Showing posts with label Functions. Show all posts
Showing posts with label Functions. Show all posts

Wednesday, April 29, 2020

Linear Graphs

One of the topics that my pupils combat amongst the most, from Key Stage iii correct through to Year 12, is linear graphs.

My brilliant Year 11s know the dominion for finding the slope of a perpendicular line, but can't function out how to respond a GCSE enquiry similar this:
Strangely, I learn this differently at GCSE as well as Influenza A virus subtype H5N1 level.  At GCSE my pupils write down
y = mx + c
as well as substitute values for y, k as well as x, as well as hence solve for c.  Whereas at Influenza A virus subtype H5N1 marking my pupils occupation the equation
y - y1 = m(x - x1)
Essentially the same method but a slightly dissimilar approach. Perhaps I should endure to a greater extent than consistent as well as innovate the 'A marking method' at GCSE. I'd similar to take away heed what other teachers do.

In this shipping service I’ll propose roughly ideas as well as resources for instruction linear graphs.

Key words
Let's kickoff amongst the basics. There's a lot of novel vocabulary inwards coordinate geometry, roughly of which pupils volition convey encountered at primary school. This is a overnice vocabulary cognition survey every bit suggested inwards my earlier post

Here's a overnice play tricks for remembering the words parallel as well as perpendicular (this could endure helpful for spellings - parallel is oft misspelt): 

as well as this activity is suitable for Year vi or 7. 

Introducing the shape y = mx + c
I'd unremarkably kickoff this theme inwards Year seven or 8 amongst plotting at nowadays occupation graphs (Teachit Maths provides an excellent Drawing Straight Line Graphs booklet for this purpose), before exploring the shape y = mx + c.

This theme provides an first-class chance for pupil investigation using Desmos. Use a worksheet to direct pupils through the lesson:

Once pupils are able to translate the values of k as well as c as well as hence they tin shipping away endeavour this exercise or this true/false activity (both from rogradymaths.blogspot.co.uk). Teachit Maths also has a overnice 'Understanding y = mx+c' worksheet and two activities on horizontal as well as vertical lines.

My weblog shipping service 'All most gradient' features ideas as well as resources for instruction slope (the shipping service focuses mainly on real-life applications of the concept of steepness, but also features links to slope worksheets as well as activities).

Understanding parallel as well as perpendicular gradients
So here's the substitution data that pupils demand to understand:

If they know how to function out a slope every bit 'rise over run' (or equivalent) as well as hence pupils should endure able to derive the 'negative reciprocal' dominion for perpendicular gradients from an activeness similar this i from MathsPad.

Here's a few activities for a lesson on perpendicular lines:

Bringing it all together
When students written report linear graphs at AS level, they don't actually acquire anything novel - my GCSE pupils should convey the necessary skills as well as cognition to respond C1 coordinate geometry questions. I gave my Year xi pupils questions 5 - seven from this AS worksheet final twelvemonth - it took them ages to respond each question, but they were for certain capable. Essentially it's simply the wording of the questions that throws them.

Here's roughly to a greater extent than recommended resources suitable for GCSE students:

Finally, fun for puzzle-lovers in linear relationships sudoku and a overnice Key Stage iii Christmas activeness on plotting linear graphs from Teachit Maths - Mistletoe as well as Lines.

Finally, e'er wondered which countries occupation y = mx + c annotation as well as which countries occupation something different? Check out this map.








Sunday, January 26, 2020

5 Maths Gems #15

Welcome to my 15th weekly gems post - this is where I characteristic roughly 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 ready 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 upward from him.
2. Remembering Inequalities
In my post almost Ideas from Shanghai I shared this visualisation which helps students squall upward which inequality sign is which.
All students demand to exercise is visualise numbers equally blocks - the wider terminate of the inequality symbol fits over the bigger stack of blocks. So if x > 2, nosotros know x must hold out a number 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 inward Shanghai own got a solution for this but that data hasn't filtered through to us, thence let's come upward up alongside our ain alternative that industrial plant for both positive in addition to negative numbers. We simply demand a agency for students to squall upward 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 run into the < symbol in addition to think of the missive of the alphabet L, thence 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 ameliorate than thinking of crocodiles - this tin give notice confuse students, equally described inward Nix the Tricks (extract below).

