5 Maths Gems #10

Have you lot ever wondered where the give-and-take mathematics comes from? Me neither. But this is genuinely quite interesting:

Latin mathematica was a plural noun, which is why mathematics has an -s at the terminate fifty-fifty though nosotros usage it every bit a singular noun. Latin had taken the give-and-take from Greek mathematikos, which inward plow was based on mathesis. That word, which was also borrowed into English linguistic communication but is at nowadays archaic, meant "mental discipline" or "learning", peculiarly mathematical learning. The Indo-European root is mendh- "to learn." Plato believed no 1 could endure considered educated without learning mathematics. Influenza A virus subtype H5N1 polymath is a individual who has learned many things, non simply mathematics (source: Math Forum).

So my boyfriend polymaths, here's my weekly maths gems. Creative maths teaching ideas, inspired past times the keen minds of Twitter.

1. Etymology

On Tuesday developing maths vocabulary before but at nowadays I own got a novel thought to share.

There's keen value inward talking to students most the etymology (origin) of mathematical words every bit they arise. It helps students brand connections as well as builds on their agreement of mathematics. Our role every bit teachers is to enrich our students' lives alongside knowledge, as well as noesis of etymology is both interesting as well as important. This fantastic article (a must read!) says "Etymology provides a security cyberspace of de-mystification. When all the words you lot listen are novel as well as confusing, or when those around you lot lay quondam words to foreign purposes, a grounding inward etymology may help".

Thanks to @CParkinson535 for telling me most etymonline.com. I've taken the next excerpts from this website, simply to give you lot an thought of the sort of affair you lot could portion alongside your students:

• hexagon (n.) 1560s, from Latin hexagonum, from Greek hexagonon, from hex "six" + gonia "angle" (see knee).
• locus (n.) (plural loci), 1715, "locality," from Latin locus "a place, spot, position," from Old Latin stlocus, literally "where something is placed," Mathematical feel past times 1750.
• vector (n.) "quantity having magnitude as well as direction," 1846; before "line joining a fixed dot as well as a variable point," 1704, from Latin vector "one who carries or conveys, carrier" (also "one who rides"), agent substantive from past times participle stalk of vehere "carry, convey" (see vehicle). 
• binomial 1550s (n.); 1560s (adj.), from Late Latin binomius "having 2 personal names," a hybrid from bi- (see bi-) + nomius, from nomen. Taken upward 16c. inward the algebraic feel "consisting of 2 terms."

Thanks also to @the_chalkface for sharing the listing of words below, most of which I'd never heard of. Although nosotros should e'er elbow grease to usage accurate mathematical vocabulary when we're teaching, some of these words may endure a pace likewise far!

2. Plickers

I've never paid much attending to interactive voting systems before because my schoolhouse doesn't ain the necessary devices. The thought is that students simultaneously respond to a multiple choice inquiry or sentiment poll using a wireless system. The instructor tin get together as well as analyse their responses instantly.

I can't give my ain sentiment on their effectiveness every bit a teaching tool, but benefits are listed here as: improved attentiveness, increased noesis retention; poll anonymously (unlike a demonstrate of hands); rails private responses; display polling results immediately; practise an interactive as well as fun learning environment; confirm audience agreement of fundamental points immediately; get together information for reporting as well as analysis. So they are similar to mini-whiteboards for formative assessment, but they own got some clear advantages. The primary disadvantage is the buy as well as maintenance cost. 

posts most Plickers lately as well as am keen to seek it out. Plickers is a free app for your telephone or tablet. Print as well as distribute voting cards and enquire students to concur upward their carte du jour inward the right orientation to betoken their answer. Scan the room alongside your telephone to collect the data. You tin charge upward questions as well as students' names on the user-friendly Plickers website. 

I've read some keen ideas to brand this operate good inward maths. One is to permanently stick the cards to the dorsum of students' books (from blog post. It plant similar this: practise a true/false board inward your classroom as well as stick a tilt on it that represents a mutual misconception. Underneath the inquiry are 2 pocket-size whiteboards - 1 for students to write their elevate if they retrieve the tilt is true, the other for students who retrieve the tilt is false. What I similar most this thought is that students tin easily switch their reply from 1 board to the other if they larn something that changes their mind. At the terminate of the calendar week the reply is revealed as well as discussed. Helpfully, Amy's post service provides some event statements to acquire you lot started.

5 Maths Gems #11

I've got roughly vivid gems for y'all this week. As park Twitter has been on overstep form.

