Showing posts with label Graphs. Show all posts
Showing posts with label Graphs. Show all posts

Friday, October 25, 2019

Linear Graphs

One of the topics that my pupils fighting amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't operate out how to respond a GCSE interrogation similar this:
Strangely, I learn this differently at GCSE too Influenza A virus subtype H5N1 level.  At GCSE my pupils write down
y = mx + c
too substitute values for y, thousand too x, too thus solve for c.  Whereas at Influenza A virus subtype H5N1 marker my pupils utilization the equation
y - y1 = m(x - x1)
Essentially the same method but a slightly dissimilar approach. Perhaps I should hold out to a greater extent than consistent too innovate the 'A marker method' at GCSE. I'd similar to remove heed what other teachers do.

In this postal service I’ll advise closed to ideas too resources for didactics linear graphs.

Key words
Let's showtime amongst the basics. There's a lot of novel vocabulary inward coordinate geometry, closed to of which pupils volition accept encountered at primary school. This is a overnice vocabulary noesis survey every bit suggested inward my earlier post

Here's a overnice play a trick on for remembering the words parallel too perpendicular (this could hold out helpful for spellings - parallel is oftentimes misspelt): 

too this activity is suitable for Year six or 7. 

Introducing the shape y = mx + c
I'd unremarkably showtime this topic inward Year seven or 8 amongst plotting conduct work graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This topic provides an splendid chance for pupil investigation using Desmos. Use a worksheet to guide pupils through the lesson:

Once pupils are able to translate the values of thousand too c too thus they tin endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal too vertical lines.

My weblog postal service 'All nigh gradient' features ideas too resources for didactics slope (the postal service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets too activities).

Understanding parallel too perpendicular gradients
So here's the primal data that pupils demand to understand:

If they know how to operate out a slope every bit 'rise over run' (or equivalent) too thus pupils should hold out able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this ane from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should accept the necessary skills too noesis to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for sure capable. Essentially it's merely the wording of the questions that throws them.

Here's closed to to a greater extent than recommended resources suitable for GCSE students:

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe too Lines.

Finally, always wondered which countries utilization y = mx + c annotation too which countries utilization something different? Check out this map.








Long Alive Stalk Together With Leaf

I planned to write a post service most instruction stalk together with leafage diagrams. But so I realised that many maths teachers reckon them to live on pointless, a waste matter of instruction fourth dimension together with a welcome removal from the curriculum.

Now let’s remember most this for a minute. Admittedly stalk together with leafage diagrams are rarely used inward ‘real life’. In fact the alone mutual examples nosotros tin abide by are timetables, such equally the Japanese develop timetable shown inward the painting exhibit below (more examples here). But does this ‘uselessness’ actually hateful that stalk together with leafage diagrams shouldn’t live on taught? If that’s the instance so a publish of the topics nosotros learn inward maths should live on taken off the curriculum. 

Japanese develop timetable. Source: Wikipedia

Much of the maths nosotros learn at Key Stage iii helps pupils access to a greater extent than advanced topics (all roads Pb to calculus?!). Maths begets maths. So practise stalk together with leafage diagrams Pb us anywhere? Do they assist pupils develop whatever useful skills together with understanding?

I'm going to tell (in a sheepish whisper) that they do. Stem together with leafage diagrams are i of a ready of tools that could live on used to develop agreement of the concepts of median, mode, quartiles, spread, skew together with outliers. I remember they are accessible to depression powerfulness pupils. I remember that pupils bask creating them. I remember they Pb to interesting discussions when comparing ii sets of data. I sure enough don't remember they should live on a compulsory theme at whatever age, but I meet no impairment inward teachers using them if they like. Isn't it prissy to receive got that freedom?

John Tukey, the inventor of stalk together with leafage diagrams, wrote "If nosotros are going to brand a mark, it may equally good live on a meaningful one. The simplest - together with most useful - meaningful score is a digit" (source). Excellent betoken Mr Tukey. Did you lot know he also invented the box together with whisker plot?

John Tukey is also quoted equally saying "There is no information that tin live on displayed inward a pie chart, that cannot live on displayed ameliorate inward another type of chart". I agree. In the same agency many of you lot don't similar stalk together with leafage diagrams, I don't similar pie charts (this excellent weblog post service most the misuse of pie charts is worth a read).

