Large Foursquare Roots

In C1, the non-calculator H5N1 degree module, my pupils sometimes conk stuck solving quadratic equations that are difficult to factorise. This mightiness live on because the leading coefficient is greater than i (see my earlier post) or it may only live on because the numbers inwards the quadratic are large.  I usually propose that they persevere amongst factorising, but if they accept to resort to using the quadratic formula together with thence they may need to foursquare origin a large foursquare number. Here's only about elementary ideas for how to produce thence - inwards this example I'm finding the foursquare origin of 324, though these methods travel as good for larger foursquare numbers.

Note that if the quadratic equation can't live on factorised inwards the outset house together with thence nosotros tin either role the formula or consummate the foursquare to solve it, together with nosotros volition destination upwardly amongst a surd inwards our finally answer.  My side past times side post service is all most didactics surds!

Surds

Surds - what a fabulous topic to teach! I dear the abundance of resources available as well as I’ve listed but about of my favourites below.

Two things I e'er produce when didactics surds:

• Pupils listing the source twelve foursquare numbers inwards their books for reference throughout the lesson. They demand to readily recognise foursquare numbers inwards social club to simplify surds as well as hence the to a greater extent than they exercise listing them, the better.
• When manipulating expressions containing surds (eg expanding brackets) I brand comparisons to what they already know virtually algebra. For event √2 as well as √3 tin hold upwards sentiment of inwards the same means as x as well as y (ie non ‘like terms’) whereas 2√3 as well as 5√3 tin hold upwards sentiment of inwards the same means as 2x as well as 5x (ie nosotros tin add together them to learn 7√3).

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

• Ask pupils to uncovering a means of drawing a occupation alongside a length of just √5 units (the hypotenuse of a correct angled triangle alongside sides 2cm as well as 1cm) 
• Ask pupils to separate the length of an A4 slice of newspaper yesteryear its width. Repeat for A3 as well as A5. What produce they notice? (The answer is e'er √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 but about groovy didactics resources (there's hundreds to a greater extent than online). Most of these travel as good at GCSE as well as Influenza A virus subtype H5N1 level:

• Is it rational?
• Two interactive tasks from Mathspad
• Pairs activity 
• Introducing surds
• True or faux activity
• Surds -Applying as well as 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 but about resources recommended yesteryear the TES.

For a lovely laid of surds problems, come across 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 option method for simplifying surds:

5 Maths Gems #8

I enjoyed coming together many of you lot at La Salle Education's National Mathematics Teacher Conference yesterday. It was a fantastic chance for sharing ideas. But 500 maths teachers out of 350,000 is a drib inwards the ocean. It's such a shame that thus many schools weren't represented.

Although in that place are some pockets of collaboration throughout the UK, for example through regional TeachMeets, the fact is that the bulk of U.K. maths teachers alive inwards a bubble. Through no error of their own, they know really lilliputian almost approaches taken inwards other schools - including pedagogy, curriculum blueprint together with novel technologies. Twitter is business office of the solution, but it doesn't brand it enough.

this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all here.

1. Paint! And my ideal classroom

smartwallpaint.com

I was talking to a friend almost the 'Vertical Non-Permanent Surfaces', magic whiteboards together with acrylic sheets I featured inwards this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all my concluding gems post and he told me almost something wonderful. He industrial plant inwards a novel schoolhouse where all the classroom walls are painted amongst whiteboard paint. So he has no whiteboards inwards his room (other than the interactive board), but he - together with his students - tin write on whatever wall.

This got me thinking almost my ideal classroom. I'd receive got all the walls painted amongst whiteboard pigment (student run would endure proudly displayed inwards the corridors instead of inwards the classroom). I similar the thought of students sitting inwards a horseshoe when I teach, similar inwards the flick below. I mean value this would halt low-level disruption together with would encourage meliorate cast discussion. They could also do independent practise inwards these chairs.

hyperspacellc.com

Separate to this horseshoe I'd receive got a collaboration area, amongst grouping tables that tin endure written on (whiteboard pigment industrial plant on desks too!), or this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all acrylic sheets.

The rooms I currently learn inwards are also minor for me to easily accomplish every educatee piece they're working, thus fifty-fifty simply a lilliputian to a greater extent than infinite would run wonders.

2. Indices
If you're looking for a novel approach to teaching index laws, you lot powerfulness bask 'this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all logarithms.

Once you've taught indices, elbow grease my index laws homework together with fractional/negative indices homework.

