Tricks Too Tips 1: Hcf

I lately presented a workshop at the National Mathematics Teacher Conference (#mathsconf2015) entitled 'Tricks as well as Tips: Clever Methods for Explaining Mathematical Concepts'. This postal service summarises the content of that workshop for those who were unable to attend. I receive got quite a lot to comprehend therefore I human face I'll demand to write 3 or 4 weblog posts. In this i I'm going to explicate the rationale for the workshop as well as depict option methods for finding a Highest Common Factor. In subsequent posts I'll comprehend sequences, linear graphs, surds, quadratics, chemical compound measures as well as a few to a greater extent than bits as well as pieces.

Workshop aim
How create you uncovering the Highest Common Factor of 2 numbers? Do yous piece of occupation a Venn method? List the factors? Use the Euclidean Algorithm? Are in that location 'better' methods that yous don't know about? (how create nosotros define 'better'?). These are the variety of questions I desire to explore. The aim of my workshop was to encourage people to reverberate on their dependent area noesis as well as the effectiveness of their explanations. I also hoped that everyone would larn novel methods that they mightiness consider using at school.

What determines the agency nosotros conduct the explicate things?

Most teachers flora pedagogy habits during their grooming as well as NQT year. The method they piece of occupation the start fourth dimension they learn a topic volition in all likelihood remain with them throughout their career - unless they brand a concious effort to assay a novel method. 

One of the few things I recall nearly GCSE maths was that I solved equations yesteryear 'moving price over the equals sign' (the 'magic portal method'). This method is straightaway considered to hold out a shortcut which stands inwards the agency of conceptual understanding. These days it is to a greater extent than acceptable to learn students to solve equations using inverse operations (ie residue the equation yesteryear 'doing the same thing' to both sides). It's lucky that during my PGCE someone told me non to piece of occupation the magic portal method because earlier therefore I was convinced that it was 'the' agency to solve equations. 

Source: https://mrjasonto.wordpress.com

When nosotros were pupil teachers, nosotros drew our methods from a multifariousness of sources. ITT courses don't comprehend much inwards the agency of mathematical methods, therefore nosotros were left to get together ideas from examples inwards textbooks, our memories from school, observations of teachers as well as conversations with colleagues. It's these conversations with colleagues that are vital, but nosotros only don't acquire plenty fourth dimension for them. Most of the novel methods I've encountered over the years receive got non been through organised CPD (ie 'collaboration sessions') inside my department, but instead through jeopardy encounters. My start always weblog postal service was nearly an option method for matrix multiplication that I'd happened to stumble across online.

During my PGCE I was asked to learn a lesson on Highest Common Factor. I recall my mentor showing me the 'Venn Method'. As a final result of that conversation I used the Venn Method for years, until yesteryear jeopardy a colleague mentioned an alternative. Let's human face at that option method now, as well as a release of others. Will yous stick with the method yous know as well as love, or volition yous assay something new?

Highest Common Factor as well as Lowest Common Multiple

I've identified 6 methods for finding the HCF as well as LCM of 2 numbers. I'll explicate each method hither as well as position whatever pros as well as cons.

1. Listing

Source: mathx.net

There's no impairment inwards the listing method. It's brilliant inwards price of underlying conceptual agreement - students tin view precisely what they're trying to arrive at here. List all the factors of the 2 numbers as well as uncovering the biggest release that's inwards both lists - that's your HCF. List all the multiples of 2 numbers as well as uncovering the smallest release that's inwards both lists - that's your LCM. Simple! Shame it's therefore time-consuming. And, inwards my experience, students sometimes immature lady factors from their list. One agency to avoid this is yesteryear listing factors using a pairing method similar this:

Factor rainbows are a pretty option (see this article from the NCTM).

