Large Foursquare Roots

In C1, the non-calculator Influenza A virus subtype H5N1 marking module, my pupils sometimes perish stuck solving quadratic equations that are difficult to factorise. This powerfulness live because the leading coefficient is greater than i (see my earlier post) or it may but live because the numbers inward the quadratic are large.  I commonly propose that they persevere amongst factorising, but if they convey to resort to using the quadratic formula in addition to thence they may require to foursquare origin a large foursquare number. Here's roughly uncomplicated ideas for how to create thence - inward this representative I'm finding the foursquare origin of 324, though these methods run every bit good for larger foursquare numbers.

Note that if the quadratic equation can't live factorised inward the commencement house in addition to thence nosotros tin either purpose the formula or consummate the foursquare to solve it, in addition to nosotros volition halt upwards amongst a surd inward our lastly answer.  My adjacent post service is all close didactics surds!

Surds

Surds - what a fabulous theme to teach! I honey the abundance of resources available in addition to I’ve listed roughly of my favourites below.

Two things I ever create when didactics surds:

• Pupils listing the starting fourth dimension twelve foursquare numbers inward their books for reference throughout the lesson. They demand to readily recognise foursquare numbers inward guild to simplify surds in addition to then the to a greater extent than they practice listing them, the better.
• When manipulating expressions containing surds (eg expanding brackets) I brand comparisons to what they already know close algebra. For representative √2 in addition to √3 tin hold upwards regard of inward the same means as x in addition to y (ie non ‘like terms’) whereas 2√3 in addition to 5√3 tin hold upwards regard of inward the same means as 2x in addition to 5x (ie nosotros tin add together them to larn 7√3).

The NCETM suggests a distich of prissy ‘hooks’ for getting started didactics surds:

• Ask pupils to notice a means of drawing a occupation alongside a length of precisely √5 units (the hypotenuse of a correct angled triangle alongside sides 2cm in addition to 1cm) 
• Ask pupils to split the length of an A4 slice of newspaper past times its width. Repeat for A3 in addition to A5. What create they notice? (The response is ever √2)

This blog post has some to a greater extent than ideas for introducing the concept of surds. And I similar this on the history of surds.

Resources
Here’s roughly bully didactics resources (there's hundreds to a greater extent than online). Most of these travel as good at GCSE in addition to Influenza A virus subtype H5N1 level:

• Is it rational?
• Two interactive tasks from Mathspad
• Pairs activity 
• Introducing surds
• True or faux activity
• Surds -Applying in addition to occupation solving
• Multiplication squares
• Mr Barton’s activity
• Standards Unit N11
• Surds Connect 4
• Surds resources - leannegadsby on TES
• Manipulating Radicals
• Tripods
• And here’s roughly resources recommended past times the TES.

For a lovely laid of surds problems, run into my Problem Sets page.

Finally, if you're looking for something actually creative, cheque out this Wheel of Theodorus Art Project.

Edit 29/12/14: Thanks to @runningtstitch for suggesting an choice method for simplifying surds:

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.