Right, directly I've attempted to justify this weblog post, here's my lesson ideas:

Starting Point
You could foremost past times presenting your cast amongst a large ready of information (like the i below) together with hollo for them what the vogue is. It's hard to spot. Ask your pupils for ideas on how could nosotros organise this information so nosotros tin easily meet the mode.

12, 54, 21, 56, 32, 14, 42, 23, 20, 48, 21, 34, 12, 15, 16, 42, 47, 46, 32, 21, 45, 43, 21, 34, 26, 32, 17, 18, 45, 21, 44, 32, 12, 23, 45, 24, 35, 38, 28, 18, 29, 20, 10, 36, 12, 42, 47, 32, 47, 37, 12, 54, 23, 17, 29, 38, 32, 12, 17, 13, 21, 34, 12, 15, 16, 42, 47, 46, 12, 16, 43, 23, 16, 46, 52

I abide by stalk together with leafage plots rather pleasing to the eye. Much nicer to await at than a ho-hum listing of unordered data.

An option starting betoken is a 'beat the teacher' game, which I've adapted from an thought past times the NCETM. In this activity, pupils remember of a publish betwixt 10 together with 40. Each publish is called out inward turn, land pupils brand a listing inward their books. Meanwhile the instructor also makes their ain list, but organises it equally a stalk together with leafage diagram. Once all the numbers are listed, the instructor asks the cast to travel out median, vogue together with range. The instructor volition practise it much quicker from their stalk together with leafage diagram, so he/she wins the race.

Physical Activities
This weblog post is most introducing stalk together with leafage diagrams using post-it notes. It's a lovely thought for an engaging together with accessible lesson. Mr Collins shared a similar thought inward this weblog post, but he uses students together with desks instead of post-its. If you lot similar the thought of human stalk together with leafage diagrams so you lot mightiness also similar these breath-holding activities - i from Don Steward together with a similar i from the NCETM.

Data Types
Encourage pupils to remember most dissimilar types of information - what is suitable for a stalk together with leafage diagram together with what isn't? For example, could the full publish of goals scored per game inward a flavor of football game matches live on displayed inward a stalk together with leafage diagram? Probably not, because the information would generally live on unmarried digit numbers. Try my worksheet for to a greater extent than on this.

Mini Projects
Don Steward has approximately prissy activities involving stalk together with leafage diagrams, such equally this this Presidents Longevity Project. I also similar Tim Jefferson's skewness).

Back-to-back stalk together with leafage diagrams are useful for comparing data. Writing comparisons betwixt information sets - whether represented past times stalk together with leafage diagrams or box together with whisker plots - is something that pupils (especially EAL pupils) ofttimes abide by difficult.

There's lots of S1 (A level) stalk together with leafage questions - similar the i below - that could live on explored at Key Stage iii (which begs the question, why were they considered suitably challenging for Influenza A virus subtype H5N1 level?).

Edexcel S1 Nov 2004, Question 1


I rarely disagree amongst people or play devil's advocate so this post service is a chip risky for me! Be nice. If you lot practise learn stalk together with leafage diagrams so I promise you lot abide by these ideas helpful. Thanks to those on twitter who shared their views together with ideas (especially @srcav - who is non a fan of stalk together with leafage diagrams!).


Scatter Graphs

This weblog is becoming a fleck statistics-heavy, which is ironic given that I don’t specially similar pedagogy statistics at Key Stage iii as well as 4.  I much prefer pedagogy algebra. I’m also quite peachy on surds as well as indices. And I similar trigonometry. In fact, apart from the strange annoying-to-teach topic similar loci as well as constructions, I’d seat most information treatment topics correct at the bottom of my ‘things I relish teaching’ list. It never fails to amaze me how long roughly teenagers receive got to plot a graph. What a faff.

Anyway, this postal service is all most ideas for pedagogy scatter graphs. And I retrieve to follow it upwards alongside a postal service looking at applications of box as well as whisker plots exterior the maths classroom.  But as well as thus I’ll halt alongside all the statistics.

