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 habitation on motherhood leave. My babe keeps me busy during the day, but my evenings are blissfully gratis from mark together with lesson planning thence I create got a rare chance to reverberate on my teaching together with assemble 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 travel inwards Jan I'll create got 100 maths teaching gems inwards my toolkit - it volition last difficult to know where to start! 

1. Two Truths together with a Lie

Two Truths together with a Lie is traditionally an icebreaker game - person tells y'all 3 facts almost themselves together with y'all jurist which ane is the lie. For event my blood brother powerfulness tell y'all that he was in ane lawsuit bitten yesteryear a donkey, he was in ane lawsuit bitten yesteryear a serpent together with he was in ane lawsuit bitten yesteryear a monkey. Bizarrely, exclusively ane of those statements is a lie. So let's accept this game together with 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 about other word for shape' when inwards fact I should last to a greater extent than specific - a polygon is a 2D figure amongst at to the lowest degree 3 conduct sides together with angles (the word derives from the Greek 'many-angled'), thence a circle is non a polygon.

The ii truths almost quadrilaterals ('a foursquare is a rectangle' together with 'a rectangle is a parallelogram') volition also prompt interesting discussions almost definitions. The quadrilateral identify unit of measurement tree powerfulness attention clarify things. The Euler diagram below is also helpful. 

Quadrilaterals (source: Wikipedia)

Here's a duet to a greater extent than examples of mathematical 'Two Truths together with a Lie' activities:

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

xkcd.com

2. Wikipedia and visualisation

From 1 to 1,000,000' from Gems 7 almost Estimation 180). Show your students the dotty pictures thence they larn a skillful feel of the magnitude of numbers. 

The paradigm higher upward reminds me of the 'If the World Were a Village of 100 People' visuals I talked almost inwards Gems 1 - this is a nice agency of conceptualising information that powerfulness attention 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 frequently reluctant to test a dissimilar approach if their get-go test at answering a enquiry is a dead end. Show this video at schoolhouse to encourage your students to last creative inwards their mathematical thinking. 

4. Communicating Reasoning
Continuing the theme of encouraging students to test 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 terminal calendar week that I was peculiarly proud of. I dearest my gems posts together with my resources library, but it's my topic specials that I intend people volition detect the most helpful. I similar to intend that novel or late qualified teachers volition actually produce goodness from these posts when planning to learn a theme for the get-go time. 

If y'all similar my weblog together with then delight vote for it inwards the Great Britain Blog Awards (click hither to vote). There are over fifty blogs inwards the freelance teaching category together with exclusively 10 volition become through to the side yesteryear side stage. My weblog is tiny compared to the super-successful, well-established blogs I'm upward against. I've exclusively been writing it since Apr but I've done a lot inwards that fourth dimension - I pose my ticker together with soul into it, thence if y'all detect it useful together with then your vote would last really much appreciated.

Finally, produce y'all receive Chris Smith's (@aap03102)  weekly newsletter?  If y'all don't already subscribe together with then email him forthwith to larn 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 first-class puzzle below, which I'm looking forrad to giving my students when I provide to travel inwards January.

Teaching Indices

Source: dotmaths.com

I've mentioned earlier that I beloved pedagogy indices, together with that's because a) there's loads of bright resources available b) the concepts are slow to explicate c) there's some lovely extension problems together with d) this is of import mathematics! You can't produce calculus without agreement indices.

I know I tin strength out programme a sequence of lessons on indices for whatever historic menses grouping (Year 8 correct through to Year 12) together with I'll live able to notice expert character engaging resources. Later inwards this shipping I'll characteristic some of my favourites.

Concepts

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

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

Fractional powers tin strength out live explained using the multiplication law.

And together with hence it's exactly a instance of students remembering the laws together with practising them until they learn fluent. Mim Gosling (@mimgosling) created the moving-picture present below to aid students recollect how fractional powers locomote -"Fractional indices are similar a bloom - the bottom's the root, the top's the power!". So if yous receive got a educatee who gets confused past times fractional indices, exactly 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 latterly - I wrote these slides to construction the degree news together with activities. After nosotros established each index law, the degree did 3 quick exercise questions earlier moving on to the adjacent law. Once we'd covered all 3 laws, the students completed this 'Powers of y eliminator' from Teachit Maths, which was fantastic. It had exactly the correct combination of independent practice, stretch together with 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 costless to borrow bits, though some formatting may live lost when yous download it (the PDF version is much prettier!).

