Surds

Surds - what a fabulous topic to teach! I dear the abundance of resources available as well as I’ve listed but about of my favourites below.

Two things I e'er produce when didactics surds:

• Pupils listing the source twelve foursquare numbers inwards their books for reference throughout the lesson. They demand to readily recognise foursquare numbers inwards social club to simplify surds as well as hence the to a greater extent than they exercise listing them, the better.
• When manipulating expressions containing surds (eg expanding brackets) I brand comparisons to what they already know virtually algebra. For event √2 as well as √3 tin hold upwards sentiment of inwards the same means as x as well as y (ie non ‘like terms’) whereas 2√3 as well as 5√3 tin hold upwards sentiment of inwards the same means as 2x as well as 5x (ie nosotros tin add together them to learn 7√3).

The NCETM suggests a yoke of prissy ‘hooks’ for getting started didactics surds:

• Ask pupils to uncovering a means of drawing a occupation alongside a length of just √5 units (the hypotenuse of a correct angled triangle alongside sides 2cm as well as 1cm) 
• Ask pupils to separate the length of an A4 slice of newspaper yesteryear its width. Repeat for A3 as well as A5. What produce they notice? (The answer is e'er √2)

This blog post has some to a greater extent than ideas for introducing the concept of surds. And I similar this on the history of surds.

Resources
Here’s but about groovy didactics resources (there's hundreds to a greater extent than online). Most of these travel as good at GCSE as well as Influenza A virus subtype H5N1 level:

• Is it rational?
• Two interactive tasks from Mathspad
• Pairs activity 
• Introducing surds
• True or faux activity
• Surds -Applying as well as occupation solving
• Multiplication squares
• Mr Barton’s activity
• Standards Unit N11
• Surds Connect 4
• Surds resources - leannegadsby on TES
• Manipulating Radicals
• Tripods
• And here’s but about resources recommended yesteryear the TES.

For a lovely laid of surds problems, come across my Problem Sets page.

Finally, if you're looking for something actually creative, cheque out this Wheel of Theodorus Art Project.

Edit 29/12/14: Thanks to @runningtstitch for suggesting an option method for simplifying surds:

Teaching Amongst Desmos

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

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

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

Desmos inwards the information technology Room

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

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

Linear Graphs

One of the topics that my pupils fighting amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't operate out how to respond a GCSE interrogation similar this:

Strangely, I learn this differently at GCSE too Influenza A virus subtype H5N1 level.  At GCSE my pupils write down

y = mx + c

too substitute values for y, thousand too x, too thus solve for c.  Whereas at Influenza A virus subtype H5N1 marker my pupils utilization the equation

y - y₁ = m(x - x₁)

Essentially the same method but a slightly dissimilar approach. Perhaps I should hold out to a greater extent than consistent too innovate the 'A marker method' at GCSE. I'd similar to remove heed what other teachers do.

In this postal service I’ll advise closed to ideas too resources for didactics linear graphs.

Key words

Let's showtime amongst the basics. There's a lot of novel vocabulary inward coordinate geometry, closed to of which pupils volition accept encountered at primary school. This is a overnice vocabulary noesis survey every bit suggested inward my earlier post. 

Here's a overnice play a trick on for remembering the words parallel too perpendicular (this could hold out helpful for spellings - parallel is oftentimes misspelt): 

too this activity is suitable for Year six or 7. 

Introducing the shape y = mx + c
I'd unremarkably showtime this topic inward Year seven or 8 amongst plotting conduct work graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This topic provides an splendid chance for pupil investigation using Desmos. Use a worksheet to guide pupils through the lesson:

• Investigating Straight Lines amongst Desmos (by Tristan Jones on TES)
• Straight Line Graphs inward Desmos (by me!)

Once pupils are able to translate the values of thousand too c too thus they tin endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal too vertical lines.

My weblog postal service 'All nigh gradient' features ideas too resources for didactics slope (the postal service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets too activities).

Understanding parallel too perpendicular gradients

So here's the primal data that pupils demand to understand:

(source)

If they know how to operate out a slope every bit 'rise over run' (or equivalent) too thus pupils should hold out able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this ane from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

• Finding Equations of Parallel too Perpendicular Lines past times Mathematics Assessment Project
• Perpendicular Lines Worksheet (by me!)
• AS marker Parallel too Perpendicular Lines  (suitable for GCSE extension)
• Perpendicular lines: equations past times toticity.co.uk

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should accept the necessary skills too noesis to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for sure capable. Essentially it's merely the wording of the questions that throws them.

Here's closed to to a greater extent than recommended resources suitable for GCSE students:

• Foundation: Linear Graphs 'I Can' from Mathsbox
• Mathattack Linear Graphs homework sheet
• Topic checklist
• MathsPad Linear Graphs Problems
• Rich activities from Five Triangles
• Rich activities from Median Don Steward

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe too Lines.

