Maths Vocabulary

I found Cav's blog shipping 'Vocabulary together with maths are non mutually exclusive' actually interesting together with it got me thinking nearly activities together with didactics techniques related to maths vocabulary.

Influenza A virus subtype H5N1 didactics tool that tin move endure used regularly throughout the twelvemonth is a source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward vocabulary noesis survey. When you lot outset didactics a topic, do a listing of the novel words that volition endure used together with inquire students to consummate a nautical chart showing their agreement of those words.  Repeat the activeness afterward to run across the improvement inward agreement - I've non tried this myself however but I intend it would generate merely about useful questions equally good equally boosting pupil confidence.

In my shipping on source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Area together with Volume I suggested these maths vocabulary exercises which brand for prissy 'end of term' lessons.  Here's an trial of an activeness from this pack:

Here's merely about to a greater extent than links that you lot mightiness honor useful:

• The Maths Magpie has created these great Maths Vocabulary Activities
• A listing of telephone commutation words for Key Stage 3
• Another vocabulary activity - perchance an choice to the noesis survey described above
• Exercises amongst a Mathematics Dictionary 
• Background reading 'Building Mathematical Vocabulary' past times Dr Madeline Kovarik

I was latterly talking to a highly intelligent together with articulate Year xiii pupil who said that she hated it when her instructor asked her to 'speak maths'. I asked her to elaborate. She said that when questioning the class, the instructor expected answers that used appropriate maths vocabulary - together with fifty-fifty this pupil (who'll endure off to Oxbridge inward September) flora this daunting.  We demand to address this trial from a immature age.  One tip is to ever require pupils to reply questions inward total sentences instead of merely numbers or words - from mind schoolhouse onwards. Influenza A virus subtype H5N1 rattling unproblematic trial - inward response to the enquiry 'what do nosotros telephone outcry upwardly a polygon amongst 8 sides?', don't bring the reply 'octagon' - inquire for a total judgement such equally 'An 8-sided polygon is called an octagon' to larn pupils used to 'speaking maths' from an early on historic menses (source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward Gems 43. I also flora the source).

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Edit: 11/11/15

Since writing this shipping final twelvemonth I've seen lots of groovy resources for developing vocabulary. I specially similar the Literacy Assessments featured inward activity below worked good amongst my Year 7s.

Here's my direct to literacy inward maths lessons:

5 Maths Gems #6

introducing calculus, a post nearly starters as well as teaching inequalities as well as a calendar of maths teaching conferences. I've also added novel bits as well as pieces to my resource libraries as well as homeworks page. I've notwithstanding works life fourth dimension for Twitter - here's this week's highlights.

1. Geogebra

For those of us who are equally good busy or non techy plenty to make clever things amongst Geogebra, at that topographic point are really helpful people who make it for us. I've mentioned Mathimation before. Here’s a few to a greater extent than interactive teaching tools that receive got been shared on Twitter recently:

• Custom Cuboid by @the_chalkface allows you lot to highlight specific cuboid faces - this is a helpful tool when teaching the surface expanse as well as book of cuboids. 
• @TheMathsTeach gives us interactive circle theorems for students to explore. Each Geogebra worksheet has uncomplicated instructions as well as questions - students tape their findings on the Student Conjecture Sheet.
• Parts of a Circle by @Mr_Mathematics is great for exploring circle vocabulary.

2. Two Superb Resources

I come across a hell of a lot of skilful maths resources inward my resource-addled life, but every straightaway as well as thus I come across ane that is absolutely superb. This calendar week was groovy because I discovered 2 such resources.

Ben Tanner (A level, my students works life them really useful for testing each other both inward shape as well as at home.

Extract from GCSE revision cards - tannermaths.co.uk

Chris Smith (@aap03102) produces a bright weekly newsletter total of fantastic maths teaching ideas - if you lot don't already subscribe thus email him straightaway to larn on the mailing list. This calendar week he tweeted nearly his relay races because they passed 100,000 downloads on TES. I can't believe that I, the resourceaholic, receive got never seen these before.

