5 Maths Gems #1

I’m fairly novel to Twitter. My absence over the final few years agency I’ve missed out on thousands of splendid pedagogy ideas. Twitter is a source of endless inspiration. So I lead keep a plan. I’m going to write a weekly post highlighting v corking novel ideas I’ve gleaned from Twitter. These posts volition assistance me recall things. And hopefully my readers volition do goodness too.

Today I’ve exceeded my limit too am presenting a listing of 6 ideas from my calendar week on Twitter (not a practiced start! I’ll aim for 5 side yesteryear side week).

1. Practical ideas from Maryse. It sounds similar Maryse (@AllThingsMaths) has done an amazing project transforming mathematics pedagogy inwards her schoolhouse too enthusing her students amongst tonnes of creative ideas. Here’s a alternative of those she’s shared this week:

• Play select handgrip of amongst eggs too run out the relative frequency of smashing.
• Get an one-time tyre, pigment it too gyre it to demonstrate circumference. 
• Have a release employment painted inwards the playground.
• Have discussions almost going dorsum inwards fourth dimension too Doctor Who amongst move graphs. 

I dear these ideas. Follow @AllThingsMaths for lots more.

Mistake Game, Colin Beveridge (My Favorite Liar’. You must read this! It prompted a give-and-take on Twitter almost whether the thought would run inwards maths. I think it would. In your outset lesson amongst a novel class, nation them that you'll nation i prevarication per lesson. Your pupils lead keep to position your lies. In the give-and-take on Twitter nosotros came upward amongst a practiced listing of lies too misconceptions, such equally 'multiplication makes numbers bigger', 'if a release has 6 zeros too so it's inwards the millions' too 'one is a prime number'. The thought is that you lot skid these lies into your pedagogy too promise that your pupils volition straightaway challenge you. And if no-one challenges you lot too so it volition brand a squeamish plenary discussion. Mr Allan (@mrallanmaths) is going to endeavour it out - I’m actually looking forwards to hearing how effective it is. I think, similar the error game, it volition hold out incredibly engaging.

3. Box plots party. In reply to my post almost teaching box plots, Pete Sides of the South Yorkshire Maths Hub (@SYMathsHub) suggested a lovely activeness inwards which pupils utter over the ages of guests at dissimilar types of party, to assistance them sympathize the concept of spread. For event you lot could inquire them to depict a box plot representing the ages of guests at an 18th birthday party, a wedding, a child’s political party etc. I similar this thought so I turned it into a worksheet too added it to my spider web log post.

Trigonometry triangles are similar. I’ve never given much thought to the fact that my students are missing an chance to practise rearranging formulae. I sympathize the argue for mixed views on these methods, but I do rather similar the triangle shared yesteryear Malc Henderson (@malc_henderson) for solving contrary per centum problems. It’s squeamish to lead keep a arrive at of tools to back upward students when they’re preparing for their GCSEs.

6. Display ideas. Clarissa Grandi (@c0mplexnumber) posted a moving painting of her novel ‘vwllss’ corridor display (inspiration from @El_Timbre). It looks fantastic - what a practiced idea!

Other practiced display ideas I’ve seen latterly include circle formulae yesteryear Dawn (@mrsdenyer), a foursquare beginning clock yesteryear Duncan Smart (@duncsmart), too an interactive release puzzle for a maths corridor or classroom, shared yesteryear Mr C Ward (@MrWardMaths).

There you lot go, half dozen maths gems from @mathsjem (my initials are JEM yesteryear the way, it’s non a spelling mistake!). This is only a pocket-size alternative of the practiced ideas I’ve seen on Twitter this week. More to come upward side yesteryear side week!

I’m working on a few posts at the moment, including i on introducing algebra too i on introducing differentiation – if you lot lead keep whatever corking ideas too so delight e-mail resourceaholic@gmail.com or tweet me.

Image sources: lightbulb tampawebdesigner.net; birds techwyse.com

Introducing Differentiation

Influenza A virus subtype H5N1 spell agone I was asked by @_JPMason to write a postal service close how I innovate differentiation to my Year 12s. I've been procrastinating for weeks simply hither I am, large drinking glass of vino inward hand, attempting to tackle this challenge. I've alone introduced calculus a few times together with I don't intend I've e'er done it peculiarly well. So this is a proficient chance for me to gain some enquiry together with some thinking which volition hopefully improve my ain teaching practice.