3. ThingLink
this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all Mathematical Concepts Wall' yesteryear this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all Samuel S. Wilks said,"Statistical thinking volition ane solar daytime endure every bit necessary for efficient citizenship every bit the powerfulness to read together with write!" (he was paraphrasing HG Wells). Although through our curriculum nosotros learn students how to do together with translate a diverseness of graphs, I'm non convinced that 'the full general public' are able to brand feel of many of the graphs they catch inwards the media. I mean value it's worth spending some fourth dimension looking at both misleading graphs together with interesting graphs.

Ridiculously misleading graph

Interesting graphs promote nifty discussions. Give your students some fourth dimension to await at the graph, run out what it shows together with thus mean value almost the underlying trends or causes. Here's a pair to acquire you lot started.

Source: 'How nosotros believe' yesteryear Micheal Shermer

Source: ONS

The 2nd graph is from '8 Facts almost Young People' yesteryear the ONS, shared this calendar week by @statshan.

Speaking of interesting graphs that spark discussion, you lot must read this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all teaching identify value. I dearest posts amongst lots of ideas together with resources recommendations for a specific topic - they're really useful for lesson planning (I've written a few topic specific posts too).

Second, I desire to bring upward this post, "in high performing countries teachers pass 30% of their fourth dimension teaching, amongst the residue spent planning, preparing together with assessing every bit good every bit working on improving their practice. Compared to the UK, where it’s 90%".

This weekend, 500 maths teachers gave upward a precious Sabbatum to larn from each other. I'm really grateful to La Salle Education for providing that opportunity. To me it farther highlighted the demand for cross-school subject-specific collaboration during term-time. Instead of spending our Inset days hearing almost our schools' latest marker policies, nosotros should all endure out having mini-conferences of our own. Let's promise that when our novel Maths Hubs acquire dorsum from their trips to Shanghai, improving collaboration is come about of their listing of priorities - together with yesteryear that I hateful collaboration amongst all schools, non simply the schools amongst tweeting teachers or a proactive Head of Maths.

Now for my weekly maths gems. For those who receive got simply started reading my blog, this is where I portion 5 nifty ideas that I've seen on Twitter each week. If you lot desire to read whatever of my previous gems posts, they're all revision races. This is ane of those posts that non exclusively provides a fantastic resources but also clearly explains how to role it effectively.

Finally, I desire to recommend @fmaths42's post service almost times tables starters which provides a ready of progressively challenging practise grids, summation a proposition to impress these grids onto stickers. Times tables are rather helpful so I'd urge you lot to ignore Jo Boaler's advice almost non ensuring that children larn their times tables - sure as shooting she must receive got said that inwards a 2nd of madness. Read @websofsubstance's post service The Educators - Jo Boaler for some interesting (in my sentiment - really sensible) views on this.

Finally, receive got a acquire at this query from Tony Gardiner's session at yesterday's conference, shared yesteryear @mrsdenyer. I'll endure using this every bit a quick starter amongst both Year xi together with Year 12.

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

5 Maths Gems #27

Hello too welcome to my 27^th gems post. This is where I percentage v of the best didactics ideas I've seen on Twitter recently. I'll survive brief today because I experience similar I'm drowning inward marking, reports too lesson planning at the moment! Thankfully it's alone ane calendar week until the Easter holidays, hence there's low-cal at the cease of the tunnel.

1. Which One Doesn't Belong?
This website is pure genius from @MaryBourassa. 'Which One Doesn't Belong?' is 'a website dedicated to providing thought-provoking puzzles for math teachers too students alike. There are no answers provided equally at that spot are many different, right ways of choosing which ane doesn't belong'.  Here's a duet of examples:

Ask students to honor a argue why each ane doesn't belong. What a fantastic tool for generating interesting shape discussion. Mary welcomes contributions to the website - details too templates are available Pythagoras Lesson. In this lesson Pythagoras problems were seat around the room too students worked inward pairs to solve the problems - they had to introduce their instructor amongst equally many right answers equally they could inward an hour. They had 3 ‘hint’ tokens that they could merchandise inward for assist at whatsoever point. I similar this sentiment - I guide maintain a habit of offering likewise much help, which tin survive counterproductive. The express provide of hint tokens volition encourage perseverance inward students - they'll alone enquire for assist when they really demand it.

Spiderbox from illustrativemathematics.org

4. Surds
Two lovely surd resources were shared on Twitter this week. First upward was @aap03102's excellent surds magic square.

And then @MathsPadJames (of awesome website mathspad.co.uk) shared this bright activity:

Followed past times some other fix of examples:

5. Sticky Maths