Dividing Past Times Zero

I found this on Pinterest and now role it to assist my pupils shout back the rules regarding segmentation too zero.  It seems to work!

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

I was really pleased when one of my pupils lately wrote this inwards a test. It's prissy to run into that approximately of them pay attention!

Most calculators laissez passer on the message ‘Maths Error’ when a publish is divided past times zero.  It’s crucial that pupils sympathise why. For didactics ideas, I recommend this first-class weblog post 'Why can't you lot split past times zero?'.

We role this agreement when solving equations similar this:  x² - 5x = 0. H5N1 mutual error is to divide past times x to buy the farm x - five = 0. This incorrectly gives alone i solution (x = 5). Knowing that nosotros shouldn't split past times x because x could locomote null (unless we're told otherwise) allows us to sympathise why the right method is to factorise ie x(x-5) = 0, giving the ii solutions x = 0 too x = 5.

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

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

Highest Mutual Ingredient Together With Lowest Mutual Multiple

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

I recently discovered an option method that is impressively quick together with simple.  It is described inwards this video every bit the 'Indian Method'. It's like to the 'upside downwardly birthday cake method' but it's much quicker because in that place is no requirement to role primes.

Say nosotros desire to detect the Highest Common Factor together with Lowest Common Multiple of 24 together with 36.
Write down the ii numbers, then (to the left, every bit inwards my illustration below) write downwardly whatever mutual element (ie 2, 3, 4, vi or 12).  I've chosen 6.  Now dissever 24 together with 36 past times vi together with write the answers underneath (4 together with vi inwards this case).  Keep repeating this procedure until the ii numbers have no mutual factors (ie 2 together with iii below).  Now, your Highest Common Factor is only the production of numbers on the left. And for the Lowest Common Multiple, detect the production of the numbers on the left together with the numbers inwards the bottom row. It's slow to hollo back which is which - to detect the LCM, await for the L shape.

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

Don Steward features an option method inwards this spider web log post.  He mentions that you lot tin detect 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 together with LCM.

Angles Facts

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

(image from greatmathsteachingideas.com)

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

Resources

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

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

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

More Angle Facts

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

• greatmathsteachingideas.com)

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

Resources

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

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

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

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

A Percentages Trick

Just a quick postal service today to portion a non bad tip:

You tin swap the percent in addition to the amount:  16% of £25 is hard to calculate inward your head, only 25% of £16 is just the same amount.

So if you lot desire to rapidly live on out 16% of £25 without a calculator, uncovering 25% of £16 instead (ie split £16 past times 4). Simple!

Think nigh why this works.

Source: www.aperiodical.com

Multiplication In Addition To Colour

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

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

Trial Too Improvement

In this post service I desire to address a mutual misconception that comes upwards when instruction lawsuit together with improvement. Here's an example which illustrates the problem:

These trials country us that the solution is betwixt 2.1 together with 2.2. The query requires an response to 1 decimal place, then our concluding solution volition live either 2.1 or 2.2.

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

We must forthwith cheque the midpoint of 2.1 together with 2.2:

Let’s depict our lastly 3 trials on a pose out line:

We tin flame encounter that the solution must prevarication betwixt 2.15 together with 2.2.  All values betwixt 2.15 together with 2.2 circular to 2.2, thus our concluding response must live 2.2. 

You tin flame encounter hither that it was absolutely necessary to cheque x = 2.15. And non only because you'd lose a score inwards a GCSE for failing to cheque it! You could plot the function, every bit shown below (use Desmos - it's fantastic!) together with zoom inwards on the solution to attention your pupils empathise this point.

I got this example from this spider web log post.

Resources
While I'm on the dependent area of lawsuit together with 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 gear upwards out.
• Justmaths.co.uk has a Whodunnit activity together with exam questions.
• Mr Barton Maths has a 'Win a Million' game.
• Teachmathematics.net has a good Excel activity.
• Mr Collins writes virtually this blog.
• Finally, an extension worksheet on linear interpolation.

