Matrix Multiplication

When I teach matrix multiplication I respect that pupils tin expire a fighting lost inwards their calculations.  I constitute a fantastic novel method on this blog.

Let's tell nosotros convey matrix A together with matrix B.  We desire to calculate AB.  Write downwards the 2 matrices side-by-side.  Then move matrix Influenza A virus subtype H5N1 down. Now write your answer inwards the infinite at the bottom right.  I intend the adjacent measurement is self-explanatory from the film below, merely read the master copy blog post for a amount explanation.

I beloved this method - it's together with then unproblematic to retrieve together with instantly virtually impossible to expire lost when multiplying matrices.

And - on the dependent area of matrices - this made me chuckle:

Logs

I similar instruction logarithms but my students abide by them genuinely hard. There's a broad multifariousness of C2 assay out questions on logs then pupils genuinely bring to sympathise the topic, they can't but acquire a gear upwards of rules to acquire by. This is a proficient affair of course.

This weblog post from Sarah Hagan has absolutely loads of activities for instruction logs too her subsequent post has roughly follow-up activities.

There's a broad arrive at of instruction ideas inward this Logarithm Functions booklet from Mathematics Vision Project, which starts amongst an ordering activity:

Mathematics Vision Project

STEM Centre render four resources designed to exercise the basics too extend agreement of logarithms, summation roughly opened upwards ended questions for tidings or a mini-whiteboard activity. I've flora the truthful or imitation exercise especially effective for identifying misconceptions inward the past times (longer version amongst answers here).

Susan Wall - via STEM Centre

Here are roughly to a greater extent than of my favourite resources for instruction logs to Year 12:

• Teachitmaths.co.uk has a pick of logs dominoes - I especially similar these. 
• SRWhitehouse on TES ever provides first-class Influenza A virus subtype H5N1 degree resources. She has a great selection of resources for logs.
• Slides - 'An introduction to logarithms' past times Teachit Maths.
• C2 Target Board - Logs too Indices - hannahlees on TES.
• Student activities on introducing logarithms - Project Maths 
• Become Friends amongst Logarithms - notes too exercises past times Scott Surgent.
• RISP 31 - edifice log equations.
• Standards Unit A13 - Simplifying Logarithmic Expressions.

Dividing Past Times Zero

I found this on Pinterest and now purpose it to assistance my pupils recollect the rules regarding segmentation as well as zero.  It seems to work!

I also similar to demo them a airheaded meme similar the i below to help the rule stick inwards their heads.  A search for 'divide past times zero' on Google Images brings upwards loads of these. I practise apologise to my pupils inwards advance for the bad language, which I intend makes it to a greater extent than memorable.

I was rattling pleased when one of my pupils late wrote this inwards a test. It's squeamish to run across that roughly of them pay attention!

Most calculators laissez passer on the message ‘Maths Error’ when a pose out is divided past times zero.  It’s crucial that pupils empathise why. For didactics ideas, I recommend this fantabulous weblog post 'Why can't you lot dissever past times zero?'.

We purpose this agreement when solving equations similar this:  x² - 5x = 0. Influenza A virus subtype H5N1 mutual error is to divide past times x to give-up the ghost x - v = 0. This incorrectly gives solely i solution (x = 5). Knowing that nosotros shouldn't dissever past times x because x could travel null (unless we're told otherwise) allows us to empathise why the right method is to factorise ie x(x-5) = 0, giving the 2 solutions x = 0 as well as x = 5.

To stretch your students, effort this interesting activeness almost the value of 0⁰, Evaluating a Special Exponential Expression from Illustrative Mathematics.

It's interesting that throughout history, many slap-up mathematicians (including Euler) possess got argued that segmentation past times null gives infinity. Most modern mathematicians accept it every bit undefined.  If you lot desire to practise roughly background reading on the ‘history’ of dividing past times zero, I recommend this article - it's an enjoyable read.

Highest Mutual Element Together With Lowest Mutual Multiple

There are many methods for finding the Highest Common Factor as well as Lowest Common Multiple of ii or to a greater extent than numbers.  For years I've been didactics pupils to pose the prime number factors into a Venn Diagram, every bit described here. 