I've used revision relays amongst my classes earlier as well as they've e'er worked really well, thus I'll definitely live using these disclose puzzle races. There are 10 relays hither including ane for Halloween, ane for Christmas as well as ane for Easter. That's halt of term sorted then.

Extract from Halloween Relay Race - Chris Smith on TES

The 100,000 downloads got me thinking nearly how many maths teachers at that topographic point are inward the UK. First I started thinking nearly how many schools at that topographic point are as well as how many maths teachers per school, but thus I thought it powerfulness live easier to starting fourth dimension from how many teenagers at that topographic point are inward the UK. This reminded me of a labor interview I ane time had. Now here's a story for your students if they ever inquire when they'll demand maths.

During my concluding twelvemonth at academy I had an interview for a graduate labor equally a administration consultant at PwC. I'd already done a summertime internship at KPMG thus was feeling fairly confident. The alternative 24-hour interval started amongst a maths seek much similar this one. After the seek I had luncheon inward a conference room amongst the other candidates. An administrator came inward after luncheon to denote who had failed the maths seek (the unsuccessful candidates had to move out at that signal - an awkward instant for all). I survived the cutting as well as proceeded to a bizarre labor interview.

The interviewer asked me how many planes were inward the heaven at that moment. He wanted an actual number, non but a method. Once I'd had a become (starting point: how many airports inward the world) he thus asked me to reply ane time to a greater extent than using a dissimilar method, thus I did (starting point: world's population). He thus asked for some other method. We went through the same procedure for 'how many babies were born inward the United Kingdom of Great Britain as well as Northern Ireland yesterday?'. I intend I did a reasonably skilful labor of answering these questions - us mathematicians are skilful at lateral thinking. The concluding query inward the interview was nearly how I would stair out the peak of a edifice using but a barometer. I gave a few sensible answers but he kept asking for more. He stopped when I gave an utterly ridiculous reply which I won't acknowledge to hither (if you're coming the conference inward 2 weeks, inquire me then). Moral of the story - maths as well as work solving skills larn you lot far. You never know what you'll live asked inward a labor interview. And don't live the mortal sent abode at lunch.

3. Two Superb Websites
@dazmck shared the website 'That Quiz' which allows you lot to laid gratis online tests as well as homeworks inward a broad hit of topics from Key Stage iii to H5N1 level. It alone takes a infinitesimal to brand a seek as well as e-mail the URL to your students. They larn instant feedback on their answers (either throughout the quiz or at the end). They also larn an chance to right their mistakes. There are a disclose of settings but it's ridiculously slowly to use.

thatquiz.org menu

If you lot register (which takes roughly 5 seconds) you lot tin also collect your students' scores online. Here's an instance of a box plot seek question:

Example query from thatquiz.org

This website is thus incredibly helpful as well as slowly to use, it reminds me of some other groovy website - Form Time Ideas. This is past times far the best tutor fourth dimension resources I've seen. It's beautifully designed as well as slowly to use. The content is spot on as well as it changes every day. Websites that salve fourth dimension are a god-send for busy teachers.

formtimeideas.com

4. Words to Avoid
Twitter had me inward stitches this week. @taylorda1 tweeted nearly something he'd said inward a lesson that his students had works life amusing. Most teachers receive got made slips similar this - they tin stimulate a lot of disruption!

