Coded Averages

Teaching coding inward Statistics i is a fleck of a pain.  My pupils simply don't similar it, in addition to it's difficult for me to larn enthusiastic most something that didn't actually be when I studied Statistics (perhaps because it's non solely necessary?). When I was revising this topic amongst my Year 12s this year, I used a actually uncomplicated real-life example:

Imagine I'm queuing upwards to purchase 4 items of clothing, which cost £29.95, £49.95, £59.95 in addition to £99.95. To hold upwards past times fourth dimension I determine to function out the hateful cost of these 4 items. To brand the numbers easier to bargain with, I add together 5p to each total in addition to and so separate past times 10, giving me £3, £5, £6 in addition to £10. It's really slow to function out the hateful of these 'coded' prices inward my caput - it's £6. And right away I tin uncode that hateful past times multiplying past times 10 in addition to so subtracting 5p (the inverse of the master copy coding).  That rapidly gives me the actual hateful cost of the clothes, which is £59.95.  

Resources

Here's a few resources I've establish for instruction this topic:

• Teachitmaths.co.uk has a lovely worksheet for helping pupils empathise the comport upon of coding. Just beware of the fault inward the extension questions - both information sets should accept 6 values, non five.
• Schoolworkout.co.uk has this sorting activity and this worksheet.
• Phildb on tes.co.uk has written this worksheet.

There's a express alternative hither so possibly I should write something myself - I'll add together it to my list!

Skewness

Let’s verbalize S1, equally this year’s essay out is fast approaching.

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

I usually piece of employment this starter interrogation inwards my get-go S1 lesson of the year:

The indicate beingness that when at that topographic point are outliers inwards a information set, the hateful becomes rather useless (unless of class you lot wishing to deceive people!).

Whilst education S1 I oftentimes uncovering myself referring dorsum to my Bibonacci starter (‘remember that CEO? He ruined the mean!’). So I decided to brand a worksheet out of it - come across below - which I used for the get-go fourth dimension this yr when education skewness (if you lot similar this thence delight acquire out me a review on TES!). My pupils enjoyed the activeness too it generated interesting discussions.

• Investigating skewness activity
• Investigating skewness instructor notes

There is a similar activeness here - from the website Illustrative Mathematics.

The substitution education indicate is that when information is skewed, the median is to a greater extent than meaningful than the mean. We convey diverse methods for identifying skewness inwards a information ready (summarised inwards these slides – sorry, master copy source unknown) - nosotros usually reckon the shape of a frequency diagram or box plot. Sometimes skewness is apparent merely from looking at the raw information (this sideways stem-and-leaf diagram is interesting). 

Pupils involve to recollect that positive skew way nosotros convey a few 'sparse' information points (possibly outliers) at the top end of the information ready – too similar inwards the Bibonacci example, this volition pull the hateful up. This volition assistance them conceptually empathise the diverse methods described inwards the textbook.

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

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Two Ways To Role Comic Strips Inwards Maths Teaching

I stumbled across a overnice instruction persuasion inwards this blog post which is all most giving pupils fourth dimension to summarise what they've learnt.  The writer of the spider web log suggests that pupils depict comic strips inwards bird or for homework. Here's but about examples:

Example worksheet

Example of pupil's work

I in ane lawsuit used comic strips for a dissimilar utilization inwards my instruction - I produced this comic strip for my GCSE class, which I showed inwards this Prezi slideshow to generate intelligence most sampling methods.  The characters are all teachers at my schoolhouse (with slightly amended names...).  It went downward good amongst my bird in addition to I laid upwards them the chore of creating their ain versions. We used Bitstrips for Schools which is lovely but tin endure really time-consuming.

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

Resources Anonymous

'Hello. My elevate is Jo together with I'm a resourceaholic'. Yes, I confess, I'm utterly addicted to searching the network for maths instruction resources.

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

I haven't had a run a endangerment to facial expression at all these websites yet, only here's around of my top resources recommendations from the websites I've looked at together with therefore far. I've focused on H5N1 marker because that's where I intend it's hardest to detect interesting instruction ideas.