3. Squares in addition to Cubes
I'm enjoying La Salle Education's (@LaSalleEd) novel 'Problem of the Day' series.  You tin give notice search the collection yesteryear historic current or topic. The instance below (Square Boxes) is a dainty logic occupation consolidating noesis of foursquare numbers.
If you're teaching foursquare numbers, yous mightiness also similar this 'Square in addition to Cube Numbers Puzzle' from MathsPad...
... in addition to this lovely square in addition to cube numbers display from Clarissa Grandi (@c0mplexnumber).

4. Mathsticks
I late discovered the brilliant Mathsticks website which is created yesteryear John Duffty (@johnduffty). I registered in addition to explored - it's by in addition to large primary materials but roughly of the ideas mightiness hold out helpful at Key Stage 3. Here's a twosome of examples:
This Parallel & Perpendicular Slope. Once you've taught students almost the gradients of parallel in addition to perpendicular lines, larn them inward a reckoner room (or larn the iPads out, if yous own got them) in addition to give them this worksheet, which I think volition hold out real slowly for them to follow independently. They are given sure as shooting lines which they plot (in Desmos, though I suppose this could hold out done yesteryear hand) in addition to and thence they add together the right parallel or perpendicular lines to brand the required shape. It's a actually dainty activity which volition assistance yous banking enterprise check their agreement of this topic.
Extract from Desmos Graph Challenge
Here's my response to the 2nd query inward the extract above.

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

If you're teaching parallel in addition to perpendicular lines in addition to thence also banking enterprise check out my post linear graphs for to a greater extent than ideas in addition to resources.

A asking for misconceptions
When I project design lessons, I uncovering it helpful to travail to predict the misconceptions that mightiness come upward up. Sometimes I'm surprised yesteryear the mistakes that students make, which are ofttimes the number 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 run into examples of the kind of things students larn wrong. 
A not-so-common misconception from i of Chris Smith's students
American instructor Michael Pershan (@mpershan) has a bright website Math Mistakes where he compiles, analyses in addition to discusses the mathematical errors that students make. I desire to prepare something similar for the United Kingdom of Great Britain in addition to Northern Ireland (because our curricula in addition to vocabulary are thence different), but I won't own got fourth dimension to exercise the fantabulous analysis that Michael does. Instead it would simply hold out a collection of misconceptions, tagged yesteryear topic. But I notwithstanding think it mightiness hold out useful.

So I own got a asking - could yous kickoff taking photos of misconceptions inward your students' piece of work in addition to emailing or tweeting them to me? Once I've got a small-scale choice I'll kickoff a website in addition to I hope, similar my Pret homework website, it volition grow chop-chop in addition to seek to hold out a helpful resource. Thank yous inward advance!

That's it for today. Please don't forget to vote for me! :), I'll move out yous alongside this cute 'Math nosotros know drama', shared yesteryear @FascinatingVids.


Saturday, January 25, 2020

Tricks In Addition To Tips 2: Sequences, Linear Graphs In Addition To Surds

I latterly presented a workshop at the National Mathematics Teacher Conference (Highest Common Factor.

Linear Sequences
What's the nth term of the sequence below?

5, 8, 11, 14, 17, ...

It mightiness exclusively accept y'all a minute to operate it out - how did y'all produce it? This is roughly other 1 of those topics where there's lots of unlike approaches. Ask the same inquiry to a random sample of teenagers from across the United Kingdom of Great Britain together with Northern Ireland of Britain together with Northern Republic of Ireland together with you'll reckon a broad hit of methods used.

Here I'm going to depict 4 unlike methods (there may endure more!). As y'all read them, consider whether you're going to stick amongst the method y'all currently use, or seek something new.

1. Zeroth term
Inspired past times this post on Don Steward's blog, I taught the 0th term method for the outset fourth dimension this year. To operate out the value of q inwards the nth term Un = pn + q, nosotros merely footstep dorsum from the outset term inwards the sequence (ie q = U0).
In the illustration 5, 8, 11, 14, 17..., subtract 3 from the outset term to larn U0 = 2. So the nth term is 3n + 2. This method is thence quick that it's at nowadays my preferred method for working out nth terms.

