prime factor decomposition and fractions

I inherit every possible method for teaching fractions under the sun. My learners come from every school across the city and all have their own way of doing things. Kiss and flick, kris kross, X marks the spot and so on are all ways for multiplying and dividing fractions. Like I always say, if you have a way that works consistently for you then use that way. I never unteach a method unless it is incorrect. Often methods have become incorrect because the learner has become confused with the method shown to them. In my experience students are more likely to become confused if they lack knowledge of the basics. One of the ‘wins’ I enjoy teaching is product of primes, prime numbers, simplifying fractions and divisibility checks. 

I like to start with prime factor decomposition. I like to call it this in my intentions on the board. I like to discuss the anxieties the learners have when they see the title and then experience the joy on their faces when they crack it in the end! There’s no fancy trick in what I am teaching, this one I am afraid requires singing and dancing as it is all about the presentation. I am not above making a fool of myself to help a concept stick in the learners minds. It all starts with some audience participation. I write up 2, 3, 5, 7, 11 on the board. We spend a few minutes shouting it as loud as we can. We play finish my sentence and I will call out 2, 3 and pick a learner to finish it off. Then we move onto questions of what is the third prime number? What is the fifth? We spend quality time recalling the first 5 prime numbers.

I don’t think I am doing anything out of the ordinary at this point for the learners. Everyone I have ever seen teach the topic as well has started by spending quality time on the first 5 primes. I tend to just stick to 2 3 5 7 11 for these early stages. An old favourite from my cover supervisor days on my PGCE was the 10 x 10 grid and playing in pairs to find all the primes up to 100. I will, if we have time, move onto games like this but in the first instance I stick to the first 5 primes. 

Here comes the singing and dancing…

“If you like it then you should have put on a ring on it”

Here is an example of the prime factor decomposition of 420:

We begin with writing our first 5 primes. We then use these as divisibility checks. I am aware that learners can find the highest prime factor and solve this problem quicker. I am not aiming for speed here. I am aiming for a consistently correct method. We always begin by seeing if 2 goes into the number. We keep the primes on the left as well.

I am aware that it may be obvious for some learners to use 5 as the prime when breaking down 105. I have no problem with this, actually in making these images that’s what I did and had to start again! Once we have broken the number down. I will then sing a bit of Beyonce or show an image of her on my board. (Beyonce also sits on my wall as well as Terry Pratchett!) The blue writing is purely for the example here, we verablise this in class but don’t write it.

Once we have really solidly grasped these divisibility checks, we can use them in a variety of ways. We can then look at simplifying fractions.

Yes this is a long way round but it ensures a consistent approach and reinforces the use of 2, 3, 5, 7, 11. It's a nice introduction in a stepping-stone to unpicking that initial knowledge that's needed to tackle a wide range of questions. Like I always say if you have your own with working things out please use your own way, but for those who struggle 2, 3, 5, 7 11 may just help with developing those core divisibility skills.

Multiplication

I'm sure by now you have heard me mention that I teach a lot of resitters where they may be sitting the GCSE for the second, third, fourth or however many time. I've also talked about those quick wins in those early weeks to earn their trust help them gaining confidence and to deepen their mathematical understanding. One of the easiest ways I've found to do this is through teaching students how to multiply correctly. As part of my PGCE training I was asked to teach a year 7 group a series of lessons covering every possible type of multiplication that I could find available. It led me to Egyptian, Chinese and many other types of multiplication. I became familiar with a wide variety of multiplication techniques that I had to fully understand before I could explain them.

My own knowledge needed to be sound and secure before I explained them to the attentive year 7’s hanging off my every word. There are some elements of teaching year 7 that I miss greatly! Chinese multiplication became my new favourite thing. I know only multiply this way, much to my builder and husband’s annoyance when planning our new extension! I'm sure you've seen it before the lattice method the Geloise method or simply Chinese multiplication. 

What I want to discuss here is the importance of being able to multiply correctly including decimals. Like I always say if you have a way that works for you than that's the way you do it what I'm offering you is a way if you can't do it consistently correctly. Many of my learner's come to me unable to multiply correctly they have been taught the grid method in primary school and they don't know what to do when they're lining them up for the final addition.

