5 Maths Gems #14

Welcome to my 14th weekly gems post - this is where I characteristic 5 of the best teaching ideas I've seen on Twitter each week.

You may or may non know that I've been writing these posts spell I've been at domicile on motherhood leave. My babe keeps me busy during the day, but my evenings are blissfully costless from marker too lesson planning hence I induce got a rare chance to reverberate on my teaching too get together novel ideas. It's a shame that all teachers can't accept a mini-sabbatical every 5 years to produce the same. When I become dorsum to function inwards Jan I'll induce got 100 maths teaching gems inwards my toolkit - it volition live on difficult to know where to start! 

1. Two Truths too a Lie

Two Truths too a Lie is traditionally an icebreaker game - somebody tells y'all 3 facts near themselves too y'all guess which 1 is the lie. For instance my blood brother mightiness tell y'all that he was 1 time bitten yesteryear a donkey, he was 1 time bitten yesteryear a serpent too he was 1 time bitten yesteryear a monkey. Bizarrely, solely 1 of those statements is a lie. So let's accept this game too plow it into an action that prompts mathematical discussion.

This thought came from a tweet yesteryear @TCM_at_NCTM:

Polygons (source: mathsisfun.com)

This tweet made me realise that I'm guilty of lazily telling my students that polygon is 'just approximately other word for shape' when inwards fact I should live on to a greater extent than specific - a polygon is a 2D figure amongst at to the lowest degree 3 at 1 time sides too angles (the word derives from the Greek 'many-angled'), hence a circle is non a polygon.

The ii truths near quadrilaterals ('a foursquare is a rectangle' too 'a rectangle is a parallelogram') volition also prompt interesting discussions near definitions. The quadrilateral solid unit of measurement tree mightiness assistance clarify things. The Euler diagram below is also helpful. 

Quadrilaterals (source: Wikipedia)

Here's a span to a greater extent than examples of mathematical 'Two Truths too a Lie' activities:

Influenza A virus subtype H5N1 related idea, Maths Lies (where the instructor tells 1 deliberate prevarication per lesson - run across my first gems post) is even hence 1 of my favourite teaching ideas ever.

xkcd.com

2. Wikipedia and visualisation

From 1 to 1,000,000' from Gems 7 near Estimation 180). Show your students the dotty pictures hence they learn a practiced feel of the magnitude of numbers. 

The epitome to a higher identify reminds me of the 'If the World Were a Village of 100 People' visuals I talked near inwards Gems 1 - this is a nice means of conceptualising information that mightiness assistance students sympathise percentages.

3. Creative Mathematicians

Thanks to @gareth_metcalfe for sharing this bright video 'What is a mathematical proof?'. The video explains why mathematicians pass most of their fourth dimension trying things that don't work. Students are oft reluctant to examine a dissimilar approach if their outset examine at answering a inquiry is a dead end. Show this video at schoolhouse to encourage your students to live on creative inwards their mathematical thinking. 

4. Communicating Reasoning
Continuing the theme of encouraging students to examine diverse approaches to solving problems, bright NQT blogger gems post (unlucky 13) was my most pop post ever, amongst almost 2,000 views inwards a week. I also wrote a post on circle theorems final calendar week that I was peculiarly proud of. I beloved my gems posts too my resources library, but it's my topic specials that I mean value people volition discovery the most helpful. I similar to mean value that novel or latterly qualified teachers volition actually produce goodness from these posts when planning to learn a theme for the outset time. 

If y'all similar my weblog hence delight vote for it inwards the Great Britain Blog Awards (click hither to vote). There are over fifty blogs inwards the freelance educational activity category too solely 10 volition become through to the side yesteryear side stage. My weblog is tiny compared to the super-successful, well-established blogs I'm upwardly against. I've solely been writing it since Apr but I've done a lot inwards that fourth dimension - I set my pump too soul into it, hence if y'all discovery it useful hence your vote would live on real much appreciated.

Finally, produce y'all receive Chris Smith's (@aap03102)  weekly newsletter?  If y'all don't already subscribe hence email him at nowadays to learn on the mailing list. This calendar week he featured Pret homeworks which y'all should accept a await at if y'all haven't seen them before. Chris also featured the fantabulous puzzle below, which I'm looking frontward to giving my students when I provide to function inwards January.