2. The Venn Method

This is a pop method inwards the UK. First, nosotros demand to create a prime number gene breakdown. By the way, if you're pedagogy prime number factorisation therefore yous mightiness similar these lovely magic portal method'). This method is straightaway considered to hold out a shortcut which stands inwards the agency of conceptual understanding. These days it is to a greater extent than acceptable to learn students to solve equations using inverse operations (ie residue the equation yesteryear 'doing the same thing' to both sides). It's lucky that during my PGCE someone told me non to piece of occupation the magic portal method because earlier therefore I was convinced that it was 'the' agency to solve equations. 

Source: https://mrjasonto.wordpress.com

When nosotros were pupil teachers, nosotros drew our methods from a multifariousness of sources. ITT courses don't comprehend much inwards the agency of mathematical methods, therefore nosotros were left to get together ideas from examples inwards textbooks, our memories from school, observations of teachers as well as conversations with colleagues. It's these conversations with colleagues that are vital, but nosotros only don't acquire plenty fourth dimension for them. Most of the novel methods I've encountered over the years receive got non been through organised CPD (ie 'collaboration sessions') inside my department, but instead through jeopardy encounters. My start always weblog postal service was nearly an option method for factor tree activities from Don Steward.

Once yous receive got the prime number factors of each number, push clitoris a Venn diagram as well as house the mutual factors inwards the intersection of 2 sets, as shown inwards the illustration below.

tutorvista.com

The HCF is the production of the elements inwards H5N1 intersection B (ie 2 x 2 x 2 x 2 inwards the illustration above) as well as the LCM is the the production of all the elements inwards H5N1 matrimony B (ie 2 x 2 x 2 x 2 x 2 x 2 x 5). Note that United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland GCSE students are non even therefore familiar with this terminology (ie intersection as well as union), but they volition hold out nether the novel GCSE syllabus.

Even though I taught the Venn method for years, I'm non a huge fan of it. In my experience, students are ok with filling inwards the Venn diagram but therefore they oft can't recall which 'bit' is the HCF. If they create recall the method therefore they in all likelihood don't receive got a clue why it works.

Confusingly, it seems that some people piece of occupation a dissimilar Venn method which involves putting all factors (not prime number factors) into a Venn diagram as well as identifying the highest gene inwards the intersection (see illustration below). This is some other cast of the listing method described higher upwards - it's just a dissimilar agency of organising the list. Let's telephone band this Lenn Method - it's a hybrid of Venn as well as Listing.

http://edtech2.boisestate.edu/brianroska/506/finalproject/gcf.html

3. Prime Factor Pairing

An alternative to the Venn Method is to create the prime factorisation but therefore skip the Venn. Write the prime number factors of each release out as shown inwards the illustration below therefore it's slow to view which factors appear inwards both release - the production of these is the HCF. This method is featured inwards magic portal method'). This method is straightaway considered to hold out a shortcut which stands inwards the agency of conceptual understanding. These days it is to a greater extent than acceptable to learn students to solve equations using inverse operations (ie residue the equation yesteryear 'doing the same thing' to both sides). It's lucky that during my PGCE someone told me non to piece of occupation the magic portal method because earlier therefore I was convinced that it was 'the' agency to solve equations. 

Source: https://mrjasonto.wordpress.com

When nosotros were pupil teachers, nosotros drew our methods from a multifariousness of sources. ITT courses don't comprehend much inwards the agency of mathematical methods, therefore nosotros were left to get together ideas from examples inwards textbooks, our memories from school, observations of teachers as well as conversations with colleagues. It's these conversations with colleagues that are vital, but nosotros only don't acquire plenty fourth dimension for them. Most of the novel methods I've encountered over the years receive got non been through organised CPD (ie 'collaboration sessions') inside my department, but instead through jeopardy encounters. My start always weblog postal service was nearly an option method for this post yesteryear Don Steward.

4. Euclidean Algorithm

I dear the subtraction-based Euclidean Algorithm. It sounds complicated but it's incredibly easy. Try a few examples yourself to view how straightforward it is.