Take a look at this work this is typical of my students work. The grid is correct but the place value when adding is appalling. Yes, I am aware I will need to re teach place value but will these mistakes arise again after we have done that unit? What would happen if we looked at Chinese multiplication instead? 

Look at the lattice method above. Here we have the correct answer in a much simpler way. Place value is correct. This makes me happy. I like the Chinese/lattice method because it promotes place value. I like the fact that it only uses the times tables up to 9 x 9 and although we teach up to 15 x 15 often up to 9x9 is secure and above that can be a bit sketchy in my experience. 

But the real reason I like the lattice method is because of the power it has to unlock learning for many resitters. I say to all my trainee teachers and staff that I mentor. Teach someone to multiply correctly and they will be set for life. It is true, multiplication is one of those skills people have had negative experiences with and switch off. To be able to show someone how to multiply correctly can sometimes be transforming. A colleague (not a student or a teacher) was trying to multiply the number of tickets and the cost of tickets to budget for the cost of a conference for her team. She was struggling. I showed her lattice multiplication ( I drew the grid) she loved it. She was so overwhelmed she began to tear up. Maths, multiplying decimals in particular, had always been a struggle for her but she felt that it wasn’t anymore. That is the power of being able to multiply correctly. Lattice may not be the best way for everyone but I think it is worth spending the time to teach learners how to multiply correctly, including with decimals, to provide the skills that are needed for life, not just GCSE.

SLED exam technique

I have mentioned before the challenge of answering A03 questions and some strategies I employ. A03 style questions are when our students are required to make connections interpret results and evaluate solutions. The easiest way I remember it and explain to student teachers is it's those questions that are open ended and they could go many different routes to find the answer generally with a full blank page underneath. I am forever looking for current relevant research that can be easily applied to my maths lessons. Last year while studying a course on a MOOC for the Friday Institute about learning differences I came across something that may help. Yes I can't quite see how course on learning differences lead me to this, but it did, and I am grateful! It just goes to show you should read as wide as possible because you never know what it will turn up. One of the things that came out of one of the pieces of reading for this course was SLED. 

sketch 

label 

explain 

discuss

It got me thinking about these complex a03 style questions where we could easily sketch a picture of what the answer might look like, the painting of the floor plan or the number of marbles in a bag whatever the question maybe about. 

We can label underline key parts of the question. Now instead of explain I switch this to estimate. This was to relieve the pressure of the learners to immediately hit upon the right answer. They are allowed to roughly approximate first. Generally they are correct but with the pressure being off it really improved their confidence in giving these types of questions a go. So the learners could estimate how many tubs of paint how many marbles in a bag and then we could discuss our answers with our peers and then choose the correct strategy for solving the question. The power in relieving the pressure in making it an estimate was immediately evident with my groups. Learners openly admitted that previously they would have skipped this type of question but were now willing to give it a go. We now had a strategy where we could pose, pause, pounce and bounce! We could now have those meaningful discussion that deepen understanding that I keep seeing in other subjects lessons! 

This is a rough example of a simple A03 question using SLED:

Being brave I asked my learner's to SLED an A03 question before the lesson. We then discussed on tables and then as a class different approaches to the same problem. Again I believe powerful learning takes place where misconceptions or different approaches to the same problem can be explored. It was an instant hit with my learners. We then began thinking about how they could adopt this in an exam. We changed discuss to DECIDE for exam situations. This is when after you have estimated, you may have created 2 or 3 different options you must decide on the correct working out and clearly state that as your answer. I like to remind students at this point that multiple workings out will attract lowest marks available and remember each question is a new opportunity to leave an impression on an examiner. 

Here is the same ratio SLED problem with the decide element added, the original working has been left in for this examples purpose but would normally be crossed out:

I like this approach as it gives confidence to tackling complex A03 problems. It provides a crutch for learners to hold on to. It promotes discussion in maths lessons, it’s not always right or wrong! It promotes deeper understanding by looking at common errors and misconceptions. One mature learner, I won’t say her age, said that this strategy gave her the confidence at work to plan her response to requests and improved her stress levels, so it worked outside the maths classroom too!