Teaching Indices

Source: dotmaths.com

I've mentioned earlier that I dear educational activity indices, in addition to that's because a) there's loads of bright resources available b) the concepts are tardily to explicate c) there's some lovely extension problems in addition to d) this is of import mathematics! You can't produce calculus without agreement indices.

I know I tin displace programme a sequence of lessons on indices for whatever historic menstruum grouping (Year 8 correct through to Year 12) in addition to I'll live able to abide by skillful lineament engaging resources. Later inwards this shipping service I'll characteristic some of my favourites.

Concepts

The concepts relating to indices are relatively tardily to explicate from kickoff principles. The reasoning behind the index laws is straightforward. We tin displace encounter that b² x b⁵ = b⁷ precisely past times writing out the expressions inwards total (ie b x b x b x b x b x b x b). Students volition rapidly spot the patterns. The 'anything to the ability of null equals one' dominion is also fairly elementary to explicate using the logic shown below.

Negative powers tin displace live explained past times extending the partitioning police pull (ie what happens when nosotros split b² past times b⁷?), or past times considering patterns (see Gems 8 for to a greater extent than on this).

Fractional powers tin displace live explained using the multiplication law.

And thence it's precisely a instance of students remembering the laws in addition to practising them until they perish fluent. Mim Gosling (@mimgosling) created the painting demonstrate below to tending students recollect how fractional powers piece of occupation -"Fractional indices are similar a blossom - the bottom's the root, the top's the power!". So if you lot receive got a pupil who gets confused past times fractional indices, precisely remind them that the root is at the bottom (like inwards a tree).

Source: @StIvoMaths

A lesson on index laws

I taught an introductory lesson on index laws lately - I wrote these slides to construction the shape give-and-take in addition to activities. After nosotros established each index law, the shape did iii quick exercise questions earlier moving on to the side past times side law. Once we'd covered all iii laws, the students completed this 'Powers of y eliminator' from Teachit Maths, which was fantastic. It had precisely the correct combination of independent practice, stretch in addition to engagement. These were the questions that most students got stuck on:

I was quite proud of the slides I made for this lesson - there's an editable version here so experience gratis to borrow bits, though some formatting may live lost when you lot download it (the PDF version is much prettier!).

Card Sorts
It's a peachy thought to receive got a well-organised furnish of sorting activities (eg Tarsia puzzles) inwards your maths department. Find a clever agency to shop them (eg inwards stackable plastic takeaway boxes) in addition to label the boxes clearly. It takes a flake of fourth dimension to educate the carte du jour sorts. If you've got the budget, it's e'er best to learn them laminated. Print each assail a dissimilar colouring cloth (eg if at that topographic point are 10 groups inwards the class, impress the carte du jour sets on 10 dissimilar colours) - this stops the sets getting mixed up. Use skillful lineament elastic bands - inexpensive ones degrade rapidly - or proceed each laid inwards an envelope.

My subdivision has a collection of 56 carte du jour sorts educate for run inwards lessons (sadly, I spent many many hours sitting at the guillotine during my summertime holidays!). We telephone outcry upwards them our 'Black Box Resources' because nosotros proceed them inwards dark CD boxes from Ikea. Two of my favourite carte du jour sorts are for indices. The first is Indices Dominoes by Teachit Maths - a truly prissy activity, alongside the added bonus that the answer is written backwards thence students can't cheat past times guessing the words. I also like Using Indices from the Standards Unit. Card laid H5N1 (pairs activity) is truly useful when you've taught fractional in addition to negative indices.

You powerfulness also similar these treasure hunts: simple index laws and negative & fractional indices, both from Teachit Maths.

Worksheets
There's loads of peachy worksheets in addition to activities for independent practice. I've already mentioned the Powers of y eliminator from Teachit Maths. Here's ii to a greater extent than first-class resources that are suitable for practising the iii index laws:

• Simplifying Indices Code Breaker - Teachit Maths 
• Collect a Joke - Number Loving

Once you've moved onto fractional in addition to negative indices, there's loads to a greater extent than first-class resources (these powerfulness live useful inwards Year 12 too):

• Mental Powers Code Breaker -Teachit Maths 
• Ever wondered why? - JustMaths 
• Indices activity - SRWhitehouse on TES

STEM Centre provides some fantastic indices activities from Susan Wall. For example, I similar 'Why does?' (extract below) inwards which students are allocated a tilt to intend virtually in addition to explicate to the class.