This postal service is primarily aimed at teachers who are teaching calculus for the starting fourth dimension time - I promise you lot honor some useful ideas here.

An Instantaneous Rate of Change
As good every bit knowing how to differentiate, students demand an intuitive agreement of the slope of a bend at a point.

Students are familiar amongst the concept of gradient as a charge per unit of measurement of change, simply alone inward the context of the steepness of direct lines. Their adjacent stride is to empathise that they tin also decide the slope of a curve. But dissimilar a direct line, the steepness of a bend changes constantly. Hence nosotros direct hold a gradient function - lay inward a value of x together with nosotros honor the derivative at a specific indicate - an 'instantaneous charge per unit of measurement of change'.

You could start past times showing your students a uncomplicated distance-time graph. Discuss how the slope changes inward each department of the graph - your students volition easily position positive, negative together with null gradients. Ask them how to assign a discover to those gradients together with they volition in all probability retrieve that slope is calculated every bit 'rise over run' ie distance divided past times time. In a distance-time graph, the value of the slope represents speed. Now beak over the sentiment that direct lines correspond constant speed. Ask your students if they tin run or wheel at a constant speed. Perhaps seek it inward the classroom - direct hold your students walk across the room simultaneously, attempting to keep constant speed. Impossible? If your schoolhouse is lucky plenty to ain a motion sensor then this is a proficient chance to utilisation it - graph matching activities are bang-up fun. The indicate is that speed varies together with thence it should live on represented past times a curve. It's slow to decide the slope of a direct delineate simply how tin nosotros decide the slope of a curve? That's the large question.

'Making feel of differentiation' by Project Maths describes the sentiment of an instantaneous charge per unit of measurement of alter inward a agency your students volition understand: "The speed of an object at an instant inward fourth dimension is surprisingly hard to define precisely. Consider the statement: 'At the instant he crossed the complete delineate inward 2009 Usain Bolt was travelling at 28 mph'. How tin such a claim live on substantiated? Influenza A virus subtype H5N1 photograph taken at that instant would live on no assist at all every bit it would demonstrate Usain Bolt motionless. There is some paradox inward trying to written report Usain’s motion at a item instant inward fourth dimension since, to focus on a unmarried instant, you lot effectively halt the motion! Problems of motion were of key occupation concern to Zeno together with other philosophers every bit early on every bit the fifth century B.C. The modern approach, made famous past times Newton's calculus, is to halt looking for a uncomplicated notion of speed at an instant, together with instead to expect at speed over pocket-size fourth dimension intervals containing the instant". Khan Academy has a truly proficient Introduction to Differential Calculus video close Usain Bolt together with instantaneous rates of change.

Once you've given students a sense of savor of what calculus involves, seek a uncomplicated activeness similar this to acquire them thinking close the changing gradients of curves:

Source: Project Maths

They should live on able to consummate the tabular array without whatever instruction, based on what they know close gradients from Key Stage 3/4. I've produced a worksheet that covers these introductory ideas. This could live on exist fix every bit a homework inward advance of the starting fourth dimension calculus lesson.

First Principles
Once students start differentiating using a set of rules, this theme is fairly straightforward. They apply a uncomplicated physical care for together with acquire the answers correct - hi presto, they're doing calculus. But it's essential that we show them where the rules come upward from, so let's expect at that.

Like most Influenza A virus subtype H5N1 degree teachers, my starting fourth dimension calculus lesson focuses on differentiation from starting fourth dimension principles. In the bang-up calculus argument of the 17th Century, Newton together with Leibniz independently invented calculus to allow the notion of charge per unit of measurement of alter to live on made mathematically precise. To quote Jonny Griffiths, "I similar the sentiment that every bit mathematics teachers nosotros are trying to rerun the history of the dependent acre within our students' heads, alone quicker! Maybe discovering the dominion for differentiating xⁿ is such an of import trial inward this history that this activeness wins its position inward an AS class where fourth dimension is tight".

In my lesson on differentiating from starting fourth dimension principles, I plot y = x² on the board together with guess the slope at x = three using a serial of increasingly brusque chords. Once we've established that the slope of the tangent (and hence the curve) at this indicate is 6, I gain the same for a duet to a greater extent than points. I together with so acquire through the algebra for the full general indicate (x, x²). We found that the slope role is 2x together with beak close how nosotros tin utilisation that role to honor the slope at whatever point.