I recently discovered an option method that is impressively quick as well as simple.  It is described inwards this video every bit the 'Indian Method'. It's like to the 'upside downwards birthday cake method' but it's much quicker because at that spot is no requirement to operate primes.

Say nosotros desire to notice the Highest Common Factor as well as Lowest Common Multiple of 24 as well as 36.
Write down the ii numbers, then (to the left, every bit inwards my representative below) write downwards whatsoever mutual component (ie 2, 3, 4, half dozen or 12).  I've chosen 6.  Now separate 24 as well as 36 past times half dozen as well as write the answers underneath (4 as well as half dozen inwards this case).  Keep repeating this procedure until the ii numbers have no mutual factors (ie 2 as well as iii below).  Now, your Highest Common Factor is merely the production of numbers on the left. And for the Lowest Common Multiple, notice the production of the numbers on the left as well as the numbers inwards the bottom row. It's slowly to retrieve which is which - to notice the LCM, await for the L shape.

It's hence quick!  And simple!  Try it.

Don Steward features an option method inwards this weblog post.  He mentions that you lot tin notice a LCM past times dividing the production of the ii numbers past times their HCF ie inwards this example, (24 x 36)/12 = 72.

See my Resources Library for resources for didactics HCF as well as LCM.

Factorising Harder Quadratics

My pupils panic at the sight of a quadratic alongside a leading coefficient greater than one.  I factorise these quadratics past times inspection (the 'guess as well as test' method) but my pupils aren't satisfied alongside this proposition - they desire a to a greater extent than structured approach.

Influenza A virus subtype H5N1 normally taught method inwards the Great Britain involves splitting the middle term inwards 2 (sometimes called the 'Grouping Method'). This is explained real clearly here (thanks to SRWhitehouse for this resource). Teachitmaths.co.uk has a PowerPoint explaining this method. It's worth watching James Tanton's video 'Splitting the Middle Term' too. He's non a fan!

'Grouping'. Source: Flat World Education

An alternative, which seems slow at commencement but paves the agency for a large publish of misconceptions, is the 'slide as well as divide' method. The method, as well as its associated problems, are nicely described inwards Nix the Tricks.

Nix the Tricks offers an interesting option - I've provided 2 examples hither but it's worth reading the majority for the total explanation.

It's also worth looking at this post past times Don Steward to run into his tap exceed method for finding factors as well as for lots of helpful practise questions.

Also worth a mention: when I commencement start didactics quadratic factorisation, I similar to role this well-designed sum-product worksheet from greatmathsteachingideas.com as a starter. It's proficient practise of an essential skill.

Angles Facts

I've e'er taught angles inward parallel lines every bit Fs, Cs in addition to Zs, simply I latterly discovered that pupils prefer to think of Fs, Us in addition to Ns, which operate inward just the same agency simply may live on easier to retrieve because they piece the discussion FUN.

(image from greatmathsteachingideas.com)

Of course of pedagogy there's nonetheless the challenge of remembering the to a greater extent than formal descriptions that they volition ask to role inward their GCSE examination (for event they are required to role the term 'corresponding angle' inward their answers, instead of F-angle).  I advise that they think of 'FC' (football lodge - every bit inward Tottenham Hotspur FC) for F angles = corresponding angles.  I besides advise they could retrieve that Z angles = alternate angles past times thinking of the commencement in addition to final letters of the alphabet. But this doesn't operate if I alter Z to N!  I'll accept to think of something else (or fifty-fifty better, larn them to come upwardly up alongside something).

Resources

There are loads of proficient resources for teaching this topic. Here are a few examples:

• I honey the 'Spot the Angle' activeness from mathspad.co.uk. This website besides has a nifty interactive Parallel Lines Tool.
• Teachitmaths.co.uk has a nifty angle bill of fare kind activity and useful revision cards.
• Mark Horley has made a Basic Angle Properties activity.
• Missbrookesmaths.com has a prissy angles inward parallel lines tick or trash activity.
• There are a give away of angle chases here - cheers to @MathedUp.
• Greatmathsteachingideas.com has a give away of lovely worksheets, activities in addition to applets including Angles inward Parallel Lines Colouring Fun and First Letter Prompts which gets pupils thinking most the language of their angle fact answers.
• This comprehensive booklet 'Introducing Angles' past times Gareth Evans is helpful. 

