Linear Graphs

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

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't function out how to respond a GCSE enquiry similar this:

Strangely, I learn this differently at GCSE as well as Influenza A virus subtype H5N1 level.  At GCSE my pupils write down

y = mx + c

as well as substitute values for y, k as well as x, as well as hence solve for c.  Whereas at Influenza A virus subtype H5N1 marking my pupils occupation the equation

y - y₁ = m(x - x₁)

Essentially the same method but a slightly dissimilar approach. Perhaps I should endure to a greater extent than consistent as well as innovate the 'A marking method' at GCSE. I'd similar to take away heed what other teachers do.

In this shipping service I’ll propose roughly ideas as well as resources for instruction linear graphs.

Key words

Let's kickoff amongst the basics. There's a lot of novel vocabulary inwards coordinate geometry, roughly of which pupils volition convey encountered at primary school. This is a overnice vocabulary cognition survey every bit suggested inwards my earlier post. 

Here's a overnice play tricks for remembering the words parallel as well as perpendicular (this could endure helpful for spellings - parallel is oft misspelt): 

as well as this activity is suitable for Year vi or 7. 

Introducing the shape y = mx + c
I'd unremarkably kickoff this theme inwards Year seven or 8 amongst plotting at nowadays occupation graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This theme provides an first-class chance for pupil investigation using Desmos. Use a worksheet to direct pupils through the lesson:

• Investigating Straight Lines amongst Desmos (by Tristan Jones on TES)
• Straight Line Graphs inwards Desmos (by me!)

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

My weblog shipping service 'All most gradient' features ideas as well as resources for instruction slope (the shipping service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets as well as activities).

Understanding parallel as well as perpendicular gradients

So here's the substitution data that pupils demand to understand:

(source)

If they know how to function out a slope every bit 'rise over run' (or equivalent) as well as hence pupils should endure able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this i from MathsPad.

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

• Finding Equations of Parallel as well as Perpendicular Lines yesteryear Mathematics Assessment Project
• Perpendicular Lines Worksheet (by me!)
• AS marking Parallel as well as Perpendicular Lines  (suitable for GCSE extension)
• Perpendicular lines: equations yesteryear toticity.co.uk

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

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

• Foundation: Linear Graphs 'I Can' from Mathsbox
• Mathattack Linear Graphs homework sheet
• Topic checklist
• MathsPad Linear Graphs Problems
• Rich activities from Five Triangles
• Rich activities from Median Don Steward

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

Finally, e'er wondered which countries occupation y = mx + c annotation as well as which countries occupation something different? Check out this map.

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.