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

• Correlation together with Regression: a lovely activity on java shops together with crime. Includes calculating a correlation coefficient, interpreting a regression equation together with considering causality together with outliers.
• Discrete Random Variables:  a brusk activity Sounds Really Good! (sort of) which features a real-life purpose of expectation. Bob's Bagel Shop is similar.
• Probability: the carte du jour action Describing Events is an splendid introduction to probability together with the activity Venn Diagrams together with the Addition Rule is skilful too. I also similar this brusk Titanic action on independence.
• Data:  These activities on Haircut Costs together with Speed Trap focus on comparison box plots. Describing Data Sets alongside Outliers and Identifying Outliers are almost outliers together with skewness inwards information (see my related postal service on instruction skewness).
• Normal Distribution: brusk contextual exercises blog. Ooh, novel websites! Heaven for a resourceaholic.
  
  I haven't had a run a endangerment to facial expression at all these websites yet, only here's around of my top resources recommendations from the websites I've looked at together with therefore far. I've focused on H5N1 marker because that's where I intend it's hardest to detect interesting instruction ideas.
  
  Statistics 1 
  Illustrative Mathematics has around fantastic ideas for instruction S1. Here's a pick of examples:
  
  • Correlation together with Regression: a lovely activity on java shops together with crime. Includes calculating a correlation coefficient, interpreting a regression equation together with considering causality together with outliers.
  • Discrete Random Variables:  a brusk activity Sounds Really Good! (sort of) which features a real-life purpose of expectation. Bob's Bagel Shop is similar.
  • Probability: the carte du jour action Describing Events is an splendid introduction to probability together with the activity Venn Diagrams together with the Addition Rule is skilful too. I also similar this brusk Titanic action on independence.
  • Data:  These activities on Haircut Costs together with Speed Trap focus on comparison box plots. Describing Data Sets alongside Outliers and Identifying Outliers are almost outliers together with skewness inwards information (see my related postal service on instruction Logs. 
  • Quadratics together with Cubics: I similar this short Cubic Graph task (answers here) from Mathematics Assessment Project. There's around great Forming Quadratics activities hither too.
  • Circles: Mathematics Assessment Project also has amount lesson plans - I've successfully used the splendid materials from Equations of Circles 1 and Equations of Circles 2 alongside my Year 12s. 
  • Surds: See resources listed inwards my before spider web log post, blog. Ooh, novel websites! Heaven for a resourceaholic.
    
    I haven't had a run a endangerment to facial expression at all these websites yet, only here's around of my top resources recommendations from the websites I've looked at together with therefore far. I've focused on H5N1 marker because that's where I intend it's hardest to detect interesting instruction ideas.
    
    Statistics 1 
    Illustrative Mathematics has around fantastic ideas for instruction S1. Here's a pick of examples:
    
    • Correlation together with Regression: a lovely activity on java shops together with crime. Includes calculating a correlation coefficient, interpreting a regression equation together with considering causality together with outliers.
    • Discrete Random Variables:  a brusk activity Sounds Really Good! (sort of) which features a real-life purpose of expectation. Bob's Bagel Shop is similar.
    • Probability: the carte du jour action Describing Events is an splendid introduction to probability together with the activity Venn Diagrams together with the Addition Rule is skilful too. I also similar this brusk Titanic action on independence.
    • Data:  These activities on Haircut Costs together with Speed Trap focus on comparison box plots. Describing Data Sets alongside Outliers and Identifying Outliers are almost outliers together with skewness inwards information (see my related postal service on instruction Surds. 

Bringing Babies Into A Statistics Lesson

I’m non especially into babies (apart from my ain lilliputian terrors darlings) merely I learn at a girls’ schoolhouse together with 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 yous thence please. I’ve already blogged virtually my Bibonacci starter. There’s besides this pregnant moo-cow evidence query (part d is the exclusively S1 evidence query I've always seen which requires students to know that 68.3% of unremarkably distributed information is inside i measure divergence of the mean).

Edexcel S1 Jan 2002, Q5

I used this query inward an S1 lesson when I was heavily pregnant, much to the entertainment of my students. It led to a tidings virtually the gestation periods of other mammals (those misfortunate elephants!). We’d clearly await a fairly strong correlation betwixt size together with gestation - when I learn a conduct 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 recollect when my due appointment for my starting fourth dimension immature lady came together with went, I tried to discovery 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 discovery much online at the fourth dimension merely i time to a greater extent than I experience it could brand for an interesting lesson.