Practical activities
Unusually for a maths lesson, there's opportunities for roughly practical activities when nosotros innovate scatter graphs. The obvious sentiment is to receive got students plot meridian or manus bridge against shoe size. If you lot desire to acquire fifty-fifty to a greater extent than practical, attempt a human scatter graph inward the classroom or inward the playground (using chalk axes).

Outliers 
I similar to purpose the ii scatter graphs shown below (stolen from a Ten Ticks worksheet) inward a shape give-and-take most outliers.  Ask your shape what could receive got caused these extreme values as well as you'll in all likelihood acquire roughly actually creative suggestions!


Line of Best Fit
I instruct my students to depict a trouble of best stand upwards for yesteryear trying to minimise the distances betwixt all the points as well as the line. That’s what a to the lowest degree squares regression does. Contrary to pop belief, at that spot doesn't receive got to live the same release of points to a higher house as well as below the line. Nor does the trouble receive got to become through whatsoever of the points. And the trouble sure enough doesn't receive got to become through the origin. Beware of dodgy methods taught inward other subjects. This misconceptions activity yesteryear frickard on TES is helpful - I've used this inward a 'hands on caput if you lot retrieve it's true, hands on hips if you lot retrieve it's false' activity.

Impossible Predictions
'Extrapolation' from regression lines is something that comes upwards at Influenza A virus subtype H5N1 level, only the sentiment tin terminate brand for interesting discussions at Key Stage iii or GCSE. The telephone substitution signal is that fifty-fifty if nosotros detect a linear human relationship inward the information we're examining, nosotros can't assume that human relationship extends beyond the make of the data. Here's a dainty instance for shape discussion:

The graph below shows a negative correlation betwixt twelvemonth as well as fourth dimension taken yesteryear athletes to run 100m. It suggests that the speed of 100m runners has increased over time. Influenza A virus subtype H5N1 trouble of best stand upwards for has been drawn. Why produce you lot retrieve 100m runners are getting faster? Do you lot retrieve this tendency volition continue?


Possible reasons for the increment inward speed include: advances inward technology (ie to a greater extent than lightweight or streamlined clothe as well as trainers), inquiry into optimal diets as well as grooming plans, sponsorship important athletes receive got to a greater extent than fourth dimension to train, the introduction of starting blocks inward the 1940s as well as an improvement inward the accuracy of timing the race.

If the tendency continues indefinitely (ie if nosotros depict the trouble of best stand upwards for into the future) as well as thus at roughly signal people would live able to run 100m inward null seconds, which is impossible. There must live a signal at which the fourth dimension volition plateau, due to limits inward humans' physical capabilities. Although at that spot is a linear correlation, nosotros must live careful non to brand predictions inward the yesteryear or futurity because the linear human relationship is over a express fourth dimension period.

The graph comes from this Minitab Blog post as well as the sentiment was seat into my caput yesteryear Kings College London PGCE tutor Chris Olley. 

"Wind is caused yesteryear the rotation of windmills"
I love the causation vs correlation discussion.  It's a real of import learning signal for students who volition come upwards across all sorts of dodgy statistics inward everyday life.

doubt.it

Influenza A virus subtype H5N1 typical instance is shoe size as well as reading age. The ii variables are positively correlated, only apparently the size of someone's feet has no demeanor on on their reading ability. For to a greater extent than ideas banking concern check out this spurious correlations website.

If you're planning a shape give-and-take on causation as well as thus receive got a quick read of 'Correlation does non imply causation'on Wikipedia (not e'er the best source only gives roughly skillful examples).

Correlation does non imply causation, only it does waggle its eyebrows suggestively as well as gesture furtively spell mouthing "look over there". – xkcd 

