Area In Addition To Volume

Every maths region should ain a giant lawn tennis ball! Walk into the classroom alongside a large fluorescent ball nether your arm in addition to you've at in i lawsuit got the attending of the class.

Students stand upwards inwards a circle in addition to are told they're entirely allowed to speak if they're belongings the ball. Ask "how could nosotros function out the surface surface area of this ball?" in addition to throw it to a random student. Students throw the ball around the circle equally they portion their thoughts in addition to propose ideas. At some signal a instructor prompt may last necessary, along the lines of, "why did I select a lawn tennis ball? Why non a football game or netball or golf game ball?". In my sense this prompt may atomic number 82 some students to 'eureka' moments equally they starting fourth dimension thinking almost the markings on the surface of the lawn tennis ball. Eventually mortal volition topographic point that the surface is made upwards of iv circles wrapped around each other, in addition to they tin so deduce that the formula for the surface surface area is 4πr². If they demand convincing, demonstrate them this slide.

This is a rattling engaging activity. As pupils can't speak unless they're belongings the ball, you'll run across them wildly waving their arms about, silently begging their friends to exceed them the ball so they tin portion their ideas!

Try it - I'd dear to listen how it goes.

Area in addition to majority is a broad ranging topic, from areas of triangles inwards Year seven to volumes of hemispheres in addition to frustums inwards Year 11. Here's a handful of my favourite resources:

• I manus out these rhymes for the surface area in addition to circumference of a circle in Year 7, tell them to alternative their favourite or come upwards up alongside their own. Love this silly song too.
• Also for Year 7, these matching cards from the Nuffield Foundation involve calculating the surface area in addition to perimeter of chemical compound shapes.
• As always, enough of dandy activities on teachitmaths.com. 
• At GCSE I purpose this problem solving challenge with questions from Median Don Steward. Pupils function on A3 newspaper inwards pairs. They demand their brains switched on for this one. There's loads of vivid activities on Don Steward's blog that could last used inwards a similar way.
• The Chalk Face has some lovely activities, including: cornflakes problem; Penny Farthing; fuel tank; golden balls and baby surface area. 
• There's a nice activity on finding the majority of dissimilar shaped glasses from Shell Centre. 
• Illustrativemathematics.org has fantastic geometry activities. I dear the rich chore Eight Circles which relates to finding the surface area of a circle.
• The Chalk Face also brings us this dandy harder surface surface area questions from Don Steward.
• Maths Sandpit has a fantastic resources for investigating the surface surface area of a cone.
• Challenging volume in addition to surface area revision questions for Year 11. Some of these are quite tricky in addition to demonstrate that this topic isn't but almost substituting into formulae.

For related degree intelligence - why produce nosotros nation hemisphere but semicircle? Why non semisphere or hemicircle? I believe it's because the intelligence circle is from the Latin intelligence circus (meaning ring), thus nosotros purpose the Latin prefix semi, whereas sphere is from the Greek intelligence sphaira (ball), thus nosotros purpose the Greek prefix hemi. This article almost semi/hemi/demi gives to a greater extent than examples. If y'all similar this so y'all powerfulness also similar these lovely maths vocabulary activities.

Finally, here's i for the teachers. It's non equally obvious equally it seems!

(answer)

Maths Vocabulary

I found Cav's blog shipping 'Vocabulary together with maths are non mutually exclusive' actually interesting together with it got me thinking nearly activities together with didactics techniques related to maths vocabulary.

Influenza A virus subtype H5N1 didactics tool that tin move endure used regularly throughout the twelvemonth is a source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward vocabulary noesis survey. When you lot outset didactics a topic, do a listing of the novel words that volition endure used together with inquire students to consummate a nautical chart showing their agreement of those words.  Repeat the activeness afterward to run across the improvement inward agreement - I've non tried this myself however but I intend it would generate merely about useful questions equally good equally boosting pupil confidence.