Card Sorts
It's a dandy thought to receive got a well-organised provide of sorting activities (eg Tarsia puzzles) inwards your maths department. Find a clever agency to shop them (eg inwards stackable plastic takeaway boxes) together with label the boxes clearly. It takes a flake of fourth dimension to laid upward the bill of fare sorts. If you've got the budget, it's ever best to learn them laminated. Print each assault a dissimilar coloring (eg if in that location are 10 groups inwards the class, impress the bill of fare sets on 10 dissimilar colours) - this stops the sets getting mixed up. Use expert character elastic bands - inexpensive ones degrade chop-chop - or perish on each laid inwards an envelope.

My subdivision has a collection of 56 bill of fare sorts create for purpose inwards lessons (sadly, I spent many many hours sitting at the guillotine during my summertime holidays!). We telephone weep upward them our 'Black Box Resources' because nosotros perish on them inwards dark CD boxes from Ikea. Two of my favourite bill of fare sorts are for indices. The first is Indices Dominoes by Teachit Maths - a genuinely dainty activity, amongst the added bonus that the answer is written backwards hence students can't cheat past times guessing the words. I also like Using Indices from the Standards Unit. Card laid H5N1 (pairs activity) is genuinely useful when you've taught fractional together with 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 dandy worksheets together with 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 3 index laws:

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

Once you've moved onto fractional together with 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 disceptation to mean value close together with explicate to the class.

Extract from 'Why does?' past times Susan Wall

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

Extract from 'True or False' past times Susan Wall

Blanks

I featured a 'blanks' draw of piece of occupation thought inwards Gems 17. Make upward some questions similar those shown below together with seat them upward to a greater extent than or less the room. Provide post-it notes hence students tin strength out propose values that fit.

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

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

together with 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, together with mayhap equally extension inwards Year 11, I similar to produce some locomote on comparison indices amongst dissimilar bases. For example, I similar this ordering starter.

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

Finally, I desire to part ii questions that I've been using for years amongst GCSE students, either when I learn indices or when I learn algebraic fractions. My students are ever horrified past times how complex these questions look, but if they're confident amongst indices together with hence both equations are genuinely surprisingly slow to solve. I'm non certain where these questions originated hence apologies to the creator for non giving credit.

That's it from me - if yous 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 5 instruction ideas I've seen on Twitter. The summertime holidays are at nowadays inward total swing thus Twitter has been placidity this week. I hold off it volition acquire busier inward August - results days volition orbit us lots to utter about, as well as and then we'll all start making preparations for September. I'm off on a position unit of measurement vacation side yesteryear side calendar week (including an exciting solar daytime out at Peppa Pig World!) thus somebody volition cause got to fill upward me inward on what I miss! I tweeted my 10,000^th tweet yesterday. I exclusively joined Twitter concluding 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 honey these - they're a groovy 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 live on groovy to pose a large angle chase up, possibly yesteryear sticking record on a large whiteboard or a wall painted amongst whiteboard paint. If anyone has done this inward their classroom, I'd honey to encounter a photo.

2. Presentation Standards
I've written earlier most setting expectations for the presentation of classwork as well as homework. The start of a novel schoolhouse yr is the fourth dimension to create upward one's hear how to approach this. latest post about Analysing Errors is no exception. From September I innovation to start setting regular low-stakes tests. For my Year 10s, I'm thinking of a brusque weekly quiz (perhaps multiple choice, marked amongst Quick Key). As suggested yesteryear Sarah, I innovation 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 get-go attempt. She's going to orbit them an mistake analysis sail that does these things:

• Require students to operate out each work correctly
• Ask students to position what they did incorrect when they get-go attempted the problem
• Direct students to reverberate on how they volition avoid making this same mistake inward the future
• Get students thinking most what types of errors they are making

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

Types of Errors by @mathequalslove

5. The Famous Five

I honey this post from @mccreaemma. It's most an approach called 'The Famous 5' that Emma uses in every lesson. When students move inward the room they are straight off presented amongst a task. The names of 5 students that begin/finish/engage good amongst the chore are written on the whiteboard. Their vantage is to exit the classroom get-go at the destination of the lesson. Emma says that her students honey it (I retrieve this would operate 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 operate 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 cheers to post most the additional sequences content on the novel GCSE. It features examples of examination questions as well as resources. I was pleased to acquire 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 likewise speedily for my liking though! It's August already, which way I'm dorsum to schoolhouse i calendar month today. #mathsconf5 is side yesteryear side calendar month too. Have you lot got your ticket yet?

