Showing posts with label GCSE. Show all posts
Showing posts with label GCSE. Show all posts

Friday, October 25, 2019

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.



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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.



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Factorising Harder Quadratics

My pupils panic at the sight of a quadratic alongside a leading coefficient greater than one.  I factorise these quadratics yesteryear 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 really 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 get-go but paves the agency for a large reveal 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 choice - 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 yesteryear Don Steward to run across his tap live yesteryear method for finding factors as well as for lots of helpful exercise questions.
Also worth a mention: when I get-go start instruction quadratic factorisation, I similar to purpose this well-designed sum-product worksheet from greatmathsteachingideas.com as a starter. It's skillful exercise of an essential skill.


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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:
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:

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:
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.



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Surds

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

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

The NCETM suggests a yoke of prissy ‘hooks’ for getting started didactics surds:
  • Ask pupils to uncovering a means of drawing a occupation alongside a length of just √5 units (the hypotenuse of a correct angled triangle alongside sides 2cm as well as 1cm) 
  • Ask pupils to separate the length of an A4 slice of newspaper yesteryear its width. Repeat for A3 as well as A5. What produce they notice? (The answer is e'er √2)
This blog post has some to a greater extent than ideas for introducing the concept of surds. And I similar this on the history of surds.

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

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

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



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



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Linear Simultaneous Equations

Solving linear simultaneous equations is rather satisfying. In this postal service I advise approximately techniques too resources for pedagogy this topic.

Equality too 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 matter are also equal to ane another’. Influenza A virus subtype H5N1 well-made betoken inward a give-and-take nearly racial equality, but also an interesting claw into a method for solving simultaneous equations such as
y = 4x + 6
y = 2x + 3
Both 4x + six too 2x + three are equal to y, thus logically nosotros convey 4x + six = 2x + three (this is essentially merely a exchange method). Why non present this this blog gives a adept explanation of Lincoln's point)

Elimination too 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils abide by it really slow to recall the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inward the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inward each equation is positive (‘same sign’), we subtract one equation from the other.

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

Graphical Solutions
It’s then of import for pupils sympathise that whenever they solve linear simultaneous equations, they are inward fact finding the betoken of intersection of 2 direct lines. It’s essential to position a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) too perish them thinking nearly why at that spot are no solutions.  I similar to present them this cute picture too.

Wordy Equations
This is ane of my favourite simultaneous equation questions: “A zoo has several ostriches too several giraffes. In full they convey xxx eyes too 44 legs. How many ostriches too how many giraffes are inward the zoo?”. Make certain you lot 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:

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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.

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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:



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Revision Alongside Twelvemonth 11

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

My Year 11s expressed their frustration inwards trying to recollect the differences betwixt statistical graphs – especially histograms, frequency polygons together with cumulative frequency graphs. Influenza A virus subtype H5N1 cardinal expanse of confusion is when to move midpoints, endpoints, course of written report widths etc. I created this for them to assist clarify these points:  GCSE Graphs Revision Summary

They besides fretted nearly which formulae they had to recollect for mass together with area. In course of written report nosotros went through this sheet - I asked them to label each formula according to whether they needed to acquire it or whether it was provided. I therefore gave them this formula summary to accept away.

In i 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, equally good equally my own mixed A* revision cards. I besides encouraged them to brand their ain cards at home.

There are many skillful 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 terminal lesson amongst my Year xi course of written report 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 pathetic for non crediting the originators of this material. It includes the rather tasteless but memorable motion-picture demonstrate below, which got a huge reaction from my class! ‘If y'all don’t similar it, don’t produce it!’ I told them. :)

Source: @mathequalslove


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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

For resources for surface area too mass of similar figures, encounter my resource library.



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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!)



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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.

    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.



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    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 4Ï€r2. 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:
    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!








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    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:

    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:






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    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:

    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:

    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:

    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:

    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.








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    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...

    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


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