1. Quick Key
Last calendar week I wrote almost Plickers, which is an app y'all tin role inward the classoom for formative assessment - y'all need a device merely your students don't. Today I'm suggesting roughly other app that y'all tin role for assessment - Quick Key. With this app y'all tin laid multiple selection homeworks or tests in addition to grade them inward seconds past times scanning the answer sheets ('Quick Tickets') with your phone.

Quick Key is the conception of American instructor Walter Duncan (@4_teachers). It "turns your cry upwardly into a scanner in addition to eliminates hand-grading of assessments, fifty-fifty for teachers working inward paper-based classrooms without a estimator or internet. Analytics in addition to information exports are easy, thence y'all tin focus on your students".

My initial thoughts were that although this app could last real useful (less fourth dimension spent marking = to a greater extent than fourth dimension spent planning character lessons), it won't allow me to banking concern gibe students' methods, which limits opportunities for useful feedback. But for straightforward cognition checks, to inform me how much my students know, it would function real well.

But thence I read this post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or render scaffolding for selected students. I mean value my boss would last happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward my reflection stickers. Students stick a 'Not withal yeti' or 'I got it' sticker inward their mass to permit y'all know whether they've understood the work.

Speaking of stickers, Adil Jaffer (@adil_3) shared his fantastic feedback stickers thence y'all don't possess got to buy the farm on writing the same affair all the fourth dimension when you're marking.

One of the post pop tweets I saw this calendar week was from @MathedUp who shared his fantastic 'request a selfie' idea. I tin come across this actually improving the character of students' function - many of my students would honey the chance to print their parents. If y'all role iDoceo thence it's slowly to accept a motion painting on your iPad in addition to electronic mail it to a parent.

Did y'all come across these practise books, tweeted by @dandesignthink? The boxes at the bottom of the pages incorporate a checklist (accuracy, spelling, grammar), telephone commutation words, farther questions, telephone commutation points, what went well, in addition to feedback. An 'Exercise mass 2.0' costs 50p - amount details are available here. There's also a maths version - Maths mass 2.0 is every bit awesome. I wishing I had a budget to pass because I'm desperate to guild these!

The to a greater extent than I role Twitter, the to a greater extent than inclined I am to hashtag everything I write (or say!). I possess got to confine myself from putting hashtags inward text messages to my hubby ('what do y'all desire for dinner tonight? #pleasesaytakeaway'). It's overnice to come across that I'm non lonely - Cathy Yenca (post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or render scaffolding for selected students. I mean value my boss would last happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward my Open Evening post where y'all concur a 'design a maths clock' competition. The clock pictures below are all taken from sbcrafts.net where y'all tin banking concern gibe out a big arrive at of clock break ideas that could also last used on break lines.

And finally...
Algebraic long partition is fun when y'all know how to do it, merely it tin last a flake tricky to learn to Year 12. It's overnice to know in that place are option methods. I've factorised polynomials past times inspection earlier merely non using a grid as suggested by post almost it. Find the Factors is designed by @IvaSallay who says it's an splendid means for children in addition to adults to review multiplication facts, role logic, in addition to strengthen encephalon power. The puzzles are based on a multiplication grid where most of the numbers possess got been removed. The grid tin last completed using logic in addition to cognition of factors - inward the illustration below y'all could commencement past times completing the 2 circled cells. The puzzles come upwardly inward varying levels of difficulty, as explained here. Find the Factors has already been real pop with tweeters who've tried it this week.

4. Chalk Pens

Kev Lister ‏(@ListerKev) tweeted almost chalk pens. I've written almost writing on desks, windows in addition to walls before, merely these are novel to me. Kev says the chalk wipes off non-porous surfaces easily with a damp cloth. He uses these pens to write targeted questions or render scaffolding for selected students. I mean value my boss would last happier with me writing on desks with these rather than whiteboard markers.

5. Alternative Number Line
I'm reluctant to include 2 ideas from Ed Southall (@solvemymaths) inward 1 post, merely he's a legend thence I'll allow it... In the same means the maths clock inward my kitchen makes a neat talking betoken for guests to my house, his alternative break line should last displayed inward Influenza A virus subtype H5N1 degree classrooms - students (and teachers!) volition last intrigued. Mr G Walton (@mr_g_walton) has made a fantastic header to larn with it.

