A Perfect Maths Lesson
Teachers have the most important job in the world. At a time when expectations and accountability are at an alltime high, delivering excellence in the classroom has never been more difficult. And this is true no more so than for maths teachers. Maligned in the press for poor international performance and relentlessly scrutinised by school leaders and government, no wonder great maths teachers are becoming difficult to find. The unique demands of our subject make it tough to apply some aspects of research on teaching and learning in our classrooms and even the best of us can, at times, become cynical about our job.
The Perfect Maths Lesson is my antidote to the above! Rather than being a subject described as boring, irrelevant and hard, outstanding maths teachers combine their passion with pragmatism to ensure that maths is intriguing, relevant and delightfully baffling. I do not believe in mechanistic checklists of expectations which headteachers or inspectors can tick for compliance but I do believe that there are common features of outstanding maths lessons and common characteristics and habits that outstanding maths teachers share.
So, what are the essential elements of The Perfect Maths Lesson?

1. Engagement
When kids are engaged in their learning, they are more ambitious in their thinking. One of the key tasks in engaging children in maths lessons is to set the pace of the learning correctly. Too easy, too slow or too repetitive and they become frustrated. Too difficult, too fast or too busy and they become bewildered.
Getting the perfect maths lesson off to the right start is crucial to engaging learners. An effective initial activity sets the tone for the rest of the learning and can determine the success (or otherwise) of the lesson. Your pupils need to be in the habit of beginning their learning as soon as they walk through the door of your classroom. As they wait for others to arrive, it is a good idea to have a little, openended challenge available on the board or on their table. For example, ‘how many ways are there to make 10 pence using British coins’?
Once all the pupils have arrived for your lesson, an effective starter is needed to help them focus on learning, make them think and provide a sense of curiosity to maintain interest. It’s best to link this learning to pupils’ own lives by using contexts sensibly.
2. Challenge
Given the right set of circumstances, all students can make progress – particularly when the teacher is determined that they will. In the perfect maths lesson, teachers help students to appreciate that effort is required for success by ensuring that the work is perplexing, mystifying and wonderfully challenging.
Ideally, you should be aiming just beyond the point students have already reached – occupying a space right at the edge of their ability. Challenge can be woven into learning by asking the right questions in the right way. Effective questioning is a central tenet of the perfect maths lesson because deep learning begins with questions, not answers.
‘Rich’ questions encourage learners to make links with previous learning, stimulate thinking, reveal misconceptions and generate even more questions. For example, the question ‘What is a rhombus?’ is made richer by becoming, ‘In what ways is a rhombus like a rectangle and in what ways is it different’?
Finally, teachers must also find a way to help all children think mathematically. For many children, procedural knowledge and rote learning have led to a void in understanding which prevents them from making the expected progress. They require conceptual understanding in order to comprehend mathematical operations and relations before they are able to apply mathematical ideas to new situations.
3. Independence
Independence is what really connects the teaching with the learning. Direct instruction on the part of the teacher (that is, deciding the learning objectives, modelling the learning, monitoring and evaluating understanding and tying the learning together) is essential if students are to make progress. However, students learn even better when they can selfselect or selfgenerate learning tasks, collaborate with peers and selfregulate their own learning.
Such is the fear of failure in maths lessons that pupils often choose to opt out of challenging learning and the words ‘I’m stuck’ resonate throughout the classroom. In the perfect maths lesson, getting stuck is celebrated because it triggers new learning and helps children to get better at maths. Helping learners to get themselves unstuck without relying on the teacher is an important precept for developing independence in maths lessons. Teachers need to rein in their impulse to answer students’ questions, instead responding by asking the question back. For example, if a pupil asks, ‘Why is the answer negative?’, the teacher replies, ‘Good question. Why do you think the answer is negative?’
4. Assessment for learning
Effective assessment is the key lever for personalising learning in maths lessons. Assessment can be done to, with or by students but, in its most emancipating form, assessment always results in the learner moving forward in their learning.
