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

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.



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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.



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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 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.


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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:
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:

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:
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.



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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:

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:



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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:

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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.

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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:



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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


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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

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



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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!)



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Venn Activities

This post service is nearly using Venn Diagrams equally a educational activity tool, rather than educational activity the concept of Venn Diagrams themselves.  To quote the first-class Johnny Griffiths, 'The Venn Diagram amongst iii bubbles is the maths teacher's friend! ... To travel able to create amount inward an eight-region diagram shows a actually deep agreement of the distinctions that a practiced pupil has to travel able to make, spell the weaker pupil finds beingness faced amongst a painting exhibit such equally this much less threatening than a page of exercises'.

Before nosotros get-go using Venn activities inward Maths lessons, let's intend nearly whether pupils are familiar amongst how Venn Diagrams work. I acknowledge to beingness a fleck clueless nearly precisely what children report at main school. The primary here), merely I at 1 time prefer the simpler method described in linear equations activity. It helped consolidate their cognition of linear graphs too allowed me to banking concern check their understanding.
  • Johnny Griffith's first-class RISPs (Rich Starting Points for H5N1 Level Core Mathematics) includes the Venn activities Risp 10 (coordinate geometry) too 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 yesteryear Factorising yesteryear aka nka on TES. 
  • A GCSE extension action on quadratic graphs from MEI.
  • I haven't tried this however merely Don Steward also gives us this lovely here), merely I at 1 time prefer the simpler method described in number activity.

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

    Other Uses
    • When I innovate complex numbers inward FP1 nosotros create a Venn Diagram during cast give-and-take nearly types of numbers (real, rational, integers etc) too 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 too Lowest Common Multiple (method explained here), merely I at 1 time prefer the simpler method described in this post.
    • Quadrilaterals tin travel classified using a Venn Diagram similar this one.  We tin 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) too Statistics 1 at H5N1 score (probability). I'm pleased to encounter that Venn Diagram methods inward probability are on the new Maths GCSE Syllabus so volition travel to a greater extent than widely studied inward future. But inward improver to beingness taught equally a topic inward their ain right, Venn Diagrams are a versatile educational activity tool amongst numerous applications inward the classroom. And they convey the added bonus of beingness created yesteryear a British Mathematican! Well done Mr Venn.



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    Area Together With Volume

    Every maths division should ain a giant lawn tennis ball! Walk into the classroom amongst a large fluorescent ball nether your arm as well as you've straight off got the attending of the class.

    Students stand upward inwards a circle as well as are told they're solely allowed to speak if they're asset the ball. Ask "how could nosotros operate out the surface surface area of this ball?" as well as throw it to a random student. Students throw the ball around the circle equally they part their thoughts as well as advise ideas. At some quest a instructor prompt may last necessary, along the lines of, "why did I convey 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 showtime thinking virtually the markings on the surface of the lawn tennis ball. Eventually person volition topographic point that the surface is made upward of iv circles wrapped around each other, as well as they tin as well as so deduce that the formula for the surface surface area is 4Ï€r2. If they demand convincing, present them this slide.


    This is a really engaging activity. As pupils can't verbalize unless they're asset the ball, you'll run across them wildly waving their arms about, silently begging their friends to move past times them the ball so they tin part their ideas!

    Try it - I'd honey to withdraw heed how it goes.

    Area as well as majority is a broad ranging topic, from areas of triangles inwards Year seven to volumes of hemispheres as well as frustums inwards Year 11. Here's a handful of my favourite resources:
    For related shape give-and-take - why produce nosotros tell hemisphere but semicircle? Why non semisphere or hemicircle? I believe it's because the news circle is from the Latin news circus (meaning ring), therefore nosotros role the Latin prefix semi, whereas sphere is from the Greek news sphaira (ball), therefore nosotros role the Greek prefix hemi. This article virtually semi/hemi/demi gives to a greater extent than examples. If y'all similar this as well as so y'all powerfulness also similar these lovely maths vocabulary activities.

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








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    Maths Vocabulary

    I found Cav's blog postal service 'Vocabulary in addition to maths are non mutually exclusive' actually interesting in addition to it got me thinking most activities in addition to instruction techniques related to maths vocabulary.

    Influenza A virus subtype H5N1 instruction tool that tin last used regularly throughout the twelvemonth is a source).



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    Edit: 11/11/15

    Since writing this postal service terminal twelvemonth I've seen lots of groovy resources for developing vocabulary. I especially similar the Literacy Assessments featured inwards vocabulary noesis survey. When y'all showtime instruction a topic, do a listing of the novel words that volition last used in addition to inquire students to consummate a nautical chart showing their agreement of those words.  Repeat the activeness subsequently to come across the improvement inwards 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 postal service on source).