Then I acquire the students to direct hold a acquire amongst y = x³ and y = x⁴. They expect for patterns together with figure out the dominion for y = xⁿ. Sounds straightforward simply the limits together with deltas may confuse your students, so don't rush them.

betterexplained.com

This starting fourth dimension principles method is clearly explained inward this article from Math Centre. If you lot haven't taught a starting fourth dimension principles lesson earlier together with are a chip unsure together with so lookout adult man this video to come across how it's explained. Most teachers I've spoken to innovate differentiation inward a similar way. Some gain a lot less explaining than me, instead getting the pupils to gain most of the piece of work themselves past times paw or using ICT. If you're looking for a resources to guide you lot inward this starting fourth dimension principles lesson together with so this worksheet from SRWhitehouse on TES mightiness live on helpful. If you'd rather students utilisation ICT (Desmos or Autograph), together with so this RISP gives some guidance.

Resources

I truly savour teaching differentiation in i trial we've got past times that tricky starting fourth dimension lesson. Optimisation is peculiarly satisfying.

I've listed a few teaching resources here.

For activities that assist students practise the basic rules, at that topographic point are simple polynomials dominoes and factorised quadratic dominoes from Teachit Maths. WJEC gives us a differentiation pelmanism for the interactive whiteboard together with the Standards Unit has a Matching Functions together with Derivatives activity.

SRWhitehouse on TES gives us pick of fantabulous differentiaton exercises.

Once you lot acquire onto stationary points, here's a few resources to try:

• Finding stationary points of cubic functions - Standards Unit
• Optimisation - The Chalk Face
• Maxima together with Minima problems (notes & slides) - Nuffield Foundation

Project Maths is a fantastic website amongst lots of proficient resources, many of which are featured inward my resource libraries. It’s based on the Irish Gaelic schoolhouse organization so is a chip hard to navigate if you’re non familiar amongst their curriculum. The best bits are the activities at the dorsum of their T&L plans - for instance Introduction to Calculus is packed total of fantabulous resources for introducing differentiation together with explaining concepts relating to rates of change. It fifty-fifty features a Usain Bolt activeness which ties inward nicely amongst the ideas above.

Final thoughts
Differentiation truly exposes gaps inward students' indices together with algebra skills. If you're looking for resources to assist you lot learn the other topics covered inward Year 12, come across my Core AS Resources Library.

I highly recommend that all maths teachers read the articles close calculus on betterexplained.com, starting amongst Calculus: Building Intuition for the Derivative.

Jo or Gottfried?

Calculus is a rare branch of mathematics inward which you lot truly desire a pupil to enquire the inquiry 'But Miss, when volition nosotros e'er demand to know this?'. There are endless applications in a broad discover of fields including engineering, architecture, medicine, physics, finance together with economics.

As usual, I'm truly keen to listen your teaching ideas - delight comment below or tweet me.

Apologies for whatever mistakes inward my terminology inward this post. I'm no Leibniz. If I've made whatever glaring errors together with so gain allow me know.

If all else fails together with so enquire your students to purchase the Cartoon Guide to Calculus. Who needs teachers?

Reflects

I began writing this weblog when I started motherhood acquire out 7 months ago. Now that my motherhood acquire out is coming to an end, I'm inwards a reflective mood. I fully intend to proceed writing it i time I provide to operate because writing a weblog - along amongst joining Twitter - has been the best affair I've always done for developing my teaching.

I've learnt to a greater extent than inwards the in conclusion 7 months than I did inwards the previous v years. I've learnt that other teachers are total of amazing ideas. I've learnt how of import it is hear to those ideas too to portion them amongst others. I've formed opinions on what plant good inwards the classroom too what doesn't. I've decided where my priorities lie. I've been inspired past times the passion too dedication of others. I've learnt lots of novel mathematics. I've also learnt close wider issues inwards education. I've learnt that it's impossible to concord amongst everyone precisely it's of import to rest positive too live supportive of my beau maths teachers. I value the advice too opinions of the Twitter community. I don't know how I survived without them.

Now I'm starting to project design lessons for the get-go fourth dimension since May, I've been looking dorsum through my posts.

Gems
Gems 13 was my most pop transportation service ever. Writing these posts takes me a goodness few hours each weekend - fourth dimension that I'll demand for marker when I kicking the bucket dorsum to work. So my v weekly gems may acquire my x monthly gems.
Posts
Ideas from Shanghai was the transportation service that made the biggest impact. I'm real proud that the ideas I featured made their agency into classrooms all over the world. Here's a pocket-size pick of the comments made:

These tweets advise that my weblog is an effective channel for sharing teaching ideas.