If yous are a nurture together with thence yous may live on familiar alongside ‘the ruddy book’, which is the Personal Child Health Record issued to all babies born inward the UK. This is a child's principal tape of immunisations, development, wellness reviews together with thence on. At the dorsum of the ruddy mass are the ‘UK-WHO Growth Charts’ where scatter graphs are plotted of the child’s tiptop together with weight against their age. On these scatter graphs are centile lines, to allow parents together with 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 alongside newborn babies, thence it occurred to me that the increment charts could assistance me explicate the concept of percentiles to my S1 classes.

The ruddy mass contains this description of the centile lines on the increment charts:

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

While I was thinking virtually how to pattern an activeness for my S1 bird based on these charts, I discovered that the writer of The Chalk Face has beaten me to it alongside this prissy 'Quartiles together with Percentiles' activity. And @srcav has already written this spider web log ship service 'the mathematics of parenthood' virtually the potential to role increment charts inward his teaching.

Incidentally, the ruddy 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 similar a shot thence I'll proceed to develop these ideas approximately other time...  Do permit me know if yous tin think of whatever other baby-related information to add together to my theme.

My mini-mathematicians.  July 2014.

Long Alive Stalk Too Leaf

I planned to write a postal service close pedagogy stalk together with foliage diagrams. But so I realised that many maths teachers reckon them to survive pointless, a waste materials of pedagogy fourth dimension together with a welcome removal from the curriculum.

Now let’s cry upwards close this for a minute. Admittedly stalk together with foliage diagrams are rarely used inwards ‘real life’. In fact the exclusively mutual examples nosotros tin abide by are timetables, such every bit the Japanese develop timetable shown inwards the moving painting below (more examples here). But does this ‘uselessness’ actually hateful that stalk together with foliage diagrams shouldn’t survive taught? If that’s the illustration so a release of the topics nosotros learn inwards maths should survive taken off the curriculum. 

Japanese develop timetable. Source: Wikipedia

Much of the maths nosotros learn at Key Stage three helps pupils access to a greater extent than advanced topics (all roads Pb to calculus?!). Maths begets maths. So exercise stalk together with foliage 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 foliage diagrams are 1 of a prepare of tools that could survive used to develop agreement of the concepts of median, mode, quartiles, spread, skew together with outliers. I cry upwards they are accessible to depression powerfulness pupils. I cry upwards that pupils bask creating them. I cry upwards they Pb to interesting discussions when comparing ii sets of data. I sure enough don't cry upwards they should survive a compulsory theme at whatever age, but I run into no terms inwards teachers using them if they like. Isn't it prissy to conduct maintain that freedom?

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

John Tukey is also quoted every bit saying "There is no information that tin survive displayed inwards a pie chart, that cannot survive displayed improve inwards another type of chart". I agree. In the same agency many of you lot don't similar stalk together with foliage diagrams, I don't similar pie charts (this excellent spider web log postal service close the misuse of pie charts is worth a read).

Right, straight off I've attempted to justify this spider web log post, here's my lesson ideas:

Starting Point
You could commencement past times presenting your shape amongst a large prepare of information (like the 1 below) together with cry for them what the trend is. It's hard to spot. Ask your pupils for ideas on how could nosotros organise this information so nosotros tin easily run into 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 foliage plots rather pleasing to the eye. Much nicer to hold off at than a dull listing of unordered data.

An option starting indicate is a 'beat the teacher' game, which I've adapted from an thought past times the NCETM. In this activity, pupils cry upwards of a release betwixt 10 together with 40. Each release is called out inwards turn, spell pupils brand a listing inwards their books. Meanwhile the instructor also makes their ain list, but organises it every bit a stalk together with foliage diagram. Once all the numbers are listed, the instructor asks the shape to run out median, trend together with range. The instructor volition exercise it much quicker from their stalk together with foliage diagram, thus he/she wins the race.