Similarity

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

Taken from Edexcel Higher Paper 1 Nov 2013

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

Two triangles are similar if they're 'equiangular' (a chip of a mouthful hence I learn 'AAA' instead). GCSE questions oft require us to kickoff jibe upward equal angles earlier nosotros start calculating unknown sides using ratio/proportional methods.  This 'matching up' usually involves using angle rules - encounter my postal service on FUN angles. The primal betoken to emphasise inward didactics is that it genuinely really helps to depict the 2 triangles separately, too inward the same orientation. Here's 3 examples to illustrate this:

Example 1 - Separate Triangles

Example 1 is straightforward - it's clear to encounter from the angle labels that the 8cm side inward the kickoff triangle is proportional to the side labelled ten inward the minute triangle.  I'd withal encourage my pupils to redraw the 2 triangles inward the same orientation though.

Example 2 - Joined Triangles

Example 2 is less obvious.  My pupils oft brand the error of thinking that side BC is proportional to side CE.  I learn them to label all equal angles inward the diagram, too hence depict triangles ABC too EDC separately. They'd too hence encounter that because <ABC = <CDE (alternate angles) too <ACB = <ECD (vertically reverse angles), the side BC is genuinely proportional to the side CD. 

Example 3 - Combined Triangles

In Example 3 we tin dismiss locomote the same approach equally inward Example 2. Label all the equal angles inward the diagram ie <ABD = <ECD (corresponding angles), too hence depict the triangles ABD too ECD separately. In this interrogation it's probable we'll live on asked to piece of occupation out the length BC, which simply requires a chip of thinking (ie calculate the length BD first, too hence subtract the length CD).  

Resources

• I honey these resources from the Mathematics Assessment Project. In particular, the sorting cards on pages fifteen - xviii render a challenging too engaging activity.  I asked my pupils to variety the cards into 3 categories (similar/not similar/can't tell), stick them onto A3 newspaper too annotate amongst reasons.  
• Similar pairs is a squeamish matching activeness from Don Steward.
• This blog post. 
• This is a great booklet of practise questions. There's also simply about 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 surface area too mass of similar figures, encounter my resource library.

Two Ways To Purpose Comic Strips Inward Maths Teaching

I stumbled across a prissy didactics sentiment inward this blog post which is all almost giving pupils fourth dimension to summarise what they've learnt.  The writer of the spider web log suggests that pupils depict comic strips inward aeroplane or for homework. Here's around examples:

Example worksheet

Example of pupil's work

I i time used comic strips for a dissimilar role inward my didactics - I produced this comic strip for my GCSE class, which I showed inward this Prezi slideshow to generate give-and-take almost sampling methods.  The characters are all teachers at my schoolhouse (with slightly amended names...).  It went downwardly good alongside my aeroplane too I laid upward them the chore of creating their ain versions. We used Bitstrips for Schools which is lovely merely tin terminate hold upward really time-consuming.

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

Binary

Maths didactics is ofttimes rushed. We encompass topics likewise quickly, nosotros show regularly, nosotros repeat the same affair every year. By Year 10 our pupils are bored. It's too then unnecessary too frustrating. If entirely nosotros spent to a greater extent than fourth dimension on rich Mathematics. I'd dearest to tiresome down, learn off on tangents, allow my pupils investigate too discover... The entirely fourth dimension I learn the run a endangerment to digress from the Scheme of Work is at the goal of the summertime term.  So I seize the chance to engage my pupils inwards interesting concepts too ideas - similar the binary system.

It's slow to learn pupils interested inwards this topic. Here's to a greater extent than or less suggestions:

• Show them a painting present of a binary watch. I i time knew a Year thirteen who genuinely wore i of these to schoolhouse every day! My pupils were intrigued past times this too wanted to know how to read it.
• You could Pb into this theme through other reveal 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 entirely 10 types of people inwards the world: those who sympathise binary too those who don't". 