Extract from 'Why does?' past times Susan Wall

There's also a truthful or faux activity which is designed to address mutual misconceptions.

Extract from 'True or False' past times Susan Wall

Blanks

I featured a 'blanks' business thought inwards Gems 17. Make upwards some questions similar those shown below in addition to seat them upwards to a greater extent than or less the room. Provide post-it notes thence students tin displace advise values that fit.

Homeworks
I've made ii Pret homeworks for this topic, both are available here.

Enrichment
There's loads of peachy extension questions for this topic. I dear these mega quadratic equations from Don Steward.

in addition to these mega difficult powers questions, also from Don Steward

And ii to a greater extent than fantastic rich tasks from Don Steward: Power Sums and Find the Power. 

At H5N1 level, in addition to peradventure every bit extension inwards Year 11, I similar to produce some piece of occupation on comparison indices alongside dissimilar bases. For example, I similar this ordering starter.

And my worksheet exponential equations has been useful. It ends alongside this lovely question. 

Finally, I desire to portion ii questions that I've been using for years alongside GCSE students, either when I learn indices or when I learn algebraic fractions. My students are e'er horrified past times how complex these questions look, but if they're confident alongside indices thence both equations are truly surprisingly tardily to solve. I'm non certain where these questions originated thence apologies to the creator for non giving credit.

That's it from me - if you lot know of whatever other fantastic indices resources, delight comment below or tweet me.

How v squared looks inwards nightmares.

5 Maths Gems #35

Hi there. Welcome to my 35^th gems post. This is where I part v educational activity ideas I've seen on Twitter. The summertime holidays are at nowadays inwards total swing thus Twitter has been serenity this week. I expression it volition acquire busier inwards August - results days volition laissez passer on us lots to utter about, as well as thus we'll all start making preparations for September. I'm off on a delineate of piece of work solid unit of measurement vacation adjacent calendar week (including an exciting twenty-four sixty minutes current out at Peppa Pig World!) thus soul volition conduct maintain to create total me inwards on what I miss! I tweeted my 10,000^th tweet yesterday. I alone joined Twitter terminal May thus I retrieve that officially makes me a chatterbox.

1. Angle Chase 
I featured angle chases in Gems 24, Gems 26 and Gems 32 . I find this type of action actually enjoyable. @MathedUp shared a whole charge of angle chases here. I dear these - they're a smashing resources both for classwork as well as for revision.

@mathninja3 suggested putting a permanent angle chase on the classroom wall. This reminded me of the display by @ExplainingMaths pictured below. I retrieve it would hold upwards smashing to lay a large angle chase up, perchance yesteryear sticking record on a large whiteboard or a wall painted amongst whiteboard paint. If anyone has done this inwards their classroom, I'd dear to come across a photo.

2. Presentation Standards
I've written earlier virtually setting expectations for the presentation of classwork as well as homework. The start of a novel schoolhouse yr is the fourth dimension to create upwards one's hear how to approach this. latest post about Analysing Errors is no exception. From September I excogitation to start setting regular low-stakes tests. For my Year 10s, I'm thinking of a curt weekly quiz (perhaps multiple choice, marked amongst Quick Key). As suggested yesteryear Sarah, I excogitation to flat these quizzes A, B or Not Yet, amongst anyone scoring a Not Yet having to accept some other test. In Sarah's postal service she suggests that earlier retaking a quiz, students are required to analyse their showtime attempt. She's going to laissez passer on them an fault analysis canvass that does these things:

• Require students to function out each employment correctly
• Ask students to position what they did incorrect when they showtime attempted the problem
• Direct students to reverberate on how they volition avoid making this same fault inwards the future
• Get students thinking virtually what types of errors they are making

Sarah has produced a fantastic poster to push clit dissimilar types of errors. Read her post for to a greater extent than virtually this as well as to download the poster.