The method (including why it works) is explained inwards James Tanton's video below. I actually similar this method but for some argue I'm hesitant to piece of occupation it with students... Would you?

Note that this method doesn't plough over yous the Lowest Common Multiple, but it's easily found i time you've got the Highest Common Factor. 

This looks similar a pain, but cancelling helps - inwards the illustration higher upwards I found the HCF of sixty as well as 84, therefore to uncovering the LCM I multiply sixty yesteryear 84 as well as dissever yesteryear the HCF.

5. The Indian Method

I've stopped using the Venn Method at schoolhouse as well as straightaway piece of occupation this instead. I'm non certain it's actually called the Indian Method, I'm solely calling it that because of this video. At my schoolhouse nosotros telephone band it the Korean Method because a Korean pupil introduced it to us! I've found that my students actually similar it. It's difficult to acquire wrong. It's slow to explore why it industrial plant too.

Say nosotros desire to uncovering the Highest Common Factor as well as Lowest Common Multiple of 315 as well as 420. Write downward the 2 numbers, therefore (to the left, as inwards my illustration above) write downward any mutual factor. I've chosen 5. Now dissever 315 as well as 420 yesteryear v as well as write the answers underneath (63 as well as 84 inwards this case). Keep repeating this procedure until the 2 numbers receive got no mutual factors (ie 3 as well as 4 above). Now, your Highest Common Factor is only the production of numbers on the left. And for the Lowest Common Multiple, uncovering the production of the numbers on the left as well as the numbers inwards the bottom row (to uncovering the LCM, human face for the L shape).

6. The 'Upside Down Birthday Cake Method'

I should scream this method because I proceed spotting it online (video here). The solely departure betwixt this as well as the Indian Method is that hither nosotros tin solely take prime factors. This seems unnecessary - the Indian Method is quicker. In the illustration below, why dissever yesteryear 2 if yous location larger mutual factors? Why non start yesteryear dividing yesteryear 4, 6 or 12?

Source: https://uk.pinterest.com/pin/13229392628819982/

So that's it - 6 methods for finding a HCF as well as LCM.

Integers
I actually similar this magic portal method'). This method is straightaway considered to hold out a shortcut which stands inwards the agency of conceptual understanding. These days it is to a greater extent than acceptable to learn students to solve equations using inverse operations (ie residue the equation yesteryear 'doing the same thing' to both sides). It's lucky that during my PGCE someone told me non to piece of occupation the magic portal method because earlier therefore I was convinced that it was 'the' agency to solve equations. 

Source: https://mrjasonto.wordpress.com

When nosotros were pupil teachers, nosotros drew our methods from a multifariousness of sources. ITT courses don't comprehend much inwards the agency of mathematical methods, therefore nosotros were left to get together ideas from examples inwards textbooks, our memories from school, observations of teachers as well as conversations with colleagues. It's these conversations with colleagues that are vital, but nosotros only don't acquire plenty fourth dimension for them. Most of the novel methods I've encountered over the years receive got non been through organised CPD (ie 'collaboration sessions') inside my department, but instead through jeopardy encounters. My start always weblog postal service was nearly an option method for set of questions from Don Steward. The next query confused i of my brightest Year 10s:

"A individual has a rectangular plot of dry reason measuring 8.4m yesteryear 5.6m. To survey the release of dandelions they desire to dissever it every bit into the minimum release of foursquare plots. What is the size of each foursquare plot as well as how many such squares volition in that location be?"

My student's approach to this query was to effort to uncovering the HCF of 8.4 as well as 5.6 using the Indian Method. This is what she did:

But she realised that her reply made no sense. 28 can't hold out the HCF of 8.4 as well as 5.6. Can yous view where she went wrong? Although yous tin dissever 8.4 yesteryear seven (indeed, yous tin dissever 8.4 yesteryear anything), it doesn't hateful than seven is a gene of 8.4. The numbers on the left must hold out factors of the numbers at the top. Non-integers don't receive got factors. H5N1 improve approach would receive got been to convert the measurements to centimetres as shown below. 