Stuart Price (@sxpmaths) suggests making an activity out of this - cutting the break job upwardly in addition to give it to your Year 13s thence they tin variety it into order. They may non last familiar with roughly of the tone merely it's a adept chance for interesting discussions (I constitute out how to read ternary to sympathise Ed's selection for break 5. I'd also non seen flooring in addition to ceiling tone before).

Stuart also suggests that students pattern their ain break lines. I honey this thought - it would function with students of whatever age, from main schoolhouse to university. It's like to an activity I suggested inward my The Art of Collaboration', it's ever neat to listen when these ideas larn far into classrooms. Have a neat half-term interruption everyone!

5 Maths Gems #12

This is going to last a relatively curt gems ship service because I'm exhausted from entertaining nineteen toddlers this afternoon at my daughter's 3rd birthday party. So I'll last brief today, but human face a lengthier ship service side past times side calendar week when I've recovered.

1. Area of a circle (again)
In my seventh gems post I shared an applet that beautifully demonstrates how to derive the surface area of a circle past times cutting it into sectors. This calendar week I establish a bright gif that shows the same thing.

This gif is taken from the animatics (animations + mathematics) section of @MathsChallenges' website. The thinking behind this method is neatly explained in Geometry: What is the intuition behind the formula for the surface area of a circle? which was shared this calendar week by @GeometryDad.

2. Standard form

'resources library has unopen to bully ideas.

3. Influenza A virus subtype H5N1 grade resources

I saw this tweet from @DrTrapezio...

as well as thence I checked this out as well as establish that the Cambridge Mathematics Education Project is inviting schools to register equally affiliates to gain early on access to their costless Influenza A virus subtype H5N1 grade maths resources nether development. I'm e'er on the human face out for Influenza A virus subtype H5N1 grade resources as well as thence I registered. There's loads of bully materials on the website as well as I human face forwards to seeing the collection develop. 

Some of the CMEP's resources are instantly featured on NRICH. For example, the question below is bright (and non equally difficult equally it looks...)

I too similar the 'always, sometimes, never' carte form 'Discriminating'.

Extract from Discriminating

And Parabella is a lovely occupation for your Year 12s studying coordinate geometry.

4. Operation Countdown

Influenza A virus subtype H5N1 combination of ideas as well as inventiveness from @LWmathsmatters, @EJmaths as well as @taylorda01 led to this splendid 'Operation Countdown'. I oftentimes role the 'four threes' action equally a plenary inward an monastic state of operations lesson alongside Year 7 but it plant alongside whatsoever historic menses group. I 1 time used it equally a Year xiii starter as well as they actually enjoyed it. The version below involves 5 threes but it's the same idea.

This painting demo is from @taylorda01. @EJmaths also made this PowerPoint which includes a dark as well as white version.

5. #units #ruler #workings 

I read the ship service 'Hashtag closure' past times A identify for gimmicks?'). David's ship service is virtually using a hashtag to summarise a lesson. 

Then A Frenzy of Marking: 'Progress Over Time' virtually feedback stickers. When I mark, I create honour that I write the same thing over as well as over again, as well as thence stickers would salvage me a lot of time. Problem is, I'm non organised plenty to role stickers. I create my marker inward a multifariousness of locations as well as unremarkably simply receive got a cherry pen to hand. Hashtags volition operate simply equally good equally stickers, equally long equally my students sympathise the important of the hashtags.

When I grade I'm non succinct enough. For instance I oftentimes write 'please become to assist lodge at 1.30pm on Midweek inward Room 111 for assist alongside this topic'. Instead, I could write #helpclub. I too write things similar 'Look at the query - y'all were meant to circular your reply to 1 important figure'. I could simply write #rounding. My students volition learn what I hateful (especially if they receive got this key inward their practise books) as well as it volition salvage me loads of time. "What's the indicate inward the # symbol?" I take away heed y'all inquire - well, yes, the symbol isn't essential, but #MrsMorganLikesHashtags as well as they're non doing whatsoever impairment are they? :)

So that's it - 5 quick gems from a busy mathematical mum. I was planning to characteristic unopen to thoughts virtually the value (or lack of value) of iPads inward maths teaching today but didn't learn fourth dimension to create the inquiry required, as well as thence volition salvage that for my side past times side gems post.

I'm too planning to write a ship service virtually circle theorems side past times side week. I've got unopen to ideas but if you

receive got an interesting agency of teaching circle theorems or whatsoever amazing resources, delight allow me know.