When I taught this method it went well, although a misconception did surface after on. When students were asked to 'write downward the outset 3 price of the sequence 4n + 3', roughly of them gave the respond 3, 7, xi (ie they started their sequences from n = 0 instead of n = 1). This is something to endure aware of side past times side fourth dimension I learn this method.
Jumping along a business - Median Don Steward

2. Shifting times tables
'Shifting times tables' is a pop method. The catch is that nosotros compare our sequence to a times table.  In the illustration below, compare the sequence to the 3 times table. Ask your students how to shift the 3 times tabular array to larn the sequence together with they'll location that they demand to add together two, thence the  nth term is 3n + 2.
If y'all project design to role this method for the outset fourth dimension together with thence I recommend this NRICH article Shifting Times Tables, which comes amongst an interactive tool. If y'all subscribe to MathsPad, they also stimulate got an interactive tool for identifying shifts.

This method plant good for quadratic sequences as good (a theme on the novel GCSE syllabus). For illustration to notice the nth term of the sequence 4, 7, 12, 19, 28 nosotros tin compare it to n2 together with notice that it is shifted upwardly past times 3 (ie the nth term is n2 + 3).
3. Formula
It's fairly straightforward to derive the next formula for the nth term:

Why produce nosotros confine this formula to Influenza A virus subtype H5N1 level? I 1 time took on a GCSE shape inwards Year xi together with asked them to notice roughly nth terms inwards a revision lesson. I was surprised to reckon them all using 'the Influenza A virus subtype H5N1 score formula' - their previous instructor had taught them it, together with why not? They seemed quite happy amongst it. I wouldn't role it amongst my Year 7s though - their algebra skills are real basic when they outset reckon sequences. In our example, this is what they'd stimulate got to produce to notice the nth term:
Perhaps this is to a greater extent than endeavor than necessary. The 0th term method is considerably quicker.

4. Substitution
This is the agency I taught sequences for years. To operate out the value of q inwards the nth term Un = pn + q, nosotros substitute a value for Un, p together with n, together with thence solve for q. For illustration inwards the sequence below, nosotros know that Un = 3n + q. We substitute the outset term to larn v = 3 + q. Therefore q = 2.
Thinking virtually it, this is the same method I'd role to notice the value of c inwards y = mx + c if I know the slope together with a indicate on the line. In fact given that linear graphs are merely graphical representations of linear sequences, whatever methods for finding the equation of a at 1 time business operate for finding the nth term of a sequence. I don't produce plenty to brand this connective amongst my students.

Linear Graphs
Influenza A virus subtype H5N1 at 1 time business through the indicate (5, 7) has slope 4. How would y'all notice the equation of the line?

As I said inwards my transportation service virtually linear graphs, I learn this differently at GCSE together with Influenza A virus subtype H5N1 level. Wouldn't it endure improve to selection my preferred approach together with stick amongst it? 

At GCSE my students write downward y = mx + c together with substitute values for y, one thousand together with x, together with thence solve for c (let's telephone vociferation upwardly this Method 1). At Influenza A virus subtype H5N1 score my pupils role the formula y - y1 = m(x - x1) (let's telephone vociferation upwardly this Method 2). Look at the steps involved - for this question, the methods are as efficient.
My electrical current Year 10s had an American instructor final term - she covered linear graphs amongst them. When nosotros came to revise this topic, they took a piece to figure out where to start. Evetually I heard 1 say, "is this the point-slope thing? What was that formula again?". 
OK, thence they'd been taught to telephone vociferation upwardly slope 'slope', that's easily fixed. But they'd also been taught Method 2 together with they couldn't recall the formula. This is a problem. Given that there's less to memorise, I intend they'd endure improve off amongst Method 1. 

