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.

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.

#Mathsconf10

Yesterday I attended #mathsconf10 inward sunny Essex. I'm really grateful to Mark McCourt together with La Salle Education for but about other fantastic solar daytime of maths CPD together with networking.

I started the solar daytime past times coming together upwards alongside here. We travelled from Central London to Essex past times educate together with had plenty of fourth dimension to banking concern gibe out the exhibition before the conference started. The format of the solar daytime was slightly dissimilar to previous conferences - because in that location were hence many workshops, in that location was an additional session added to the programme together with no keynote at the start. This worked good - it was expert to hold out able to select 5 workshops, though choices were every bit hard every bit ever.

In the outset session I presented my 'Angles inward Depth' workshop. This is the outset inward a novel serial of workshops where I expression at a theme inward depth (misconceptions, explanations, resources etc). I experience quite strongly that this is something that maths teachers need, though I mean value it volition accept me a spell to convince people of this! I blogged most it here.

Apart from the uncomfortably hot room together with the glare on the screen, I mean value my session went well. I focused specifically on 2 angle facts - following angles on direct lines together with angles inward a triangle. After my workshop, lots of members of the audience told me stories of their experience teaching angles - the misconceptions they'd seen together with the approaches they'd used - which was brilliant.

Lots of people at the conference requested that I portion my session online. It makes a lot to a greater extent than feel if y'all genuinely listen me verbalise through it, but hither y'all go:

• PowerPoint (includes links together with animations)
• PDF version 
• Workshop handout (angles problems for Year 7)

Links together with sources are inward the notes at the bottom of each slide.

Once I've made a few to a greater extent than of these I'll pose them on a split page hence they're all inward 1 place.

The thought is that these slide packs are shared alongside trainee teachers the outset fourth dimension they learn these topics. My following session, at Sheffield inward September, volition focus on angles inward parallel lines.

After my session Charlie Dawson showed me a bright manipulative which is genuinely elementary to make:

Simple manipulatives to assistance empathise angles: present me a crimson acuate angle, present me a yellowish angle of 295 degrees etc. pic.twitter.com/AzAwxJR48m

— Charlie Dawson (@dawsonmaths) 24 June 2017

In the 2d session I attended Mark McCourt's workshop on the history of maths education. I did a lot of query on this before inward the twelvemonth because I ran a session on it for my SCITT trainees, but I felt that I had but about gaps inward my noesis hence it was worth aid Mark's session to uncovering out more. As expected, this was a genuinely interesting session. It's fascinating that maths teaching keeps swinging from progressive to traditional together with dorsum again.

I together with then went to Andrew Taylor's session where he talked most his personal history of employment solving. He shared but about lovely Malcolm Swan problems, including Skeleton Tower from the blue box.

When he shared the mark guides for the sometime maths GCSE coursework it made me really happy that I became a instructor subsequently coursework was removed from GCSE. Tilly's tweet most this genuinely made me laugh:

Andrew spoke most the reasons that coursework was discontinued together with how exams straightaway endeavor to show employment solving skills, though of course of instruction nosotros know that conducting mathematical investigations nether fourth dimension atmospheric condition is non ideal.

During this workshop a lot of people attended the lovely here together with included but about links to learn out ticket resources (though, arguably, an learn out ticket should solely accept a few minutes to create hence teachers may hold out amend off making their ain tailored learn out tickets instead of using pre-made ones).

At tiffin I popped along to the tweet-up together with tried (unsuccessfully!) to brand a cobra weave stick bomb alongside Lucy Rycroft-Smith.

After tiffin I attended Rachel Horsman's session 'Geometrical Gems'. This was a lovely session total of practical activities. My favourite purpose was the Area Game, which I played alongside Martin Noon. The thought is to accept it inward turns to describe lines within a rectangle to cast triangles. When y'all cast a triangle y'all claim it past times colouring or labelling it. Each business y'all describe must start where the previous business finished together with has to encounter the other side of the rectangle. The mortal alongside the biggest total expanse at the terminate wins.