The conversation that followed this tweet was really funny. For the sake of novel or trainee teachers, here's a listing of things to avoid maxim inward maths lessons:

• In probability, don't toss a money as well as larn a head. In a room total of teenagers, far improve to flip a money as well as larn a tail.
• Avoid examples involving 'balls inward a bag'. 'Discs inward a bag' tin live but equally problematic if non said clearly. Try counters instead.
• Also inward probability, live careful how you lot nation 'the or rule'.
• When writing on the board make non shorten the discussion cumulative. Cum freq is probable to stimulate a stir.
• Don't brand c proportional to k (c∝k).
• Careful what you lot nation (and how you lot gesture) when talking nearly enlargements, top heavy fractions as well as going downward the disclose line.
• Be prepared for giggles if an reply is 69.
• Avoid having refer to 'the d' or maxim 4q ('4q too!').
• We can't avoid f(x) but live prepared for 'f off' silliness. Avoid f(u).
• When writing page numbers on the board, beware of p155.
• Don't nation cos. Say cosine. Cos Omac is an insult as well as surely non suitable for a maths lesson if whatsoever of your students speak Arabic!

Thanks to all the tweeters who contributed to this list.

It works both ways. I had to stifle my young giggles when I attended a Year 13's utter on the dangers of fracking.

There's to a greater extent than 'dirty mathematics' here.

5. Calligrams
@edsouthall tweeted some of these Minimal Math Concepts.

I honey these as well as was really pleased to uncovering that you lot tin purchase them equally a sheet or framed impress - some other affair for my christmas list! I've added this to my mathsy gifts page.

@tessmaths shared her lovely thought for a shape activity on Maths Calligrams. A calligram is a phrase or discussion inward which the text is arranged inward a agency that creates a visual image. The paradigm created past times the words expresses visually what the discussion says. This could live incorporated into a chief or secondary maths lesson - give students a listing of maths vocabulary as well as inquire them to create pictures to assist agreement as well as recall.

Maths Calligram by @JonTrebyAAN

I promise you've works life some of these ideas helpful. I'm taking requests for time to come resources posts thus if there's a detail theme you'd similar me to feature, delight email or tweet me.

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.

Ideas For Education Circle Theorems

There was no inquiry nearly whether circle theorems should earn their house on the novel mathematics curriculum. They are the perfect representative of a theme that is good placed inward secondary schoolhouse mathematics. In teaching this topic, nosotros receive got the pleasance of exploring a prepare of theorems - a pocket-size alternative of the many fascinating properties of circles - thence teaching students how to apply their novel mathematical noesis to solve geometrical problems.

Background
Imagine designing a mathematics GCSE from scratch. What topics would yous include? There's a lot of mathematics to select from. You exclusively receive got to glance at an quondam textbook or O score newspaper to come across that the topics studied at secondary schoolhouse receive got changed considerably over the final century. Have circle theorems ever featured on the United Kingdom of Great Britain together with Northern Ireland of Britain together with Northern Republic of Ireland curriculum?

Looking dorsum at the 1957 O score Syllabus, nosotros receive got the following:

Extract from 1957 O score maths syllabus

Most of this looks really familiar, although the theorem 'if 2 circles touch, the indicate of contact is on the business of the centres' is non covered anymore. Note that the term 'cyclic quadrilateral' isn't used, but instead 'angles inward contrary segments are supplementary'.

In the 1957 O score exam there were many questions relating to circle theorems, including a seat out of proofs. The inquiry below is perchance the easiest, together with is similar inward mode to the questions seen on electrical flow GCSE papers. Our students mightiness relish having a become at questions similar this - the maths that their grandparents did at school.

1957 O score question

There was also a inquiry inward the 1957 newspaper relating to the Power of a Point Theorem, which at in ane lawsuit features inward iGCSE (specifically the Intersecting Chords Theorem) but non GCSE.

Interestingly the wording (but non the substance) of the circle theorems content on the 1974 O score Syllabus differs notably from the 1957 Syllabus. Again, circle theorems characteristic heavily inward the Geometry department of the 1974 O score exam. In the inquiry below, our electrical flow GCSE students would live able to do purpose a, but non purpose b.

1974 O score question

Over the next forty years, circle theorems content was reduced (in business amongst a gradual displace to include more topics inward secondary mathematics, but less depth). The 1984 O level (an splendid seek - similar to today's higher GCSE but to a greater extent than challenging) contained exclusively 2 circle theorem questions. Here's ane of them:

1984 O score question

The electrical flow GCSE specifications are really specific nearly which theorems are included (most of circle theorems on the 1957 Syllabus receive got stood the seek of time). The extract below is from the 2012 Edexcel GCSE specification.