Finally, always wondered which countries utilization y = mx + c annotation too which countries utilization something different? Check out this map.

Scatter Graphs

This weblog is becoming a fleck statistics-heavy, which is ironic given that I don’t specially similar pedagogy statistics at Key Stage iii as well as 4.  I much prefer pedagogy algebra. I’m also quite peachy on surds as well as indices. And I similar trigonometry. In fact, apart from the strange annoying-to-teach topic similar loci as well as constructions, I’d seat most information treatment topics correct at the bottom of my ‘things I relish teaching’ list. It never fails to amaze me how long roughly teenagers receive got to plot a graph. What a faff.

Anyway, this postal service is all most ideas for pedagogy scatter graphs. And I retrieve to follow it upwards alongside a postal service looking at applications of box as well as whisker plots exterior the maths classroom.  But as well as thus I’ll halt alongside all the statistics.

Practical activities

Unusually for a maths lesson, there's opportunities for roughly practical activities when nosotros innovate scatter graphs. The obvious sentiment is to receive got students plot meridian or manus bridge against shoe size. If you lot desire to acquire fifty-fifty to a greater extent than practical, attempt a human scatter graph inward the classroom or inward the playground (using chalk axes).

Outliers 

I similar to purpose the ii scatter graphs shown below (stolen from a Ten Ticks worksheet) inward a shape give-and-take most outliers.  Ask your shape what could receive got caused these extreme values as well as you'll in all likelihood acquire roughly actually creative suggestions!

Line of Best Fit

I instruct my students to depict a trouble of best stand upwards for yesteryear trying to minimise the distances betwixt all the points as well as the line. That’s what a to the lowest degree squares regression does. Contrary to pop belief, at that spot doesn't receive got to live the same release of points to a higher house as well as below the line. Nor does the trouble receive got to become through whatsoever of the points. And the trouble sure enough doesn't receive got to become through the origin. Beware of dodgy methods taught inward other subjects. This misconceptions activity yesteryear frickard on TES is helpful - I've used this inward a 'hands on caput if you lot retrieve it's true, hands on hips if you lot retrieve it's false' activity.

Impossible Predictions

'Extrapolation' from regression lines is something that comes upwards at Influenza A virus subtype H5N1 level, only the sentiment tin terminate brand for interesting discussions at Key Stage iii or GCSE. The telephone substitution signal is that fifty-fifty if nosotros detect a linear human relationship inward the information we're examining, nosotros can't assume that human relationship extends beyond the make of the data. Here's a dainty instance for shape discussion:

The graph below shows a negative correlation betwixt twelvemonth as well as fourth dimension taken yesteryear athletes to run 100m. It suggests that the speed of 100m runners has increased over time. Influenza A virus subtype H5N1 trouble of best stand upwards for has been drawn. Why produce you lot retrieve 100m runners are getting faster? Do you lot retrieve this tendency volition continue?

Possible reasons for the increment inward speed include: advances inward technology (ie to a greater extent than lightweight or streamlined clothe as well as trainers), inquiry into optimal diets as well as grooming plans, sponsorship important athletes receive got to a greater extent than fourth dimension to train, the introduction of starting blocks inward the 1940s as well as an improvement inward the accuracy of timing the race.

If the tendency continues indefinitely (ie if nosotros depict the trouble of best stand upwards for into the future) as well as thus at roughly signal people would live able to run 100m inward null seconds, which is impossible. There must live a signal at which the fourth dimension volition plateau, due to limits inward humans' physical capabilities. Although at that spot is a linear correlation, nosotros must live careful non to brand predictions inward the yesteryear or futurity because the linear human relationship is over a express fourth dimension period.

The graph comes from this Minitab Blog post as well as the sentiment was seat into my caput yesteryear Kings College London PGCE tutor Chris Olley. 

"Wind is caused yesteryear the rotation of windmills"

I love the causation vs correlation discussion.  It's a real of import learning signal for students who volition come upwards across all sorts of dodgy statistics inward everyday life.

doubt.it

Influenza A virus subtype H5N1 typical instance is shoe size as well as reading age. The ii variables are positively correlated, only apparently the size of someone's feet has no demeanor on on their reading ability. For to a greater extent than ideas banking concern check out this spurious correlations website.

If you're planning a shape give-and-take on causation as well as thus receive got a quick read of 'Correlation does non imply causation'on Wikipedia (not e'er the best source only gives roughly skillful examples).