Finally, I honey 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 as well as welcome to my 37^th gems post. This is where I part around of the best maths teaching ideas I've seen on Twitter. If y'all bask reading these posts as well as thus y'all mightiness similar to explore my novel hashtag #mathsgems to view highlights from previous posts.

Last calendar week I attended #pieandmaths - this was an trial organised past times La Salle Education inwards which a grouping of maths teachers got together to utter over issues inwards maths education. It was a bully twenty-four hr current as well as I've included a curt write-up at the terminate of this post.

I get got a surplus of gems this calendar week thus here's the starting fourth dimension five, alongside v to a greater extent than to follow subsequently this week.

1. Brilliant Indices Question
I starting fourth dimension wrote most Gems 21. I 'like' Brilliant's Facebook page which agency 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 flake this calendar week working on my novel Facebook page. Luckily that agency that I spotted this awesome interrogation from Brilliant:

My Year 12s volition endure 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 unproblematic as well as middle schoolhouse children. The problems are accessible as well as engaging. Solutions are included.

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

The problems are mainly suitable for Key Stage two as well as 3. I dearest 'The Spilled Juice Problem'.

3. Simulations
Last August I wrote a post service Animations as well as Simulations, as well as since as well as thus I've occasionally featured animations inwards my gems posts, similar this lovely demonstration of the expanse 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 as well as 4, such equally this estimation activity. Do get got a play alongside this activity, it's great.

Thanks to a tweet from @ChristinaGawlik I've also discovered the lately revamped website www.explorelearning.com. This is the 'world's largest library of math as well as scientific discipline simulations'. These simulations (called Gizmos) are actually good. Unfortunately unless y'all pay a subscription, y'all tin move alone access each Gizmo for 5 minutes. Worth a aspect though.

4. VideoScribe

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

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



Since starting at a novel schoolhouse as well as having to produce 'proper' deportment administration for the starting fourth dimension time, I've realised the importance of setting expectations for students. I retrieve 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 conception to present this brief video I created using a free 7-day trial of VideoScribe as well as give students a difficult re-create of classroom expectations to create total inwards a few blanks equally they watch. I may present this several times during the starting fourth dimension few weeks of school, post service it on my website, as well as generate a QR code to link to it when individual needs a reminder".

I spotted Cathy's video inwards her fantabulous post service Primary Maths page which links to blogs as well as resources. I updated my tangents as well as areas based on the novel GCSE specification.

Pie as well as Maths
La Salle Education is a companionship dedicated to improving mathematics education. I dearest La Salle's conferences as well as volition endure presenting at their side past times side conference inwards Sheffield inwards September. Last calendar week La Salle hosted an trial called Pie as well as Maths which was attended past times around of my Twitter buddies, thus it was a proficient run a hazard to grab upwards alongside people as well as utter most maths.

The trial started alongside a demonstration of Complete Mathematics. This is a actually impressive organization as well as if you've non seen it earlier as well as thus it's worth exploring - La Salle tin move come upwards to your schoolhouse to demonstrate it. I actually back upwards the underlying principles of Complete Mathematics - it has the potential to endure the ultimate collaboration tool for maths teachers. The content as well as functionality get got developed good since I starting fourth dimension saw it final summer. The interface is actually user-friendly, allowing teachers to efficiently conception lessons alongside access to well-written objectives, pedagogical notes, resources as well as assessment tools. Complete Mathematics currently covers Key Stage 1 through to GCSE. New content is existence developed for Core Maths, providing much needed construction as well as resources for this novel post-16 qualification.

Can y'all cite the Twitter handles?

We enjoyed a lovely luncheon as well as and thus went to the pub for a debate, led past times Mark McCourt (@EmathsUK). We discussed a number of issues including behaviour, parenting, teaching methods, instructor grooming as well as research.

Afterwards nosotros had lots of fourth dimension to chat as well as play maths games - I ended upwards 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 as well as Mark McCourt for organising a actually enjoyable event. I loved catching upwards alongside Twitter friends as well as 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 as well as @mathsjem.