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

More Angle Facts

On a related note, here's closed to tips for teaching to a greater extent than basic angle facts:

• greatmathsteachingideas.com)

Of course of pedagogy there's nonetheless the challenge of remembering the to a greater extent than formal descriptions that they volition ask to role inward their GCSE examination (for event they are required to role the term 'corresponding angle' inward their answers, instead of F-angle).  I advise that they think of 'FC' (football lodge - every bit inward Tottenham Hotspur FC) for F angles = corresponding angles.  I besides advise they could retrieve that Z angles = alternate angles past times thinking of the commencement in addition to final letters of the alphabet. But this doesn't operate if I alter Z to N!  I'll accept to think of something else (or fifty-fifty better, larn them to come upwardly up alongside something).

Resources

There are loads of proficient resources for teaching this topic. Here are a few examples:

• I honey the 'Spot the Angle' activeness from mathspad.co.uk. This website besides has a nifty interactive Parallel Lines Tool.
• Teachitmaths.co.uk has a nifty angle bill of fare kind activity and useful revision cards.
• Mark Horley has made a Basic Angle Properties activity.
• Missbrookesmaths.com has a prissy angles inward parallel lines tick or trash activity.
• There are a give away of angle chases here - cheers to @MathedUp.
• Greatmathsteachingideas.com has a give away of lovely worksheets, activities in addition to applets including Angles inward Parallel Lines Colouring Fun and First Letter Prompts which gets pupils thinking most the language of their angle fact answers.
• This comprehensive booklet 'Introducing Angles' past times Gareth Evans is helpful. 

There are loads to a greater extent than resources for this theme inward my mathsisfun.com has a distich to a greater extent than ideas - I similar their proffer that the C of the discussion complementary stands for 'corner' (ie a correct angle) in addition to the due south inward supplementary stands for 'straight' (ie 180 degrees on a withdraw line).

Interestingly, the discussion complementary comes from Latin completum (meaning completed) because the correct angle is persuasion of every bit a consummate angle.

Coded Averages

Teaching coding inward Statistics i is a fleck of a pain.  My pupils simply don't similar it, in addition to it's difficult for me to larn enthusiastic most something that didn't actually be when I studied Statistics (perhaps because it's non solely necessary?). When I was revising this topic amongst my Year 12s this year, I used a actually uncomplicated real-life example:

Imagine I'm queuing upwards to purchase 4 items of clothing, which cost £29.95, £49.95, £59.95 in addition to £99.95. To hold upwards past times fourth dimension I determine to function out the hateful cost of these 4 items. To brand the numbers easier to bargain with, I add together 5p to each total in addition to and so separate past times 10, giving me £3, £5, £6 in addition to £10. It's really slow to function out the hateful of these 'coded' prices inward my caput - it's £6. And right away I tin uncode that hateful past times multiplying past times 10 in addition to so subtracting 5p (the inverse of the master copy coding).  That rapidly gives me the actual hateful cost of the clothes, which is £59.95.  

Resources

Here's a few resources I've establish for instruction this topic:

• Teachitmaths.co.uk has a lovely worksheet for helping pupils empathise the comport upon of coding. Just beware of the fault inward the extension questions - both information sets should accept 6 values, non five.
• Schoolworkout.co.uk has this sorting activity and this worksheet.
• Phildb on tes.co.uk has written this worksheet.

There's a express alternative hither so possibly I should write something myself - I'll add together it to my list!