Correlation does non imply causation, only it does waggle its eyebrows suggestively as well as gesture furtively spell mouthing "look over there". – xkcd 

Resources

Finally, here's a few resources that you lot could purpose inward your lessons:

• I love this Bee Aware action from Don Steward. It could easily live made into a mini-project/display move most the campaign as well as demeanor on of the demise of dear bees.
• The first-class Mathematics Assessment Project gives us ii tasks - Scatter Diagram and Birds' Eggs
• There's no shortage of real-life applications of scatter graphs. This worksheet 'Shake It Up alongside Scatterplots' is 1 of many examples (here's the solutions).
• Nrich gives us this nice David as well as Goliath activity.
• 'Foldables' seem to live a big matter inward U.S.A. math lessons, only I've never seen them inward the UK. I retrieve my students would quite similar them. Here's an sentiment for correlation foldables from the weblog 'Everybody is a Genius'.
• I similar this online tool for checking the accuracy of lines of best stand upwards for from Mark Ritchings
• Here's an interesting group project. I similar the sentiment of giving each pair/group ii options thus they tin terminate select the variables they prefer, as well as that everyone inward the shape is working on something different. Also, the 'assigned tasks' for each grouping fellow member (see in conclusion page) is an sentiment I haven't seen earlier for organising grouping work. These detail tasks may non live suitable for a United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland lesson because nosotros don't hold off students to calculate the equations of lines of best fit, only the sentiment could live adapted.

I promise this postal service has been helpful.  Please comment if you lot receive got whatsoever ideas to share. 

By the way, this cool moving scatter graph is worth a look.

xkcd.com

Consistent Mathematics

‘But Miss, that’s non what our lastly instructor said’

I read an interesting Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.

As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the Poorly Executed Mnemonics Definitely Addle Students' by Bill Shillito - so I won’t go through it all again, but let’s think almost how to develop it.

As a minimum, nosotros postulate all teachers inward a schoolhouse to live on board alongside a novel approach. In an ideal province of affairs we’d acquire all maths teachers inward the province – no actually, inward the footing – on board. Now, inward a rather tiny pace towards changing the footing – I’ll start past times discussing this inward my division coming together on the commencement solar daytime of term inward September.

If our pupils take away maintain met BODMAS at master copy school, we’ll take away maintain to tell them to disregard it, in addition to we’ll take away maintain to demonstrate them why past times demonstrating the misconceptions it may Pb to. Like many others, I’m an advocate of teaching GEMA or GEMS instead. Some American maths teachers take away maintain already written blog posts almost this approach. It’s a hurting that most of my lovely resources reference the term BODMAS though. If I acquire fourth dimension over summertime I’ll brand roughly choice GEMA resources.

Changing quartile terminology
Now I don’t think I’m going to brand whatever progress alongside this i because it doesn’t termination inward whatever serious misconceptions. Am I the alone someone bothered past times the fact that nosotros work the term ‘lower quartile’ to depict both the bottom 25% of the information in addition to the cut-off value 25% of the means through the data? John Tukey, inventor of the box plot, used the tidings ‘hinge’ instead ie the lower quartile consists of the values betwixt the minimum value in addition to the lower hinge. I prefer this terminology, in addition to I’ve seen it used inward a few places, but I doubtfulness it volition live widely adopted.

Maths nosotros desire to alter but can’t
When nosotros innovate the thought of squaring sinx at Influenza A virus subtype H5N1 level, nosotros tell pupils to write sin²x instead of sinx² (to clarify that it’s non the x that’s beingness squared). But nosotros take away maintain to carefully explicate that sin^-1x doesn't hateful the reciprocal of sinx, but truly the inverse ie arcsin. The obvious solution to this confusing annotation is to halt using -1 to dot inverse functions – but in addition to so we’d postulate to redesign estimator buttons! Why didn’t estimator designers write arcsin, arccos in addition to arctan on the inverse trig buttons?

The work of -1 to hateful both a reciprocal in addition to an inverse business office is i of the many mathematical annoyances discussed inward this ship on Reddit ‘What Mathematical Conventions would yous change?’. You mightiness also live interested inward this article ‘The most mutual errors inward undergraduate mathematics’.

Inconsistent mathematical methods
I don’t think it’s a job if pupils work a diversity of methods to respond the same question. Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.

As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the best method though!). Another representative is the approach nosotros take away maintain to exchange in addition to rearranging. When I work the Cosine Rule to notice an angle, I substitute the numbers into the formula a² = b² + c² - 2bcCosA then I rearrange. But I’ve noticed that most of my colleagues tell students to rearrange the algebra before they substitute. It mightiness confuse students when they commencement catch a novel approach, but this opens upward a useful dialogue almost the equivalence of dissimilar methods.

Here’s a few to a greater extent than examples of where teachers take away maintain dissimilar approaches:

• When teaching trigonometry inward right-angled triangles, non everyone says ‘SOHCAHTOA’. At schoolhouse I learnt a Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.
  
  As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the trigonometry triangles too.
• I’ve already written almost differing methods for finding the equation of a at i time draw inward my Multiplication methods are a practiced representative of this. There’s been roughly tidings almost multiplication methods lately on twitter - most people concord that if nosotros acquire the right respond in addition to so it shouldn't affair what method nosotros use.
  