I was pleased that most readers understood why I chose to focus on mathematical methods instead of discussing wider issues relating to the cultural, political too structural comparisons.

And it was a goodness demonstration of the ability of Twitter for sharing ideas on a global scale.

  

Thoughts on Teaching Fractions, Introducing Algebra and Introducing Differentiation. I flora these posts especially challenging to write - precisely worthwhile. For event I project design to totally alter the agency I innovate calculus to my Year 12s afterwards researching option approaches. If I didn't write a weblog I never would receive got taken the fourth dimension to retrieve close it. Other pop topic posts included Ideas for Teaching Circle Theorems, Pythagoras' Theorem and Teaching Trigonometry. I welcome requests for time to come posts.

I've written 74 weblog posts thus far, thus yous mightiness live wondering where to start if you're novel to reading my blog. If you're planning lessons too then I advise yous role the search component division or the Practical Tips for (Newly) Qualified Teachers which has loads of ideas that mightiness brand your life easier. If yous instruct H5N1 grade too then yous mightiness desire to read Bridging the Gap to H5N1 Level which, cheers to Andrew Old, featured inwards the Academies Week column Top Blogs of the Week.

My post Why Teach?, which gives an insight into why I became teacher, was also popular. 

It was my post Long Live Stem too Leaf that get-go got my weblog to a greater extent than or less attention. In this post I argued against Cav's sentiment that Stem too Leaf Diagrams were a welcome removal from the curriculum. This was the get-go fourth dimension I was brave plenty to assert an opinion! Since too then I've acquire a to a greater extent than confident blogger.

#PREThomeworks

In August, Kathryn Forster tweeted to a greater extent than or less photos of her novel homework template:

I thought this was a genuinely goodness homework format - it would sure enough operate good amongst my students - thus I asked Kathryn if I could characteristic her template inwards my adjacent gems transportation service (Gems 3). There was a non bad answer to this post, thus Kathryn too I started working on edifice upward a large collection of these homeworks. I gave them a get upward - 'Pret homeworks' - too nosotros asked for contributions through Twitter. I ready a page on resourceaholic.com to portion contributions. This rapidly became the busiest page on my website. I felt that these pop homeworks deserved their ain dedicated site thus I moved them to prethomework.weebly.com in October. We immediately receive got 69 homeworks (the collection grows every week) from 27 contributors. The format has been adopted past times Science too English linguistic communication too. Again, this demonstrates the ability of Twitter every bit a collaboration tool.

Sphere Pret homework by @_rhi_rhi

Resource Libraries
My resource libraries are total of recommendations. The Number page has been the most popular, closely followed by Algebra and Shape.  Interestingly, the Data resources are barely used inwards comparison. When I kicking the bucket dorsum to operate I retrieve my Core AS and Statistics AS pages are going to live genuinely helpful because it's difficult to detect goodness Post-16 resources.

Misconceptions
I'm working on another project, a misconceptions website. You're welcome to receive got a hold off at it too give me to a greater extent than or less feedback, precisely acquit inwards heed that it's very early on days. I demand to give it its ain URL too I receive got loads to a greater extent than materials to add. But if yous receive got a quick look, you'll acquire an thought of what I receive got inwards mind. I promise it volition live a useful tool, especially for novel teachers. I retrieve I mightiness demand a twain of volunteers to add together posts i time it's upward too running thus delight allow me know if you're interested inwards helping.

Still addicted?
I'm even thus real much addicted to searching the cyberspace for maths resources too immediately I tin forcefulness out add together blogging to my listing of addictions... has acquire blogaholic! It's been a non bad 7 months. I mightiness receive got to cutting downward soon, precisely at to the lowest degree i time I'm dorsum at schoolhouse I'll genuinely acquire to endeavor things out earlier I recommend them. I can't write a goodness weblog close maths teaching if I'm non genuinely teaching whatever maths.

Please vote for me!
If you're a regular reader of my weblog too then you'll know that lately I've been asking people to vote for me inwards the 2015 Great Britain Blog Awards. The listing of entrants inwards the individual/freelance instruction category is immense too many of the other entrants receive got tens of thousands of followers. Only i inwards v of the blogs inwards my category volition acquire through to the final. If yous could spare a infinitesimal that would live fantastic - delight click hither to vote. Voting closes on third Dec 2014.