Challenge for all2

As I said in the previous post the 'challenge for all' really changed my teaching from stretching the more able to challenging everyone and not by giving them more activities to do. Dylan Wiliam is just a treasure trove of hints and tips every time he writes or speaks. In one piece I read (the full article is here) he talks about activating students as instructional resources for one another. In its simplest terms he talks about before a piece of work is handed in a peer marks it and signs to say they have done so. If there are any remedial actions needed the peer must let the learner know, as if there’s anything missing when the teacher marks the work it is the peer that is responsible not the original learner. I liked this as I could easily see this in maths working well. You could give some learners a mark sheet to help them and for others you could ask them to do it without. Everyone could be involved. I was then browsing the brilliant trythisteaching and came across this Doctor’s Diagnosis It takes Wiliam’s idea and asks learners to prescribe remedial work to the originator. 

I took some prescriptions from the trythisteaching templates into my lesson. We were looking at sequences. 

Ben has completed the task. Stacey has marked his work and corrected his error. What I like about this is the level of differentiation available. Depending on my instruction Stacey could have just asked Ben to look again at part B, she could indicate the date we looked at the topic, or she could research a resource online that would help Ben and share that with him. I also like that they don’t need to be in the same class. Stacey is from group B and Ben group A, same set just opposite timetable. The possibilities of this are endless. You could do it verbally in class. However, when I tried this all I heard was “good try” “you did this bit great”. I found that when students had to put their comments in writing they became more focussed in their feedback. I find that many great teaching and feedback ideas are tricky to fit with maths as a subject but this one worked for me!

I am known when mentoring to say “if it isn’t in the plan it won’t happen” I am not pushing lesson plans, please don’t mistake me! What I mean is, whatever you use to plan, make sure all your activities and episodes are planned. For example, for progress checks against the learning intentions I encourage student teachers to have a slide in their presentation to ensure that they happen. (It’s not just student teachers that need reminding of this, I am more than aware!) I needed to ensure that I remembered to include a 'challenge for all' element in my lessons. As I have an open door policy for all staff, and especially mentees, I always need to be on point. I like doing one thing once and doing it well so that it is always the same level of planning from me. I found that whilst creating all these 'challenge for all' activities I found that some worked and some didn’t. So I hit upon a choice board. I created a Padlet of my 'challenge for all' activities. If you are unfamiliar with Padlet, it can be used as a virtual noticeboard with ideas pinned to it. If you are out of free usage of Padlet there are alternatives, try Linoit. My padlet looks like this:

I loved Fighting Talk on BBC Radio Five Live when I was younger. It was part of my pre match routine. The game ends with defend the indefensible. Two players were given opposing sides of a statement to defend. The statement was purposely controversial or opposing to the participant views. For example, one participant was asked to defend the statement that his wife’s cooking was terrible. He refused to engage! I have found that this format plays great in maths lessons. 

Imagine we are looking at solving equations x^2 = 36

Ben is asked to defend that x=6

Stacey is asked to defend that x=18

What I like about this is that both need to calculate the correct answer. Stacey needs to identify where the misconception has come from in order to defend it. I am a big fan of learners knowing the common misconceptions in order to avoid them. All to often in maths I see the power of 2 mis-interpreted as multiplying by 2! 

I found that defend the indefensible worked in many lessons and I could generally think of them on the spot! Any time solving or rearranging with algebra was involved I would challenge the whole class with defend the indefensible. We would do it as 2 teams against each other or lots of small pairs debating to the class. I found it a nice way to promote respect and listening along with developing debate and argument forming skills.

Spot my error and tick or trash were brought to my attention via TES. Spot my error came from the fabulous alutwyche https://www.tes.com/teaching-resources/shop/alutwyche  (he is also on Twitter https://twitter.com/andylutwyche) and tick or trash I originally found on the old but brilliant Number Loving from Laura Rees Hughes A lot of the Number loving resources are now to pay for on TES. Tick or trash has a question in the middle and to the left and right are two answers, one is correct, to be ticked, and one is incorrect, to be trashed.