Resources
Finally, here's a few resources that you lot could purpose inward your lessons:
  • I love this Bee Aware action from Don Steward. It could easily live made into a mini-project/display move most the campaign as well as demeanor on of the demise of dear bees.
  • The first-class Mathematics Assessment Project gives us ii tasks - Scatter Diagram and Birds' Eggs
  • There's no shortage of real-life applications of scatter graphs. This worksheet 'Shake It Up alongside Scatterplots' is 1 of many examples (here's the solutions).
  • Nrich gives us this nice David as well as Goliath activity.
  • 'Foldables' seem to live a big matter inward U.S.A. math lessons, only I've never seen them inward the UK. I retrieve my students would quite similar them. Here's an sentiment for correlation foldables from the weblog 'Everybody is a Genius'.
  • I similar this online tool for checking the accuracy of lines of best stand upwards for from Mark Ritchings
  • Here's an interesting group project. I similar the sentiment of giving each pair/group ii options thus they tin terminate select the variables they prefer, as well as that everyone inward the shape is working on something different. Also, the 'assigned tasks' for each grouping fellow member (see in conclusion page) is an sentiment I haven't seen earlier for organising grouping work. These detail tasks may non live suitable for a United Kingdom of Great Britain as well as Northern Ireland of Britain as well as Northern Republic of Ireland lesson because nosotros don't hold off students to calculate the equations of lines of best fit, only the sentiment could live adapted.

I promise this postal service has been helpful.  Please comment if you lot receive got whatsoever ideas to share. 

By the way, this cool moving scatter graph is worth a look.


xkcd.com

Teaching Box As Well As Whisker Plots

Image: ruthmaas.com
When I wrote Long Live Stem together with Leaf, I'd been challenged to uncovering a practical application of stalk together with foliage diagrams exterior the maths classroom. After extensive googling - together with helpful input from twitter - the alone examples I could uncovering were motorbus together with prepare timetables. But I argued that existent life application isn't the last all together with destination all.

Stem together with foliage diagrams were invented inwards the 1970s past times Consistent Mathematics if you lot desire to know why). This is a lovely activeness inwards a lesson introducing the thought of median, precisely non hence effective inwards a box plot lesson. Because fifty-fifty though you lot tin purpose a bedsheet together with string to larn the students to hold off similar a box plot, if they’re non appropriately spaced out (ie if there’s no scale) hence it’s non a box plot. If you lot desire a proper box plot you’ll accept to truly mensurate the heights together with depict a scale on the floor.

An choice thought (inspired past times this post) involves newspaper aeroplanes. You’ll necessitate a large infinite for this - the schoolhouse hall or playground. Tape (or depict inwards chalk) a long scale on the floor. Have each of your pupils brand a newspaper aeroplane, write their elevate on it, together with throw it from the outset of the scale. Leave the aeroplanes where they land. Once all pupils accept thrown their aeroplane, you lot tin depict or record a box plot on the flooring or hence the planes to stand upwardly for the distance flown. Pupils volition last able to run into which quartile their plane landed in. Hopefully ane futurity engineer volition throw an amazing outlier which volition brand a skilful give-and-take point! You could fifty-fifty separate the flat inwards one-half together with do ii box plots on the flooring side past times side, hence the flat could hash out which squad had meliorate aeroplanes together with which team’s planes were to a greater extent than consistent.

If you lot similar practical activities, here’s ii more:
  • This uncomplicated newspaper folding activeness is a overnice introduction to median together with quartiles.
Source: bigideasmath.com


Resources
There’s surprisingly few skilful box plot resources online. But Don Steward never lets us down. His website has a discover of box plot activities - my favourite is this truthful or imitation activity.


I also similar the activeness below from bigideasmath.com:

If you’re looking to generate box plots on your interactive whiteboard for flat discussion, this online tool is overnice – it has pre-populated information or you lot tin input your own.

I've listed some to a greater extent than skilful box plot resources below. I’ve constitute that many resources enquire questions almost skewness, which nosotros don’t encompass until S1 (but mayhap nosotros should encompass earlier). Treatment of outliers is also non covered at GCSE precisely makes for a overnice discussion.

If you lot desire to demo your flat some ‘real world’ box plots hence these box plots showing the ages of World Cup players could prompt some skilful discussions almost comparisons. Read @loumeracy’s blog post for to a greater extent than on this.


If you lot desire to ‘wow’ your flat amongst an instance of how box plots tin last used to compare huge amounts of information inwards a modest space, demo them this example which shows the historic menstruation distribution of Olympics athletes (more of this here).

Final thoughts
In French the box plot is called boîte à moustaches (box amongst a moustache). The author of this article attempts to create a box together with beard plot!

There are many variations to the box together with whisker plot, such equally the edible bean plot together with violin plot. Look these upwardly on google images for lots of examples.