  As teachers nosotros take away maintain our ain preferences. And pupils may take away maintain their ain methods too, learnt from teachers, parents, tutors, Kumon (grrr...) in addition to so on. Influenza A virus subtype H5N1 practiced representative is the means nosotros notice a highest mutual factor - there’s many dissimilar methods, all as valid (I'm convinced I've finally flora the linear graphs post.
• I i time had a Year eleven degree who’d been taught past times their previous instructor to notice the nth term of a sequence using the a + (n-1)d formula that nosotros usually learn at Influenza A virus subtype H5N1 level. It worked well.
• I don’t work the ‘FOIL’ social club when I expand brackets on the board in addition to this confuses roughly of my pupils who appear to think that FOIL is the alone right method.

Inconsistent vocabulary in addition to pronunciation
I state parab-ola, my colleague says para-bola. I’m pretty certain I state it right (in fact, I only checked here to brand sure!). But I had a minute of doubtfulness when my pupils all laughed at my pronunciation because they’d heard it pronounced differently the previous year. Now this truly isn’t the destination of the world, but it made me wonder almost my pronunciation of other words, such as cyclic (as inward cyclic quadrilateral), alternate (as inward alternate angles) in addition to ln (as inward natural log).

As for vocabulary, I switch betwixt the price 'index' in addition to 'power' all the time. This is only i representative of my inconsistencies. I don't think it's a job to work a diversity of words, inward fact it mightiness live a practiced thing, as long as all novel vocabulary is explained to students.

Inconsistent standards
I taught a Year 12 lastly twelvemonth whose piece of work was laid out so badly it was almost impossible to follow. She scattered her workings all over the page, sometimes showing me where to hold off adjacent alongside flowery arrows. She set multiple equals signs on the same draw of working, in addition to her lastly respond was e'er hidden away somewhere. Her piece of work was also mathematically incorrect. Although I commented - many times - on the province of her workings, I decided it was to a greater extent than of import to focus our express fourth dimension together on fixing her mathematical misconceptions. I felt frustrated that her appalling approach to setting out her piece of work hadn’t been dealt alongside at an before age.

I recollect when I was a pupil inward the Upper Sixth Form, my maths instructor wrote on a homework that I’d used the symbols for 'equals' in addition to 'therefore' interchangeably. I’d seen her work a double arrow symbol on the board in addition to misunderstood its meaning. I was utterly confused (and embarrassed!) because I’d been doing it wrong for over a twelvemonth in addition to she’d never mentioned it before!

I also think nosotros could create a lot to a greater extent than to encourage clearer mathematical handwriting (both numbers in addition to algebra). We all take away maintain our ain styles though. I’m guilty of writing diagonal lines inward fractions on the board fifty-fifty though I know I shouldn’t.

A instance study
It’s worth reading this good practise written report from Ofsted: “In many schools, students’ long-term progress inward mathematics is slowed past times inconsistent teaching. At Archbishop Temple School, really effective leadership of a potent squad of teachers ensures that students sense teaching that is consistently practiced or better. Students inward all groups create goodness because dissimilar teachers work mutual approaches in addition to teaching styles”. There are lots of practiced ideas inward this instance study, such as the formal sharing of resources betwixt teachers in addition to ‘book swapping’ – non inward the critical ‘how much marker create yous do?’ form of way, but alongside a stance to encouraging consistent practice.

I think that novel products in addition to technologies similar Complete Mathematics past times La Salle Education volition create a lot to back upward teachers, improve consistency in addition to heighten teaching standards. The flipped classroom approach, which has been gaining popularity recently, may also take away maintain an touching on on consistency.

I’d live interested to take away heed your views on whether nosotros postulate to improve consistency inward maths teaching in addition to how nosotros could become almost doing so.

Image: mentalfloss.com

5 Maths Gems #3

Well it's been an emotional twain of weeks. Influenza A virus subtype H5N1 plane in addition to GCSE results kept many of us upwards at black in addition to nosotros experienced the green feelings of joy, pride, relief in addition to sometimes disappointment. But nevertheless nosotros perish along to gear upwards for the novel schoolhouse twelvemonth in addition to intend nearly what we'll produce differently.

The hardest matter nearly writing these weekly posts is deciding which ideas to feature. I take away keep an increasingly long listing of unused fabric because fifty-fifty when Twitter's teachers are preoccupied alongside results, the incredible inventiveness in addition to spirit of collaboration remains. In this postal service I'll showcase only v of the real many ideas shared on Twitter this week.

1. Homework
Kathryn Forster (@DIRT_expert) shared a novel laid of homeworks that she has designed. Each homework consists of v sections: literacy, research, memory, skills in addition to stretch. These homeworks would live on followed upwards past times starter activities such equally spelling or retentiveness tests in addition to discussions nearly enquiry findings. Kathryn has real helpfully shared iv of her homeworks for us to borrow:

• Negative numbers  
• Rounding
• Fractions, Decimals in addition to Percentages
• Wordy arithmetic

These are actually goodness ideas.