Types of Errors by @mathequalslove

5. The Famous Five

I dear this post from @mccreaemma. It's virtually an approach called 'The Famous 5' that Emma uses in every lesson. When students acquire into the room they are forthwith presented amongst a task. The names of v students that begin/finish/engage good amongst the employment are written on the whiteboard. Their vantage is to move out the classroom showtime at the goal of the lesson. Emma says that her students dear it (I retrieve this would function actually good for my students too) as well as it reduces wasted fourth dimension at the start of lessons. Her postal service is good worth a read.

Update
I'm continuing to function on resourceaholic.com behind the scenes when I acquire a chance. I've added some resources to my libraries as well as made updates to my New GCSE Support page. If you've got some fourth dimension over summertime to brand resources, here's a listing of topics that nosotros demand to a greater extent than resources for:

Huge thank y'all to post virtually the additional sequences content on the novel GCSE. It features examples of testify questions as well as resources. I was pleased to larn a novel method for finding the nth term of a quadratic sequence.

I'm enjoying spending lots of fourth dimension amongst my daughters this summer. It's all going also speedily for my liking though! It's August already, which agency I'm dorsum to schoolhouse 1 calendar month today. #mathsconf5 is adjacent calendar month too. Have y'all got your ticket yet?

Finally, I dear this homework for the summertime holidays that's been going circular Twitter. What a lovely idea.

Holiday homework yesteryear Tom Christy

5 Maths Gems #37

Hello too welcome to my 37^th gems post. This is where I portion about of the best maths teaching ideas I've seen on Twitter. If you lot bask reading these posts therefore you lot mightiness similar to explore my novel hashtag #mathsgems to reckon highlights from previous posts.

Last calendar week I attended #pieandmaths - this was an lawsuit organised yesteryear La Salle Education inwards which a grouping of maths teachers got together to verbalize over issues inwards maths education. It was a non bad solar daytime too I've included a brusk write-up at the terminate of this post.

I stimulate got a surplus of gems this calendar week therefore here's the kickoff five, amongst 5 to a greater extent than to follow afterwards this week.

1. Brilliant Indices Question
I kickoff wrote close Gems 21. I 'like' Brilliant's Facebook page which way I acquire regular maths problems inwards my Facebook feed. Since I joined Twitter I haven't used Facebook much, simply I've been on in that place quite a fleck this calendar week working on my novel Facebook page. Luckily that way that I spotted this awesome query from Brilliant:

My Year 12s volition live on treated to this inwards September! 

2. 1001 Math Problems
Thanks to Denise Gaskins (@letsplaymath) for sharing the website 1001 Math Problems. This American website was created equally a rootage of problem-solving activities for simple too middle schoolhouse children. The problems are accessible too engaging. Solutions are included.

Here's a lovely example, taken from the pick of puzzles that explore factors/divisibility:

The problems are mainly suitable for Key Stage ii too 3. I honey 'The Spilled Juice Problem'.

3. Simulations
Last August I wrote a postal service Animations too Simulations, too since therefore I've occasionally featured animations inwards my gems posts, similar this lovely demonstration of the surface area of a circle from Gems 12.

One of my favourite simulation websites is PhET Interactive Simulations which I'm told is peculiarly useful for teaching Mechanics at Influenza A virus subtype H5N1 level. Some of the simulations on PhET are suitable for Key Stage three too 4, such equally this estimation activity. Do stimulate got a play amongst this activity, it's great.

Thanks to a tweet from @ChristinaGawlik I've also discovered the late revamped website www.explorelearning.com. This is the 'world's largest library of math too scientific discipline simulations'. These simulations (called Gizmos) are actually good. Unfortunately unless you lot pay a subscription, you lot tin dismiss entirely access each Gizmo for 5 minutes. Worth a expression though.