In my shipping on source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Area together with Volume I suggested these maths vocabulary exercises which brand for prissy 'end of term' lessons.  Here's an trial of an activeness from this pack:

Here's merely about to a greater extent than links that you lot mightiness honor useful:

• The Maths Magpie has created these great Maths Vocabulary Activities
• A listing of telephone commutation words for Key Stage 3
• Another vocabulary activity - perchance an choice to the noesis survey described above
• Exercises amongst a Mathematics Dictionary 
• Background reading 'Building Mathematical Vocabulary' past times Dr Madeline Kovarik

I was latterly talking to a highly intelligent together with articulate Year xiii pupil who said that she hated it when her instructor asked her to 'speak maths'. I asked her to elaborate. She said that when questioning the class, the instructor expected answers that used appropriate maths vocabulary - together with fifty-fifty this pupil (who'll endure off to Oxbridge inward September) flora this daunting.  We demand to address this trial from a immature age.  One tip is to ever require pupils to reply questions inward total sentences instead of merely numbers or words - from mind schoolhouse onwards. Influenza A virus subtype H5N1 rattling unproblematic trial - inward response to the enquiry 'what do nosotros telephone outcry upwardly a polygon amongst 8 sides?', don't bring the reply 'octagon' - inquire for a total judgement such equally 'An 8-sided polygon is called an octagon' to larn pupils used to 'speaking maths' from an early on historic menses (source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Gems 43. I also flora the source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward activity below worked good amongst my Year 7s.

Here's my direct to literacy inward maths lessons:

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.

Resources, Resources, Resources...

Inequalities activeness - Project Maths

I've been working actually difficult on my resources libraries lately, hence I'm pleased to nation I'm lastly cook to part them! They tin live accessed through the tabs at the exceed of the page.

This is where I've set all my resources recommendations for you lot to browse when you're planning lessons. The A' degree pages volition in all probability live the most helpful every bit it tin live difficult to detect practiced resources for Key Stage 5. 

My recommendations are yesteryear no agency exhaustive - there's loads of practiced resources I haven't discovered withal (the cyberspace is also big, I can't hap upwards alongside it!). But I volition update my listings whenever I come upwards across something specially good. To clarify what I hateful yesteryear 'good' - my recommendations include well-designed activities, rich tasks and worksheets for topics where I yell back it tin live difficult to detect suitable do questions. 

My Top three Websites

The resources I've recommended are all gratis in addition to come upwards from a broad make of sources.  Here's my electrical flow favourite websites, inward no detail order.

1. Roof Truss task (trigonometry) and Bee Aware (scatter graphs) - at that topographic point are hundreds to a greater extent than in addition to they're all awesome.  
2. MathsPad has enough of first-class gratis resources. Subscription (£3 per month) gives access to their total range. I dear the way their resources are designed, including their interactive activities which are all rattling engaging in addition to slowly to use. Example resources include this lovely Square in addition to Cube Numbers Puzzle, and for older pupils I actually like Is it Rational?. 
3. Teachit Maths has large, well-organised resources libraries.  Free registration gives access to resources inward pdf form, which is fine for all their printable activities in addition to worksheets. You'll demand a subscription (£25 per year) if you lot also desire to access PowerPoints, interactive activities, didactics tools etc. Worksheets are well-designed, engaging in addition to include solutions. Examples of their resources include this Mental Powers Code Breaker in addition to this Transforming Graphs carte form activity, which I accept used successfully alongside both my Year 11s in addition to Year 12s.

Special advert to The Chalk Face and Mathematics Assessment Project - both of these websites are total of first-class ideas. I also larn a lot of resources from TES. One of my favourite TES contributors is SRWhitehouse who creates first-class Influenza A virus subtype H5N1 degree activities. For a total (and ever-expanding) listing of recommended resources websites, come across my links page.

Factor Trees - Median Don Steward

My Blog
Now I've finished creating my resources libraries, I tin larn dorsum to focussing on my blog. Here's approximately of the highlights hence far...