Thanks for reading. ☺

My daughters too my blog!

Tricks In Addition To Tips 3: Quadratics

highest mutual factor and methods for sequences, linear graphs too surds.

The vertex of a quadratic graph
This comes upward inwards the novel maths GCSE, inwards questions similar this which is taken from the Pearson Edexcel GCSE (9-1) Mathematics Sample Assessment Materials:

Pause for a infinitesimal too expect at this question, because it's a non bad instance of the modify inwards difficulty inwards the novel GCSE. Note the utilisation of business office annotation too the term turning point. The equation doesn't factorise. The graph doesn't cross the x-axis. The coordinates of the turning betoken aren't integers. This is a notable footstep upward from the type of questions asked inwards electrical current GCSE exams.

For the purpose of this post, let's consider the business office y = x² - 6x + 10. There are a give away of ways to notice the coordinates of the turning betoken - how would y'all create it?

1. Vertex Form
The term 'vertex form' is non unremarkably used inwards the UK. Vertex shape is what y'all acquire when y'all consummate the square. So we'd write the business office equally follows:

y = (x - 3)² + 1

Now nosotros tin sack position the turning betoken at in 1 trial away. I've e'er explained it a chip similar this:

"The (x - 3)²  is squared thence it tin sack never move negative. The lowest it tin sack move is zero. It's null when x is 3. The lowest possible y value is 0 + 1. So nosotros know that the minimum is at (3,1)..."

This explanation is inwards draw alongside my idea procedure - it's the agency I position the turning betoken - but my students actually create out alongside it. Of all the things I teach, this is the explanation that gets the most blank looks! So this yr I tried a dissimilar approach when revising this theme alongside my Year 11s. This fourth dimension I relied on my students' noesis of graph transformations. I told them to intend of the graph y = (x - 3)² + 1 equally a transformation of the graph y = x². It's been translated iii units correct too 1 unit of measurement up. The vertex moves from (0,0) to (3,1). They constitute this approach actually slowly - it made a lot to a greater extent than feel to them. Suddenly all my students were able to notice the vertex of a quadratic function.

As long equally students own got studied graph transformations thence this approach seems to work. This instruction gild is worth bearing inwards hear when designing a Scheme of Work. 

From at nowadays on, I'm going to utilisation the transformation method. But at that topographic point are alternatives...

2. H5N1 formula
In unopen to countries, students only memorise a formula. They larn that the x coordinate of the vertex is -b/2a. They thence notice the y coordinate yesteryear substituting that value into the equation.

By memorising this formula, y'all tin sack notice the coordinates of the turning betoken of whatever quadratic function without completing the square. At my conference session I showed the video below - lookout it to encounter how the method is explained. I'm non a fan of this approach. I don't desire my students to only memorise a formula - there's no conceptual agreement here.


3. Differentiation
Differentiation is e'er a pleasure. We don't create calculus at GCSE, but I idea it worth mentioning hither that unopen to other method to notice a turning betoken of a business office is to laid upward the derivative equal to zero. As y'all tin sack encounter below, for a quadratic that volition e'er hand us x = -b/2a.

4. Symmetry
For a quadratic that intercepts the x axis, the vertex is the midpoint of the 2 roots. This plant because parabolas are symmetrical. Up until late I idea this approach wasn't possible for quadratics that don't intercept the x axis, but thence I discovered James Tanton's method. It's described below for the business office  y = x² + 4x + 5  - for to a greater extent than exceptional too examples, encounter this Algebra too Core AS resource libraries are packed total of recommended resources for instruction this fantastic topic, such as this activity from Susan Wall.

Preparing for the novel GCSE
As I was writing this postal service it occurred to me that there's a lot of actually of import things that maths departments demand to do this term to cook for the novel GCSE. Writing novel Schemes of Work is a huge job, equally is finding suitable resources for instruction the novel GCSE topics.

CPD for maths teachers is likewise actually important. All maths teachers demand to move familiar alongside the novel GCSE content - they demand to know what's been added too what's been removed. They demand to expect at lots of instance questions.

The other affair that all teachers demand to create at nowadays is a patch of written report noesis banking concern gibe - are at that topographic point whatever topics on the novel GCSE syllabus that you're non familiar with? This is specially relevant for teachers who've never taught H5N1 degree maths. Has everyone inwards your subdivision idea close how to learn the novel GCSE topics? It's fourth dimension for unopen to vital maths subdivision CPD.