4. VideoScribe

Chris Smith (@aap03102) shared an impressive promotional video for his newsletters. He said it entirely took him fifteen minutes to brand this video too I didn't believe him! I ready a trial of VideoScribe and flora out he was correct - it's real quick to brand a video using this software. Here's my endeavor - a fun (but pointless!) promo video for resourceaholic.com:

I was wondering if in that place were whatever opportunities to work this software inwards the classroom when I coincidentally stumbled across this Classroom Expectations video from Cathy Yenca (@mathycathy):



Since starting at a novel schoolhouse too having to create 'proper' behavior administration for the kickoff time, I've realised the importance of setting expectations for students. I recollect this approach mightiness brand those expectations to a greater extent than memorable (and fifty-fifty if it doesn't, it's fun to brand the video!). Cathy says, "I innovation to demo this brief video I created using a free 7-day trial of VideoScribe too give students a difficult re-create of classroom expectations to fill upward inwards a few blanks equally they watch. I may demo this several times during the kickoff few weeks of school, postal service it on my website, too generate a QR code to link to it when individual needs a reminder".

I spotted Cathy's video inwards her first-class postal service Primary Maths page which links to blogs too resources. I updated my tangents too areas based on the novel GCSE specification.

Pie too Maths
La Salle Education is a fellowship dedicated to improving mathematics education. I honey La Salle's conferences too volition live on presenting at their adjacent conference inwards Sheffield inwards September. Last calendar week La Salle hosted an lawsuit called Pie too Maths which was attended yesteryear about of my Twitter buddies, therefore it was a skillful run a jeopardy to grab upward amongst people too verbalize close maths.

The lawsuit started amongst a demonstration of Complete Mathematics. This is a actually impressive organization too if you've non seen it earlier therefore it's worth exploring - La Salle tin dismiss come upward to your schoolhouse to demonstrate it. I actually back upward the underlying principles of Complete Mathematics - it has the potential to live on the ultimate collaboration tool for maths teachers. The content too functionality stimulate got developed good since I kickoff saw it concluding summer. The interface is actually user-friendly, allowing teachers to efficiently innovation lessons amongst access to well-written objectives, pedagogical notes, resources too assessment tools. Complete Mathematics currently covers Key Stage 1 through to GCSE. New content is beingness developed for Core Maths, providing much needed construction too resources for this novel post-16 qualification.

Can you lot advert the Twitter handles?

We enjoyed a lovely tiffin too therefore went to the pub for a debate, led yesteryear Mark McCourt (@EmathsUK). We discussed a number of issues including behaviour, parenting, teaching methods, instructor grooming too research.

Afterwards nosotros had lots of fourth dimension to chat too play maths games - I ended upward tied to Bruno Reddy (@MrReddyMaths). This video shows how nosotros got out of it (well done Bruno, I had no idea!).

Thanks to La Salle too Mark McCourt for organising a actually enjoyable event. I loved catching upward amongst Twitter friends too coming together novel people - here's the listing of attendees (sorry if I've missed anyone!): @getdiagnostics, @nishadealwis, @mrdrapermaths, @naveenfrizvi, @MissBsResources, @MissBaileyMaths, @kris_boulton, @DrTrapezio, @craigos87, @EJmaths, @tessmaths, @ColinTheTrainer, @MrMattock, @dannytybrown, @RJS2212, @mrreddymaths, @mathsatschool, @MrBenWard, @xanbritt, @CubbonSue too @mathsjem.

That's it for today's post. Good luck amongst GCSE results everyone! I'll acquire out you lot amongst this cute Nonagon video shared yesteryear @solvemymaths.

Icebreakers

I've seen a lot of non bad icebreaker ideas this calendar week hence I thought it mightiness hold upward helpful to percentage to a greater extent than or less of my favourites here. Most of us volition hold upward coming together novel classes for the kickoff fourth dimension side past times side week. I'll hold upward getting a novel tutor grouping - I demand activities that volition attention me teach to know my students as well as attention them teach to know each other too.

Creeping Death
First, a floor close what not do. When I was at academy I attended a two-day residential choice centre for a graduate chore at Esso. I intend at that topographic point were twelve candidates, all Russell Group, all inwards smart novel suits. Naturally nosotros started amongst an icebreaker. We were told to tell something interesting close ourselves. I had a few ideas for what I was going to tell - I used to alive inwards Africa as well as convey a dyad of stories to tell - merely all of a abrupt I had argue to panic. The other candidates - every i of them - had far to a greater extent than interesting stories than me. They'd met royalty, they'd been on TV, they'd won awards, they were related to celebrities, they'd saved lives. I'll never forget that feeling of impending doom every bit I waited for my plough to speak, as well as then the embarrassment as well as feeling of inferiority. It shook my confidence for the residue of the choice centre.