The spot my error tasks from alutwyche are quite comprehensive. I have enjoyed adapting this idea. I will present and incorrectly answered question on the board and ask the learners to spot my error. This also helps with the inevitable board work mistakes I make daily as it gives me a great cover story! The spot my error from alutwyche and my own ones all focus on displaying a common misconception. Again if learners know the common misconception and can realise where it comes from they can avoid it. Both STEM and NCETM have resources and evidence explaining the common misconceptions in maths. You can find them here and here. The NCTEM also has a great paper on inspection worthy mistakes made by students here. It makes a great read. Broadly it suggests that “Conducting appropriate class inspections of mistakes in student work can create pedagogically powerful moments in the classroom.” One of the most powerful types of mistake to investigate, the article says, are those that approach the problem from a different way that the broad solutions from the class, as if the problem had been interpreted differently. This is my aim when I create either defend the indefensible, spot my error or tick or trash activities. How could the problem be interpreted and how different will the answer be?

My final activity in challenge for all is to create cheat sheets. I was shown these by my mentor in my NQT year and they have been with me every since. Do you remember the old, make a poster lesson? I hated them in school as I would rather be at home watching MTV Select than in school making posters! As a teacher I also dislike them as really, what are the learners learning apart from how to use fineliners of contrasting colours to make 3D lettering? A cheat sheet is like a poster but different! Have you ever had this... You ask the learners after a lesson, how much of this are you going to remember? Queue awkward faces and panic! It happens multiple times a day to me! A cheat sheet gives the learners a way out of this. You ask learners to imagine that they have 2 minutes before the exam and their present self wants to tell their future self all about this topic and they need to make a cheat sheet to record it. I normally model one as an example. I follow a thought or spider diagram. I encourage the learners to make it personal to them. A specific error they made in class they may want to clarify or they may want to emphasise a specific stage of the process. 

This rough example (apologies!) is personal to the learner. They are clearly wanting to remember interior means inside the shape angles. They are also keen to remember it’s angles around a point rather than in a circle! With my adult learners, evening class learners specifically, we do this weekly as they worry they won’t be able to remember it. I don’t blame them, maths is hard, many are working and raising families as well as coming to maths. We end up with a bank of 20 or so personalised cheat sheets. The learners then have a revision guide ready to go when exam day comes.

I am now pleased with where I have got to with my 'challenge for all'. There is challenge for all available in every learning episode via my padlet or prepared activities (if I remember!) It has been powerful in helping me develop skills to enable understanding rather than offering more tasks for my learners to complete. My learners were initially sceptical but embrace the challenge now and enjoy unpicking where the incorrect answers have come from.

Challenge for all

You know the feeling when you return in September, feeling prepared, lessons ready, imagining your groups, beautiful 5 minute lesson plans for the first 12 weeks that took an hour each all ready….smug! Then day 1 you are hit with...right so today we thought we could spend some time planning the first few weeks of term given our new lesson plan and scheme of work structure….Argh!!!! It’s all changed! Into the bin goes your summer work and rapidly you pray to get through at least the first 4 weeks worth of work in a day. No idea what I am on about, then you are very fortunate as this happens to me every year! Thankfully every year’s change or tweak to the lesson plans or schemes of work are positive and eventually I am pleased they have changed but those first few weeks are gruelling!

A few years ago I was introduced to the 'challenge for all'. (Cue images of Tower of Terror ride at Disneyland and the Twilight zone music!) As part of the team responsible for coaching and mentoring staff to meet standards it was quite complex to get across to staff what the 'challenge for all' is. I can take no credit it was all the work of my amazing teaching and learning colleagues but I am more than happy to share it!

To be clear, this is not stretch and challenge in the sense that you plan for the HATs (oldie but a goodie term!) top end of the group some extension activities. There is an element of that but it is actually about challenging all learners no matter where they sit in your group. What often comes up as good ideas for challenging all are, design a tweet, create a mnemonic, promote a discussion with deeper probing questions. Some of these techniques are useful and appropriate to maths lessons but often they are not. Discussions and opinions about who is right and wrong are very limited in their applicability in maths in my opinion. 

Imagine we are teaching expanding brackets, something like 2(x+5). 