That's it for today's post. Good luck alongside GCSE results everyone! I'll acquire out y'all alongside this cute Nonagon video shared past times @solvemymaths.

Icebreakers

I've seen a lot of dandy icebreaker ideas this calendar week therefore I thought it mightiness endure helpful to portion simply about of my favourites here. Most of us volition endure coming together novel classes for the offset fourth dimension adjacent week. I'll endure getting a novel tutor grouping - I demand activities that volition assist me larn to know my students together with assist them larn to know each other too.

Creeping Death
First, a floor nigh what not do. When I was at academy I attended a two-day residential alternative centre for a graduate project at Esso. I intend at that spot were twelve candidates, all Russell Group, all inwards smart novel suits. Naturally nosotros started alongside an icebreaker. We were told to nation something interesting nigh ourselves. I had a few ideas for what I was going to nation - I used to alive inwards Africa together with convey a duet of stories to tell - but all of a abrupt I had argue to panic. The other candidates - every ane 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 equally I waited for my plough to speak, together with therefore the embarrassment together with feeling of inferiority. It shook my confidence for the residuum of the alternative centre.

'Say something interesting nigh yourself' is non a proficient means to intermission the ice, especially alongside xi yr olds who may good intend they convey goose egg interesting to say. If yous must ask a tike to nation something interesting nigh themselves, position simply about suggestions on the board inwards instance they're stuck for ideas (eg publish of siblings, what they did over summertime etc). Or, fifty-fifty better, purpose simply about of the activities listed below.

Me... By the Numbers
Donna Boucher (post. Students gain total inwards the template alongside numerical facts nigh themselves.

Numbers Quiz
H5N1 related thought comes from this post from Sarah Hagan. Ask each educatee to brand a quiz nigh themselves. The answers should endure numerical together with students should furnish an reply depository fiscal establishment at the bottom, similar my illustration below. Sarah completed all her students' quizzes together with they marked her answers. Alternatively, if students haven't met each other before, they could inquire simply about other educatee to consummate their quiz. This gives them a run a peril to chat nigh their answers together with larn to know each other. Even the shy students should endure happy alongside this activity.

Two Truths together with a Lie

When I returned from motherhood exit inwards Jan I took over a Year xi tutor group. To larn to know them I did 'Two truths together with a lie'. I told them 2 facts nigh myself together with ane prevarication - they had to approximate which was the lie. Then I gave them simply about fourth dimension to write downward their 2 truths together with 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 proficient 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 together with Lines
This post service Icebreakers That Rock is bright - it's total of proficient ideas. I specially similar Blobs together with Lines - students are prompted to either employment upward inwards simply about item companionship (eg past times birthday) or get together inwards 'blobs' based on something they convey inwards mutual (eg how they larn to school). Students rapidly uncovering things they convey inwards common.

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

His post service also features a flat scavenger hunt, shown below. I innovation to purpose adaptations of both activities alongside my novel Year 12 tutor grouping adjacent calendar week - my versions are here.

Dan's post service also includes a shape that students consummate piece yous beak through rules together with expectations.

If you're looking for to a greater extent than ideas for communicating expectations, depository fiscal establishment lucifer out the videos inwards my recent post service post. Students gain total inwards the template alongside numerical facts nigh themselves.

Numbers Quiz
H5N1 related thought comes from Behaviour Management for Beginners.

Also, shape tutors looking for ideas to gain total daily shape fourth dimension volition dear formtimeideas.com.

First Maths Lessons
In this post service I've focused on icebreakers. I've written previously nigh maths activities for offset lessons - reckon post. Students gain total inwards the template alongside numerical facts nigh themselves.

Numbers Quiz
H5N1 related thought comes from Gems 2, addition the lovely alphabet thought inwards post. Students gain total inwards the template alongside numerical facts nigh themselves.

Numbers Quiz
H5N1 related thought comes from Gems 34. I also convey 2 posts that mightiness endure of interest:

• post. Students gain total inwards the template alongside numerical facts nigh themselves.
  
  
  Numbers Quiz
  H5N1 related thought comes from Your First Maths Lesson alongside Year 7 
• post. Students gain total inwards the template alongside numerical facts nigh themselves.
  
  
  Numbers Quiz
  H5N1 related thought comes from Kicking off Year 12

I promise these ideas are helpful. Good luck everyone!