New Gcse: Tangents In Addition To Areas

At commencement glance it appears that calculus features inwards the novel GCSE specification. On closer inspection it turns out that our students volition detect the slope of a plication past times drawing a suitable tangent rather than past times differentiating. And instead of integrating, students volition use the trapezium rule (or similar) to detect the expanse nether a curve. So calculus remains reserved for Key Stage 5, merely our students volition straightaway go amend prepared for calculus when they commencement regard it. GCSE volition create got given them a conceptual agreement of charge per unit of measurement of modify together with an powerfulness to translate this contextually.

This postal service talks you lot through this novel GCSE topic - it tells you lot what you lot demand to learn together with provides links to resources.

Specification together with Exam Questions
Here's the relevant extracts from the novel GCSE specification:

This all becomes clearer when nosotros await at example examination questions. Huge thank you lot to Tom Bennison (@DrBennison) for doing the difficult operate for me hither - he's been through the sample assessment materials for all examination boards together with collated the relevant questions inwards this Subject Knowledge Check. In a typical question, students are given a velocity-time graph together with asked to detect the amount distance travelled and/or the acceleration at a specific time.

AQA helpfully provides additional clarification nigh the specification inwards their instructor guide. The extract below is from GCSE Mathematics (8300) Teaching Guidance (available to All About Maths members) which provides a release of additional example questions.

Methods
The diagrams below are taken from this extract from a novel GCSE textbook which sets out the criterion methods that our students volition use.

Students volition already know how to detect the slope of a direct business (ie 'rise over run' or equivalent). To guess the slope of a plication they volition create got to pull a tangent, every bit shown here:

They'll also demand to create upward one's hear whether the slope is positive or negative.

To guess the expanse nether a graph, students volition create got to dissever the expanse into sections. The AQA Teaching Guidance says 'the trapezium dominion demand non go known merely it is recommended every bit the most efficient way of calculating the expanse nether a curve'. Unlike at Influenza A virus subtype H5N1 level, they won't go given the formula inwards the exam.

The option to using the trapezium dominion is to dissever the expanse into a release of triangles together with rectangles.

Motion Graphs

The methods described to a higher house are fairly straightforward. I recall interpretation powerfulness examine trickier (eg agreement what motion graphs are showing). Students volition demand to know that speed, acceleration together with deceleration are rates of change, together with that the expanse nether a velocity-time graph represents distance. There's a lot of novel concepts together with vocabulary here.

Bear inwards hear that motion graphs come upward up inwards Physics GCSE too. As shown inwards this extract from the AQA Physics GCSE Specification, it's precisely the same content:

Other Contexts
I was initially confused past times the cite of 'graphs inwards fiscal contexts' inwards this department of the specification - I've seen questions inwards which students create got to interpret fiscal graphs merely cypher involving tangents or areas. Thanks to @DJUdall for sharing the moving painting below (taken from this novel GCSE textbook) which shows an example of estimating a charge per unit of measurement of modify inwards a fiscal context.

Could examination questions encompass other contexts, also motion together with finance? It's possible. In the example below from CIMT students are asked to detect the majority of H2O represented past times the shaded area. To empathise why the expanse nether the graph represents majority nosotros tin dismiss consider the units - the units on the horizontal axis are seconds, together with the units on the vertical axis are m³/s, then when nosotros multiply the 2 together nosotros larn m³.

Instantaneous Rate of Change

Students volition demand to empathise the divergence betwixt an average charge per unit of measurement of modify over a menstruum of fourth dimension together with an instantaneous charge per unit of measurement of change. In my postal service 'Introducing Differentiation' I talked nigh how to give students an intuitive agreement of the slope of a plication at a point. It's worth reading the department entitled 'An Instantaneous Rate of Change' for ideas, videos together with resources (including my worksheet 'Thinking About Gradient' which was designed for Influenza A virus subtype H5N1 degree merely is straightaway suitable for GCSE).

Resources
Resources for this topic are listed below. I'll add together these to my library together with volition go along to add together novel resources every bit I detect them.

