Showing posts with label Statistics. Show all posts
Showing posts with label Statistics. Show all posts

Friday, October 25, 2019

Coded Averages

Teaching coding inwards Statistics 1 is a flake of a pain.  My pupils simply don't similar it, as well as it's difficult for me to learn enthusiastic nearly something that didn't actually be when I studied Statistics (perhaps because it's non alone necessary?). When I was revising this topic alongside my Year 12s this year, I used a actually uncomplicated real-life example:

Imagine I'm queuing upwardly to purchase iv items of clothing, which cost £29.95, £49.95, £59.95 as well as £99.95. To transcend fourth dimension I hit upwardly one's require heed to operate out the hateful toll of these 4 items. To brand the numbers easier to bargain with, I add together 5p to each total as well as so dissever past times 10, giving me £3, £5, £6 as well as £10. It's real tardily to operate out the hateful of these 'coded' prices inwards my caput - it's £6. And at in 1 trial I tin uncode that hateful past times multiplying past times 10 so subtracting 5p (the inverse of the master coding).  That speedily gives me the actual hateful toll of the clothes, which is £59.95.  

Resources
Here's a few resources I've constitute for didactics this topic:
There's a express alternative hither so mayhap I should write something myself - I'll add together it to my list!


Skewness

Let’s beak S1, equally this year’s examine is fast approaching.

I don’t similar the way my S1 textbook deals alongside skewness. It basically only sets out methods for identifying skewness without actually explaining what it is. In this post service I hash out an choice approach.

I unremarkably operate this starter inquiry inwards my commencement S1 lesson of the year:

The quest existence that when in that place are outliers inwards a information set, the hateful becomes rather useless (unless of course of report you lot want to deceive people!).
Whilst instruction S1 I oft detect myself referring dorsum to my Bibonacci starter (‘remember that CEO? He ruined the mean!’). So I decided to brand a worksheet out of it - run across below - which I used for the commencement fourth dimension this twelvemonth when instruction skewness (if you lot similar this thence delight endure out me a review on TES!). My pupils enjoyed the action in addition to it generated interesting discussions.
There is a similar action here - from the website Illustrative Mathematics.

The fundamental instruction quest is that when information is skewed, the median is to a greater extent than meaningful than the mean. We bring diverse methods for identifying skewness inwards a information laid upwardly (summarised inwards these slides – sorry, master copy source unknown) - nosotros unremarkably reckon the shape of a frequency diagram or box plot. Sometimes skewness is apparent only from looking at the raw information (this sideways stem-and-leaf diagram is interesting). 


Pupils necessitate to retrieve that positive skew agency nosotros bring a few 'sparse' information points (possibly outliers) at the top end of the information laid upwardly – in addition to similar inwards the Bibonacci example, this volition pull the hateful up. This volition help them conceptually sympathise the diverse methods described inwards the textbook.

Finally, here's a keen fob that I learnt from my colleague Lizzie... Imagine a cute puppy sitting on the left of the graph. Influenza A virus subtype H5N1 positive skew is going to run across the puppy (positive = yay, a puppy!) in addition to a negative skew is going away from the puppy (negative = acquire away from this puppy!). It's a giddy but uncomplicated in addition to memorable way of ensuring that students don't acquire the graphs mixed up.






Two Ways To Purpose Comic Strips Inward Maths Teaching

I stumbled across a prissy didactics sentiment inward this blog post which is all almost giving pupils fourth dimension to summarise what they've learnt.  The writer of the spider web log suggests that pupils depict comic strips inward aeroplane or for homework. Here's around examples:
Example worksheet

Example of pupil's work


I i time used comic strips for a dissimilar role inward my didactics - I produced this comic strip for my GCSE class, which I showed inward this Prezi slideshow to generate give-and-take almost sampling methods.  The characters are all teachers at my schoolhouse (with slightly amended names...).  It went downwardly good alongside my aeroplane too I laid upward them the chore of creating their ain versions. We used Bitstrips for Schools which is lovely merely tin terminate hold upward really time-consuming.

(that's meant to hold upward me past times the way!)