Traditionally to stretch and challenge the high attainers we might ask them to move onto expanding double brackets, for example (x+5) (x+3). This stretches their skills to a new level. However it can be argued that they are actually learning a new skill in moving on to double brackets. In my experience of doing this, more teacher input is required meaning that the learner isn’t being stretched but that the teacher is guiding them to the next activity. Yes you can set them off with scaffolded worksheets to relieve this but I always have Dylan Wiliam ringing in my ears at this point. Wiliam (on the amazing Mr Barton Maths Blog) talks about a hysteria of a few years ago which came from observations where teachers, observers and OFSTED all wanted to see more activities to evidence the learning. Thankfully this is less so now, we recognise it’s not the busyness of the learner it’s the engagement that tells us if learning is taking place. This is why I like the 'challenge for all' element. It’s not about keeping them busy with the next thing, it’s not about more teacher input, it’s about deepening the learners understanding of the topic covered in that lesson.

So let’s return to our expanding brackets of 2(x+5). We could ask learners to create a tweet, a diagram of the stages or a cheat sheet (see next blog). However, if we could apply their knowledge to new concept we could evidence a deeper understanding. Asking them to move onto double brackets wouldn’t necessarily achieve this. We could take expanding brackets to solving a worded problem, an AO3 style question.  We could ask the learners how old Millie is if Billie is 5 years older than Ellie and Millie is twice as old as Billie.  For the lower attainers we could form the expressions as Billie is (x+5) and Millie then is 2(x+5). For the middle attainers we could give them the problem without the expressions. For the high attainers we could ask them how old Millie is if Billie is 12 and they could solve the expressions. We could ask all of them the age difference between the oldest and youngest and see if they can work this out algebraically rather than by solving. This got me thinking, would this work with any AO3 style question? Could we give a 'challenge for all' opportunity for all just by looking at the AO3 style problems. 

I am a big fan of doing something well once and it will save you time in the long run. I created a lucky dip box and cut up AO3 questions and put them in the box. The 'challenge for all' then became about learners applying their knowledge to an AO3 style question. It started off as random and they could pick a number AO3 question out and we had been learning data but it worked as a nice retrieval element as well. Reflecting on this,  I created an algebra AO3 lucky dip, a shape AO3, a number one, data and finally the really tricky crossover problems box lucky dip. Depending on the topic would depend on which lucky dip box we used. The beauty of this was high attainers could pull their own AO3 out. Mid and low attainers we could work on as groups and collaboratively solve. 

As with anything once it becomes routine it is expected. Learners would race through activities to get to the lucky dip. There was a leader board of who answered which question quickest. We would discuss if one question was harder than the other, and if so why. Given that we think one is harder than the other, should they be worth the same amount of points for the leaderboard. This then got learners thinking about the design on the question. One healthcare student said “the maths isn’t any harder in that one it’s just spotting what it’s asking” I think if we are aiming for learners to deepen their knowledge that quote sums it up beautifully. If learners know why they are doing something and can explain what the aim of the task is they have begun to understand the topic. We will cover understanding another time….

Retrieval Practice

I love to read, and I read widely around education, teaching. Maths, anything that interests me. However, no matter how much I love to read the amount of time I am able to spend reading is significantly less than I would like it to be. Prior to my current position, unfortunately the only real time I devoted to reading was when there was an urgent need. I was preparing for interview for my previous position I was trying to find some research that was relevant to what I was discussing in my presentation. 

I know this is the wrong way round to do things the research should have informed what I was doing beforehand but we were where we were and the interview was in 2 days. I am pleased that I now allocate myself coffee and reading time once a week to keep up with the latest blogs and developments. I love my coffee and reading time and it is sacred, I need it to be so. That doesn’t mean that if work is busy and I don’t get time to read at work I will make time to sit at home with a coffee and read, point is I read weekly! Whilst preparing for my  interview I came across retrieval practice. Retrieval practice had nothing to do with what I was presenting in interview but it instantly sparked my interest. 