It's obvious now, but whatever y'all do you'll terminate upwards alongside a describe - because you'll both receive got the length of the rectangle every bit your total base, together with all the triangles receive got the same height. Clever!

In the terminal session Dani together with Rose headlined alongside a workshop on workload. I didn't become to this session because I experience that my workload is every bit nether command every bit it tin be. Most of the large drains on my workload (UCAS references, mock mark etc) are unavoidable. Influenza A virus subtype H5N1 lot of the tweets mentioned quizzes, which I've been using for a twain of years straightaway together with absolutely love. Regular depression stakes quizzes are 1 of the best changes to my practise that I've made inward recent years together with I cannot recommend them plenty (I blogged most it here). Influenza A virus subtype H5N1 flat mark together with feedback for a giant cast of 28 is the primary affair that's caused me ongoing workload issues this twelvemonth - I'm non convinced that quizzes are a suitable option at Influenza A virus subtype H5N1 level, but I suppose it's worth considering.

Instead I went to Peter Mattock's session 'Opportunities for Reasoning' inward which he shared lots of interesting activities together with resources, including this from the Standards Unit which requires students to explicate what's happening inward each step:

He likewise shared his lovely fractions activity which y'all tin download here.

I stayed for a twain of drinks subsequently the conference together with had a lovely chat alongside swain maths teachers. Overall it was a slap-up solar daytime together with I expression forrad to the Sheffield conference inward September.

In illustration you're interested, my previous maths conference weblog posts tin hold out institute here:

#mathsconf9 (March 2017)
#mathsconf8 (September 2016)
#mathsconf6 (March 2016)
#mathsconf5 (September 2015)
#mathsconf4 (June 2015)
#mathsconf2015 (March 2015)
Gems 8 (September 2014)

I'm going to the JustMaths Conference on Tuesday (two maths conferences inward 4 days!) - if you're going, catch y'all there.

#Mathsconf10

Yesterday I attended #mathsconf10 inward sunny Essex. I'm really grateful to Mark McCourt together with La Salle Education for but about other fantastic solar daytime of maths CPD together with networking.

I started the solar daytime past times coming together upwards alongside here. We travelled from Central London to Essex past times educate together with had plenty of fourth dimension to banking concern gibe out the exhibition before the conference started. The format of the solar daytime was slightly dissimilar to previous conferences - because in that location were hence many workshops, in that location was an additional session added to the programme together with no keynote at the start. This worked good - it was expert to hold out able to select 5 workshops, though choices were every bit hard every bit ever.

In the outset session I presented my 'Angles inward Depth' workshop. This is the outset inward a novel serial of workshops where I expression at a theme inward depth (misconceptions, explanations, resources etc). I experience quite strongly that this is something that maths teachers need, though I mean value it volition accept me a spell to convince people of this! I blogged most it here.

Apart from the uncomfortably hot room together with the glare on the screen, I mean value my session went well. I focused specifically on 2 angle facts - following angles on direct lines together with angles inward a triangle. After my workshop, lots of members of the audience told me stories of their experience teaching angles - the misconceptions they'd seen together with the approaches they'd used - which was brilliant.

Lots of people at the conference requested that I portion my session online. It makes a lot to a greater extent than feel if y'all genuinely listen me verbalise through it, but hither y'all go:

• PowerPoint (includes links together with animations)
• PDF version 
• Workshop handout (angles problems for Year 7)

Links together with sources are inward the notes at the bottom of each slide.

Once I've made a few to a greater extent than of these I'll pose them on a split page hence they're all inward 1 place.

The thought is that these slide packs are shared alongside trainee teachers the outset fourth dimension they learn these topics. My following session, at Sheffield inward September, volition focus on angles inward parallel lines.