• My Area in addition to Volume postal service - featuring a giant lawn tennis ball - was rattling popular.
• My suggestions for terminate of term lessons on Binary in addition to Fermat also went downward well.
• Have you lot tried this method for finding inward HCFs in addition to LCMs?  It's hence much quicker than the Venn method.
• Have you lot read the majority post most it.
• I set a lot of sentiment into my postal service All About Gradient. I'm certain that pupils would savour the lesson ideas I've suggested for investigating steepness - accept you lot watched the video of the cyclist attempting a 38% gradient? My legs wound simply thinking most it!
• I've written a publish of posts focussing on specific topics or concepts such every bit dividing yesteryear zero, angle facts, skewness in addition to simultaneous equations.  I've also discussed didactics tools such every bit Desmos, comic strips, blogs in addition to methods for developing vocabulary. 
• It was my uncovering of a novel matrix multiplication method that brought me to blogging - if you lot instruct matrices hence create depository fiscal establishment tally it out.
• Finally, something fun for the teachers - evidence the Maths Movie Quiz.

For a total listing of my weblog posts come across the blog archive.  Not bad going for three months!

'Find the Coordinates' chore yesteryear Susan Wall

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

Teaching Box As Well As Whisker Plots

Image: ruthmaas.com

When I wrote Long Live Stem together with Leaf, I'd been challenged to uncovering a practical application of stalk together with foliage diagrams exterior the maths classroom. After extensive googling - together with helpful input from twitter - the alone examples I could uncovering were motorbus together with prepare timetables. But I argued that existent life application isn't the last all together with destination all.

Stem together with foliage diagrams were invented inwards the 1970s past times Consistent Mathematics if you lot desire to know why). This is a lovely activeness inwards a lesson introducing the thought of median, precisely non hence effective inwards a box plot lesson. Because fifty-fifty though you lot tin purpose a bedsheet together with string to larn the students to hold off similar a box plot, if they’re non appropriately spaced out (ie if there’s no scale) hence it’s non a box plot. If you lot desire a proper box plot you’ll accept to truly mensurate the heights together with depict a scale on the floor.

An choice thought (inspired past times this post) involves newspaper aeroplanes. You’ll necessitate a large infinite for this - the schoolhouse hall or playground. Tape (or depict inwards chalk) a long scale on the floor. Have each of your pupils brand a newspaper aeroplane, write their elevate on it, together with throw it from the outset of the scale. Leave the aeroplanes where they land. Once all pupils accept thrown their aeroplane, you lot tin depict or record a box plot on the flooring or hence the planes to stand upwardly for the distance flown. Pupils volition last able to run into which quartile their plane landed in. Hopefully ane futurity engineer volition throw an amazing outlier which volition brand a skilful give-and-take point! You could fifty-fifty separate the flat inwards one-half together with do ii box plots on the flooring side past times side, hence the flat could hash out which squad had meliorate aeroplanes together with which team’s planes were to a greater extent than consistent.

If you lot similar practical activities, here’s ii more:

• This uncomplicated newspaper folding activeness is a overnice introduction to median together with quartiles.

Source: bigideasmath.com

• This Cheerios activity explores mean, median, manner together with box plots.

Resources
There’s surprisingly few skilful box plot resources online. But Don Steward never lets us down. His website has a discover of box plot activities - my favourite is this truthful or imitation activity.

I also similar the activeness below from bigideasmath.com:

If you’re looking to generate box plots on your interactive whiteboard for flat discussion, this online tool is overnice – it has pre-populated information or you lot tin input your own.

I've listed some to a greater extent than skilful box plot resources below. I’ve constitute that many resources enquire questions almost skewness, which nosotros don’t encompass until S1 (but mayhap nosotros should encompass earlier). Treatment of outliers is also non covered at GCSE precisely makes for a overnice discussion.