Large Foursquare Roots

In C1, the non-calculator Influenza A virus subtype H5N1 marking module, my pupils sometimes perish stuck solving quadratic equations that are difficult to factorise. This powerfulness live because the leading coefficient is greater than i (see my earlier post) or it may but live because the numbers inward the quadratic are large.  I commonly propose that they persevere amongst factorising, but if they convey to resort to using the quadratic formula in addition to thence they may require to foursquare origin a large foursquare number. Here's roughly uncomplicated ideas for how to create thence - inward this representative I'm finding the foursquare origin of 324, though these methods run every bit good for larger foursquare numbers.

Note that if the quadratic equation can't live factorised inward the commencement house in addition to thence nosotros tin either purpose the formula or consummate the foursquare to solve it, in addition to nosotros volition halt upwards amongst a surd inward our lastly answer.  My adjacent post service is all close didactics surds!

Surds

Surds - what a fabulous theme to teach! I honey the abundance of resources available in addition to I’ve listed roughly of my favourites below.

Two things I ever create when didactics surds:

• Pupils listing the starting fourth dimension twelve foursquare numbers inward their books for reference throughout the lesson. They demand to readily recognise foursquare numbers inward guild to simplify surds in addition to then the to a greater extent than they practice listing them, the better.
• When manipulating expressions containing surds (eg expanding brackets) I brand comparisons to what they already know close algebra. For representative √2 in addition to √3 tin hold upwards regard of inward the same means as x in addition to y (ie non ‘like terms’) whereas 2√3 in addition to 5√3 tin hold upwards regard of inward the same means as 2x in addition to 5x (ie nosotros tin add together them to larn 7√3).

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

• Ask pupils to notice a means of drawing a occupation alongside a length of precisely √5 units (the hypotenuse of a correct angled triangle alongside sides 2cm in addition to 1cm) 
• Ask pupils to split the length of an A4 slice of newspaper past times its width. Repeat for A3 in addition to A5. What create they notice? (The response is ever √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 roughly bully didactics resources (there's hundreds to a greater extent than online). Most of these travel as good at GCSE in addition to Influenza A virus subtype H5N1 level:

• Is it rational?
• Two interactive tasks from Mathspad
• Pairs activity 
• Introducing surds
• True or faux activity
• Surds -Applying in addition to 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 roughly resources recommended past times the TES.

For a lovely laid of surds problems, run into 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 choice method for simplifying surds:

Linear Simultaneous Equations

Solving linear simultaneous equations is rather satisfying. In this postal service I advise unopen to techniques as well as resources for pedagogy this topic.

Equality as well as Lincoln
When I saw the cinema Lincoln I was struck yesteryear Abraham Lincoln’s reference to Euclid’s First Axiom ‘Things which are equal to the same affair are also equal to 1 another’. Influenza A virus subtype H5N1 well-made indicate inwards a tidings nigh racial equality, but also an interesting claw into a method for solving simultaneous equations such as

y = 4x + 6

y = 2x + 3

Both 4x + vi as well as 2x + three are equal to y, hence logically nosotros convey 4x + vi = 2x + three (this is essentially simply a exchange method). Why non demo this this blog gives a proficient explanation of Lincoln's point)

Elimination as well as 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils uncovering it real tardily to shout out back the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inwards the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inwards each equation is positive (‘same sign’), we subtract one equation from the other.

However, I noticed that when solving simultaneous equations such every 2nd -3x + 5y = 41; 2x + 5y = 56, unopen to pupils saw that the -3x as well as the 2x were different signs as well as incorrectly decided that this meant they should add the 2 equations. So it’s worth clarifying which signs nosotros are referring to inwards the ‘Same Sign Subtract’/’Different Sign Add’ approach.

Graphical Solutions
It’s as well as then of import for pupils empathise that whenever they solve linear simultaneous equations, they are inwards fact finding the indicate of intersection of 2 conduct lines. It’s essential to put a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) as well as decease them thinking nigh why at that spot are no solutions.  I similar to demo them this cute picture too.

Wordy Equations
This is 1 of my favourite simultaneous equation questions: “A zoo has several ostriches as well as several giraffes. In full they convey xxx eyes as well as 44 legs. How many ostriches as well as how many giraffes are inwards the zoo?”. Make certain yous discourage pupils from using the missive of the alphabet O for ostrich, because it looks similar a zero.