Physical Activities
This spider web log post is close introducing stalk together with foliage diagrams using post-it notes. It's a lovely thought for an engaging together with accessible lesson. Mr Collins shared a similar thought inwards this spider web log post, but he uses students together with desks instead of post-its. If you lot similar the thought of human stalk together with foliage diagrams so you lot powerfulness also similar these breath-holding activities - 1 from Don Steward together with a similar 1 from the NCETM.

Data Types
Encourage pupils to cry upwards close dissimilar types of information - what is suitable for a stalk together with foliage diagram together with what isn't? For example, could the full release of goals scored per game inwards a flavor of football game matches survive displayed inwards a stalk together with foliage diagram? Probably not, because the information would by together with large survive unmarried digit numbers. Try my worksheet for to a greater extent than on this.

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

Back-to-back stalk together with foliage diagrams are useful for comparing data. Writing comparisons betwixt information sets - whether represented past times stalk together with foliage 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 foliage questions - similar the 1 below - that could survive explored at Key Stage three (which begs the question, why were they considered suitably challenging for H5N1 level?).

Edexcel S1 Nov 2004, Question 1

I rarely disagree amongst people or play devil's advocate so this postal service is a chip risky for me! Be nice. If you lot exercise learn stalk together with foliage 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 foliage diagrams!).

Scatter Graphs

This weblog is becoming a fleck statistics-heavy, which is ironic given that I don’t peculiarly similar instruction statistics at Key Stage three in addition to 4.  I much prefer instruction algebra. I’m also quite dandy on surds in addition to indices. And I similar trigonometry. In fact, apart from the strange annoying-to-teach topic similar loci in addition to 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 accept to plot a graph. What a faff.

Anyway, this ship service is all nigh ideas for instruction scatter graphs. And I intend to follow it upward amongst a ship service looking at applications of box in addition to whisker plots exterior the maths classroom.  But in addition to hence I’ll halt amongst all the statistics.

Practical activities

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

Outliers 

I similar to purpose the ii scatter graphs shown below (stolen from a Ten Ticks worksheet) inwards a class give-and-take nigh outliers.  Ask your class what could receive got caused these extreme values in addition to you'll in all probability acquire roughly actually creative suggestions!

Line of Best Fit

I learn my students to depict a employment of best check past times trying to minimise the distances betwixt all the points in addition to the line. That’s what a to the lowest degree squares regression does. Contrary to pop belief, in that place doesn't receive got to live the same seat out of points to a higher house in addition to below the line. Nor does the employment receive got to become through whatsoever of the points. And the employment for certain doesn't receive got to become through the origin. Beware of dodgy methods taught inwards other subjects. This misconceptions activity past times frickard on TES is helpful - I've used this inwards 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 upward at Influenza A virus subtype H5N1 level, simply the watch tin brand for interesting discussions at Key Stage three or GCSE. The cardinal shout out for is that fifty-fifty if nosotros bring out a linear human relationship inwards the information we're examining, nosotros can't assume that human relationship extends beyond the attain of the data. Here's a prissy instance for class discussion:

The graph below shows a negative correlation betwixt yr in addition to fourth dimension taken past times athletes to run 100m. It suggests that the speed of 100m runners has increased over time. Influenza A virus subtype H5N1 employment of best check 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 inwards speed include: advances inwards technology (ie to a greater extent than lightweight or streamlined wearing clothing in addition to trainers), query into optimal diets in addition to grooming plans, sponsorship important athletes receive got to a greater extent than fourth dimension to train, the introduction of starting blocks inwards the 1940s in addition to an improvement inwards the accuracy of timing the race.

If the tendency continues indefinitely (ie if nosotros depict the employment of best check into the future) in addition to hence at roughly shout out for people would live able to run 100m inwards null seconds, which is impossible. There must live a shout out for at which the fourth dimension volition plateau, due to limits inwards humans' physical capabilities. Although in that place is a linear correlation, nosotros must live careful non to brand predictions inwards the past times or time to come because the linear human relationship is over a express fourth dimension period.

The graph comes from this Minitab Blog post in addition to the watch was seat into my caput past times Kings College London PGCE tutor Chris Olley. 