• Standards unit of measurement activities S5 together with S6, which tin last constitute on Mr Barton’s website. 
• Illustrative Mathematics has loads of first-class statistics questions, similar Haircut Costs together with Speed Trap.
• Interpreting Box Plots Treasure Hunt from numberloving.co.uk.
• Representing Data Using Box Plots from Mathematics Assessment Project (activities at the back)
• Lots of exercises from CIMT inwards this chapter – I specially similar the comparing questions on the final few pages 
• Using NBA Statistics for Box together with Whisker Plots from NCTM 
• The variability exercise (starting on page 8) inwards this lesson plan could last helpful when didactics the concept of spread. 
• My Describing Box Plots activeness on TES helps pupils do reading together with drawing box plots together with emphasises the purpose of the right vocabulary.
• My Party Box Plots activeness on TES helps pupils empathize the concept of spread.

If you lot desire to demo your flat some ‘real world’ box plots hence these box plots showing the ages of World Cup players could prompt some skilful discussions almost comparisons. Read @loumeracy’s blog post for to a greater extent than on this.

If you lot desire to ‘wow’ your flat amongst an instance of how box plots tin last used to compare huge amounts of information inwards a modest space, demo them this example which shows the historic menstruation distribution of Olympics athletes (more of this here).

Final thoughts
In French the box plot is called boîte à moustaches (box amongst a moustache). The author of this article attempts to create a box together with beard plot!

There are many variations to the box together with whisker plot, such equally the edible bean plot together with violin plot. Look these upwardly on google images for lots of examples.

I read an interesting thought here that I’d never thought of before: “One agency to assistance you lot translate box plots is to imagine that the agency a information ready looks equally a histogram is something similar a mount viewed from Earth flat together with a box together with whisker diagram is something similar a contour map of that mount equally viewed from above”.

Well, at that topographic point you lot are – a 'box plot weblog post'. Try maxim that 5 times out loud. I've invented a novel natural language twister.

Pythagoras' Theorem

Pythagoras' Theorem is ane of my favourite topics to teach. In my experience, students quite similar it too. At outset they may hold out intimidated past times the novel as well as seemingly complex mathematics. It's in all probability the outset fourth dimension they've seen words such equally theorem, proof as well as hypotenuse thus no wonder they're apprehensive. But they'll rapidly larn the hang of it.

When H5N1 score students receive got to discovery the distance betwixt 2 points or verify that a triangle is right-angled, their outset thought should hold out Pythagoras. By Year 12, Pythagoras' Theorem should hold out a staple inwards their mathematical toolkit, along alongside other skills such equally arithmetic, fractions, simplifying algebra, using index laws as well as factorising quadratics. In my sentiment these things are the breadstuff as well as butter of secondary schoolhouse higher mathematics.

I'm going to affect briefly on proofs at the terminate of this postal service but my master copy focus is on interesting Pythagoras questions as well as resources for Key Stage 3 as well as 4. Before nosotros start, I should number my commons caveat - there's absolutely loads of fantabulous Pythagoras resources online as well as hither I'm exactly showcasing a small-scale selection.

Interesting Questions
It's non ever necessary to strength a inquiry into a 'real world' context to larn inwards engaging. Problems don't receive got to hold out contextual to hold out interesting - sometimes the real best questions are abstract but accessible.

In this example from illustrativemathematics.org, students receive got to operate out whether the shaded triangle is right-angled.

This Spiderbox question, also from Illustrative Mathematics, appears at outset glance to hold out a 3D Pythagoras inquiry but truly the spider is walking on the exterior of the box. Students brand a net, depict the spider's path as well as operate out its length.

amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this two diagonals' as well as exactly about other called 'amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this kite areas'.

Helpful Worksheets

horacek.com.au

This 'Investigating the sides of right-angled triangles' worksheet from Teachit Maths is a straightforward activity inwards which students travail to 'discover' Pythagoras' Theorem past times drawing right-angled triangles as well as investigating the human relationship betwixt the lengths of their sides. Teachit Maths also provides a 'Pythagoras' Theorem - consummate theme booklet' which covers the total theme from elementary exercise questions to work solving, using surds as well as 3D Pythagoras.