Resources
There's lots of resources online – here’s a few I’ve picked out:

• Don Steward’s Median blog has a huge arrive at of fantastic questions as well as activities.
• TeachitMaths has a slap-up ‘wordy question’ worksheet as well as clear slides on elimination as well as substitution.
• UEA has a worksheet on linear simultaneous equations amongst a overnice progression of questions.
• There is a useful worksheet on Solving Simultaneous Equations Graphically yesteryear Tristan Jones on TES. 
• This Geogebra worksheet yesteryear themathsteacher.com is a proficient practice inwards solving simultaneous equations graphically amongst ICT.
• Peter Bland and JustMaths both supply examination questions on this topic.
• MEI has a overnice extension activity. 

A Percentages Trick

Just a quick post service today to portion a groovy tip:

You tin rate notice swap the per centum as well as the amount:  16% of £25 is hard to calculate inwards your head, just 25% of £16 is exactly the same amount.

So if you lot desire to speedily function out 16% of £25 without a calculator, honour 25% of £16 instead (ie split £16 past times 4). Simple!

Think most why this works.

Source: www.aperiodical.com

Radians

Radians scare my Year 12s. They oftentimes select to 'think' inwards degrees together with only convert their answers into radians. I wonder if I could produce a meliorate undertaking of introducing the concept.  I've only discovered this animation that is hence absolutely fantastic, I had to part it.

I works life it inwards this blog post but it originated here.  Both are worth a read.  

I honey this post service 'Degrees vs Radians' which presents an opened upward missive of the alphabet to students wondering, “Why Do We Use Radians Instead of Degrees?”.  

Colin Beveridge has rigid feelings on the discipline - both teachers together with students would produce goodness from reading his post service 'Why Radians Rock (and Degrees Don't)', inwards which he convinces the reader of the unquestionable benefits of using radians.

Next Level Maths has a dainty explanation of radians, including an interactive activity.

Incidentally, if you're excited past times animations together with hence yous mightiness similar the other animations inwards this article '7 Animated GIFs That Will Make You Instantly Understand Trigonometry'.

Multiplication As Well As Colour

This uncomplicated persuasion shows how of import it is to role unlike colours when writing on the board - no affair what topic you're teaching.  It actually helps pupils decease along rails of what you're doing.

Source: http://www.jandmranch.com/2013/02/09/teaching-three-digit-multiplication-to-my-aspergers-daughter/ 

Trial As Well As Improvement

In this post I desire to address a mutual misconception that comes upward when instruction case too improvement. Here's an representative which illustrates the problem:

These trials say us that the solution is betwixt 2.1 too 2.2. The inquiry requires an response to 1 decimal place, too then our concluding solution volition last either 2.1 or 2.2.

At this betoken it looks similar our solution volition last 2.1, because x = 2.1 gives us the closest response to five. But this is a cubic function, non a linear function, too then this is an incorrect supposition (and a mutual misconception alongside students).

We must similar a shot banking corporation jibe the midpoint of 2.1 too 2.2:

Let’s depict our in conclusion iii trials on a set out line:

We tin come across that the solution must prevarication betwixt 2.15 too 2.2.  All values betwixt 2.15 too 2.2 circular to 2.2, hence our concluding response must last 2.2. 

You tin come across hither that it was absolutely necessary to banking corporation jibe x = 2.15. And non merely because you'd lose a grade inward a GCSE for failing to banking corporation jibe it! You could plot the function, every bit shown below (use Desmos - it's fantastic!) too zoom inward on the solution to aid your pupils sympathise this point.

I got this representative from this weblog post.

Resources
While I'm on the dependent patch of case too improvement, let's receive got a quick await at a few instruction resources:

• Teachitmaths has a smashing PowerPoint explaining the method.
• I peculiarly similar the agency this worksheet yesteryear jhofmannmaths is fix out.
• Justmaths.co.uk has a Whodunnit activity too exam questions.
• Mr Barton Maths has a 'Win a Million' game.
• Teachmathematics.net has a good Excel activity.
• Mr Collins writes almost this blog.
• Finally, an extension worksheet on linear interpolation.

