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

• This Cheerios activity explores mean, median, manner together with box plots.

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.

• Standards unit of measurement activities S5 together with S6, which tin last constitute on Mr Barton’s website. 
• Illustrative Mathematics has loads of first-class statistics questions, similar Haircut Costs together with 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 specially similar the comparing questions on the final few pages 
• Using NBA Statistics for Box together with Whisker Plots from NCTM 
• The variability exercise (starting on page 8) inwards this lesson plan could last helpful when didactics the concept of spread. 
• My Describing Box Plots activeness on TES helps pupils do reading together with drawing box plots together with emphasises the purpose of the right vocabulary.
• My Party Box Plots activeness on TES helps pupils empathize the concept of spread.

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.

5 Maths Gems #1

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

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

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

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

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

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

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

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

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

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

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

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

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

5 Maths Gems #91

Welcome to my 91^st gems post. This is where I percentage merely about of the latest news, ideas in addition to resources for maths teachers.

1. World Cup Box Plots
Thanks to Southborough Maths (@Mathsteam1) for sharing these box plots created past times @johnwmillr. They present the distributions of acme past times seat for players inwards the World Cup. They brand for smashing discussions with students, in addition to supply a prissy demonstration of how box plots tin assistance us brand comparisons.

I've been using a like laid of graphs for years, every fourth dimension I instruct box plots (see my post on teaching box plots for to a greater extent than on this). It ever goes downwards well.

2. Variation Theory
Last calendar week Craig Barton launched a novel website packed sum of sets of good written questions for intelligent practice. Do banking enterprise friction match out variationtheory.com if y'all haven't already seen it.

'Rearranging formulae' past times Danielle Moosajee

'Mixed Bases' past times Joe Berwick 

Like Craig's other resources websites (SSDDs, Venns in addition to Diagnostic Questions), y'all tin submit your ain resources for inclusion on this website.

3. Fractions
Thanks to Berkeley Everett‏ (@BerkeleyEverett) for sharing this animation. This tin endure found, along alongside loads of other smashing animations, on the Math Visuals website. 

4. Compound Shapes
Thanks to Mark Ives (@MarkIvesTeach) for showing us how he used Numicon to back upwards students inwards identifying the lengths of sides inwards chemical compound shapes.

5. Coordinates Problems
Thanks to Dave Taylor (@taylorda01) for a sharing a laid of challenging coordinates problems (see this tweet in addition to this tweet) . Here are a duet of examples:

Update
Do maths teachers all nation things inwards the same way? At the Tweet Up inwards Manchester in conclusion weekend, I recorded a grouping of teachers maxim words that I've heard pronounced differently past times dissimilar maths teachers. I've picked 3 of these words for the start video from my pronunciation project:

Thank y'all to everyone who took part! It may non endure the most exciting video ever but I mean value it's actually interesting that students postulate heed dissimilar things from dissimilar teachers.

Here are a few other things y'all powerfulness stimulate got missed recently:

• ThinkMaths (@thinkmaths) are doing their annual giveaway of maths goodies - the 'Exciting Maths Toys for Excited Maths Teachers Mailout' - sign upwards now!
• I'll endure taking role inwards the Big Internet Math-Off inwards July - in addition to I'd actually appreciate your support! 
• Check out this great post from Alex Cutbill (@intersectarian) most the Definition of 'power' inwards maths. This is what I was talking most inwards my conference session in conclusion Saturday.
• Do banking enterprise friction match out the fantabulous laid of surds questions from Gillian Matthewson (@gmathewson1) on her new blog.
• The Nuffield Foundation written report "How create shortages of maths teachers impact the within-school allotment of maths teachers to pupils?" is worth a read.
• I recorded a podcast afterward the JustMaths conference alongside Craig Barton which is directly online - y'all tin head to it here. It's solely one-half an hour!

Ten years afterward nosotros did our PGCE together, I finally met upwards alongside Colin Hegarty! He came to my schoolhouse to launch Hegarty Maths at our start annual trust maths conference. This is actually exciting - Hegarty Maths is awesome. I loved trialling it alongside my Year 11s this year. Thank y'all to both Colin in addition to Simon Petri from the Surrey Plus Maths Hub for their fantabulous presentations.

It's all been a fleck crazy lately. Next calendar week I stimulate got an AQA Expert Panel Meeting, the BBO Maths Hub conference, a TTRS Rock Wrangle trip, in addition to prom. Then I tin relax!

I'll learn out y'all alongside this lovely ingredient tree puzzle from Sarah Carter (@mathequalslove), inspired by @HaroldReiter.