If you're thinking nearly trying out around unlike approaches to homework I recommend reading Cav's (Homework in addition to Retention and Take Away Homework.

2. Influenza A virus subtype H5N1 Scavenger Hunt

Speaking of homework, the Mailbox (@TheMailbox) shared a 'scavenger hunt' which could live on adapted equally starting fourth dimension homework for Year seven or 8.  Alternatively yous could pick out a pile of newspapers in addition to magazines into i of your starting fourth dimension Year seven lessons so your pupils tin create a poster inward shape using this idea.

Wouldn't this live on dandy for the starting fourth dimension calendar week of schoolhouse & slow to revise for whatsoever degree level? http://t.co/lpCN5KrS88 pic.twitter.com/i9wghJFQtk
— The Mailbox (@TheMailbox) August 22, 2014

3. Oh for a room to telephone telephone my own...

There's nevertheless a lot of classroom display ideas going circular Twitter. One of my most retweeted retweets this calendar week was this 'Change your words' display:

@mathequalslove what produce yous think? Thanks for the inspiration in addition to the files! You. Are. Awesome! pic.twitter.com/vEeTQ2fCdl
— casey mccormick (@cmmteach) August 19, 2014

It's of import to communicate these messages in addition to a display similar this is a goodness agency of doing so. The see originally came from Sarah Hagan's (@mathequalslove) post '2014-2015 Classroom Pics - My Most Colorful Room Yet!'. Sarah may good live on i of the most enthusiastic maths teachers inward the world! Her weblog is real popular, in addition to rightly so. Check out this lectern inward her room - yes, a lectern! Is this measure inward American classrooms? I must acquire one!

I saw lots of prissy display ideas inward Sarah's Homework in addition to Retention and Take Away Homework.

2. Influenza A virus subtype H5N1 Scavenger Hunt

Speaking of homework, the Mailbox (@TheMailbox) shared a 'scavenger hunt' which could live on adapted equally starting fourth dimension homework for Year seven or 8.  Alternatively yous could pick out a pile of newspapers in addition to magazines into i of your starting fourth dimension Year seven lessons so your pupils tin create a poster inward shape using this idea.

Wouldn't this live on dandy for the starting fourth dimension calendar week of schoolhouse & slow to revise for whatsoever degree level? http://t.co/lpCN5KrS88 pic.twitter.com/i9wghJFQtk
— The Mailbox (@TheMailbox) August 22, 2014

3. Oh for a room to telephone telephone my own...

There's nevertheless a lot of classroom display ideas going circular Twitter. One of my most retweeted retweets this calendar week was this 'Change your words' display:

@mathequalslove what produce yous think? Thanks for the inspiration in addition to the files! You. Are. Awesome! pic.twitter.com/vEeTQ2fCdl
— casey mccormick (@cmmteach) August 19, 2014

It's of import to communicate these messages in addition to a display similar this is a goodness agency of doing so. The see originally came from Sarah Hagan's (@mathequalslove) post 'post - similar the reckoner posters below - in addition to it made me long for my ain classroom. Whilst inward the baby-making phase of my life I'm having a brief piece equally a part-timer. It's a mixed blessing. One disadvantage is that I don't take away keep my ain classroom so I learn inward rooms all over the school. Between lessons I take away keep to squash downwards crowded corridors alongside my huge pocketbook of books in addition to equipment (this was a nightmare when I was heavily pregnant!). There are lots of other disadvantages to beingness part-time such equally missing of import information from unminuted meetings in addition to a total lack of career progression opportunities. Of class this is all outweighed past times the massive wages of getting to pass fourth dimension alongside my children, so I'm non complaining... (much).

Another display see I've seen this calendar week is this classroom rules poster, shared by @TeachThought inward this post. I intend pupils would appreciate these real clear in addition to reasonable messages.

On the land of written report of conduct management, I enjoyed David Didau's (@learningspy) post on schoolhouse routines.

If yous desire to brand your ain classroom posters so recitethis.com is dandy for creating pretty quotes in addition to notices - cheers to @mathminds for sharing the link.

And if you're looking to render your classroom, Stephen Harris (@Stephen_H) shared a twain of awesome write-on tabular array designs: these ones are dandy for collaboration and tangram tables are perfect for a maths classroom.

And in conclusion on display ideas, Mr Allan (@mrallanmaths) shared his RAG123 display, Chris Smith (@aap03102) shared a motion-picture present of his 'Mathematician of the month' board, in addition to Mr Taylor (@taylorda01) adapted Spiked Math's Mathagasm comic so it's suitable for display. I'm going to steal all 3 ideas - if I always acquire my ain classroom.