I read an interesting thought here that I’d never thought of before: “One agency to assistance you lot translate box plots is to imagine that the agency a information ready looks equally a histogram is something similar a mount viewed from Earth flat together with a box together with whisker diagram is something similar a contour map of that mount equally viewed from above”.

Well, at that topographic point you lot are – a 'box plot weblog post'. Try maxim that 5 times out loud. I've invented a novel natural language twister.



Thursday, October 24, 2019

5 Maths Gems #8

I enjoyed coming together many of you lot at La Salle Education's National Mathematics Teacher Conference yesterday. It was a fantastic chance for sharing ideas. But 500 maths teachers out of 350,000 is a drib inwards the ocean. It's such a shame that thus many schools weren't represented.

Although in that place are some pockets of collaboration throughout the UK, for example through regional TeachMeets, the fact is that the bulk of U.K. maths teachers alive inwards a bubble. Through no error of their own, they know really lilliputian almost approaches taken inwards other schools - including pedagogy, curriculum blueprint together with novel technologies. Twitter is business office of the solution, but it doesn't brand it enough.

this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all here.

1. Paint! And my ideal classroom
smartwallpaint.com
I was talking to a friend almost the 'Vertical Non-Permanent Surfaces', magic whiteboards together with acrylic sheets I featured inwards this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all my concluding gems post and he told me almost something wonderful. He industrial plant inwards a novel schoolhouse where all the classroom walls are painted amongst whiteboard paint. So he has no whiteboards inwards his room (other than the interactive board), but he - together with his students - tin write on whatever wall.

This got me thinking almost my ideal classroom. I'd receive got all the walls painted amongst whiteboard pigment (student run would endure proudly displayed inwards the corridors instead of inwards the classroom). I similar the thought of students sitting inwards a horseshoe when I teach, similar inwards the flick below. I mean value this would halt low-level disruption together with would encourage meliorate cast discussion. They could also do independent practise inwards these chairs.

hyperspacellc.com
Separate to this horseshoe I'd receive got a collaboration area, amongst grouping tables that tin endure written on (whiteboard pigment industrial plant on desks too!), or this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all acrylic sheets.

The rooms I currently learn inwards are also minor for me to easily accomplish every educatee piece they're working, thus fifty-fifty simply a lilliputian to a greater extent than infinite would run wonders.

2. Indices
If you're looking for a novel approach to teaching index laws, you lot powerfulness bask 'this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all logarithms.

Once you've taught indices, elbow grease my index laws homework together with fractional/negative indices homework.

3. ThingLink
this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all Mathematical Concepts Wall' yesteryear this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all Samuel S. Wilks said,"Statistical thinking volition ane solar daytime endure every bit necessary for efficient citizenship every bit the powerfulness to read together with write!" (he was paraphrasing HG Wells). Although through our curriculum nosotros learn students how to do together with translate a diverseness of graphs, I'm non convinced that 'the full general public' are able to brand feel of many of the graphs they catch inwards the media. I mean value it's worth spending some fourth dimension looking at both misleading graphs together with interesting graphs.
Ridiculously misleading graph
Interesting graphs promote nifty discussions. Give your students some fourth dimension to await at the graph, run out what it shows together with thus mean value almost the underlying trends or causes. Here's a pair to acquire you lot started.
Source: 'How nosotros believe' yesteryear Micheal Shermer

Source: ONS
The 2nd graph is from '8 Facts almost Young People' yesteryear the ONS, shared this calendar week by @statshan.

Speaking of interesting graphs that spark discussion, you lot must read this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all teaching identify value. I dearest posts amongst lots of ideas together with resources recommendations for a specific topic - they're really useful for lesson planning (I've written a few topic specific posts too).

Second, I desire to bring upward this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all revision races. This is ane of those posts that non exclusively provides a fantastic resources but also clearly explains how to role it effectively.

Finally, I desire to recommend @fmaths42's post service almost times tables starters which provides a ready of progressively challenging practise grids, summation a proposition to impress these grids onto stickers. Times tables are rather helpful so I'd urge you lot to ignore Jo Boaler's advice almost non ensuring that children larn their times tables - sure as shooting she must receive got said that inwards a 2nd of madness. Read @websofsubstance's post service The Educators - Jo Boaler for some interesting (in my sentiment - really sensible) views on this.