Resources Anonymous

'Hello. My refer is Jo as well as I'm a resourceaholic'. Yes, I confess, I'm utterly addicted to searching the mesh for maths didactics resources.

It all started when I saw a PGCE pupil photocopying this blog. Ooh, novel websites! Heaven for a resourceaholic.

I haven't had a remove chances to aspect at all these websites yet, exactly here's around of my transcend resources recommendations from the websites I've looked at as well as thence far. I've focused on Influenza A virus subtype H5N1 score because that's where I mean value it's hardest to abide by interesting didactics ideas.

Statistics 1 
Illustrative Mathematics has around fantastic ideas for didactics S1. Here's a alternative of examples:

Finally, I stance it powerfulness last helpful to part this quadratic activeness 'Find the coordinates' - my schoolhouse uses this on Sixth Form Induction Day inwards our maths taster sessions (thanks to Susan Wall at Wilberforce College for this activity).

I'll croak on to piece of occupation my agency through the website listing as well as volition characteristic recommended Key Stage three as well as GCSE resources inwards afterward posts.




Bringing Babies Into A Statistics Lesson

I’m non specially into babies (apart from my ain niggling terrors darlings) precisely I learn at a girls’ schoolhouse in addition to the bulk of my students response rather good to babe materials (apologies for the stereotyping). It’s surprisingly tardily to characteristic babies inward your statistics lessons if y'all thus please. I’ve already blogged near my Bibonacci starter. There’s likewise this pregnant moo-cow attempt enquiry (part d is the entirely S1 attempt enquiry I've e'er seen which requires students to know that 68.3% of usually distributed information is inside 1 measure difference of the mean).

Edexcel S1 Jan 2002, Q5

I used this enquiry inward an S1 lesson when I was heavily pregnant, much to the entertainment of my students. It led to a give-and-take near the gestation periods of other mammals (those pitiable elephants!). We’d clearly hold back a fairly strong correlation betwixt size in addition to gestation - when I learn a lead chances I'll run into if I tin pattern an interesting activeness using this information (I wonder whether anything similar is done inward biology).

Speaking of gestation periods - I retrieve when my due appointment for my get-go immature lady came in addition to went, I tried to respect statistics online to tell me how far overdue I mightiness go. I wanted to know the probability of babe arriving at 42 weeks. I didn’t respect much online at the fourth dimension precisely 1 time to a greater extent than I experience it could brand for an interesting lesson.

If y'all are a rear in addition to then y'all may move familiar amongst ‘the ruby-red book’, which is the Personal Child Health Record issued to all babies born inward the UK. This is a child's main tape of immunisations, development, wellness reviews in addition to thus on. At the dorsum of the ruby-red mass are the ‘UK-WHO Growth Charts’ where scatter graphs are plotted of the child’s tiptop in addition to weight against their age. On these scatter graphs are centile lines, to allow parents in addition to wellness professionals to compare the child’s measurements against other children of the same age. On a few occasions, I’ve been asked to explicate the pregnant of these charts to friends amongst newborn babies, thus it occurred to me that the increment charts could help me explicate the concept of percentiles to my S1 classes.

The ruby-red mass contains this description of the centile lines on the increment charts:


More information near the charts is available inward this fact sheet from the RCPCH.

While I was thinking near how to pattern an activeness for my S1 course of didactics based on these charts, I discovered that the writer of The Chalk Face has beaten me to it amongst this dainty 'Quartiles in addition to Percentiles' activity. And @srcav has already written this weblog postal service 'the mathematics of parenthood' near the potential to run increment charts inward his teaching.

Incidentally, the ruby-red mass says ‘someone who has been appropriately trained should consummate the increment chart’. Hmm. I promise they're non suggesting that members of the populace are incapable of adding a dot to a uncomplicated scatter graph?!

Right, my babe is awake directly thus I'll expire along to develop these ideas about other time...  Do permit me know if y'all tin think of whatever other baby-related information to add together to my theme.


My mini-mathematicians.  July 2014.


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 #21

Happy New Year's Day as well as welcome to my 21st gems post - this is where I portion v pedagogy ideas that I've seen on Twitter inwards the yesteryear week. Now I'm dorsum at travel from motherhood leave, I await these posts volition cash inwards one's chips fortnightly rather than weekly. Sadly, marker as well as lesson planning volition hateful I select less fourth dimension to get together ideas from Twitter.