4. Teaching ideas from #mathschat
Weekly maths chats accept identify on Twitter every Midweek at 8pm, organised by @BetterMaths. This calendar week nosotros discussed our favourite topics, tasks, resources in addition to investigations, so the goodness ideas were coming thick in addition to fast! I've got a long listing to form through.

There were lots of ideas nearly getting out of the classroom. Jon Treby (@JonTrebyAAN) suggested instruction loci exterior using buildings in addition to string. He too puts record on the flooring of the schoolhouse hall when he teaches angles inward parallel lines. Dawn (@mrsdenyer) has a schoolhouse treasure hunt for 3D trigonometry in addition to Martin Noon (@letsgetmathing) suggests using a clinometer to mensurate the summit of schoolhouse buildings in addition to trees.

There was too a lot of verbalize nearly popcorn! Dawn (@mrsdenyer) gets her students to blueprint a popcorn cone - an activity that involves sectors in addition to arcs, Pythagoras in addition to volume. If students tin function out the volume of their cone, they tin create total it alongside popcorn! Miss Ren (@ReynoldsBSGD) shared Dan Meyer's popcorn picker chore - 'all yous demand is A4 paper. I only stand upwards dorsum in addition to spotter the kids acquire stuck in!'.

5. Mistakes in addition to feedback
I've written a lot nearly learning from mistakes lately so this tweet was real relevant:

@Maths4ukplc @ccampbel14 Pupils copy/stick their error inward the box in addition to so right it. pic.twitter.com/C8TSaVApDo
— Helen Hindle (@HelenHindle1) July 30, 2014

And here's a dandy see for marker from @ChrisHildrew.

So at that spot yous become - a pocket-sized option of ideas from a calendar week on Twitter. I promise that's helpful. If yous missed the previous ii Maths Gems posts, yous tin honor them here. I'll locomote out yous alongside a prissy inquiry for your students from Big Ideas Math.

Starters Together With Inequalities

I lately participated inwards a Twitter chat well-nigh lesson starters. Initially a forum for sharing ideas, it turned into a ground well-nigh whether starters are necessary inwards maths lessons. In my persuasion in that place is no correct or incorrect lesson construction - every instructor does what plant best for them together with their students. For me together with my students, starters travel well. I exercise them inwards the vast bulk of my lessons.

What is a starter?
Presumably inwards a lesson without a starter, students acquire inwards the classroom, sit down downwards together with at in i trial take away heed to an exposition. In a lesson alongside a starter, students produce unopen to maths at in i trial on arrival, before the principal pedagogy chemical factor begins. Lesson starters (or 'bell work') accept many forms. Every instructor has a unlike approach.

Purpose

My starters receive got i of iii purposes:

(a) recap together with practice of what students learnt inwards the previous lesson.
(b) prerequisite skills check to assess a starting point.
(c) a hook to engage together with intrigue.

Starters also assist to awaken my students' brains - they acquire into a mathematical means of thinking before I firstly pedagogy them something new. 

Logistics
When students brand it I greet them at the door alongside their starter, usually a printed question. They're used to this format hence they sit down downwards together with firstly immediately. They produce the starter independently spell their peers brand it together with I laid up.

My starters are usually real brusk - no to a greater extent than than five minutes - because this minimises the variation inwards how long students accept to consummate them. H5N1 starter that takes anywhere betwixt 10 together with twenty minutes to consummate could travel problematic (early finishers are left waiting) but inwards a starter that takes 3 - five minutes this is less of an issue. The early on finishers stick their completed starter inwards their books together with yesteryear the fourth dimension they've done that, the residual are ready hence nosotros together with hence review it equally a class. There's rarely a indicate at which students are non occupied.

Sometimes starters atomic number 82 to interesting questions. Sometimes they effect inwards me changing my lesson innovation on the spot. This is a challenge for me, but I'm getting amend at thinking on my feet equally I acquire to a greater extent than experienced.

Typical Examples
I'll laissez passer you lot an thought of what my typical starters seem like. Bear inwards mind, equally I said earlier, every instructor does this differently. I've picked a theme at random: inwards iii lessons on inequalities alongside Year 10 final year, these were my iii starters.

In lesson 1 we're solving linear inequalities together with representing solutions on number lines. They've done this before hence I firstly alongside a skills cheque to brand certain they scream back the basics:

Inequalities starter - lesson 1

In lesson 2 we're going to firstly looking at graphical inequalities - for this they request to know how to plot direct lines hence I laissez passer them unopen to other skills cheque starter to run into if I request to become through this:

Inequalities starter - lesson 2

In lesson 3 we're looking at unopen to harder graphical inequalities hence I desire to remind them of what they did inwards the previous lesson together with laissez passer them a gustatory modality of the kind of inquiry they volition travel seeing today:

Inequalities starter - lesson 3

The 'list the integer coordinates' business office of this inquiry is novel to them hence requires unopen to thinking. I seem it to generate questions which link smoothly into my exposition. I similar my students to intend that the direction of the lesson is prompted yesteryear the questions that arise during the starter, when inwards reality I've usually pre-empted their questions together with planned accordingly.