Finally, receive got a acquire at this query from Tony Gardiner's session at yesterday's conference, shared yesteryear @mrsdenyer. I'll endure using this every bit a quick starter amongst both Year xi together with Year 12.


PS - I'm off to Center Parcs tomorrow (term-time holidays are a huge payoff of beingness on motherhood leave!) thus in that place won't endure a gems post service side yesteryear side Saturday. I'll endure dorsum the next calendar week though. 

5 Maths Gems #13

In my gems posts I portion roughly of the best teaching ideas I've seen on Twitter each week. This is my 13th gems post. I promise you're non triskaidekaphobic.

1. Flying Numbers
At Julia Smith's (@tessmaths) creativity workshop at the lastly maths conference, she shared an activeness inwards which students brand 'Flying Numbers' to hang from the ceiling inwards the classroom or corridor. It industrial plant similar this: they direct a release in addition to brand that release from forest inwards Design & Technology (drill a hole at the overstep for hanging). They pigment their release in addition to then role fine markers or chalk pens to decorate it amongst facts virtually that number. This is a lovely chance for students to role the cyberspace to explore release properties in addition to detect out all sorts of wonderful mathematical things that are non on the curriculum. The examples below were made at the maths conference - it was a actually enjoyable exercise.
Ed Southall (post virtually teaching a binary lesson).

Alice inwards FractalLand is a stunning animated slideshow. Show it to your shape in addition to explore sequences, fractals, the golden ratio in addition to more. The text at the bottom explains each concept really clearly. I love this! This is just the kind of affair I was referring to inwards my postal service 'A house for gimmicks?' when I said that nosotros should brand fourth dimension to enrich our students' instruction amongst interesting mathematics that is non on the GCSE syllabus.
  • The Primary and Secondary Treasure Hunts are really good designed. Full instructions are included in addition to in that place are questions on areas of mathematics such every bit cryptography, primes in addition to probability. The questions are rather challenging for the intended historic catamenia groups - if I was organising an inter-school maths contender in addition to then I mightiness role these questions.
  • The video collection is due to grow - an exciting prospect if this 2 infinitesimal wordless video exploring triangles is a gustatory modality of things to come. 

  • 3. Imbalance Problems
    If you're non familiar amongst Don Steward's resources in addition to then halt reading this postal service straight off in addition to banking concern lucifer out his mobiles', in addition to then 'mobile inequalities' in addition to finally 'mobile moments'.

    In mobiles, the activities kickoff amongst release problems that larn progressively harder, in addition to then motion on to algebraic balancing problems. Here's a numerical instance which tin live solved amongst arithmetics in addition to logic (fill inwards the missing weights thence that everything balances correctly). 
    There are lots of variations, such every bit this 1 where the weights must add together upwardly to the release inwards the triangle (this is a straightforward example):
    The algebraic problems railroad train skills inwards writing algebraically in addition to simplifying expressions. In the occupation below, students accept to consummate the missing weights to brand the combined hanging weight equal to 8n.
    These are dandy problems. Check out all 3 posts to run into how Mr Steward developed the idea. It's every bit good worth reading Paul Salomon's (last week's gems post has paid off - both Debbie Hart ‏(@Debbie_Hart_UK) and Jane Appleton (‏@JaneAppleton24) accept tried it.

    I've been busy writing a postal service virtually circle theorems which volition live attain soon. Also, later seeing roughly dandy Halloween in addition to Guy Fawkes maths resources, I've started to collate a 'seasonal resources' page. I've seen thence many adept Christmas resources, it's difficult to direct the best only I'm getting there.

    So in that place yous go, my 13th gems post. It wasn't scary at all.

    Image source: guernseydonkey.com



    5 Maths Gems #15

    Welcome to my 15th weekly gems post - this is where I characteristic to a greater extent than or less of the best teaching ideas I've seen on Twitter each week.