"Wind is caused past times the rotation of windmills"

I love the causation vs correlation discussion.  It's a really of import learning shout out for for students who volition come upward across all sorts of dodgy statistics inwards everyday life.

doubt.it

Influenza A virus subtype H5N1 typical instance is shoe size in addition to reading age. The ii variables are positively correlated, simply apparently the size of someone's feet has no comport upon on their reading ability. For to a greater extent than ideas depository fiscal establishment check out this spurious correlations website.

If you're planning a class give-and-take on causation in addition to hence receive got a quick read of 'Correlation does non imply causation'on Wikipedia (not e'er the best source simply gives roughly skillful examples).

Correlation does non imply causation, simply it does waggle its eyebrows suggestively in addition to gesture furtively land mouthing "look over there". – xkcd 

Resources

Finally, here's a few resources that you lot could purpose inwards your lessons:

• I love this Bee Aware action from Don Steward. It could easily live made into a mini-project/display move nigh the drive in addition to comport upon of the demise of dearest bees.
• The fantabulous 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 amongst Scatterplots' is i of many examples (here's the solutions).
• Nrich gives us this nice David in addition to Goliath activity.
• 'Foldables' seem to live a big affair inwards the US math lessons, simply I've never seen them inwards the UK. I retrieve my students would quite similar them. Here's an watch for correlation foldables from the weblog 'Everybody is a Genius'.
• I similar this online tool for checking the accuracy of lines of best check from Mark Ritchings
• Here's an interesting group project. I similar the watch of giving each pair/group ii options hence they tin pick out the variables they prefer, in addition to that everyone inwards the class is working on something different. Also, the 'assigned tasks' for each grouping fellow member (see lastly page) is an watch I haven't seen earlier for organising grouping work. These item tasks may non live suitable for a U.K. lesson because nosotros don't await students to calculate the equations of lines of best fit, simply the watch could live adapted.

I promise this ship 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 as well as Leaf, I'd been challenged to detect a practical application of stalk as well as foliage diagrams exterior the maths classroom. After extensive googling - as well as helpful input from twitter - the exclusively examples I could detect were motorcoach as well as prepare timetables. But I argued that existent life application isn't the hold upward all as well as goal all.

Stem as well as foliage diagrams were invented inwards the 1970s yesteryear Consistent Mathematics if y'all desire to know why). This is a lovely action inwards a lesson introducing the thought of median, exactly non thus effective inwards a box plot lesson. Because fifty-fifty though y'all tin role a bedsheet as well as string to larn the students to expect similar a box plot, if they’re non appropriately spaced out (ie if there’s no scale) as well as thus it’s non a box plot. If y'all desire a proper box plot you’ll bring to truly mensurate the heights as well as depict a scale on the floor.

An option thought (inspired yesteryear this post) involves newspaper aeroplanes. You’ll quest 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 cite on it, as well as throw it from the outset of the scale. Leave the aeroplanes where they land. Once all pupils bring thrown their aeroplane, y'all tin depict or record a box plot on the flooring approximately the planes to correspond the distance flown. Pupils volition hold upward able to run across which quartile their plane landed in. Hopefully 1 hereafter engineer volition throw an amazing outlier which volition brand a skillful tidings point! You could fifty-fifty dissever the degree inwards one-half as well as do 2 box plots on the flooring side yesteryear side, as well as thus the degree could verbalise over which squad had amend aeroplanes as well as which team’s planes were to a greater extent than consistent.

If y'all similar practical activities, here’s 2 more:

• This uncomplicated newspaper folding action is a overnice introduction to median as well as quartiles.

Source: bigideasmath.com

• This Cheerios activity explores mean, median, fashion as well as box plots.

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

I also similar the action below from bigideasmath.com:

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

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

• Standards unit of measurement activities S5 as well as S6, which tin hold upward constitute on Mr Barton’s website. 
• Illustrative Mathematics has loads of first-class statistics questions, similar Haircut Costs as well as Speed Trap.
• Interpreting Box Plots Treasure Hunt from numberloving.co.uk.
• Representing Data Using Box Plots from Mathematics Assessment Project (activities at the back)
• Lots of exercises from CIMT inwards this chapter – I especially similar the comparing questions on the final few pages 
• Using NBA Statistics for Box as well as Whisker Plots from NCTM 
• The variability exercise (starting on page 8) inwards this lesson plan could hold upward helpful when educational activity the concept of spread. 
• My Describing Box Plots action on TES helps pupils practice reading as well as drawing box plots as well as emphasises the role of the right vocabulary.
• My Party Box Plots action on TES helps pupils empathise the concept of spread.