So you lot tin run into that my starters are naught special but to me they are an essential business office of the lesson.

Exam Questions

Sometimes, peculiarly at H5N1 level, I exercise the starter equally an chance to produce an examination manner question. For event if I instruct a Year 12 lesson on finding the equation of a circle using these excellent activities from Mathematics Assessment Project, together with hence the side yesteryear side lesson I would laissez passer students an equation of a circle yesteryear examination inquiry on arrival. This gets them used to the format together with wording of examination questions together with recaps what they learnt inwards the previous lesson. H5N1 unmarried iv or five grade examination inquiry is the perfect length for an H5N1 grade starter.

With GCSE classes, I sometimes laissez passer a QWC examination inquiry (a 'star' question) equally a starter.

More Inequalities Starters
So at nowadays I've described my typical starters, let's seem unopen to option activities. I've featured iii starters here, in i trial again focusing on inequalities.

Most maths teachers are familiar alongside Transum's 'starter of the day'. What I similar well-nigh the Transum website is that starters are also listed by topic. Here's an event of an inequalities starter.

'Less than' yesteryear Transum

Short card sorts tin travel good equally starters. This number draw of piece of occupation card matching activity is suitable for an inequalities lesson.

There's also a nifty card gibe (and other first-class activities) inwards Evaluating Statements well-nigh Number Operations from Mathematics Assessment Project. Some of these mightiness travel likewise long for a starter but would travel suitable for a principal lesson activity.

When is the arguing true? - Mathematics Assessment Project

If you're looking for to a greater extent than principal lesson activities on inequalities together with hence these 2 resources are superb: Introduction to inequalities by Project Maths (activities towards the dorsum of the pdf) and Defining Regions Using Inequalities by Mathematics Assessment Project. There are lots to a greater extent than resources inwards my algebra resources library.

Project Maths

Sources of Starters
These ideas are merely the tip of the iceberg. There are loads to a greater extent than sources of starters - a classic is 30 Maths Starters from Subtangent. MathsPad has unopen to nifty interactives similar this Simplifying Magic Square. FlashMaths has skillful interactives too. I could become on but there's no indicate reinventing the wheel. Colleen Young has an amazing website 'Mathematics Starters together with Plenaries' which I highly recommend.

5 Maths Gems #6

introducing calculus, a post nearly starters as well as teaching inequalities as well as a calendar of maths teaching conferences. I've also added novel bits as well as pieces to my resource libraries as well as homeworks page. I've notwithstanding works life fourth dimension for Twitter - here's this week's highlights.

1. Geogebra

For those of us who are equally good busy or non techy plenty to make clever things amongst Geogebra, at that topographic point are really helpful people who make it for us. I've mentioned Mathimation before. Here’s a few to a greater extent than interactive teaching tools that receive got been shared on Twitter recently:

• Custom Cuboid by @the_chalkface allows you lot to highlight specific cuboid faces - this is a helpful tool when teaching the surface expanse as well as book of cuboids. 
• @TheMathsTeach gives us interactive circle theorems for students to explore. Each Geogebra worksheet has uncomplicated instructions as well as questions - students tape their findings on the Student Conjecture Sheet.
• Parts of a Circle by @Mr_Mathematics is great for exploring circle vocabulary.

2. Two Superb Resources

I come across a hell of a lot of skilful maths resources inward my resource-addled life, but every straightaway as well as thus I come across ane that is absolutely superb. This calendar week was groovy because I discovered 2 such resources.

Ben Tanner (A level, my students works life them really useful for testing each other both inward shape as well as at home.

Extract from GCSE revision cards - tannermaths.co.uk

Chris Smith (@aap03102) produces a bright weekly newsletter total of fantastic maths teaching ideas - if you lot don't already subscribe thus email him straightaway to larn on the mailing list. This calendar week he tweeted nearly his relay races because they passed 100,000 downloads on TES. I can't believe that I, the resourceaholic, receive got never seen these before.

I've used revision relays amongst my classes earlier as well as they've e'er worked really well, thus I'll definitely live using these disclose puzzle races. There are 10 relays hither including ane for Halloween, ane for Christmas as well as ane for Easter. That's halt of term sorted then.

Extract from Halloween Relay Race - Chris Smith on TES

The 100,000 downloads got me thinking nearly how many maths teachers at that topographic point are inward the UK. First I started thinking nearly how many schools at that topographic point are as well as how many maths teachers per school, but thus I thought it powerfulness live easier to starting fourth dimension from how many teenagers at that topographic point are inward the UK. This reminded me of a labor interview I ane time had. Now here's a story for your students if they ever inquire when they'll demand maths.