A Degree Revision

I created these revision cards for a classroom activity, simply they're as helpful for pupils studying at home. These cards comprehend all the facts as well as definitions that pupils bespeak to larn for each module - I haven't included anything that is given inward the formula booklet.

These cards are based on the Edexcel specification.

Core ane as well as Core two revision cards
Core three revision cards
Statistics ane revision cards
Statistics two revision cards
Decision ane revision cards
Mechanics ane formulae revision  (thanks to my boss for creating the M1 cards!)

I promise to create C4 as well as FP1 adjacent year!

Hope they're helpful!  If yous desire to run out me a review or brand suggestions, delight create through TES or Twitter.

Revision Alongside Yr 11

As this year's Maths GCSE exams are fast approaching, I idea it powerfulness endure helpful to percentage a few of my revision resources.

My Year 11s expressed their frustration inwards trying to recall the differences betwixt statistical graphs – peculiarly histograms, frequency polygons together with cumulative frequency graphs. H5N1 telephone substitution surface area of confusion is when to role midpoints, endpoints, aeroplane widths etc. I created this for them to manage clarify these points:  GCSE Graphs Revision Summary

They likewise fretted close which formulae they had to recall for mass together with area. In aeroplane nosotros went through this sheet - I asked them to label each formula according to whether they needed to larn it or whether it was provided. I together with therefore gave them this formula summary to accept away.

In ane revision lesson my Year 11s tested each other using these circle theorem revision cards from teachitmaths.co.uk. They loved this lesson together with demanded cards for every topic! I supplied them amongst the other cards from teachitmaths.co.uk, every bit good every bit my own mixed A* revision cards. I likewise encouraged them to brand their ain cards at home.

There are many skilful revision checklists together with progress trackers available online.  I've but discovered this great progress booklet for Higher GCSE, created past times Emily Hughes who writes the blog http://ilovemathsgames.wordpress.com/.

Finally, inwards my concluding lesson amongst my Year xi aeroplane I went through these ‘hints together with tips’ slides (while they ate cake, of course!). I pulled these slides together over fourth dimension from a diverseness of sources therefore lamentable for non crediting the originators of this material. It includes the rather tasteless but memorable painting demo below, which got a huge reaction from my class! ‘If you lot don’t similar it, don’t create it!’ I told them. :)

Source: @mathequalslove

Similarity

I saw this neat monster GCSE enquiry on Twitter (thanks @ReviseJustMaths) - it inspired me to write a postal service most similarity!

Taken from Edexcel Higher Paper ane Nov 2013

In this postal service I'll focus on resources as well as methods for didactics similar triangles.

Two triangles are similar if they're 'equiangular' (a flake of a mouthful thence I instruct 'AAA' instead). GCSE questions oftentimes require us to outset tally upwards equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' unremarkably involves using angle rules - come across my postal service on FUN angles. The cardinal betoken to emphasise inward didactics is that it truly really helps to describe the ii triangles separately, as well as inward the same orientation. Here's iii examples to illustrate this:

Example ane - Separate Triangles

Example 1 is straightforward - it's clear to come across from the angle labels that the 8cm side inward the outset triangle is proportional to the side labelled x inward the minute triangle.  I'd yet encourage my pupils to redraw the ii triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oftentimes brand the error of thinking that side BC is proportional to side CE.  I instruct them to label all equal angles inward the diagram, thence describe triangles ABC as well as EDC separately. They'd thence come across that because <ABC = <CDE (alternate angles) as well as <ACB = <ECD (vertically contrary angles), the side BC is truly proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin role the same approach every bit inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), thence describe the triangles ABD as well as ECD separately. In this enquiry it's probable we'll endure asked to function out the length BC, which simply requires a flake of thinking (ie calculate the length BD first, thence subtract the length CD).  

