than reflective teacher. In this post I desire to part a twosome of things that accept gone good this week.

Angles with Year 7
The matter I uncovering hardest most teaching Year seven is that I don't actually know what maths they've done inward previous years. I demand to see simply about local primary schools together with uncovering simply about Year half dozen maths lessons. This calendar week I found out that most of my students were aware that the interior angles of a triangle amount to 180^o, but non aware that vertically contrary angles are equal. I found simply about questions (example below) inward which they had to combine their existing noesis with their newly acquired knowledge. They found these quite challenging - I don't holler back they're used to multi-step questions similar this.

Brilliant.org is an fantabulous source of extension questions for lessons on angles, similar the instance shown below.

I'll survive moving onto angles inward parallel lines with Year seven adjacent calendar week together with I'm looking forrad to using 'Angle Facts.

I did quite a lot on vocabulary with Year seven this calendar week because there's lots of novel words inward this topic. When I was defining 'vertically contrary angles', I spotted the fact below on mathsisfun.com. This was novel to me - I in all likelihood should accept known this! It was helpful to part this with my students because I'd simply taught them the pregnant of the word vertex.

Finally, I recommend the brusk video Gems 19). I showed it inward my lesson on triangles together with it went downwards well.

Problem Solving with Year 11
It's of import that I apace flora a skillful human relationship with my Year eleven class. I've acquire their instructor at a belatedly phase inward their GCSE course, but I withal accept fourth dimension to brand a difference. I demand this aeroplane to trust me. I meet them 5 times a fortnight together with that gives me 36 lessons to complete the syllabus together with fix for their exams. This calendar week I decided to pass a lesson getting to know them. I handed out a problem solving activity then went circular together with met each educatee individually, chatting to them most their predicted grades together with the topics they desire me to review. While I circulated, they worked on viii problems of varying levels of difficulty. In the halt I ran out of fourth dimension to verbalize to everyone but I withal holler back the lesson went good - they were actually engaged inward solving the problems together with I heard lots of discussions most mathematics.

These problems are from a multifariousness of sources (thanks to all originators!). At the halt of the lesson the solely work that remained unanswered was the 'find the radius of the circle' work from Chris Smith's newsletter - most students hadn't fifty-fifty attempted it but I promised them we'd await at it simply about other day.

I did a similar lesson with Year 8 (top set), except all their problems involved Pythagoras' Theorem (I told them to exercise Pythagoras, pregnant they had a starting indicate for each question. Perhaps I shouldn't accept told them). Again, my students were actually engaged inward this activity. They peculiarly liked the 'Spider Box' question. The solely enquiry that no-one answered was Ed Southall's semi-circle work (I suggested they challenge parents or older siblings to accept a go). Also, the enquiry below was answered incorrectly yesteryear almost every educatee (they squared the superlative to acquire 4w² instead of 16w²).

Support
Student Communication using Blogs). I'm trying Twitter equally an choice this year, the thought beingness that students (or their parents) follow me for useful links (eg for examine revision), interesting maths, reminders (eg 'you accept a examine adjacent week') together with therefore on. I've already started tweeting links to homeworks therefore students tin sack impress a re-create if they lose their sheet. I've also said that I volition offering maths back upwards through Twitter, therefore they tin sack inquire for assist anytime they acquire stuck on a homework or when revising.

I'm non certain how successful this volition be. Other schools are much to a greater extent than Twitter-friendly than mine. We don't accept a schoolhouse Twitter draw of piece of work organisation human relationship to communicate with parents, together with I holler back I'm the start instructor at my schoolhouse to essay to exercise Twitter for educational purposes. So I got nervous giggles from my classes when I told them most it. I incertitude many of them accept a Twitter draw of piece of work organisation human relationship therefore it mightiness non work, but we'll see. I'll study dorsum on this inward a few months!

What's Next?
Well it's solely been a calendar week therefore I've withal got loads to try. I downloaded iDoceo but haven't had a adventure to await at it yet. I'm also increasingly great on setting upwards a visualiser (via my iPad), to demo examples of educatee run on the IWB (amongst other things). Funnily plenty i of the most useful things I've done this calendar week is exercise my ain website, resourceaholic.com, to uncovering resources! My resources libraries accept saved me a lot of time. I've already noticed gaps inward them though - goose egg on angles inward triangles for instance - therefore I'll run on boosting my libraries over the adjacent few months.