• @DJUdall has produced this first-class graphing activity which covers both tangents together with areas nether graphs. 
• @jase_wanner has written this super hero activity on distance-time together with speed-time graphs to prepare students' agreement of how to translate these graphs.
• Gradient on a curved graph by Owen134866 on TES gives students the chance to practice drawing graphs together with tangents. My worksheet Finding the slope of a plication using a tangent is similar, merely students aren't required to pull the graphs themselves.
• Using Graphs from CIMT covers a broad arrive at of graph topics. Section 17.2 covers areas nether graphs using the trapezium dominion together with Section 17.3 covers tangents to curves. The amount arrive at of resources for this module are available on TES.
• Nuffield Mathematics provides a Free-Standing Mathematics Activity 'Speed together with Distance' which is nigh finding the expanse nether a speed-distance graph. Resources include slides, a student sheet and teacher notes.

'Graphing' by @DJUdall

I promise this postal service has been useful inwards helping you lot fix to learn this novel GCSE topic. Please permit me know if you lot create got whatever resources to share.

You powerfulness also detect my other posts nigh novel GCSE topics helpful: Sequences, Inequalities together with Quadratic Graphs.

See my New GCSE Support Page for resources together with links for all novel GCSE content. 

'Drawing a Tangent Line' past times NCTM

A Degree Resources

At #mathsconf5 I delivered a workshop entitled 'Resources for Teaching Maths at AS Level'. I thought it mightiness hold upwards helpful to portion highlights from that presentation here. I'm going to separate my ideas into 2 separate posts - inwards today's postal service I'll listing recommended sources of Influenza A virus subtype H5N1 degree resources. In my adjacent postal service I'll utter over some ideas on how to construction Influenza A virus subtype H5N1 degree lessons, how to operate resources as well as how to organise as well as portion resources.

Here's the slides as well as handout from my conference session.

My Top 10
In my workshop I talked through my favourite sources of Influenza A virus subtype H5N1 degree resources. I narrowed it downwardly to ten, but in that place were many to a greater extent than I wanted to include.

1. Solomon Worksheets
I tend to operate extracts from Solomon worksheets for starters, plenaries or extension work. For example, if I've taught quadratic inequalities hence the interrogation below makes a overnice starter interrogation inwards the adjacent lesson:

Solomon worksheets come upwards amongst rattling clear worked solutions hence you lot could also give these worksheets to students for independent exercise at home. It's non helpful when teachers tell their students to do ongoing independent report but don't supply (or indicate them inwards the direction of) suitable exercise questions.

You likely direct maintain these worksheets on your network at school, if non hence they tin hold upwards purchased here.

2. Activities from Susan Wall
Susan Wall is considered the queen of rich tasks at Influenza A virus subtype H5N1 Level. Some of her resources are on Integral, which I'll utter close inwards a infinitesimal - but some other expert agency to discovery her cloth is to search for 'Susan Wall' inwards the National STEM Centre eLibrary.

Have a larn at the interrogation below. It may solely accept you lot a minute, but it's an first-class interrogation for students who discovery this notation tricky (plus anything that involves graph sketching is worthwhile).

I also dearest Susan Wall's integration activity below. Again, this is bully for getting students to intend rather than simply follow procedures.

3. Integral
Every schoolhouse should direct maintain a subscription to integralmaths.org. Provided yesteryear the MEI as well as FMSP, it's an extensive collection of notes, activities, worksheets as well as assessments for every Influenza A virus subtype H5N1 degree module as well as seek out board. The indices maze below is simply ane instance of MEI/FMSP cloth - there's a huge diversity of resources on Integral hence it's worth spending a hateful solar daytime inwards the holidays exploring.

This guide provides detailed data close the content of Integral. Another instance of an Integral activity is shown below. I dearest this activity!

4. TES - SRWhitehouse

There's loads of Influenza A virus subtype H5N1 degree resources on TES - my favourite contributor is Susan Whitehouse. I operate her resources inwards almost every lesson. I discovery her materials especially useful when instruction C3 as well as C4 - you'll discovery lots of links to these inwards my A2 resources library.

Her indices activity (extract below) is excellent. I await that most people operate this when instruction indices at Influenza A virus subtype H5N1 degree or GCSE, but it also makes a helpful starter inwards a lesson on differentiating expressions amongst negative as well as fractions indices. Question half dozen as well as vii below frequently stimulate confusion for students - they desire to write both equally 2x^-3.

The logs activity shown below is some other instance of a Susan Whitehouse activity that I operate regularly.

5. Teachit Maths
Teachit Maths is a bully website for Key Stage iii as well as GCSE. PDF resources are available for free. Their collection of Key Stage v resources is growing. I don't frequently operate card-based activities but I do similar their log dominoes. I've used them earlier as well as they worked well.