My aim for 2015 is to cash inwards one's chips on to travel towards a post for every topic, therefore that when you're planning lessons you lot tin refer to these posts as well as there's everything you lot demand - concepts, ideas, resources, enrichment as well as links. I truly promise these posts cut back the amount of fourth dimension you lot select to pass searching the internet. My latest post was on Teaching Indices, as well as you lot tin come across the total attain here.

1. Brilliant
I've been enjoying the questions from brilliant.org this week. It has a big attain of mathematical problems that you lot could purpose inwards lessons (algebra, geometry, calculus, mechanics etc). Plenty of the problems are available for gratis - total solutions, extra problems as well as a bunch of other materials is available for a small-scale subscription.

Here's a couplet of examples of problems for your students:
Some topics also select explanations as well as interesting worked examples - depository fiscal establishment represent out the chapter on the volume of a pyramid. The associated quiz has questions similar the ane shown below.
So if you're looking for interesting questions to purpose when pedagogy a specific theme therefore you lot mightiness discovery Brilliant helpful.

Also, if you're looking for some challenging problems to select a cash inwards one's chips at yourself, I recommend you lot similar Brilliant.org on Facebook - you'll acquire a overnice menstruum of problems inwards your newsfeed. Here's what Facebook presented me amongst this morn - this is a degree 2 enquiry (levels cash inwards one's chips from 1 to 5, amongst 5 existence the most difficult).
2. FOIL
Whether or non you lot learn 'FOIL' every bit a method for expanding brackets, sentry the video below.

By the way, I don't intend there's necessarily anything terribly incorrect amongst pedagogy 'FOIL' every bit long every bit students know that the gild doesn't matter. When I was at schoolhouse I was merely told to 'multiply everything inwards the outset bracket yesteryear everything inwards the 2d bracket' as well as every bit a upshot I purpose a attain of FOIL, FIOL, FOLI as well as FILO on the board... sometimes my students who've been taught FOIL intend I'm doing it wrong. It's truly of import that nosotros emphasise that at that topographic point is no laid upward order. I suppose FOIL merely helps students hold rail of their workings.

3. BODMAS
Sticking amongst the first-class videos from @minutephysics, if you lot haven't seen this ane close PEDMAS (that's BODMAS inwards the UK), it's good worth a sentry (thanks to @JustinAion for sharing). The gild of operations turns humans into robots!


4. Furbles
I may last the in conclusion maths instructor to take away heed close Furbles, but inwards illustration anyone else hasn't heard of them, they deserve a get upward here. Thanks to Hannah (@missradders) for bringing this cute statistics pedagogy tool to my attention.

Furbles tin last used to learn statistical graphs as well as probability - if you've non seen them earlier therefore select a play or therefore - there's ii web-based versions on the website, summation a downloadable version here. Examples of Furbles-related questions are shown below, as well as there's a to a greater extent than comprehensive listing here (thanks to @clwatson999 for sharing this link).
  • Which is the best graph to present you lot which is the most as well as the least? 
  • What would the telephone substitution for this pie nautical chart facial expression like? 
  • What is the probability the adjacent starred Furble volition last … a regal triangle amongst iv eyes?
You tin also enquire students to brand a laid upward of Furbles to laissez passer detail nautical chart properties or a specified probability distribution.

5. Euclid the Game
H5N1 few people select recommended Euclid the Game to me as well as I finally got circular to having a skillful facial expression at it. I come across what all the fuss is close now. I'm pedagogy loci as well as constructions shortly therefore I intend I'll mass an information technology room to permit my students select a cash inwards one's chips at this game. After a curt tutorial inwards which they acquire how to purpose the basics of GeoGebra, students are asked to create a serial of constructions.
What I similar close it is that students who unremarkably merely acquire a physical care for for these constructions select to intend close how the constructions truly travel (ie they're non merely drawing arcs). It's a cracking game therefore if you've non seen it before, create select a look.

Well that's it from me today. Hope you lot all select a skillful outset calendar week dorsum at school!