I ended up spending all my interview talking about retrieval practice and openly admitted that I haven't used it yet because I just found it but since I got the job and have begun using retrieval practice. I am not an expert but am happy to signpost you to the experts here: https://www.retrievalpractice.org/

Retrieval practice works on the basis that if you regularly retrieve small bits of information you will deepen your understanding. It was really nice to finally find something that was current, relevant to my teaching and unusually appropriate to a maths lesson. Too many times as a maths teacher I have felt left behind. Whilst other subjects make huge strides in questioning and feedback I find myself trying my hardest to make it work in maths but most of the time answers are right or wrong. The guys at https://www.retrievalpractice.org/ shared a retrieval practice grid where the topics that have been covered previously were colour-coded by how far in the past they had been. This was easily replicated into my lessons and it looks a little bit like this. 

Share £60 in the ratio 7:5	Find the nth term of this sequence: 32, 26, 20, 14, 8	Simplify: f + f -f +2f -2f + e	Multiply: 5.4 x 3.2
What is the 100th term of the sequence 5n-6?	Tickets cost £3.50, we need 18 tickets in total.  Calculate the total cost.	Share £125 in the ratio 18:7	Simplify: d x d x d
Simplify: 2k - 3g + 5g + 4k	The next term in a sequence is 15. The start number is 9. What is the nth term rule?	Multiply:  2.5 x 1.2	Aliaa and Steve share £45 in the ratio 5:4. How much do they each get?
Multiply: 4.4 x 3.2	Gray and Teag share some money in the ratio 2:3. Teag gets £45. How much was the total amount shared?	Simplify: e x j x j x e x e	Is the term 54 in the sequence 6n-6?

Red is 4 lessons ago, orange is 3 lessons ago, green is 2 lessons ago and blue is last lesson. This replaced my bellwork. Students arrive and these are on their desks already they sit down and begin working through the grid. Every lesson I would change the questions and colours. It really wasn’t an onerous task. The aim of it being a little reminder a little refresher and in total would take less than 5 minutes to go through the board. So I would give the learner's 5 minutes to come in and do it and then 5 minutes to run through at the board I felt that it was worth the sacrifice in my lesson time but I appreciate not everyone has 90 minute lessons like we have. (We only have 1 90 minute lesson a week though!)

My adult resit learners would sit and discuss the questions. You would overhear questions about when to use ADAM or DINO. I would spend the 5 minutes catching up with any absentees from the previous week or any messages that I needed to pass on to my learners. The next time when I would look up the powerful maths discussions that were taking place were jaw dropping. The collaboration and cooperation of learners in reminding and refreshing each other with how to answer the questions was lovely to see. Age gaps disappeared and mature adult learners were working at the same pace and stage collaboratively with teenage adult learners. Over time our little routine expanded into each table being responsible for sharing the answers rather than me standing at the board. My application of the grids also evolved in that the red section became a place for poorly answered topics to be repeated and recovered. For example nth term would be in the red section for one class for a few weeks whereas for another class it was factorising. Using these grids I was able to personalise the retrieval practice that each group needed.

Having taught resit groups for a number of years the impact in my results was significant. The topics that have been regularly and consistently answered correctly on my retrieval practice grids were regularly and consistently answered correctly in my mock exam papers. It was evident that those 5 minutes made all the difference in keeping topics ticking over. When we came to the actual exam one learner asked me for a copy of all the previous retrieval practice grids to revise from. This was a Eureka moment. Thanks to Google Docs I had a bank of sheets that I could print off and issue meaning we had instant revision packs ready to go! Google docs is brilliant for this because it has version history allowing you to revert to previous versions. If you would like to know more about Google docs I will talk about this at a later date. 

Not only did retrieval practice improve my in class testing, it helped create an empowering collaborative working environment which was an outcome I wasn’t expecting. It also enabled me to have a class specific time relevant revision pack for learners appropriate to their stage and ability. I am a big fan of curating revision collections for my learners based on the topics and how well they have done in them. Retrieval practice did this for me! 

Nth Term Sequences

I love teaching nth term! I am not going to lie it is one of my favourite favourite lessons. 