I similar this Pairs of Lines activity besides - it would piece of employment inwards both a Higher GCSE lesson as well as inwards an AS coordinate geometry lesson.

6. Mathematics Assessment Project
The materials of the Shell Centre) remind me of the Standards Unit materials (more on that inwards a minute). They supply well-designed tasks for formative as well as summative assessment. Although these materials are designed for the United States curriculum, there's enough of first-class resources for Key Stage 3, iv as well as 5. There's 2 lessons that I especially like: Sorting Equations of Circles 1 as well as Sorting Equations of Circles 2. I frequently operate the 'Going circular inwards circles' poster chore (solution shown below). I operate this when I've simply taught students the equation of a circle - instead of giving them a textbook exercise, I give them this grid on A3 paper. Working inwards pairs, they direct maintain to identify diverse equations of circles on the grid.

The 2nd circles lesson is also total of first-class tasks - an extract is shown below.

7. CMEP
We're rattling lucky that the Cambridge Mathematics Enhancement Project - an initiatory to prepare Influenza A virus subtype H5N1 degree resources - is currently producing loads of fantastic novel material. If you lot desire to access these resources spell they're nevertheless nether evolution hence you'll demand to register amongst CMEP (although some materials are currently available through NRICH). It won't hold upwards long though until the total collection of CMEP resources are made available to all. Some of their materials are enrichment problems for high attainers, but there's also fluency exercises as well as scaffolded tasks. For instance I similar this 'Logarithm lattice':

as well as this 'Integral chasing' activity:

8. Don Steward
I can't utter close resources without recommending my hero Don Steward. His weblog (Median) contains rich tasks for xi - xvi twelvemonth olds, but many of his higher halt GCSE resources are suitable for Influenza A virus subtype H5N1 degree too. Topics include algebra, quadratics, trigonometry, sequences, surds, indices, cubics, graph transformations as well as coordinate geometry. An instance is his activity 'geometric series, some amongst surds' which was designed for the novel GCSE but is suitable for C2 (Edexcel).

I've already blogged close his 'one wrong simplification' tasks which worked brilliantly on Year 12 induction day.

And here's some other typical Don Steward chore - this ane is on cubics:

9. The Standards Unit
We all know as well as dearest the "Improving Learning inwards Mathematics" (or Standards Units) resources. There's a expert alternative for Influenza A virus subtype H5N1 degree that are good worth exploring. In the yesteryear I've e'er gone instantly for the resources at the back, but late I've discovered that the lesson ideas as well as questioning prompts are also incredibly helpful.  Here's an instance from Matching Functions as well as Derivatives:

10. as well as #mathsTLP
The libraries at resourceaholic.com comprise hundreds of links to hand-picked Influenza A virus subtype H5N1 degree resources. My AS Core library is e'er the commencement identify I cheque when planning a C1 or C2 lesson. Resources are grouped yesteryear topic. The extract below is from a 'Fun Sheet' (I can't discovery a re-create of the master copy mass it came from) - it's a lovely activity for simplifying elementary trigonometric expressions earlier coming together trigonometric identities.

On my weblog you'll also discovery lots of Introducing Differentiation, Algebraic Division, Radians, Logs as well as Factorising Harder Quadratics. I frequently characteristic Influenza A virus subtype H5N1 degree ideas inwards my Gems posts besides - here's ane from John Smith.

Finally, #mathsTLP is every Dominicus eve 7pm - 8pm. This is a Twitter chat inwards which lesson ideas as well as resources are shared. Join inwards to inquire for assist or offering ideas. This is the form of matter you lot mightiness tweet:

More sources
I used to intend that in that place weren't many Influenza A virus subtype H5N1 degree resources around, but it turns out there's enough out there. Every schoolhouse needs a difficult working Key Stage v Coordinator to come upwards into schoolhouse during the holidays as well as pass a hateful solar daytime or 2 downloading as well as organising resources! I'll tell to a greater extent than close this inwards my adjacent post.

There were lots of websites that I didn't get upwards inwards the listing to a higher identify that should definitely hold upwards on your radar. If I'd had longer than l minutes for my workshop, I'd direct maintain included the websites listed below (and many more!):

• MathedUp! - lots of first-class Influenza A virus subtype H5N1 degree links including activities, PowerPoints as well as videos.
• next post volition characteristic to a greater extent than ideas for instruction Influenza A virus subtype H5N1 degree maths.