Resources

• I dearest these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages xv - eighteen furnish a challenging as well as engaging activity.  I asked my pupils to form the cards into iii categories (similar/not similar/can't tell), stick them onto A3 newspaper as well as annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of exercise questions. There's also closed to challenging questions inward this worksheet from mathsmalakiss.com.
• CIMT has lots of first-class similarity resources.
• This is a lovely rich task from Shell Centre

For resources for expanse as well as mass of similar figures, come across my resource library.

Skewness

Let’s verbalize S1, equally this year’s essay out is fast approaching.

I don’t similar the way my S1 textbook deals alongside skewness. It basically merely sets out methods for identifying skewness without actually explaining what it is. In this postal service I hash out an choice approach.

I usually piece of employment this starter interrogation inwards my get-go S1 lesson of the year:

The indicate beingness that when at that topographic point are outliers inwards a information set, the hateful becomes rather useless (unless of class you lot wishing to deceive people!).

Whilst education S1 I oftentimes uncovering myself referring dorsum to my Bibonacci starter (‘remember that CEO? He ruined the mean!’). So I decided to brand a worksheet out of it - come across below - which I used for the get-go fourth dimension this yr when education skewness (if you lot similar this thence delight acquire out me a review on TES!). My pupils enjoyed the activeness too it generated interesting discussions.

• Investigating skewness activity
• Investigating skewness instructor notes

There is a similar activeness here - from the website Illustrative Mathematics.

The substitution education indicate is that when information is skewed, the median is to a greater extent than meaningful than the mean. We convey diverse methods for identifying skewness inwards a information ready (summarised inwards these slides – sorry, master copy source unknown) - nosotros usually reckon the shape of a frequency diagram or box plot. Sometimes skewness is apparent merely from looking at the raw information (this sideways stem-and-leaf diagram is interesting). 

Pupils involve to recollect that positive skew way nosotros convey a few 'sparse' information points (possibly outliers) at the top end of the information ready – too similar inwards the Bibonacci example, this volition pull the hateful up. This volition assistance them conceptually empathise the diverse methods described inwards the textbook.

Finally, here's a keen play a trick on that I learnt from my colleague Lizzie... Imagine a cute puppy sitting on the left of the graph. H5N1 positive skew is going to come across the puppy (positive = yay, a puppy!) too a negative skew is going away from the puppy (negative = acquire away from this puppy!). It's a giddy but uncomplicated too memorable way of ensuring that students don't acquire the graphs mixed up.

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Two Ways To Role Comic Strips Inwards Maths Teaching

I stumbled across a overnice instruction persuasion inwards this blog post which is all most giving pupils fourth dimension to summarise what they've learnt.  The writer of the spider web log suggests that pupils depict comic strips inwards bird or for homework. Here's but about examples:

Example worksheet

Example of pupil's work

I in ane lawsuit used comic strips for a dissimilar utilization inwards my instruction - I produced this comic strip for my GCSE class, which I showed inwards this Prezi slideshow to generate intelligence most sampling methods.  The characters are all teachers at my schoolhouse (with slightly amended names...).  It went downward good amongst my bird in addition to I laid upwards them the chore of creating their ain versions. We used Bitstrips for Schools which is lovely but tin endure really time-consuming.

(that's meant to endure me past times the way!)

Maths Painting Quiz

Spiked Math has approximately first-class Maths Movie Quizzes.  I chose these ones to entertain my Year 13s at Christmas.  Great fun for Maths teachers too!

Student Communication Using Blogs

I've taken a few days away from posting on hither because my babe was born on Monday... But fifty-fifty though I've been a flake tied up, I've even then been able to part concluding infinitesimal motivational messages amongst my show classes using 2 pupil blogs - i for my GCSE class too i for the whole Sixth Form. In this post I beak over my experience of communicating inwards this way.

GCSE Class
I started example post).  I also posted classwork answers too links to worksheets too homework sheets inwards instance they missed a lesson or lost a homework. I works life this was the most useful appear of the spider web log - my pupils never had an excuse for missing a homework!

I works life it a flake time-consuming to write a spider web log post 3 times a calendar week too yesteryear the fourth dimension this shape were inwards Year eleven I was updating the spider web log less often, too my posts got shorter. To last honest at that topographic point were times when I felt far also busy to post, simply I did persevere.