    1. Slice The Pie
    Paul Rehmet (@prehmet) has built an interactive tool to help students construct numerical fluency. It's a uncomplicated fraction game - Slice The Pie - which helps students railroad train an intuitive sense of the relative sizes of numbers. It's non compatible alongside mobiles yet but would piece of work on your interactive whiteboard. I honey this. Have a play alongside it, I think you'll honey it too. And follow Paul on Twitter because there's to a greater extent than to come upwardly from him.
    2. Remembering Inequalities
    In my post virtually Ideas from Shanghai I shared this visualisation which helps students cry back which inequality sign is which.
    All students demand to exercise is visualise numbers equally blocks - the wider halt of the inequality symbol fits over the bigger stack of blocks. So if x > 2, nosotros know x must last a divulge bigger than 2. 

    Chris Smith (@aap03102) pointed out that this doesn't piece of work for negative numbers. 
    I'm sure as shooting our friends inwards Shanghai possess got a solution for this but that data hasn't filtered through to us, therefore let's come upwardly up alongside our ain alternative that industrial plant for both positive together with negative numbers. We only demand a agency for students to cry back which symbol is which.

    I'm actually grateful to all the lovely creative tweeters who offered ideas - my favourite was this calligram from Chris. 
    So if x < - 8, nosotros encounter the < symbol together with think of the alphabetic character L, therefore nosotros know x is less than -8.

    Eventually students volition automatically know the important of the symbols on sight, without having to visualise blocks or words.

    These methods are far meliorate than thinking of crocodiles - this tin confuse students, equally described inwards Nix the Tricks (extract below).

    3. Squares together with Cubes
    I'm enjoying La Salle Education's (@LaSalleEd) novel 'Problem of the Day' series.  You tin search the collection past times historic menses or topic. The instance below (Square Boxes) is a prissy logic occupation consolidating noesis of foursquare numbers.
    If you're teaching foursquare numbers, you lot powerfulness also similar this 'Square together with Cube Numbers Puzzle' from MathsPad...
    ... together with this lovely square together with cube numbers display from Clarissa Grandi (@c0mplexnumber).

    4. Mathsticks
    I lately discovered the brilliant Mathsticks website which is created past times John Duffty (@johnduffty). I registered together with explored - it's to a greater extent than oftentimes than non primary materials but to a greater extent than or less of the ideas powerfulness last helpful at Key Stage 3. Here's a pair of examples:
    This Parallel & Perpendicular Slope. Once you've taught students virtually the gradients of parallel together with perpendicular lines, larn them inwards a calculator room (or larn the iPads out, if you lot possess got them) together with give them this worksheet, which I think volition last really slow for them to follow independently. They are given sure as shooting lines which they plot (in Desmos, though I suppose this could last done past times hand) together with therefore they add together the right parallel or perpendicular lines to brand the required shape. It's a actually prissy activity which volition assistance you lot cheque their agreement of this topic.
    Extract from Desmos Graph Challenge
    Here's my respond to the minute interrogation inwards the extract above.

    To extend this task, you lot could possess got students trammel the domains of the functions, equally I've done below. If you lot exercise this, it's of import that they figure out how to calculate the coordinates of the vertices.

    If you're teaching parallel together with perpendicular lines therefore also cheque out my post linear graphs for to a greater extent than ideas together with resources.

    A asking for misconceptions
    When I project design lessons, I abide by it helpful to endeavour to predict the misconceptions that powerfulness come upwardly up. Sometimes I'm surprised past times the mistakes that students make, which are oftentimes the effect of my explanations non beingness clear enough. Knowledge of mutual misconceptions comes alongside sense but I think it would exercise goodness novel maths teachers if they could consult a website to encounter examples of the form of things students larn wrong. 
    A not-so-common misconception from 1 of Chris Smith's students
    American instructor Michael Pershan (@mpershan) has a bright website Math Mistakes where he compiles, analyses together with discusses the mathematical errors that students make. I desire to prepare something similar for the Great Britain (because our curricula together with vocabulary are therefore different), but I won't possess got fourth dimension to exercise the first-class analysis that Michael does. Instead it would only last a collection of misconceptions, tagged past times topic. But I even therefore think it powerfulness last useful.

    So I possess got a asking - could you lot outset taking photos of misconceptions inwards your students' piece of work together with emailing or tweeting them to me? Once I've got a modest alternative I'll outset a website together with I hope, similar my Pret homework website, it volition grow speedily together with attempt to last a helpful resource. Thank you lot inwards advance!