That's it from me. I've found it quite therapeutic to reverberate on my start calendar week dorsum at schoolhouse together with I hope there's been something helpful for you lot hither too. There'll survive no gems post this calendar week because I've non had much fourth dimension to acquire on Twitter, but I'll write i adjacent week. Please don't forget to acquire a complimentary ticket to La Salle's National Mathematics Teacher Conference which is on Pi Day inward Birmingham (I'm delivering a session). I hope to meet you lot there. Also, White Rose Math Hub's Celebration of Maths is definitely worth attending. I'm gutted I can't conk (I can't afford the prepare fare to Leeds!) but it looks awesome.

Selfie with my girls on my final solar daytime of motherhood leave

5 Maths Gems #22

Hello as well as welcome to my 22^nd gems postal service - this is where I part 5 instruction ideas I've seen on Twitter.

I've discovered at schoolhouse this calendar week that alter is hard. It's slowly to tell 'I'm non going to learn it similar that anymore' or 'I get got a fantastic novel thought for instruction this topic' but when it comes to truly delivering lessons it's slowly to stick with tried as well as tested methods as well as resources. We desire our students to accept risks but how oft do nosotros accept risks equally teachers? This has been on my hear a lot this calendar week - I'll write a postal service close this soon.

1. 2015

Every yr Chris Smith features the Math Forum Year Game inward his newsletter. The idea is to purpose the digits inward the yr 2015 as well as the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), as well as ! (factorial), to write expressions for the integers 1 to 100. Answers tin last submitted through the Math Forum website, or perchance you lot could brand a classroom/corridor display similar these examples:

2015 Challenge classroom display by @Jeremy_Denton

Challenge 2015 display by @c0mplexnumber

post close the 2014 challenge is besides worth a read if you're going to displace this.

2. The Constant Character
Teaching indefinite integration? I loved this tweet from @inFinnityPi.

This lovely thought originated from @edenspresence who shared the student-decorated constant characters below. When students forget the 'plus C' they get got to decorate a grapheme - a skilful agency to larn inward stick!

3. 'I helped'
H5N1 prissy thought from @GiftedBA - 'I helped' stickers to encourage students to offering each other meaningful assist as well as to recognise those who do so. Download a sticker template here.

4. What's the question?
H5N1 truly prissy thought from Marcus Fleet is to write an reply on the board as well as enquire students for possible questions.

It's prissy that the shape get got chosen a winning question!

I'm quite surprised to encounter the sort of algebra students are doing inward Year half dozen - it's to a greater extent than advanced than I realised.

In the conversation that followed this tweet, Miss_Ren said that she likes to write a issue on the board as well as enquire what the enquiry could get got been. It links to all areas of maths as well as requires no printed resources. Paul Godding shared about similar ideas - such equally writing 5, nine as well as 10 on the board as well as scream for for the strange i out (students get got to come upwards up with ii reasons for each answer). There's charge to a greater extent than fantastic problems similar this on Paul's website 7puzzleblog.com.

5. What the examiner sees
If you're instruction a Year xi shape I retrieve it's good worth showing them this moving painting from @TheMathsMagpie to ensure they are aware that they shouldn't function exterior the allocated spaces inward their exams.

This post gives to a greater extent than data close the moving painting above. Use it with this rattling helpful develop of slides GCSE Maths - Easy Ways to Make Sure You Don't Lose Marks, besides from @TheMathsMagpie.

WWW/EBI

I'm resisting the urge to write a weekly postal service reflecting on what went good (and what didn't become well) at school. Instead I'll but characteristic i personal reflection inward each of my gems posts.

I'm instruction angles to Year seven at the moment. I gave them a homework inward which they were required to orbit reasons for their answers. Some students gave vivid reasons as well as I was pleased to encounter the right purpose of mathematical price I'd taught them such equally 'supplementary'. But many students but wrote out their calculations inward words instead of stating the angle facts they'd used.

In their defence, nosotros hadn't practised 'giving reasons' inward class, as well as so I decided to address this past times setting about angle problems as well as scream for for total reasons with each answer. Conveniently Don Steward has but published a develop of angle problems that were the right degree of challenge.

It seemed similar a skilful thought but I wouldn't tell the lesson went well. What happened was that my students were writing such detailed reasons inward total sentences that it became truly time-consuming (for instance solving enquiry 8 inward a higher identify involves using 3 dissimilar angle facts, therefore 3 sentences). They were doing as well as so much writing that they weren't doing plenty maths for my liking. Plus you lot could hear a pivot drib inward my classroom, as well as that makes me uncomfortable. In the halt I told them to halt writing total sentences as well as write one-word bullet points instead (eg isoscoles/triangle/straight line/complementary etc). They were truly relieved! I'd beloved to hear my readers' thoughts on this - should I get got persevered with the irksome but of import sentence-writing practice? I'm non sure. Please tweet me your opinion!