It's worth reading Nix the Tricks (essential reading for all maths teachers), we're shown a didactics play tricks called 'Jailbreak Radicals'. Thankfully I've never seen this 'zero conceptual agreement method' used inwards the UK.
Instead, most teachers tell students to position a foursquare element together with and thence separate the surd accordingly eg √45 = √9√5 = 3√5.
Sometimes students fighting to location foursquare factors. In this illustration they mightiness prefer to simplify using prime number factors.
Influenza A virus subtype H5N1 geometric method is explained inwards the extract from Nix the Tricks below. Try to simplify a few surds similar this yourself together with reckon what y'all think. Notice that y'all all the same demand to position a foursquare factor.
Source: Nix the Tricks
The feedback from my conference workshop suggests that roughly people notice this unnecessarily complicated. But if you're going to seek it, I recommend this post by @ChrisHunter36 and this resource (pages v - 6) past times @314Piman.

That's it for today's post. I promise you've flora it helpful. Please comment below or tweet me if y'all know of whatever choice methods for didactics these topics. My side past times side transportation service volition endure all virtually quadratics - sketching, expanding together with factorising.

5 Maths Gems #34

Hello in addition to welcome to my 34th gems post. This is where I percentage 5 educational activity ideas I've seen on Twitter. The summertime holidays are survive here! Let's live honest though - although it's lovely to conduct maintain the chance to remainder in addition to play, the bulk of us practise a fair amount of schoolhouse operate over summertime - creating resources, organising in addition to tidying, preparing for September, catching upward on reading... Have yous read all 34 of my gems posts? Now's a skillful fourth dimension to start!

1. Magnitude
Standard Form is all nigh actually large numbers in addition to actually pocket-size numbers. It's overnice to set the theme into context - I've written a few times nigh The beauty of the real very large in addition to the real very pocket-size – Standard form' by @mhorley. Thanks too to the lovely @MissBLilley who shared this video which puts size into context - she used it to innovate Standard Form in addition to her students were amazed!



2. Prime Time
@MathedUp shared a overnice activity on prime number element decomposition. I actually similar this because it makes it hence clear that every set out is either prime number or composed of primes.
I honey this prime clock from the vivid Minimal Math Concepts. Influenza A virus subtype H5N1 few tweeters were unhappy to reckon the set out i on it though!
Whilst on the dependent area of primes, banking concern gibe out this first-class primes in addition to factors puzzle from @LearningMaths:
@LearningMaths ever produces first-class resources. Here's to a greater extent than or less other twosome of examples:
Fractions starter by @LearningMaths
Number machines by @LearningMaths


3. Alphabet Lesson
In a Twitter news nigh commencement lessons of the year, the ever creative @missradders shared an thought for a Maths Alphabet lesson. In this lesson, students come upward up with the best news they tin for each letter. They need to live able to tell yous what it agency - for instance for the missive of the alphabet Influenza A virus subtype H5N1 they mightiness define add, angle, area, average, astute or adjacent... As Hannah says, "this is a skillful estimate of prior knowledge/ability ... in addition to gives yous fourth dimension to chat to them". What a lovely thought for a commencement lesson with Year 7.

If yous desire to conduct maintain this thought further, your class could blueprint in addition to attain a maths alphabet poster similar the examples shown below. 
Source: http://www.vernalpool.org/treefrog/pop/09F-MPS-MATH.htm
Source: http://www.vernalpool.org/treefrog/pop/04R-B-M.htm

Last twelvemonth I wrote a post 'Your First Maths Lesson with Year 7' which has lots to a greater extent than ideas for September.

4. Influenza A virus subtype H5N1 Level Prompts
@dannytybrown has been busy developing a serial of pre-teaching prompts for Influenza A virus subtype H5N1 score topics. These are designed to live given to students a few days earlier a theme is taught. They are intended to prompt shape news in addition to potentially trim back the variation inwards prior noesis alongside students. Influenza A virus subtype H5N1 few examples are shown below. Do go on an optic on Danny's weblog squeaktime.com for to a greater extent than on this.
 5. Maths with Pizzazz
Thank yous to @japleen_kaur1 for sharing a prepare of resources I've never seen earlier - Maths with Pizzazz worksheets. Hundreds of topics are covered. Many of the activities involve practising skills in addition to using answers to operate out riddles in addition to jokes. Here's a twosome of extracts:
Extract from Page 211 - Algebra with Pizzazz!
Extract from Page 159 - Pre-Algebra with Pizzazz!
I could pass days looking through these resources! Thankfully there's an index. What I actually need to practise is split upward the PDFs into separate worksheets, labelled in addition to grouped past times topic. But that would conduct maintain weeks. Any volunteers?!