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

• This Cheerios activity explores mean, median, manner together with box plots.

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.

• Standards unit of measurement activities S5 together with S6, which tin last constitute on Mr Barton’s website. 
• Illustrative Mathematics has loads of first-class statistics questions, similar Haircut Costs together with 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 specially similar the comparing questions on the final few pages 
• Using NBA Statistics for Box together with Whisker Plots from NCTM 
• The variability exercise (starting on page 8) inwards this lesson plan could last helpful when didactics the concept of spread. 
• My Describing Box Plots activeness on TES helps pupils do reading together with drawing box plots together with emphasises the purpose of the right vocabulary.
• My Party Box Plots activeness on TES helps pupils empathize the concept of spread.

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.

5 Maths Gems #1

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

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

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

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

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

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

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

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

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

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

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

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

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

5 Maths Gems #91

Welcome to my 91^st gems post. This is where I percentage merely about of the latest news, ideas in addition to resources for maths teachers.

1. World Cup Box Plots
Thanks to Southborough Maths (@Mathsteam1) for sharing these box plots created past times @johnwmillr. They present the distributions of acme past times seat for players inwards the World Cup. They brand for smashing discussions with students, in addition to supply a prissy demonstration of how box plots tin assistance us brand comparisons.

I've been using a like laid of graphs for years, every fourth dimension I instruct box plots (see my post on teaching box plots for to a greater extent than on this). It ever goes downwards well.

2. Variation Theory
Last calendar week Craig Barton launched a novel website packed sum of sets of good written questions for intelligent practice. Do banking enterprise friction match out variationtheory.com if y'all haven't already seen it.

'Rearranging formulae' past times Danielle Moosajee

'Mixed Bases' past times Joe Berwick 

Like Craig's other resources websites (SSDDs, Venns in addition to Diagnostic Questions), y'all tin submit your ain resources for inclusion on this website.

3. Fractions
Thanks to Berkeley Everett‏ (@BerkeleyEverett) for sharing this animation. This tin endure found, along alongside loads of other smashing animations, on the Math Visuals website. 

4. Compound Shapes
Thanks to Mark Ives (@MarkIvesTeach) for showing us how he used Numicon to back upwards students inwards identifying the lengths of sides inwards chemical compound shapes.

5. Coordinates Problems
Thanks to Dave Taylor (@taylorda01) for a sharing a laid of challenging coordinates problems (see this tweet in addition to this tweet) . Here are a duet of examples:

Update
Do maths teachers all nation things inwards the same way? At the Tweet Up inwards Manchester in conclusion weekend, I recorded a grouping of teachers maxim words that I've heard pronounced differently past times dissimilar maths teachers. I've picked 3 of these words for the start video from my pronunciation project:

Thank y'all to everyone who took part! It may non endure the most exciting video ever but I mean value it's actually interesting that students postulate heed dissimilar things from dissimilar teachers.

Here are a few other things y'all powerfulness stimulate got missed recently:

• ThinkMaths (@thinkmaths) are doing their annual giveaway of maths goodies - the 'Exciting Maths Toys for Excited Maths Teachers Mailout' - sign upwards now!
• I'll endure taking role inwards the Big Internet Math-Off inwards July - in addition to I'd actually appreciate your support! 
• Check out this great post from Alex Cutbill (@intersectarian) most the Definition of 'power' inwards maths. This is what I was talking most inwards my conference session in conclusion Saturday.
• Do banking enterprise friction match out the fantabulous laid of surds questions from Gillian Matthewson (@gmathewson1) on her new blog.
• The Nuffield Foundation written report "How create shortages of maths teachers impact the within-school allotment of maths teachers to pupils?" is worth a read.
• I recorded a podcast afterward the JustMaths conference alongside Craig Barton which is directly online - y'all tin head to it here. It's solely one-half an hour!

Ten years afterward nosotros did our PGCE together, I finally met upwards alongside Colin Hegarty! He came to my schoolhouse to launch Hegarty Maths at our start annual trust maths conference. This is actually exciting - Hegarty Maths is awesome. I loved trialling it alongside my Year 11s this year. Thank y'all to both Colin in addition to Simon Petri from the Surrey Plus Maths Hub for their fantabulous presentations.

It's all been a fleck crazy lately. Next calendar week I stimulate got an AQA Expert Panel Meeting, the BBO Maths Hub conference, a TTRS Rock Wrangle trip, in addition to prom. Then I tin relax!

I'll learn out y'all alongside this lovely ingredient tree puzzle from Sarah Carter (@mathequalslove), inspired by @HaroldReiter.