Factors vs Multiples

If your students fighting to recall the departure betwixt factors as well as multiples therefore they mightiness uncovering this helpful: for factors, mean value of a factory (where separate parts are set together). For multiples, mean value of multi-packs eg if cokes are sold inwards multi-packs of 6 therefore I tin purchase 6, 12, eighteen etc. These ideas are taken from this resource from the thechalkface.net.

Conclusion

Did yous know all of these methods? Will yous assay something new? Please allow me know of whatever skillful methods that I've missed.

Even if you create upwards one's hear to stick with the method you're currently using, at to the lowest degree you've now reflected on how yous learn this topic. Teachers rarely receive got the chance to interruption as well as reflect.

This postal service should hold out read amongst Ed Southall's post Complements #9 LCM as well as HCF which explains the underlying concepts.

The whole presentation from my workshop is here. In my adjacent postal service (give me a few days to write it!) I'll comprehend methods for pedagogy sequences, linear graphs as well as surds.

Mei Conference 2015

Last calendar week was an incredibly busy calendar week for me. On overstep of a number of occupation solid unit of measurement events too personal commitments, I did the following:

• Attended #mathsconf4 inwards London too helped run the TweetUp
• Hosted #mathsTLP on Lord's Day nighttime too #mathscpdchat (on behalf of the NCETM) on Tuesday night
• Had my source SLT lesson observation at my novel school
• Did my source e'er TeachMeet presentation at #TMEpsom
• Wrote 3 weblog posts too processed a dozen novel Pret Homeworks
• Travelled to Bath to attend too introduce at the MEI Conference.

It was a slap-up calendar week but I'm therefore pleased it's over! I've already written virtually #mathsconf4, the #mathscpdchat virtually Problem Solving too #TMEpsom virtually Pret Homeworks, therefore this is my lastly ship service virtually the events of my busy calendar week - this ship service is virtually my sense of the MEI Conference.

Maths CPD

subject specific CPD. Although I produce pick upwards closed to ideas from generic T&L events, my instruction benefits the most from conversations virtually maths - both the pedagogy too the subject. Unfortunately, aside from on Twitter, opportunities for such conversations are few too far between. My previous school's budget for external courses was null (I'm non exaggerating! No external CPD allowed at all). So at the MEI Conference it was refreshing to run across that closed to schools produce withal let their teachers to attend conferences. I chop-chop discovered that the chance to larn virtually maths too educate equally a instructor was immense.

Because I was presenting on the Sat I got to attend that hateful solar daytime for free, too I was staggered past times both how much I learnt too past times how much I enjoyed learning. The alternative of sessions was huge - over the 3 days at that spot were 12 sessions too inwards each session delegates could select from 8 options. Many, but non all, sessions were focussed on Influenza A virus subtype H5N1 flat instruction and/or the purpose of technology.

Ideas for Influenza A virus subtype H5N1 Level

The source session I attended was "The aspirational flat due east student" past times David Philip too Claire Phillips. The session was virtually how to back upwards AS maths students who convey an due east equally their baseline/target grade. We started past times discussing the reasons that therefore many students neglect AS flat maths too therefore flora out what David too Claire convey done at their schoolhouse to improve results. I've persuasion virtually this number earlier (see my post Bridging the Gap to Influenza A virus subtype H5N1 level) therefore it was slap-up to take away heed what they've been doing, including:

• They run an algebra bootcamp inwards the 3 days earlier term starts for flat B GCSE students.
• They number students alongside a self-assessment workbook containing the MEI exercise for each chapter (and links to solutions).
• They purpose a flipped learning approach for the basics (ie students spotter videos at dwelling occupation solid inwards advance of closed to lessons). Feedback from students has been good.
• They convey a department Twitter account (@mathsnewvic) which is the exclusively agency they communicate sure enough pieces of vital data (eg when the side past times side evidence is).
• They make students information virtually what questions volition live inwards assessments inwards advance (eg 'the side past times side evidence volition consist questions from 2011 past times papers') - students therefore produce all those questions to ready for the assessment, which is amend than doing zip at all.
• They convey whiteboard pigment on the walls. I wrote virtually Vertical Whiteboards in Gems 7 and i time again I've been convinced of their effectiveness. There are lots of alternatives (eg magic whiteboards or writing on windows) if yous can't purpose whiteboard paint. David too Claire said that oft their students brand it inwards lessons too start solving problems on the walls conduct away - sometimes they don't fifty-fifty pose their bags down! If they acquire stuck they are much to a greater extent than probable to inquire closed to other pupil for aid than if they were sitting down. Another delegate said that this approach had transformed her teaching.

There's likewise a few things that David too Claire innovation to implement side past times side year. They recall to brand assessment results (broken downward past times question) world therefore students know who the practiced is inwards each topic, too they tin therefore acquire to their peers for help. They are likewise going to brand purpose of the MathsWatch App which is gratis for students when the schoolhouse subscribes to MathsWatch (the Influenza A virus subtype H5N1 flat video collection is growing).

Problem Solving
I likewise attended a session on Problem Solving at Key Stage 3 too four alongside Phil Chaffé. During this session I had fun trying out a make of maths problems.

My favourite problem, which I recall would live peculiarly suitable for Year 8 or 9, was 'Zag Area 1', which is shown below too available to download (with solution) from Integral (login required).

The session notes likewise featured these concern carte problems from the FMSP - these volition live available online from September.

All the problems featured inwards this session were drawn from Integral, the FMSP too Nrich. If you're looking for occupation solving resources therefore produce likewise banking venture check out my recent ship service Favourite Problems.

Mathematical Methods
National Mathematics Teacher Conference inwards March. It was virtually alternative mathematical approaches (eg all the unlike methods nosotros tin purpose to discovery the highest mutual constituent of 2 numbers). If yous await my 'Methods' page then you'll run across the posts I wrote after the lastly conference explaining the content of my workshop.

This fourth dimension I added an extra subdivision to my presentation - I spoke virtually how to factorise harder quadratics. I demonstrated 3 methods. The source was the 'guess too test' method (commonly used past times anyone over the historic catamenia of 20), the 2d was the 'grouping' method (used past times many U.K. teachers) too the tertiary was the 'slide too divide' method (sometimes used inwards the US, but considered a 'trick' past times many). We talked virtually advantages, disadvantages too alternatives. If you're interested inwards finding out to a greater extent than therefore run across my ship service Factorising Harder Quadratics, which I've but updated. An interesting alternative approach that many delegates had non seen earlier was 'the monic method', which is demonstrated inwards these 2 examples:

I promise that delegates flora my session useful. I did acquire closed to prissy encouraging feedback subsequently therefore I recall it went well.

Summary

The plenary 'Bouncing Bombs too Boomerangs' past times Dr Hugh Hunt, Senior Lecturer inwards the Department of Engineering at Cambridge University, was entertaining too fascinating. Overall my whole hateful solar daytime at the MEI Conference was fantastic too I regret non beingness able to attend to a greater extent than sessions.

So at that spot ends my busy week. I've fallen agency behind alongside my to-do listing therefore forthwith it's fourth dimension to acquire dorsum on track. First up, I'll proceed to locomote on my page of resources for the new GCSE specification.

Thanks to MEI for organising such a high character conference - I actually promise I'm able to attend i time again side past times side year.

5 Maths Gems #58

This is my 58^th update from the Blue Planet of Maths EduTwitter. Here I summarise about of the latest ideas as well as resources for didactics maths.