    That's it for today. Please don't forget to vote for me! :), I'll larn out you lot alongside this cute 'Math nosotros know drama', shared past times @FascinatingVids.


    5 Maths Gems #19

    Hello in addition to welcome to my 19th gems post. This is where I part approximately of the best didactics ideas I've seen on Twitter each week. Most of my gems convey come upwards from across the Atlantic today.

    1. Polygraph
    There's been a lot of buzz almost Desmos' novel Polygraph activities. They're mathematical versions of Guess Who, designed to 'foster the pleasance in addition to the ability of words without the drudgery of the lists'. There are currently 4 Polygraph activities:

    Let's expect at Polygraph: Parabolas. Students move inwards pairs (a picker in addition to a guesser) on split upwards tablets, phones or computers. The picker selects a graph from a ready of parabolas. The guesser sees the same ready of parabolas - their trace is to position which graph the picker has chosen past times cry for a serial of yes/no questions. For instance they mightiness inquire almost the seat out of roots or the place of the vertex or y-intercept. The guesser types their questions in addition to the picker responds alongside yes, no, or don't know. The guesser keeps cry for questions until they are able to position the chosen graph.
    Students in addition to then convey the chance to analyse in addition to refine their questioning, in addition to y'all convey a flat discussion to formalise the mathematical vocabulary.

    As alongside Desmos' awesome Gems 13, it's incredibly quick in addition to slow to larn started. I'm going to survive didactics quadratics to Year 10 before long in addition to can't hold back to purpose the Parabolas activity. And I computer program to purpose the Linear Graphs version alongside my Year 9s too.
    Extract from Polygraph: Lines
    2. Point, Point, Gradient
    Tina Cardone (@crstn85) shared this lovely activity 'Point, Point, Slope' past times Michael Fenton (@mjfenton). It's a unproblematic precisely effective lesson stance inwards which students convey to purpose whatsoever digit from 2 to ix to create 2 points - y'all could rank them post-its or seat out tiles to shuffle around. You furnish criteria, such every bit 'create 2 points which create upwards one's heed a trace alongside the greatest possible gradient'. Read the amount post for to a greater extent than ideas. There's loads y'all could create alongside this activity, for instance y'all could inquire your students to use half dozen unlike digits (from 0 - 9) to create iii points which prevarication on the same line. It's a expert agency to railroad train agreement of linear graphs in addition to I cry back it would move good at both GCSE in addition to AS level.

    Michael's spider web log is amount of fantabulous ideas. For instance in Two Fractions students house digits in addition to operators inwards the boxes below to brand an facial expression alongside the greatest possible value.
    This reminds me of the Blanks activities I featured inwards Gems 17, which y'all tin rank the axe read to a greater extent than almost inwards Sarah Aldous' post Gems 13 I talked almost making your students 'Number Experts'. I shared 2 websites that are useful for finding out properties of numbers (numbergossip.com in addition to numdic.com). Both websites are fantabulous - for example, numbergossip.com tells me that 28 is a perfect, composite, happy number, and numdic.com (which wins the prize for funniest URL) gives me the binary in addition to Roman Numeral representations of 28. I've immediately discovered a novel website - the Number Property Calculator - which I similar because of the agency it gives data almost the important of the seat out properties. Here's a small extract from what comes upwards when I search for 28:
    I flora this website when I was browsing through sometime posts on Math Munch. Math Munch is a 'Weekly Digest of the Mathematical Internet'. It's packed amount of fantastic resources in addition to ideas thus it's definitely worth subscribing to have weekly e-mail updates, in addition to y'all tin rank the axe follow them on Twitter also (@MathMunch).

    5. Drawing Euclid
    Andy Shaw (@Squidworm74) pointed me inwards the direction of these lovely Euclid videos on YouTube past times Shoo Rayner (@shoorayner). They are fantastic videos in addition to I can't hold back to part them alongside my Year vii students. Check out the amount playlist here. Here's an instance almost unlike types of triangles:



    That's it for this week. I promise you've flora approximately inspiration inwards this post. I'll move out y'all alongside this bright video past times the always awesome Vi Hart - The Gauss Christmath Special. Thanks to Chris Smith (@app03102) for sharing this.




    Have a wonderful Christmas!