Recommended Reading
This summer @DrBennison in addition to @MissNorledge are task an impressive #summerblogchallenge. They intend to write a post every day, hence go on an optic on their blogs this summertime - blog.ifem.co.uk in addition to storeroom.norledgemaths.com.

Here's a few recent posts that I recommend:
  • The beauty of the real very large in addition to the real very pocket-size – Standard form' by @mhorley. Thanks too to the lovely @MissBLilley who shared this video which puts size into context - she used it to innovate Standard Form in addition to her students were amazed!



    2. Prime Time
    @MathedUp shared a overnice activity on prime number element decomposition. I actually similar this because it makes it hence clear that every set out is either prime number or composed of primes.
    I honey this prime clock from the vivid Minimal Math Concepts. Influenza A virus subtype H5N1 few tweeters were unhappy to reckon the set out i on it though!
    Whilst on the dependent area of primes, banking concern gibe out this first-class primes in addition to factors puzzle from @LearningMaths:
    @LearningMaths ever produces first-class resources. Here's to a greater extent than or less other twosome of examples:
    Fractions starter by @LearningMaths
    Number machines by @LearningMaths


    3. Alphabet Lesson
    In a Twitter news nigh commencement lessons of the year, the ever creative @missradders shared an thought for a Maths Alphabet lesson. In this lesson, students come upward up with the best news they tin for each letter. They need to live able to tell yous what it agency - for instance for the missive of the alphabet Influenza A virus subtype H5N1 they mightiness define add, angle, area, average, astute or adjacent... As Hannah says, "this is a skillful estimate of prior knowledge/ability ... in addition to gives yous fourth dimension to chat to them". What a lovely thought for a commencement lesson with Year 7.

    If yous desire to conduct maintain this thought further, your class could blueprint in addition to attain a maths alphabet poster similar the examples shown below. 
    Source: http://www.vernalpool.org/treefrog/pop/09F-MPS-MATH.htm
    Source: http://www.vernalpool.org/treefrog/pop/04R-B-M.htm

    Last twelvemonth I wrote a post 'Well whistle me Dixie, the reply is Pi!" nigh maths inwards the movies.
  • The beauty of the real very large in addition to the real very pocket-size – Standard form' by @mhorley. Thanks too to the lovely @MissBLilley who shared this video which puts size into context - she used it to innovate Standard Form in addition to her students were amazed!



    2. Prime Time
    @MathedUp shared a overnice activity on prime number element decomposition. I actually similar this because it makes it hence clear that every set out is either prime number or composed of primes.
    I honey this prime clock from the vivid Minimal Math Concepts. Influenza A virus subtype H5N1 few tweeters were unhappy to reckon the set out i on it though!
    Whilst on the dependent area of primes, banking concern gibe out this first-class primes in addition to factors puzzle from @LearningMaths:
    @LearningMaths ever produces first-class resources. Here's to a greater extent than or less other twosome of examples:
    Fractions starter by @LearningMaths
    Number machines by @LearningMaths


    3. Alphabet Lesson
    In a Twitter news nigh commencement lessons of the year, the ever creative @missradders shared an thought for a Maths Alphabet lesson. In this lesson, students come upward up with the best news they tin for each letter. They need to live able to tell yous what it agency - for instance for the missive of the alphabet Influenza A virus subtype H5N1 they mightiness define add, angle, area, average, astute or adjacent... As Hannah says, "this is a skillful estimate of prior knowledge/ability ... in addition to gives yous fourth dimension to chat to them". What a lovely thought for a commencement lesson with Year 7.

    If yous desire to conduct maintain this thought further, your class could blueprint in addition to attain a maths alphabet poster similar the examples shown below. 
    Source: http://www.vernalpool.org/treefrog/pop/09F-MPS-MATH.htm
    Source: http://www.vernalpool.org/treefrog/pop/04R-B-M.htm

    Last twelvemonth I wrote a post 'A score resources libraries. My presentation is nearly finished in addition to I'm actually pleased with it - if yous learn Influenza A virus subtype H5N1 score in addition to you're coming to the conference hence practise come upward to my workshop to reckon what I've discovered.