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    Edit: 11/11/15

    Since writing this postal service terminal twelvemonth I've seen lots of groovy resources for developing vocabulary. I especially similar the Literacy Assessments featured inwards Area in addition to Volume I suggested these maths vocabulary exercises which brand for overnice 'end of term' lessons.  Here's an illustration of an activeness from this pack:



    Here's merely about to a greater extent than links that y'all powerfulness detect useful:

    I was of late talking to a highly intelligent in addition to 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 - in addition to fifty-fifty this pupil (who'll last off to Oxbridge inwards September) constitute this daunting.  We demand to address this effect from a immature age.  One tip is to ever require pupils to respond questions inwards total sentences instead of merely numbers or words - from main schoolhouse onwards. Influenza A virus subtype H5N1 rattling unproblematic illustration - inwards response to the interrogation 'what do nosotros telephone telephone a polygon amongst 8 sides?', don't convey the respond '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 current (source).



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    Edit: 11/11/15

    Since writing this postal service terminal twelvemonth I've seen lots of groovy resources for developing vocabulary. I especially similar the Literacy Assessments featured inwards Gems 43. I also constitute the source).



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    Edit: 11/11/15

    Since writing this postal service terminal twelvemonth I've seen lots of groovy resources for developing vocabulary. I especially similar the Literacy Assessments featured inwards activity below worked good amongst my Year 7s.

    Here's my take away to literacy inwards maths lessons:






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    Linear Graphs

    One of the topics that my pupils combat 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 function out how to respond a GCSE enquiry similar this:
    Strangely, I learn this differently at GCSE as well as Influenza A virus subtype H5N1 level.  At GCSE my pupils write down
    y = mx + c
    as well as substitute values for y, k as well as x, as well as hence solve for c.  Whereas at Influenza A virus subtype H5N1 marking my pupils occupation the equation
    y - y1 = m(x - x1)
    Essentially the same method but a slightly dissimilar approach. Perhaps I should endure to a greater extent than consistent as well as innovate the 'A marking method' at GCSE. I'd similar to take away heed what other teachers do.

    In this shipping service I’ll propose roughly ideas as well as resources for instruction linear graphs.

    Key words
    Let's kickoff amongst the basics. There's a lot of novel vocabulary inwards coordinate geometry, roughly of which pupils volition convey encountered at primary school. This is a overnice vocabulary cognition survey every bit suggested inwards my earlier post. 

    Here's a overnice play tricks for remembering the words parallel as well as perpendicular (this could endure helpful for spellings - parallel is oft misspelt): 

    as well as this activity is suitable for Year vi or 7. 

    Introducing the shape y = mx + c
    I'd unremarkably kickoff this theme inwards Year seven or 8 amongst plotting at nowadays occupation graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

    This theme provides an first-class chance for pupil investigation using Desmos. Use a worksheet to direct pupils through the lesson:

    Once pupils are able to translate the values of k as well as c as well as hence they tin shipping away 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 as well as vertical lines.

    My weblog shipping service 'All most gradient' features ideas as well as resources for instruction slope (the shipping service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets as well as activities).

    Understanding parallel as well as perpendicular gradients
    So here's the substitution data that pupils demand to understand:

    If they know how to function out a slope every bit 'rise over run' (or equivalent) as well as hence pupils should endure able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this i 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 convey the necessary skills as well as cognition 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 certain capable. Essentially it's simply the wording of the questions that throws them.

    Here's roughly 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 as well as Lines.

    Finally, e'er wondered which countries occupation y = mx + c annotation as well as which countries occupation 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 tell I'm live fix to portion them! They tin flame live accessed through the tabs at the move past times of the page.

    This is where I've lay all my resources recommendations for you lot to browse when you're planning lessons. The A' degree pages volition in all likelihood live the most helpful equally it tin flame live difficult to notice practiced resources for Key Stage 5. 

     My recommendations are past times no agency exhaustive - there's loads of practiced resources I haven't discovered nonetheless (the meshing is likewise big, I can't proceed upward alongside it!). But I volition update my listings whenever I come upward across something peculiarly good. To clarify what I hateful past times 'good' - my recommendations include well-designed activities, rich tasks and worksheets for topics where I retrieve it tin flame live difficult to notice suitable practise questions. 

     My Top three Websites
    The resources I've recommended are all gratis as well as come upward from a broad arrive at of sources.  Here's my electrical current favourite websites, inwards no detail order.
    1. Roof Truss task (trigonometry) and Bee Aware (scatter graphs) - at that topographic point are hundreds to a greater extent than as well as 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 really engaging as well as slowly to use. Example resources include this lovely Square as well as 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 inwards pdf form, which is fine for all their printable activities as well as worksheets. You'll demand a subscription (£25 per year) if you lot also desire to access PowerPoints, interactive activities, pedagogy tools etc. Worksheets are well-designed, engaging as well as include solutions. Examples of their resources include this Mental Powers Code Breaker as well as this Transforming Graphs carte kind activity, which I accept used successfully alongside both my Year 11s as well as Year 12s.
    Special get upward 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 H5N1 degree activities. For a total (and ever-expanding) listing of recommended resources websites, meet my links page.

    Factor Trees - Median Don Steward

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

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

    'Find the Coordinates' chore past times Susan Wall


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