Extract from Edexcel GCSE 2012 Mathematics Influenza A virus subtype H5N1 specification

The novel Edexcel GCSE maths specification (effective from 2015) is far less specific, only stating:

Thankfully the new AQA specification is less vague, confirming the continuation of the existing content.

The novel OCR specification contains a similar score of detail.

Source: Wikipedia

So it's long been accepted that circle theorems are worth including inward secondary mathematics education. Although there's been a pocket-size reduction inward the attain of theorems covered over the final lx years, the bulk receive got survived. Circle theorems may receive got petty straight application inward 'real life', but that doesn't matter. Mathematicians relish applying circle theorems to solve interesting geometrical problems. The trickier problems tin actually seek our logical thinking skills together with are especially satisfying. I'm pleased that circle theorems are hither to stay. So let's expect at a few teaching ideas.

Influenza A virus subtype H5N1 skillful house to start when teaching circle theorems is a recap of angle facts relating to triangles together with parallel lines. Most teachers thence acquire their students doing some exploration into angles inward circles. Once each theorem is established, students should do a lot of practice, starting amongst uncomplicated cases thence moving onto to a greater extent than complex questions involving to a greater extent than than ane theorem. We ask to expect at proofs along the way too.

Vocabulary

Paper plate vocab from Mr Collins

There's a lot of novel vocabulary inward this topic. First nosotros receive got the parts of a circle - your students could explore these using this blog post from Mr Collins.

This is also a skillful chance to verbalize about etymology - tangent originates from the Latin tangere 'to touch' and arc originally referred to the sun's apparent motility inward the sky. Segment (think oranges) and sector (think pie charts) are both from the Latin secare 'to cut'. Diameter is from the Greek dia- "across, through" and metron "a measure".

As good every bit the parts of a circle, nosotros also receive got novel words inward the descriptions of the theorems. For example vocabulary I brand some suggestions for activities to back upwards students when yous innovate novel cardinal words, such every bit vocabulary noesis surveys together with literacy walls.

'Name the line'
vocabulary exercise

Investigations
It's squeamish to give students the chance to investigate the angles inward a circle using ICT, geoboards (virtual or real), worksheet investigations or paper folding.  I honey this serial of Geogebra worksheets from The Maths Teacher. Students tin play around amongst the angles on enshroud thence respond the questions provided. In Folding Circles: Exploring Circle Theorems through Paper Folding from the NCTM, students manipulate newspaper circles to explore circle theorems (scroll downwardly to theorems 3 together with iv inward the instructions). I also similar these 2 uncomplicated paper-based demonstrations: angle at the centre and angles inward the same segment.

Extract from Folding Circles (NCTM)

Another persuasion for investigating angles inward circles involves hula hoops - this originates from the invitee post this post by Kelly Achtymichuk (source of the pictures below) together with Mr Collins' post 'Circle Theorems & Hula Hoops!!' to come across how other teachers receive got adapted the idea.

Cyclic Quadrilaterals

I'm non going to become into item nearly each theorem but I do desire to call cyclic quadrilaterals. The give-and-take cyclic is from the Greek kuklos which agency 'circle' or 'wheel'. A cyclic quadrilateral is a quadrilateral whose vertices all prevarication on a unmarried circle (ie the vertices are concyclic).

All triangles receive got a circumcircle but non all quadrilaterals do. Ask your students to sketch an representative of a quadrilateral amongst circumcircle (eg a square) together with ane without (eg a rhombus).

I similar the inquiry below (from this CIMT exercise) to develop understanding of the give-and-take concyclic.