1. New GCSE Revision Resources

Thanks to @pixi_17 for sharing a fantastic develop of revision resources for novel GCSE students. This good designed develop of 9 - 1 revision booklets for 4 dissimilar degree levels (eg 'Aiming for a Grade 5') has come upward inwards handy for my Year 10s this week, equally they revise for their upcoming terminate of twelvemonth exams.

2. Whack a Prime 

I honey the Is This Prime? game simply about of my students learn disheartened past times depression scores. It's quite a stressful game to play! Slow it downwards with this choice 'Whack a Prime' game from @prehmet.

3. Polygons Angles

This novel tool from MathsPad is awesome. I've seen similar tools earlier simply this is the best yet. Click 'play' below for a demonstration.

#mathschat #mtbos Take a expect at our novel gratis interactive tool for exploring outside angles https://t.co/lPy5lvOUVf pic.twitter.com/nHrt19Ai56

— James Pearce (@MathsPadJames) 9 June 2016

4. Key Stage iii Scheme of Work

At this fourth dimension of twelvemonth many schools are thinking nearly their schemes of run for side past times side year. I actually similar the Year seven Scheme of Learning from the White Rose Maths Hub. Schools looking to alter their approach at Key Stage iii (less 'spiral', to a greater extent than 'mastery') volition uncovering this helpful. There's primary schemes hither too.

5. Interesting Exam Questions

Did you lot especially similar whatever of the questions inwards this year's GCSE papers? Share them on Twitter! For representative this inquiry was inwards the Edexcel Linked Pair Methods ii newspaper - it volition come upward inwards handy when teaching/revising recurring decimal proofs inwards hereafter years.

This circle theorems inquiry from Edexcel Methods 1 was a flake harder than commons - there's lots to produce here! Have a become at it.

For Influenza A virus subtype H5N1 flat teachers, this MEI inquiry is actually squeamish - it was sent to me past times a pupil who got stuck on it when revising.

Update
Did you lot grab my latest posts? One was nearly my twenty-four hours at researchED Maths as well as Science as well as the other was nearly maths schoolhouse trips.

On Mon I presented at LIME Oldham, focusing on mathematical methods. My slides are here.

Because I'm an Influenza A virus subtype H5N1 flat teacher, examination stream is nevertheless inwards total swing for me. The final examination is S2 side past times side Mon - phew! I'm looking frontward to Edexcel's conference inwards Warwick on s July, I should endure far less stressed past times then!

I've got a engagement inwards heed for here. This twelvemonth it volition belike accept a slightly dissimilar format - less CPD, to a greater extent than enrichment - simply I volition hold the 'Christmas political party for maths teachers' social element. Watch this space!

Finally, I'll locomote out with you lot with this squeamish action from James Tanton that I found, amongst other interesting tasks, inwards his 9th curriculum essay.

New Gcse Cpd

Towards the terminate of the summertime term I visited some other schoolhouse to deliver some preparation on the novel GCSE.

I thought it mightiness last helpful to part the slides together with materials from this preparation session here, inwards instance anyone wants to deliver a similar update at their schoolhouse inwards September. It's a adept fourth dimension for maths departments to halt together with mean value almost whether they're on rail amongst Year xi together with whether they're going to produce anything differently amongst Year 10.

1. Example of GCSE questions
I started past times holler for the squad to hold off at examples of attempt questions together with create upwardly one's heed whether or non the questions were from novel GCSE specimen papers. For illustration I included a query on moving averages from a Linked Pair newspaper (time serial are on the novel GCSE, exactly non moving averages).

This action helped me larn a sense of how familiar the squad were amongst the novel GCSE specification. You tin download the questions here. The answers are inwards the slides, which yous tin download at the terminate of this post.

2. Misconceptions
I thence talked through 10 fundamental points which were mainly drawn from the 2 posts I wrote:

• Five things yous mightiness non know almost the novel GCSE content #1
• Five things yous mightiness non know almost the novel GCSE content #2

It's worth noting that whenever I enquire the query 'has this topic gone from GCSE?', the attempt boards are careful non to commit to anything. They are allowed to include questions on topics that aren't specifically mentioned inwards their specification, as long as the text inwards the query provides plenty data for students to piece of work it out for themselves.