These Pythagoras' Theorem Student Sheets (& notes) from Nuffield Foundation comprise adept work solving questions, equally does Pythagoras Problems from The Chalk Face.

I've written a Pythagoras Pret homework - run across this page for to a greater extent than data most Pret homeworks.

Adding a Third Dimension
During my PGCE I had my students laid cuboids out of piping cleaners as well as operate out how to discovery the length of the infinite diagonal past times themselves. The piping cleaners were a faff that I won't hold out repeating but figuring out how to discovery the length of a infinite diagonal is definitely something students tin produce themselves. Perhaps the easiest prop to role is your classroom. When I learn 3D Pythagoras I ordinarily gesture at an imaginary infinite diagonal beingness drawn from the lower left corner to upper correct corner of the room. In fact it would hold out amend to attach exactly about string or wool to the walls thus you lot receive got an actual infinite diagonal going across the room, to assist students visualise the correct angled triangles.

There's 2 approaches to pedagogy 3D Pythagoras. One is to receive got the pupils derive the formula for the infinite diagonal (eg d² =  x² + y² + z²) as well as and thus memorise it. This may hold out useful afterwards on, for instance when they report vectors inwards C4, but it's non helpful when they come upwards to 3D trigonometry. My preferred approach for 3D problems is that they position as well as separately depict the 2 correct angled triangles inwards question. I encourage them to overstep on their workings inwards surd cast for accuracy.

Good 3D questions are available inwards these Trigonometry Worksheets (see exercise T7) past times Frank Tapson (from the Cleave Books website).

Also, here's a prissy 3D Pythagoras activity 'amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this Cuboid Diagonal' from Don Steward.

Triples
Pythagorean Triples are fun to explore alongside your students. Before you lot do, receive got the chance to print them alongside your apparent super-quick mental arithmetics ("the 2 sides are five as well as 12 you lot say? Well the hypotenuse must hold out 13").

Activity 3.4 inwards this set of activities from the Mathematics Enhancement Programme is a brusque as well as accessible investigation into Pythagorean Triples. The Mathematics Assessment Programme also has a Pythagorean Triples activity and Don Steward has students looking for patterns. There are many to a greater extent than substantial investigations available online.

Vocabulary

amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this here.

Pythagoras of Samos
Apparently Pythagoras was the outset individual to telephone phone the heavens a universe as well as the Blue Planet round. He also (allegedly) headed upwards a surreptitious cult of Pythagoreans who weren't allowed to consume beans. Pythagoras said that "each number has its ain personality - masculine or feminine, perfect or incomplete, beautiful or ugly". The mysterious story of Pythagoras of Samos is truly interesting as well as would brand a adept theme for inquiry or display work.

Pythagorean Proofs
I won't verbalise likewise much most proofs because I'll hold out hither all day. I must advert this vivid H2O demonstration video though.



If you lot desire your students to attempt exactly about proof activities, this line 'Proofs of the Pythagorean Theorem' from Mathematics Assessment Project is most comparison 3 unlike proofs.

Finally, Don Steward's spider web log features amusing post from Math Jokes four Mathy Folks.

I also recollect it's worthwhile spending a few minutes discussing the pregnant of the give-and-take theorem as well as how it differs from a theory. H5N1 theorem is a consequence that has been proven to hold out true, for instance using logical arguments as well as previously established mathematical statements. Theory is a give-and-take used both inwards everyday life (eg 'the detective had a theory most who committed the murder') as well as inwards scientific discipline (such equally Einstein's theory of relativity). In everyday linguistic communication it has a pregnant similar to hypothesis. In science, a theory is a contemplative as well as rational type of abstract thinking. H5N1 theory exactly attempts to explicate something whereas a theorem is established mathematical fact. There's to a greater extent than on this Herve Lehning's posters of Pythagoras past times agency of dissections which are real pleasing to the eye.

I promise this has been helpful if you're planning Pythagoras lessons. Please comment if you lot receive got whatever ideas to add.

I've similar a shot seat all my theme resources specials here so they are easier to browse.

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.