Question from CIMT

Proof

Students should receive got a become at working the proofs out themselves. But they're non accustomed to proof, thence they'll in all likelihood ask some direction. For example, when they're proving that the angle inward a semicircle is a right-angle, yous could exhibit them the pace pictured together with inquire 'how would yous acquire to this step?' And where would yous become from here?'.

I also actually similar this activity from rhemsley on TES which makes the proofs to a greater extent than accessible yesteryear starting amongst numbers earlier generalising.

The NCETM also gives us this proof worksheet where students create total inward the missing words.

Tangent proofs are non currently on the GCSE syllabus but if yous desire to evidence the tangent theorems amongst your class, scout James Tanton's video Tangent Theorems for Circles together with the Pythagorean Theorem beforehand - the explanations are really clear.

If yous desire circle theorems together with proofs on your classroom wall thence these posters from danbar1000 on TES are great.

Resources
If you're planning a sequence of lessons on circle theorems thence you'll detect enough of useful worksheets together with activities listed inward my shape resources library. 

In my final gems post I mentioned the costless app Angles? - Let's solve figures problems! by Gakko Net Inc. If your students receive got access to iPads inward lessons thence this is a bright app for practice. It starts off amongst triangles together with parallel lines but yous tin skip ahead to circle theorems.

Particularly complex circle theorem questions, or 'busy' diagrams (like the inquiry below), could live enlarged on A3 newspaper - this would live a skillful chance to job the acrylic sheets suggested inward Jeremy Denton's post 'Improving students' collaboration using acrylic sheets'.

Source: CIMT

Memorising the theorems

Circle theorems are ane of those topics that require think every bit good every bit understanding. If students acquire by to spot the solution to a job thence I encourage them to become through a checklist of circle theorems inward their head, annotating the diagram where they can. Often students missy the 'angles inward the same segment are equal' steps because they aren't ever every bit obvious every bit others (as inward the representative shown below).

Enough practise of using circle theorems mightiness live sufficient to memorise them, but in this post Don Steward suggests that at that spot mightiness live do goodness inward chanting the theorems. I've non tried this yet but dorsum inward chief schoolhouse I learnt my times tables yesteryear chanting - it seemed to operate well. He suggests that the instructor taps on a diagram together with the cast telephone phone out the theorem (see his post for associated resources).

Chanting exercise from Don Steward

Off on a tangent
I desire to cease amongst a twain of curt non-syllabus ideas that would live squeamish to expect at amongst your students if yous receive got time.

Have yous ever looked at a regular This post nearly Thales Theorem describes how the presenter of children's TV programme Art Attack demonstrated how to detect the centre of a circle. If it featured on Art Attack thence why non do it inward a maths lesson? There is a squeamish interactive demonstration of the method here including printable instructions.

If you're teaching circle theorems for the start fourth dimension or yous precisely wanted some fresh ideas, I promise this post has been helpful. Please percentage your ideas together with favourite resources inward the comments below, or through Twitter. 

This was a rather long post thence if yous made it this far together with it's nonetheless Nov 2014, delight vote for me inward the United Kingdom of Great Britain together with Northern Ireland of Britain together with Northern Republic of Ireland Blog Awards! Thank you.

All O score cloth inward this post was taken from Cambridge Assessment.

5 Maths Gems #15

Welcome to my 15th weekly gems post - this is where I characteristic to a greater extent than or less of the best teaching ideas I've seen on Twitter each week.

1. Slice The Pie

Paul Rehmet (@prehmet) has built an interactive tool to help students construct numerical fluency. It's a uncomplicated fraction game - Slice The Pie - which helps students railroad train an intuitive sense of the relative sizes of numbers. It's non compatible alongside mobiles yet but would piece of work on your interactive whiteboard. I honey this. Have a play alongside it, I think you'll honey it too. And follow Paul on Twitter because there's to a greater extent than to come upwardly from him.

2. Remembering Inequalities

In my post virtually Ideas from Shanghai I shared this visualisation which helps students cry back which inequality sign is which.