I follow a great guy on TES called alutwyche https://www.tes.com/teaching-resources/shop/alutwyche  (he is also on Twitter https://twitter.com/andylutwyche) from the very beginning of my teaching career his resources have saved me from dreary worksheets consistently. When you are teaching mixed ability groups his bank of lessons of grade A to G of the old GCSEs are a lifesaver. His explanation of the nth term was completely different to how I had been taught it how I've seen it before when I was training and how my department taught it when I qualified. I love seeing something taught in a different way.

I was taught, and I saw be taught and my colleagues were teaching, nth term as you work out the difference and then you write that in front of the n and then you work out what you would do to get to the 0th term, like this:

This guy introduced me to the times table method you may have seen it before but it blew my mind. You work out the difference then you write the times table of that number above the sequence then you calculate the difference and you end up with the nth term rule. Have a look at this example.

Learner's really respond to this because if they have been taught a way that hasn’t worked before for them, it's nice to give them something different. But like I always say if you have a way that works for you you use that way. I only offer alternatives when you don't have your own way of working things out consistently correctly. 

Thinking about the working out the difference and what would the 0 term be I began to think about the steps that we were doing. We work out the difference you put that in front of the n and then you work out what the 0 term would be I wonder if there was a way we could make an acronym or a mnemonic for this and I thought Dino. A quick Google later and nth term with Dino is a thing and there are loads of resources out there! Phew I’m not going mad, others are thinking the same as me! So just like at famous Adams and famous Terry's appearing my lessons the amazing Rex the dinosaur from toy story also appears in my lessons. And it works like this 

D is for difference 

I in front of 

N 

and then the letter o is actually a number

0

This really helps learner's remember the steps they often know how to work out the difference and they know it goes in front of an it's just what are they adding or subtracting it's the final stages. With my famous Adams my famous Terry's my female mathematicians and now Rex the dinosaur from Toy Story on my walls hopefully now you can picture what my classroom looks like. 

Transformation Terry

So I have introduced you to ADAM, my SASSYLASS, and my magic triangles you can imagine what my walls are full of in my classroom along with my equality and diversity posters my safeguarding policy and my famous mathematicians through time. I only ever pick female mathematicians it provides an interesting discussion point for those that take notice of my boards. I recently walked past the pub with an a board outside it that said my manager told me to write something good on here to get customers to come in but nobody reads these anyway. This is true of my teaching boards I spend ages making them look wonderful and I really enjoy it when they ask questions about my famous female mathematicians. 

Let me introduce you to Terry, famous Terry’s are also on my walls! I've just mentioned before about a teaching transformations and how the learner's missed me and my experience and what I say and do when I teach transformations. I think this may be something to do with Terry. Terry is one of those lessons where learner's leave laughing and I mean genuinely laughing about a maths lesson and then can apply it straight away into an exam style question. So nothing difficult nothing tricky and I can't remember where it came from, it may even have come from me but I've been using Terry for years now. As well as famous Adams who appear in my lessons famous Terry's, Terry Pratchett, Terry from The Word (if you are as old enough as I am to remember The Word) Terry Butcher... all sorts of Terry's randomly appearing my lessons when it is a transformation question to remind them that they need a Terry. 

Terry applies to the “describe a single transformation” question that has been a mainstay throughout all the incarnations of GSCE specifications in my teaching career. How often do we see “it was flipped and then rotated”? (One of my favourite always incorrect answers!) No matter how I teach transformations someone always tells me a shape has been flipped!!!!! So to avoid the flipped and rotated or it was moved and turned or it was made bigger and turned round I decided to talk about Terry. 

Terry is Translation Enlargement Rotation Reflection whY? you only need one Terry in your life. 

Lessons have been completed on transformations. We are looking at completed transformations now so we have an understanding of the fundamentals of transformations. We look at a completed transformation and I will ask the class what has happened here?

I then follow it up with, pick a Terry and stick with a Terry, don’t ever change your Terry. It's the opposite of Bruce Forsyth's play your cards right, there’s no swapping your base card here! You can see how the students start to laugh. The learners enjoy the humour of talking about Terry and how you pick a Terry, you stick with a Terry and be loyal to your Terry. I have found this a useful way to ensure the correct language is used in answering these questions and thankfully the number of times I have read “it has been flipped” as been significantly reduced!