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

• Nice PowerPoint 'Binary Bot' from MauveStorm on TES (designed for Key Stage two simply could survive used for Year 7/8)
• The slides that I operate 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 do converting to too from binary
• Binary Crossums
• PowerPoint from teachitmaths.co.uk on binary, denary too 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) well-nigh Maths inwards the Simpsons.  His book 'The Simpsons too their Mathematical Secrets' is absolutely brilliant, a must-read for all Maths teachers.  Singh writes well-nigh 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 well-nigh this - they loved it. I wanted to present them the clip from Futurama simply all I constitute was this YouTube video in Castilian (?) which they sentiment was hilarious. I also explained the reference to the 'Redrum' scene inwards The Shining - most of them had never seen the celluloid too then I showed them this clip too managed to terrify one-half the class! Myself included. :)

Venn Activities

This post service is nigh using Venn Diagrams equally a didactics tool, rather than didactics the concept of Venn Diagrams themselves.  To quote the splendid Johnny Griffiths, 'The Venn Diagram amongst iii bubbles is the maths teacher's friend! ... To move able to fill upward inward an eight-region diagram shows a actually deep agreement of the distinctions that a practiced pupil has to move able to make, spell the weaker pupil finds beingness faced amongst a moving-picture exhibit such equally this much less threatening than a page of exercises'.

Before nosotros foremost using Venn activities inward Maths lessons, let's mean value nigh whether pupils are familiar amongst how Venn Diagrams work. I acknowledge to beingness a flake clueless nigh just what children written report at master copy school. The primary here), only I straight off prefer the simpler method described in linear equations activity. It helped consolidate their noesis of linear graphs in addition to allowed me to banking concern check their understanding.

Johnny Griffith's splendid RISPs (Rich Starting Points for H5N1 Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) in addition to Risp 4 (periodic functions).  In the instructor notes for Risp 10 Johnny shares his views on the usefulness of Venns.

A Venn action for Solving Quadratics past times Factorising past times aka nka on TES. 

A GCSE extension action on quadratic graphs from MEI.

I haven't tried this all the same only Don Steward also gives us this lovely here), only I straight off prefer the simpler method described in number activity.

Interactive Venns

Venns piece of occupation good on the Interactive Whiteboard - here's roughly examples.

• Nrich has roughly interactive Venn diagrams on types of number.
• MathsPad has roughly lovely Venn activities (most ask a subscription). I've successfully used this Factors, Primes in addition to Multiples Activity with my Year 8s.   
• Teachitmaths.co.uk has interactive Venn activities - for instance for shapes and prime factors, or y'all tin create your ain (subscription required).

Other Uses

• When I innovate complex numbers inward FP1 nosotros create a Venn Diagram during degree news nigh types of numbers (real, rational, integers etc) in addition to their Greek symbol notation.  The NCETM has a similar Venn action inward this resource sheet.
• Up until lately I used Venn Diagrams to learn Highest Common Factor in addition to Lowest Common Multiple (method explained here), only I straight off prefer the simpler method described in this post.
• Quadrilaterals tin move classified using a Venn Diagram similar this one.  We tin in addition to hence answer questions such as 'Is every foursquare a rectangle? Is every rhomb a square?' A 'family tree' also plant well.

In determination - Venns are everywhere! But inward secondary Maths they are alone formally taught to those studying iGCSE (set theory) in addition to Statistics 1 at H5N1 flat (probability). I'm pleased to run across that Venn Diagram methods inward probability are on the new Maths GCSE Syllabus so volition move to a greater extent than widely studied inward future. But inward add-on to beingness taught equally a topic inward their ain right, Venn Diagrams are a versatile didactics tool amongst numerous applications inward the classroom. And they bring the added bonus of beingness created past times a British Mathematican! Well done Mr Venn.

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)

All Most Gradient

When nosotros learn linear graphs at Key Stage 3, nosotros oft fille the chance to explore useful real-life mathematics. In this post service I portion practical ideas in addition to resources for pedagogy the concept of gradient.

A feel of steepness
At schoolhouse nosotros usually limited gradients every bit integers or fractions exactly route signs inwards the Britain present gradients every bit percentages.  Older signs showed ratios (rise:run) - arguably these were easier to interpret.

The route sign pictured indicates a slope of 25% ie 1 quarter. We nation the slope of this route is 'one inwards four'. Think almost this every bit 'rise over run' in addition to thus translate this every bit 'we become upward 1 unit of measurement for every 4 units nosotros become across'. Wouldn't it last keen if nosotros could saltation inwards the schoolhouse minibus amongst our marker in addition to crusade to a route amongst a 25% slope to reckon how steep it is? Unfortunately this is in all probability impractical (though it could last develop every bit a homework, depending on how hilly your local expanse is!).