All students demand to exercise is visualise numbers equally blocks - the wider halt of the inequality symbol fits over the bigger stack of blocks. So if x > 2, nosotros know x must last a divulge bigger than 2. 

Chris Smith (@aap03102) pointed out that this doesn't piece of work for negative numbers. 

I'm sure as shooting our friends inwards Shanghai possess got a solution for this but that data hasn't filtered through to us, therefore let's come upwardly up alongside our ain alternative that industrial plant for both positive together with negative numbers. We only demand a agency for students to cry back which symbol is which.

I'm actually grateful to all the lovely creative tweeters who offered ideas - my favourite was this calligram from Chris. 

So if x < - 8, nosotros encounter the < symbol together with think of the alphabetic character L, therefore nosotros know x is less than -8.

Eventually students volition automatically know the important of the symbols on sight, without having to visualise blocks or words.

These methods are far meliorate than thinking of crocodiles - this tin confuse students, equally described inwards Nix the Tricks (extract below).

3. Squares together with Cubes
I'm enjoying La Salle Education's (@LaSalleEd) novel 'Problem of the Day' series.  You tin search the collection past times historic menses or topic. The instance below (Square Boxes) is a prissy logic occupation consolidating noesis of foursquare numbers.

If you're teaching foursquare numbers, you lot powerfulness also similar this 'Square together with Cube Numbers Puzzle' from MathsPad...

... together with this lovely square together with cube numbers display from Clarissa Grandi (@c0mplexnumber).

4. Mathsticks
I lately discovered the brilliant Mathsticks website which is created past times John Duffty (@johnduffty). I registered together with explored - it's to a greater extent than oftentimes than non primary materials but to a greater extent than or less of the ideas powerfulness last helpful at Key Stage 3. Here's a pair of examples:

This Parallel & Perpendicular Slope. Once you've taught students virtually the gradients of parallel together with perpendicular lines, larn them inwards a calculator room (or larn the iPads out, if you lot possess got them) together with give them this worksheet, which I think volition last really slow for them to follow independently. They are given sure as shooting lines which they plot (in Desmos, though I suppose this could last done past times hand) together with therefore they add together the right parallel or perpendicular lines to brand the required shape. It's a actually prissy activity which volition assistance you lot cheque their agreement of this topic.

Extract from Desmos Graph Challenge

Here's my respond to the minute interrogation inwards the extract above.

To extend this task, you lot could possess got students trammel the domains of the functions, equally I've done below. If you lot exercise this, it's of import that they figure out how to calculate the coordinates of the vertices.

If you're teaching parallel together with perpendicular lines therefore also cheque out my post linear graphs for to a greater extent than ideas together with resources.

A asking for misconceptions
When I project design lessons, I abide by it helpful to endeavour to predict the misconceptions that powerfulness come upwardly up. Sometimes I'm surprised past times the mistakes that students make, which are oftentimes the effect of my explanations non beingness clear enough. Knowledge of mutual misconceptions comes alongside sense but I think it would exercise goodness novel maths teachers if they could consult a website to encounter examples of the form of things students larn wrong. 

A not-so-common misconception from 1 of Chris Smith's students

American instructor Michael Pershan (@mpershan) has a bright website Math Mistakes where he compiles, analyses together with discusses the mathematical errors that students make. I desire to prepare something similar for the Great Britain (because our curricula together with vocabulary are therefore different), but I won't possess got fourth dimension to exercise the first-class analysis that Michael does. Instead it would only last a collection of misconceptions, tagged past times topic. But I even therefore think it powerfulness last useful.

So I possess got a asking - could you lot outset taking photos of misconceptions inwards your students' piece of work together with emailing or tweeting them to me? Once I've got a modest alternative I'll outset a website together with I hope, similar my Pret homework website, it volition grow speedily together with attempt to last a helpful resource. Thank you lot inwards advance!

That's it for today. Please don't forget to vote for me! :), I'll larn out you lot alongside this cute 'Math nosotros know drama', shared past times @FascinatingVids.