After my session Charlie Dawson showed me a bright manipulative which is genuinely elementary to make:

Simple manipulatives to assistance empathise angles: present me a crimson acuate angle, present me a yellowish angle of 295 degrees etc. pic.twitter.com/AzAwxJR48m

— Charlie Dawson (@dawsonmaths) 24 June 2017

In the 2d session I attended Mark McCourt's workshop on the history of maths education. I did a lot of query on this before inward the twelvemonth because I ran a session on it for my SCITT trainees, but I felt that I had but about gaps inward my noesis hence it was worth aid Mark's session to uncovering out more. As expected, this was a genuinely interesting session. It's fascinating that maths teaching keeps swinging from progressive to traditional together with dorsum again.

I together with then went to Andrew Taylor's session where he talked most his personal history of employment solving. He shared but about lovely Malcolm Swan problems, including Skeleton Tower from the blue box.

When he shared the mark guides for the sometime maths GCSE coursework it made me really happy that I became a instructor subsequently coursework was removed from GCSE. Tilly's tweet most this genuinely made me laugh:

Andrew spoke most the reasons that coursework was discontinued together with how exams straightaway endeavor to show employment solving skills, though of course of instruction nosotros know that conducting mathematical investigations nether fourth dimension atmospheric condition is non ideal.

During this workshop a lot of people attended the lovely here together with included but about links to learn out ticket resources (though, arguably, an learn out ticket should solely accept a few minutes to create hence teachers may hold out amend off making their ain tailored learn out tickets instead of using pre-made ones).

At tiffin I popped along to the tweet-up together with tried (unsuccessfully!) to brand a cobra weave stick bomb alongside Lucy Rycroft-Smith.

After tiffin I attended Rachel Horsman's session 'Geometrical Gems'. This was a lovely session total of practical activities. My favourite purpose was the Area Game, which I played alongside Martin Noon. The thought is to accept it inward turns to describe lines within a rectangle to cast triangles. When y'all cast a triangle y'all claim it past times colouring or labelling it. Each business y'all describe must start where the previous business finished together with has to encounter the other side of the rectangle. The mortal alongside the biggest total expanse at the terminate wins.

It's obvious now, but whatever y'all do you'll terminate upwards alongside a describe - because you'll both receive got the length of the rectangle every bit your total base, together with all the triangles receive got the same height. Clever!

In the terminal session Dani together with Rose headlined alongside a workshop on workload. I didn't become to this session because I experience that my workload is every bit nether command every bit it tin be. Most of the large drains on my workload (UCAS references, mock mark etc) are unavoidable. Influenza A virus subtype H5N1 lot of the tweets mentioned quizzes, which I've been using for a twain of years straightaway together with absolutely love. Regular depression stakes quizzes are 1 of the best changes to my practise that I've made inward recent years together with I cannot recommend them plenty (I blogged most it here). Influenza A virus subtype H5N1 flat mark together with feedback for a giant cast of 28 is the primary affair that's caused me ongoing workload issues this twelvemonth - I'm non convinced that quizzes are a suitable option at Influenza A virus subtype H5N1 level, but I suppose it's worth considering.

Instead I went to Peter Mattock's session 'Opportunities for Reasoning' inward which he shared lots of interesting activities together with resources, including this from the Standards Unit which requires students to explicate what's happening inward each step:

He likewise shared his lovely fractions activity which y'all tin download here.

I stayed for a twain of drinks subsequently the conference together with had a lovely chat alongside swain maths teachers. Overall it was a slap-up solar daytime together with I expression forrad to the Sheffield conference inward September.

In illustration you're interested, my previous maths conference weblog posts tin hold out institute here:

#mathsconf9 (March 2017)
#mathsconf8 (September 2016)
#mathsconf6 (March 2016)
#mathsconf5 (September 2015)
#mathsconf4 (June 2015)
#mathsconf2015 (March 2015)
Gems 8 (September 2014)

I'm going to the JustMaths Conference on Tuesday (two maths conferences inward 4 days!) - if you're going, catch y'all there.

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

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

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.