For illustration Edexcel lists stalk together with leafage diagrams together with frequency polygons inwards their GCSE (9-1) Mathematics Content Guidance FAQs, thence I'd definitely instruct these topics if my students were going to sit down the Edexcel exams. AQA does non specify these topics inwards their Teaching Guidance, exactly this doesn't guarantee they won't come upwardly up. If students are asked to translate a stalk together with leafage diagram inwards an AQA paper, the query volition receive got to clearly explicate how to read a stalk together with leafage diagram earlier holler for students to produce so.

3. New topics
I attempted to listing all the topics that are novel to Higher together with Foundation tier (as best I could - at that topographic point is no definitive list!). The listing of novel Foundation topics is a employment - I deal to sympathise why some of these topics are considered suitable for Foundation tier.

4. Exam Structure, Tiering together with Grading 
I talked almost attempt construction (three papers, the outset of which is earlier one-half term) together with grading. No 1 tin predict aeroplane boundaries together with I won't endeavor to produce so, exactly 2 points did come upwardly up:

Beware the drop
If yous larn inwards students for the Higher tier together with they alone handle to larn a handful of marks, they may good larn a U. Bear inwards heed that the Higher tier newspaper volition no longer start amongst a charge of 'easy' questions similar it used to, thence some students may good deal amongst the entire paper. If they barely pick upwardly whatsoever marks, they volition autumn off the bottom of the aeroplane boundaries together with terminate upwardly amongst a U when they may receive got picked upwardly a Grade 3 or four from the Foundation tier. I've seen speculation that this cut-off bespeak on the Higher tier volition last anywhere betwixt 10% together with 20%, exactly this is totally unknown at the moment. The proposition is that 'borderline' students would last safer on the Foundation tier, exactly delight don't quote me on that!

50% H5N1 together with A* content
This is a actually of import quote, taken from Edexcel's Guide to Edexcel GCSE Mathematics (9-1):

"Previously, 25% of questions were targeted at A/A*, exactly instantly 50% of questions inwards each newspaper are targeted at the equivalent grades, 7–9".

That's quite a ramp upwardly inwards difficultly level!

At my preparation session, a instructor suggested that the aeroplane boundary for a Grade half-dozen is unlikely to last higher than 50%, because a pupil who gets to a greater extent than than 50% of the marks on the Higher tier attempt has clearly accessed some Grade seven - nine material.

I receive got no idea almost aeroplane boundaries exactly if you're interested inwards reading more, receive got a hold off at Mel's post service 'here.

Mel's Mind the Gap Maths Toolbox for to a greater extent than ideas.

At my preparation session I also showed some examples of revision workbooks. Most of my Year 10s bought a workbook to prepare for their terminate of twelvemonth exams. There are plenty of resources available for students to purchase on Amazon including revision guides, revision cards together with sets of practise papers. This mightiness last a adept move of pupil premium coin for Year 11s who can't afford to purchase these resources themselves.

Note that Edexcel are instantly making a choice of printed past times papers available for yous to move for mock exams. These volition relieve schools both fourth dimension together with money. Preparing papers for mocks is a hassle thence this is a actually adept idea!

5. Checklist together with Scheme of Work
I finished my session past times issuing the squad amongst this topic checklist together with holler for them to tick off what they'd covered inwards Year 10 thence they could position which topics they even thence had left to encompass inwards Year 11.

My schoolhouse is almost halfway through the list. Given that nosotros alone receive got until early on May, together with that our students larn off timetable twice during the twelvemonth for mocks, I mean value we're all feeling the fourth dimension pressure! Thankfully our Year 11s volition receive got ix lessons a fortnight adjacent twelvemonth - this volition assistance considerably.