If y'all desire to exhibit your degree some ‘real world’ box plots as well as thus these box plots showing the ages of World Cup players could prompt some skillful discussions almost comparisons. Read @loumeracy’s blog post for to a greater extent than on this.

If y'all desire to ‘wow’ your degree amongst an instance of how box plots tin hold upward used to compare huge amounts of information inwards a pocket-size space, exhibit them this example which shows the historic menses 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 as well as beard plot!

There are many variations to the box as well as whisker plot, such every bit the edible bean plot as well as violin plot. Look these upward on google images for lots of examples.

I read an interesting thought here that I’d never thought of before: “One agency to assistance y'all translate box plots is to imagine that the agency a information gear upward looks every bit a histogram is something similar a mount viewed from the world plane as well as a box as well as whisker diagram is something similar a contour map of that mount every bit viewed from above”.

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

5 Maths Gems #8

I enjoyed coming together many of yous 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 inward the ocean. It's such a shame that thence many schools weren't represented.

Although at that spot are some pockets of collaboration throughout the UK, for event through regional TeachMeets, the fact is that the bulk of U.K. maths teachers alive inward a bubble. Through no error of their own, they know really niggling almost approaches taken inward other schools - including pedagogy, curriculum pattern together with novel technologies. Twitter is purpose of the solution, but it doesn't acquire inward enough.

this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever 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 inward this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all my final gems post and he told me almost something wonderful. He plant inward a novel schoolhouse where all the classroom walls are painted alongside whiteboard paint. So he has no whiteboards inward his room (other than the interactive board), but he - together with his students - tin write on whatsoever wall.

This got me thinking almost my ideal classroom. I'd receive got all the walls painted alongside whiteboard pigment (student operate would live on proudly displayed inward the corridors instead of inward the classroom). I similar the thought of students sitting inward a horseshoe when I teach, similar inward the motion-picture demo below. I intend this would halt low-level disruption together with would encourage meliorate course of written report discussion. They could also do independent practise inward these chairs.

hyperspacellc.com

Separate to this horseshoe I'd receive got a collaboration area, alongside grouping tables that tin live on written on (whiteboard pigment plant on desks too!), or this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all acrylic sheets.

The rooms I currently learn inward are every bit good minor for me to easily accomplish every pupil piece they're working, thence fifty-fifty simply a niggling to a greater extent than infinite would operate wonders.

2. Indices
If you're looking for a novel approach to teaching index laws, yous mightiness taste 'this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all logarithms.

Once you've taught indices, endeavor 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, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever 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, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all Samuel S. Wilks said,"Statistical thinking volition ane twenty-four hr menstruation live on 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 see inward the media. I intend it's worth spending some fourth dimension looking at both misleading graphs together with interesting graphs.

Ridiculously misleading graph

Interesting graphs promote non bad discussions. Give your students some fourth dimension to expect at the graph, operate out what it shows together with and thence intend almost the underlying trends or causes. Here's a distich to acquire yous 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, yous must read this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all teaching identify value. I honey posts alongside 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 elevate this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, alongside the residual 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 quest for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest mark policies, nosotros should all live on 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 spill out of their listing of priorities - together with yesteryear that I hateful collaboration alongside all schools, non simply the schools alongside 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 part 5 non bad ideas that I've seen on Twitter each week. If yous desire to read whatsoever of my previous gems posts, they're all revision races. This is ane of those posts that non alone provides a fantastic resources but also clearly explains how to utilisation it effectively.

Finally, I desire to recommend @fmaths42's post service almost times tables starters which provides a railroad train of progressively challenging practise grids, addition a proposition to impress these grids onto stickers. Times tables are rather helpful so I'd urge yous to ignore Jo Boaler's advice almost non ensuring that children larn their times tables - sure she must receive got said that inward a 2nd of madness. Read @websofsubstance's post service The Educators - Jo Boaler for some interesting (in my see - 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 live on using this every bit a quick starter alongside both Year eleven together with Year 12.

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