Also, don't forget to banking concern friction match out my other website, prethomework.weebly.com - the extensive collection has grown over half-term.

I'll exit y'all alongside a base of operations eleven abacus which I recollect is cute but volition annoy @solvemymaths (see his ship service 'My Base eleven Abacus Bugbear').

5 Maths Gems #22

Hello as well as welcome to my 22^nd gems postal service - this is where I part 5 instruction ideas I've seen on Twitter.

I've discovered at schoolhouse this calendar week that alter is hard. It's slowly to tell 'I'm non going to learn it similar that anymore' or 'I get got a fantastic novel thought for instruction this topic' but when it comes to truly delivering lessons it's slowly to stick with tried as well as tested methods as well as resources. We desire our students to accept risks but how oft do nosotros accept risks equally teachers? This has been on my hear a lot this calendar week - I'll write a postal service close this soon.

1. 2015

Every yr Chris Smith features the Math Forum Year Game inward his newsletter. The idea is to purpose the digits inward the yr 2015 as well as the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), as well as ! (factorial), to write expressions for the integers 1 to 100. Answers tin last submitted through the Math Forum website, or perchance you lot could brand a classroom/corridor display similar these examples:

2015 Challenge classroom display by @Jeremy_Denton

Challenge 2015 display by @c0mplexnumber

post close the 2014 challenge is besides worth a read if you're going to displace this.

2. The Constant Character
Teaching indefinite integration? I loved this tweet from @inFinnityPi.

This lovely thought originated from @edenspresence who shared the student-decorated constant characters below. When students forget the 'plus C' they get got to decorate a grapheme - a skilful agency to larn inward stick!

3. 'I helped'
H5N1 prissy thought from @GiftedBA - 'I helped' stickers to encourage students to offering each other meaningful assist as well as to recognise those who do so. Download a sticker template here.

4. What's the question?
H5N1 truly prissy thought from Marcus Fleet is to write an reply on the board as well as enquire students for possible questions.

It's prissy that the shape get got chosen a winning question!

I'm quite surprised to encounter the sort of algebra students are doing inward Year half dozen - it's to a greater extent than advanced than I realised.

In the conversation that followed this tweet, Miss_Ren said that she likes to write a issue on the board as well as enquire what the enquiry could get got been. It links to all areas of maths as well as requires no printed resources. Paul Godding shared about similar ideas - such equally writing 5, nine as well as 10 on the board as well as scream for for the strange i out (students get got to come upwards up with ii reasons for each answer). There's charge to a greater extent than fantastic problems similar this on Paul's website 7puzzleblog.com.

5. What the examiner sees
If you're instruction a Year xi shape I retrieve it's good worth showing them this moving painting from @TheMathsMagpie to ensure they are aware that they shouldn't function exterior the allocated spaces inward their exams.

This post gives to a greater extent than data close the moving painting above. Use it with this rattling helpful develop of slides GCSE Maths - Easy Ways to Make Sure You Don't Lose Marks, besides from @TheMathsMagpie.

WWW/EBI

I'm resisting the urge to write a weekly postal service reflecting on what went good (and what didn't become well) at school. Instead I'll but characteristic i personal reflection inward each of my gems posts.

I'm instruction angles to Year seven at the moment. I gave them a homework inward which they were required to orbit reasons for their answers. Some students gave vivid reasons as well as I was pleased to encounter the right purpose of mathematical price I'd taught them such equally 'supplementary'. But many students but wrote out their calculations inward words instead of stating the angle facts they'd used.

In their defence, nosotros hadn't practised 'giving reasons' inward class, as well as so I decided to address this past times setting about angle problems as well as scream for for total reasons with each answer. Conveniently Don Steward has but published a develop of angle problems that were the right degree of challenge.

It seemed similar a skilful thought but I wouldn't tell the lesson went well. What happened was that my students were writing such detailed reasons inward total sentences that it became truly time-consuming (for instance solving enquiry 8 inward a higher identify involves using 3 dissimilar angle facts, therefore 3 sentences). They were doing as well as so much writing that they weren't doing plenty maths for my liking. Plus you lot could hear a pivot drib inward my classroom, as well as that makes me uncomfortable. In the halt I told them to halt writing total sentences as well as write one-word bullet points instead (eg isoscoles/triangle/straight line/complementary etc). They were truly relieved! I'd beloved to hear my readers' thoughts on this - should I get got persevered with the irksome but of import sentence-writing practice? I'm non sure. Please tweet me your opinion!