'Say something interesting close yourself' is non a practiced means to interruption the ice, especially amongst eleven yr olds who may good intend they convey nix interesting to say. If y'all must ask a child to tell something interesting close themselves, pose to a greater extent than or less suggestions on the board inwards instance they're stuck for ideas (eg pose out of siblings, what they did over summertime etc). Or, fifty-fifty better, role to a greater extent than or less of the activities listed below.

Me... By the Numbers
Donna Boucher (post. Students fill upward inwards the template amongst numerical facts close themselves.

Numbers Quiz
Influenza A virus subtype H5N1 related thought comes from this post from Sarah Hagan. Ask each pupil to brand a quiz close themselves. The answers should hold upward numerical as well as students should render an reply depository fiscal establishment at the bottom, similar my instance below. Sarah completed all her students' quizzes as well as they marked her answers. Alternatively, if students haven't met each other before, they could inquire to a greater extent than or less other pupil to consummate their quiz. This gives them a peril to chat close their answers as well as teach to know each other. Even the shy students should hold upward happy amongst this activity.

Two Truths as well as a Lie

When I returned from motherhood teach out inwards Jan I took over a Year eleven tutor group. To teach to know them I did 'Two truths as well as a lie'. I told them ii facts close myself as well as i prevarication - they had to approximate which was the lie. Then I gave them to a greater extent than or less fourth dimension to write downwards their ii truths as well as a lie. I allow them volunteer to read their facts out - each fourth dimension I had to approximate the lie. It was a actually fun action (they were surprised past times how practiced I was at detecting their lies!). They all enjoyed it and, because they were confident students who already knew each other well, most volunteered to convey a go.

Blobs as well as Lines
This shipping service Icebreakers That Rock is bright - it's total of practiced ideas. I peculiarly similar Blobs as well as Lines - students are prompted to either trouble upward inwards to a greater extent than or less detail fellowship (eg past times birthday) or assemble inwards 'blobs' based on something they convey inwards mutual (eg how they teach to school). Students speedily uncovering things they convey inwards common.

Who I Am
Dan Meyer's shipping service The First Day Wiki from dorsum inwards 2007 provides a link to his well-known 'Who I Am' activity.

His shipping service also features a course of report scavenger hunt, shown below. I excogitation to role adaptations of both activities amongst my novel Year 12 tutor grouping side past times side calendar week - my versions are here.

Dan's shipping service also includes a shape that students consummate spell y'all verbalize through rules as well as expectations.

If you're looking for to a greater extent than ideas for communicating expectations, cheque out the videos inwards my recent shipping service post. Students fill upward inwards the template amongst numerical facts close themselves.

Numbers Quiz
Influenza A virus subtype H5N1 related thought comes from Behaviour Management for Beginners.

Also, shape tutors looking for ideas to fill upward daily shape fourth dimension volition dearest formtimeideas.com.

First Maths Lessons
In this shipping service I've focused on icebreakers. I've written previously close maths activities for kickoff lessons - watch post. Students fill upward inwards the template amongst numerical facts close themselves.

Numbers Quiz
Influenza A virus subtype H5N1 related thought comes from Gems 2, addition the lovely alphabet thought inwards post. Students fill upward inwards the template amongst numerical facts close themselves.

Numbers Quiz
Influenza A virus subtype H5N1 related thought comes from Gems 34. I also convey ii posts that mightiness hold upward of interest:

• post. Students fill upward inwards the template amongst numerical facts close themselves.
  
  
  Numbers Quiz
  Influenza A virus subtype H5N1 related thought comes from Your First Maths Lesson amongst Year 7 
• post. Students fill upward inwards the template amongst numerical facts close themselves.
  
  
  Numbers Quiz
  Influenza A virus subtype H5N1 related thought comes from Kicking off Year 12

I promise these ideas are helpful. Good luck everyone!