I shared my scheme of piece of work - you tin download it here exactly send inwards heed that most of the links won't piece of work as they're linked to documents on my school's network.

6. Slides
As far as I know, the content of my preparation session applies every bit to Edexcel, AQA together with OCR. My slides comprise a position out of graphics from Edexcel's excellent Guide to Edexcel GCSE Mathematics (9-1). The slides for this session (which took around 1 hour) are here together with you're real welcome to borrow them if yous experience that your squad needs an update inwards September.

5 Maths Gems #61

Welcome to my 61^st update from the globe of Maths EduTwitter. Here I summarise unopen to of the latest ideas together with resources for educational activity maths.

I promise everyone is enjoying their summertime break. I've been busy having lots of fun amongst my lovely daughters. We're going to rest on a farm close Hastings side past times side calendar week - looks similar I powerfulness fifty-fifty larn skillful weather! I'm starting to experience a chip nervous (and excited!) close Influenza A virus subtype H5N1 grade together with GCSE results - non long to hold back now...

1. Magic
Thanks to Susan Russo (@Dsrussosusan) for sharing this Crystal Ball activity from @Yummymath. It's neat fun! This powerfulness non operate on a mobile - create crusade it on a estimator if you lot can. Everyone likes a chip of mathematical sorcery... together with the interesting chip is trying to figure out how it works.

2. Planet Nutshell
I spotted unopen to skillful maths clips at Planet Nutshell. For instance you lot could demo this brusk proportional relationships video every bit purpose of a GCSE lesson (proportional graphs are featured on the novel GCSE specification).



It's worth checking out the total attain of videos. Short video clips tin dismiss sometimes complement a lesson nicely.

3. Puzzles 
Through the Sacks' which I'd non seen before.

Do banking concern agree out Don's latest ready of number puzzles too.

I've also been enjoying the problems shared past times Five Triangles (@Five_Triangles) recently. These 2 problems would operate good at Key Stage iii or 4:

a. Find x

b. The trapezium has meridian 22cm. The ratio of areas of triangles ⓐ to ⓑ is 4:5. Find expanse of shaded triangle.

4. Infinite Fractions

If you lot convey fourteen minutes spare for mathematical enrichment this summer, I recommend this video:



I actually enjoyed this.

5. Planner 
I know this won't appeal to everyone, simply if you're a fan of pretty stationery than you lot powerfulness desire to design your ain planner...  I've done it for the commencement fourth dimension this year. The website is real tardily to utilization together with it's amazing how much you lot tin dismiss customise - size, cover, binding, contents (which tin dismiss include seating plans, grade sheets, demeanour logs etc...). If you lot desire i for September I recommend ordering soon. I've been sent a code for 10% off (YDJ5PLX) which mortal powerfulness create goodness from. I honey my novel planner!

Update
In instance you lot missed them, hither are my recent posts:

• New GCSE CPD
• Misspelt Words Display 
• Divisibility Rules

I also created a novel page of classroom display ideas from diverse sources.

I was pleased that my spider web log was ranked 2nd inwards Vuelio's Top 10 Great Britain Education Blogs 2016.

Today I went to Bletchley Park amongst a lovely grouping of maths teachers from Twitter. We had a fantastic solar daytime together with were treated to a particular demonstration of an Enigma car from @TeaKayB. If you lot haven't been to Bletchley Park earlier thence I actually recommend a visit.

La Salle convey directly confirmed the appointment of their side past times side Pie together with Maths event. It's on Tuesday 23rd August together with you lot tin dismiss mass Gems 37 for my write-up of terminal summer's event. I'm hoping to become along for the drinks this year.

#mathsconf6, #mathsconf5, #mathsconf4, #mathsconf2015 together with Gems 8.

Finally, I'll live out you lot amongst this joke - I spotted it inwards a dorsum number of Chris Smith's weekly maths newsletter.