During my concluding twelvemonth at academy I had an interview for a graduate labor equally a administration consultant at PwC. I'd already done a summertime internship at KPMG thus was feeling fairly confident. The alternative 24-hour interval started amongst a maths seek much similar this one. After the seek I had luncheon inward a conference room amongst the other candidates. An administrator came inward after luncheon to denote who had failed the maths seek (the unsuccessful candidates had to move out at that signal - an awkward instant for all). I survived the cutting as well as proceeded to a bizarre labor interview.

The interviewer asked me how many planes were inward the heaven at that moment. He wanted an actual number, non but a method. Once I'd had a become (starting point: how many airports inward the world) he thus asked me to reply ane time to a greater extent than using a dissimilar method, thus I did (starting point: world's population). He thus asked for some other method. We went through the same procedure for 'how many babies were born inward the United Kingdom of Great Britain as well as Northern Ireland yesterday?'. I intend I did a reasonably skilful labor of answering these questions - us mathematicians are skilful at lateral thinking. The concluding query inward the interview was nearly how I would stair out the peak of a edifice using but a barometer. I gave a few sensible answers but he kept asking for more. He stopped when I gave an utterly ridiculous reply which I won't acknowledge to hither (if you're coming the conference inward 2 weeks, inquire me then). Moral of the story - maths as well as work solving skills larn you lot far. You never know what you'll live asked inward a labor interview. And don't live the mortal sent abode at lunch.

3. Two Superb Websites
@dazmck shared the website 'That Quiz' which allows you lot to laid gratis online tests as well as homeworks inward a broad hit of topics from Key Stage iii to H5N1 level. It alone takes a infinitesimal to brand a seek as well as e-mail the URL to your students. They larn instant feedback on their answers (either throughout the quiz or at the end). They also larn an chance to right their mistakes. There are a disclose of settings but it's ridiculously slowly to use.

thatquiz.org menu

If you lot register (which takes roughly 5 seconds) you lot tin also collect your students' scores online. Here's an instance of a box plot seek question:

Example query from thatquiz.org

This website is thus incredibly helpful as well as slowly to use, it reminds me of some other groovy website - Form Time Ideas. This is past times far the best tutor fourth dimension resources I've seen. It's beautifully designed as well as slowly to use. The content is spot on as well as it changes every day. Websites that salve fourth dimension are a god-send for busy teachers.

formtimeideas.com

4. Words to Avoid
Twitter had me inward stitches this week. @taylorda1 tweeted nearly something he'd said inward a lesson that his students had works life amusing. Most teachers receive got made slips similar this - they tin stimulate a lot of disruption!

The conversation that followed this tweet was really funny. For the sake of novel or trainee teachers, here's a listing of things to avoid maxim inward maths lessons:

• In probability, don't toss a money as well as larn a head. In a room total of teenagers, far improve to flip a money as well as larn a tail.
• Avoid examples involving 'balls inward a bag'. 'Discs inward a bag' tin live but equally problematic if non said clearly. Try counters instead.
• Also inward probability, live careful how you lot nation 'the or rule'.
• When writing on the board make non shorten the discussion cumulative. Cum freq is probable to stimulate a stir.
• Don't brand c proportional to k (c∝k).
• Careful what you lot nation (and how you lot gesture) when talking nearly enlargements, top heavy fractions as well as going downward the disclose line.
• Be prepared for giggles if an reply is 69.
• Avoid having refer to 'the d' or maxim 4q ('4q too!').
• We can't avoid f(x) but live prepared for 'f off' silliness. Avoid f(u).
• When writing page numbers on the board, beware of p155.
• Don't nation cos. Say cosine. Cos Omac is an insult as well as surely non suitable for a maths lesson if whatsoever of your students speak Arabic!

Thanks to all the tweeters who contributed to this list.

It works both ways. I had to stifle my young giggles when I attended a Year 13's utter on the dangers of fracking.

There's to a greater extent than 'dirty mathematics' here.

5. Calligrams
@edsouthall tweeted some of these Minimal Math Concepts.

I honey these as well as was really pleased to uncovering that you lot tin purchase them equally a sheet or framed impress - some other affair for my christmas list! I've added this to my mathsy gifts page.

@tessmaths shared her lovely thought for a shape activity on Maths Calligrams. A calligram is a phrase or discussion inward which the text is arranged inward a agency that creates a visual image. The paradigm created past times the words expresses visually what the discussion says. This could live incorporated into a chief or secondary maths lesson - give students a listing of maths vocabulary as well as inquire them to create pictures to assist agreement as well as recall.

Maths Calligram by @JonTrebyAAN

I promise you've works life some of these ideas helpful. I'm taking requests for time to come resources posts thus if there's a detail theme you'd similar me to feature, delight email or tweet me.