    My 2 most recent weblog posts both characteristic inwards my 5 most pop posts ever - i was nigh The beauty of the real very large in addition to the real very pocket-size – Standard form' by @mhorley. Thanks too to the lovely @MissBLilley who shared this video which puts size into context - she used it to innovate Standard Form in addition to her students were amazed!



    2. Prime Time
    @MathedUp shared a overnice activity on prime number element decomposition. I actually similar this because it makes it hence clear that every set out is either prime number or composed of primes.
    I honey this prime clock from the vivid Minimal Math Concepts. Influenza A virus subtype H5N1 few tweeters were unhappy to reckon the set out i on it though!
    Whilst on the dependent area of primes, banking concern gibe out this first-class primes in addition to factors puzzle from @LearningMaths:
    @LearningMaths ever produces first-class resources. Here's to a greater extent than or less other twosome of examples:
    Fractions starter by @LearningMaths
    Number machines by @LearningMaths


    3. Alphabet Lesson
    In a Twitter news nigh commencement lessons of the year, the ever creative @missradders shared an thought for a Maths Alphabet lesson. In this lesson, students come upward up with the best news they tin for each letter. They need to live able to tell yous what it agency - for instance for the missive of the alphabet Influenza A virus subtype H5N1 they mightiness define add, angle, area, average, astute or adjacent... As Hannah says, "this is a skillful estimate of prior knowledge/ability ... in addition to gives yous fourth dimension to chat to them". What a lovely thought for a commencement lesson with Year 7.

    If yous desire to conduct maintain this thought further, your class could blueprint in addition to attain a maths alphabet poster similar the examples shown below. 
    Source: http://www.vernalpool.org/treefrog/pop/09F-MPS-MATH.htm
    Source: http://www.vernalpool.org/treefrog/pop/04R-B-M.htm

    Last twelvemonth I wrote a post 'resources for halt of term lessons, the other The beauty of the real very large in addition to the real very pocket-size – Standard form' by @mhorley. Thanks too to the lovely @MissBLilley who shared this video which puts size into context - she used it to innovate Standard Form in addition to her students were amazed!



    2. Prime Time
    @MathedUp shared a overnice activity on prime number element decomposition. I actually similar this because it makes it hence clear that every set out is either prime number or composed of primes.
    I honey this prime clock from the vivid Minimal Math Concepts. Influenza A virus subtype H5N1 few tweeters were unhappy to reckon the set out i on it though!
    Whilst on the dependent area of primes, banking concern gibe out this first-class primes in addition to factors puzzle from @LearningMaths:
    @LearningMaths ever produces first-class resources. Here's to a greater extent than or less other twosome of examples:
    Fractions starter by @LearningMaths
    Number machines by @LearningMaths


    3. Alphabet Lesson
    In a Twitter news nigh commencement lessons of the year, the ever creative @missradders shared an thought for a Maths Alphabet lesson. In this lesson, students come upward up with the best news they tin for each letter. They need to live able to tell yous what it agency - for instance for the missive of the alphabet Influenza A virus subtype H5N1 they mightiness define add, angle, area, average, astute or adjacent... As Hannah says, "this is a skillful estimate of prior knowledge/ability ... in addition to gives yous fourth dimension to chat to them". What a lovely thought for a commencement lesson with Year 7.

    If yous desire to conduct maintain this thought further, your class could blueprint in addition to attain a maths alphabet poster similar the examples shown below. 
    Source: http://www.vernalpool.org/treefrog/pop/09F-MPS-MATH.htm
    Source: http://www.vernalpool.org/treefrog/pop/04R-B-M.htm

    Last twelvemonth I wrote a post 'shared advice for educational activity depression attaining students.

    My youngest missy Hettie in addition to I had the pleasance of coming together Rob Smith (@RJS2212) yesterday. Rob has spent the commencement calendar week of the summertime holidays travelling the length of the province to see equally many tweeting maths teachers equally he tin - banking concern gibe out #48hourmathstour to reckon what he's been upward to.

    Finally, expect what I've got - Mathematical Mr Men stickers! If you've non seen the l Mathematical Mr Men earlier hence practise banking concern gibe out them out on solvemymaths.com. They're awesome.