Since this shape direct maintain been on written report leave, I've been posting motivational messages too concluding infinitesimal revision resources. I tin run into from the striking tracker on Blogger that my pupils direct maintain been receiving these messages.

Sixth Form
When I took on the piece of occupation of Key Stage v Coordinator I decided to fix this blog every bit the original tool for communicating amongst H5N1 score pupils.  My schoolhouse has 200 pupils studying AS too A2 Maths too Further Maths.  Around twenty pupils subscribe to my spider web log yesteryear e-mail too I promise that position out volition growth greatly adjacent twelvemonth (if I successfully promote it to the incoming Year 12s inwards September). It's been a really useful means of sharing resources too word - for instance almost trips, courses, opened upward days too competitions.  Over the class of the twelvemonth I've done an average of 3 - iv posts per calendar month then it's been less time-consuming than my other blog.

Summary
Although I've continued to utilisation 'old-fashioned' forms of communication (noticeboards, handouts etc), I experience that blogging has been an splendid method for communicating amongst pupils, peculiarly during written report leave. Blogger - too similar tools - are really quick too slow to use.

My blogs direct maintain been primarily for communicating amongst pupils, dissimilar other blogs run yesteryear my schoolhouse (like this one) which give pupils the chance to part spider web log posts themselves.

I've seen Twitter used yesteryear other Maths Departments to communicate amongst pupils - I mean value this is an splendid sentiment too my adjacent destination is to encourage my Head of Department to laid this upward for my school.

Binary

Maths pedagogy is oft rushed. We encompass topics also quickly, nosotros essay regularly, nosotros repeat the same matter every year. By Year 10 our pupils are bored. It's as well as then unnecessary as well as frustrating. If alone nosotros spent to a greater extent than fourth dimension on rich Mathematics. I'd honey to deadening down, become off on tangents, permit my pupils investigate as well as discover... The alone fourth dimension I learn the hazard to digress from the Scheme of Work is at the destination of the summertime term.  So I seize the chance to engage my pupils inwards interesting concepts as well as ideas - similar the binary system.

It's tardily to learn pupils interested inwards this topic. Here's around suggestions:

• Show them a painting demo of a binary watch. I 1 time knew a Year xiii who genuinely wore 1 of these to schoolhouse every day! My pupils were intrigued past times this as well as wanted to know how to read it.
• You could atomic number 82 into this theme through other seat out systems (Roman Numerals etc).
• Perform this fantastic binary magic trick.  My pupils loved it! They were desperate to know how it worked.
• Tell them the joke "There are alone 10 types of people inwards the world: those who sympathize binary as well as those who don't". 

Here's a few examples of resources y'all could purpose inwards a binary lesson:

• Nice PowerPoint 'Binary Bot' from MauveStorm on TES (designed for Key Stage two only could live on used for Year 7/8)
• The slides that I purpose when I learn binary.  Includes how to count binary on your fingers! 
• Binary Window Frames from mathsticks.com (free registration to access)
• A worksheet to practice converting to as well as from binary
• Binary Crossums
• PowerPoint from teachitmaths.co.uk on binary, denary as well as hexadecimal numbers
• Teaching binary using cups
• Lots to a greater extent than resources listed inwards this blog.

Last twelvemonth I went to a fantastic lecture past times Simon Singh (@SLSingh) close Maths inwards the Simpsons.  His book 'The Simpsons as well as their Mathematical Secrets' is absolutely brilliant, a must-read for all Maths teachers.  Singh writes close a scene inwards the Futurama episode 'The Honking' inwards which Bender is alarmed when he reads the binary code 0101100101. When read inwards a mirror, the code reads '666'.  I told my Year 13s close this - they loved it. I wanted to demo them the clip from Futurama only all I institute was this YouTube video in Castilian (?) which they view was hilarious. I also explained the reference to the 'Redrum' scene inwards The Shining - most of them had never seen the cinema as well as then I showed them this clip as well as managed to terrify one-half the class! Myself included. :)