There are some impressively steep roads in article attempts to calculate the steepest slope that 1 tin cycle up.  This article says that anything over 16% is considered rattling challenging for cyclists of all abilities.

Ripley Street Ridge, San Francisco

Practical activities using trigonometry
In existent life it is ordinarily impossible to mensurate the rising in addition to run of a slope so nosotros piece of job trigonometry to calculate these lengths. Picture a slope every bit a right-angled triangle - nosotros tin piece of job a clinometer to mensurate the angle of elevation in addition to mayhap a trundle wheel to mensurate the length of the hypotenuse. Trigonometry tin in addition to then last used to calculate the rising in addition to run inwards lodge to detect the gradient. The tabular array below shows gradients in addition to their equivalent angles of elevation.  I intend it's of import that students empathise the connection betwixt a 100% slope in addition to a 45 aeroplane angle.

Source: Wikipedia

Gradient tin too last calculated using Pythagoras' Theorem. Say a human cycles 5km on a slope in addition to knows (from his altimeter watch) that he has climbed 250m vertically.  Again, flick a right-angled triangle - the hypotenuse is 5000m in addition to the superlative is 250m. Use Pythagoras to calculate the base of operations (4994m).  Now piece of job 'rise over run' to calculate the slope - inwards this illustration nosotros learn 5%.

These real-life applications of mathematics tin easily last made into practical marker activities. For illustration y'all could use home-made clinometers and trigonometry to calculate the gradients of slopes inwards in addition to around school, similar staircases in addition to ramps.

Resources for pedagogy gradient

• My worksheet on real-life gradients on TES
• A broad gain of exercises inwards this pack. Note that this is a American resources so uses the price slope in addition to marker instead of gradient.
• A mensurate of slope - lesson in addition to activities from Mathematics Assessment Project
• A worksheet of contextual slope problems
• A gradient activity from Nrich
• Mixed slope questions by linzbfc on TES
• PowerPoint on gradients yesteryear Andrea Frame on TES
• What is gradient? worksheet yesteryear MathsPad
• this curt video of person cycling upward a route amongst 38% gradient. Looks similar difficult work! As a affair of interest, this rather technical article attempts to calculate the steepest slope that 1 tin cycle up.  This article says that anything over 16% is considered rattling challenging for cyclists of all abilities.
  
  

  

  Ripley Street Ridge, San Francisco

  Practical activities using trigonometry
  In existent life it is ordinarily impossible to mensurate the rising in addition to run of a slope so nosotros piece of job trigonometry to calculate these lengths. Picture a slope every bit a right-angled triangle - nosotros tin piece of job a clinometer to mensurate the angle of elevation in addition to mayhap a trundle wheel to mensurate the length of the hypotenuse. Trigonometry tin in addition to then last used to calculate the rising in addition to run inwards lodge to detect the gradient. The tabular array below shows gradients in addition to their equivalent angles of elevation.  I intend it's of import that students empathise the connection betwixt a 100% slope in addition to a 45 aeroplane angle.
  
  

  

  Source: Wikipedia

  Gradient tin too last calculated using Pythagoras' Theorem. Say a human cycles 5km on a slope in addition to knows (from his altimeter watch) that he has climbed 250m vertically.  Again, flick a right-angled triangle - the hypotenuse is 5000m in addition to the superlative is 250m. Use Pythagoras to calculate the base of operations (4994m).  Now piece of job 'rise over run' to calculate the slope - inwards this illustration nosotros learn 5%.
  
  These real-life applications of mathematics tin easily last made into practical marker activities. For illustration y'all could use home-made clinometers and trigonometry to calculate the gradients of slopes inwards in addition to around school, similar staircases in addition to ramps.
  
  Resources for pedagogy gradient
  
  • My worksheet on real-life gradients on TES
  • A broad gain of exercises inwards this pack. Note that this is a American resources so uses the price slope in addition to marker instead of gradient.
  • A mensurate of slope - lesson in addition to activities from Mathematics Assessment Project
  • A worksheet of contextual slope problems
  • A gradient activity from Nrich
  • Mixed slope questions by linzbfc on TES
  • PowerPoint on gradients yesteryear Andrea Frame on TES
  • What is gradient? worksheet yesteryear MathsPad
  • Alphabet slopes activity
  
  Possible homework investigation questions
  What is a funicular? Why tin funiculars go at steeper than 90 degrees?
  What’s the maximum marker allowed for a railway without cable or cogs?
  Why produce y'all intend route builders convey to worry about the marker of the road?
  Why produce y'all intend nosotros convey regulations for building wheelchair ramps?
  At what steepness produce avalanches occur?
  Is it possible to ski at xc degrees steepness?
  (source)
  
  I promise this post service has inspired y'all to seek out out some novel ideas when pedagogy gradient!  Let me know how y'all learn on (@mathsjem).
  

  

  Unusual slope sign inwards Hertfordshire, UK

  
  

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.

End Of Term!

The summertime holidays are fast approaching. Although I'm a believer inwards didactics maths correct upwardly to the halt of term, it tin give the axe live difficult to learn a topic properly when lessons are existence interrupted past times sports day, assemblies, schoolhouse trips etc. But if nosotros don't deliver worthwhile lessons until the terminal solar daytime of term, as well as therefore nosotros can't complain when parents desire to possess got their children on vacation during term-time.

I'm non against the sentiment of watching a video or playing games inwards maths lesson, only let's brand certain our students are either learning something novel or becoming to a greater extent than engaged as well as excited past times mathematics.

My schoolhouse has a criterion laid upwardly of challenges, games, projects as well as investigations that nosotros role every year, only here's a few of my option suggestions for halt of term activities:

Fermat's Last Theorem as well as Pythagoras
Have yous read The Simpsons as well as their Mathematical Secrets by Simon Singh? It's a bright book. Influenza A virus subtype H5N1 dainty halt of term lesson could involve yous explaining Fermat's Last Theorem (or role this BBC video to explicate it for you) as well as showing your degree how it features inwards the Simpsons (it's actually rather clever that Homer seems to possess got disproved it - inwards fact it's a 'near miss' solution - every bit explained past times Simon Singh in this video from Numberphile).

In this lesson your pupils could exercise approximately question into Fermat, or perchance other famous mathematicians - they could create a poster every bit suggested inwards this lovely activity from Interactive Maths.  Alternatively, they could await at related Pythagorean problems, such every bit proving Pythagoras' Theorem (which tin give the axe live done amongst Origami!), finding Pythagorean triples or investigating Pythagoras amongst other polygons.

BBC iPlayer is currently showing the Fermat's Last Theorem episode of Horizon - although the maths is rather advanced (it made my encephalon hurt!), it's an interesting episode as well as gives an insight into the operate of mathematicians.

If yous similar these Fermat lesson ideas, yous mightiness also similar my postal service on teaching binary which features to a greater extent than ideas from Simon Singh's book.

Pascal Investigations
Pascal's Triangle contains lots of amazing patterns as well as yous tin give the axe easily create total a lesson exploring them. Teachit Maths has a smashing PowerPoint as well as activity sheet for this lesson. In this short video a maths instructor briefly explains this history of the triangle. For older students yous could also innovate 'choose' musical note as well as link the triangle to binomial expansions.

Pi week
My colleague ane time had a Pi themed terminal calendar week of term amongst ane of his classes. The students all brought inwards cakes as well as pies, they watched Life of Pi (a lovely cinema only non mathematical!) as well as they did Pi-based activities including a Pi recital competition, a freehand circle drawing contest as well as making a giant Pi paperchain (a dissimilar coloring per digit).

If yous possess got whatsoever other creative ideas for halt of term lessons, I'd honey to demand heed them.

Inspiration

I was real lucky to encounter Simon Singh verbalise at the Maths inwards Action lectures inwards London terminal year. My schoolhouse took xx Year 12s to the consequence only this twelvemonth nosotros conception to possess got forty because it was such a bright solar daytime of lectures. I came away feeling inspired. I actually recommend these lectures, which are for both Influenza A virus subtype H5N1 flat as well as GCSE students.

Do yous know what makes the numbers on this jumbotron interesting?  Find out inwards this article.

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