The use of a learning continuum, based on the objectives for the lesson, is an effective way of helping students to be clear about how they can make progress in maths. It allows them to assess where they are in their learning journey and where they need to go. In this way, the emphasis is on the pupils’ continuing learning journey over the course of the lesson (or series of lessons), as opposed to believing that they are simply able to ‘do’ or ‘not do’ maths.
Because the process of learning is a journey, it is important to remind students to frequently check their own progress in relation to the distance travelled towards the learning outcome. Dedicated Improvement and Reflection Time (DIRT) means spending quality time in your lesson returning their work, letting them read your comments, soaking in the feedback and then responding to it.
5. Relationships for learning
The challenge for maths teachers is to help pupils enjoy their maths lessons (even if it isn’t their favourite subject) because positive emotions are essential for learning. Dopamine is the number one, learningrelated, memoryboosting neurochemical – and a teacher’s best friend. Managing the emotional climate of your classroom to produce the right levels of dopamine in learners’ brains means that they will have no choice but to learn, whether they want to or not! The most effective means of achieving this is through reward or the anticipation of reward. In a maths lesson, rewards might include a joke, opportunities for movement, a puzzle, group work, a giggle, a game, listening to music or a curiosity or surprise.
The fear of failure is amplified in the maths classroom because children believe that, above all other subjects, failure in maths is the worst of all failures. In the perfect maths lesson, then, the teacher must obviate the fear of failure. Indeed, we must encourage students to fail better! Maths teachers can convey a growth mindset to students by using language carefully and communicating praise with purpose.
So, there we have it! If you’d like an insight into the ‘how to do it’ (and why it works) of outstanding lessons, get yourself a copy of The Perfect Maths Lesson. Having observed hundreds of brilliant teachers during my career, this little book neatly summarises their best ideas, unashamedly stolen, tried and tested.
If you are looking for ideas to breathe new life into your lessons or tops tips to gain that elusive ‘outstanding’ judgement, you’ll find plenty in The Perfect Maths Lesson. My aim in the book is to provide practical ideas and commonsense methods that can help every teacher to be excellent, and uncover the essential strategies that help teachers appear to walk on water!
Ian Loynd is a teacher, school leader, governor, author, educational consultant and trainer. Follow Ian on twitter @IanLoynd or visit www.ianloynd.com

Factors and Multiples Math App
Math Raps: Factors & Multiples is available on iTunes and Android now. The app is composed of videos and songs about particular math skills with exciting games to follow so the user can practice mastering the concept. I created this app because students as well as parents are having trouble doing the basic math concepts. While teaching middle school math, homework would be sent home often. Too often the homework would be incomplete and followed with a letter from the parents stating that neither the parent nor the student knew how to complete the assignment. So I created this app (with more to come) as a tool to help parents and students understand and master the basic concepts of math. Once the basic concepts of these skills are mastered, common core math will be much easier.
Comments are FREE, so please leave one below. How did you find the app? Do you want to write a review?
This is the best 99 cents you will ever spend so please support this!
Math RAPS: Factors and Multiples, Prime and Composite, and Prime Factorization
FOR ITUNES: https://appsto.re/us/3Exa0.i
FOR ANDROID: https://play.google.com/store/apps/details?id=com.aplusssolutions.mathrapvol
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This is another classic Math problem that has gone viral on the internet specifically on Facebook and Twitter. However, it doubles up as a great Math problem starter to a lesson that generates great discussion and debate. It is said and I do not have the evidence of this that children can solve this far better than adults, and on average children find the solution within 30 seconds.
Please do not reveal the answer to anyone once you have solve it, just share it to annoy others : )
Do not forget to check out the other Magical Math Lesson starters on the site. Comments are FREE, please leave one below. What is your answer?
Math problem: What is the missing number under the arrow?
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Why not set your class a challenge to be able to work out the pin code to your credit card! This is a fun and engaging Mathematical starter that will get any pupil motivated to answer a great Math question. It is best used as a starter to a lesson, possibly on financial mathematics or a number lesson. Open your wallet and present to the class your credit card and tell them that the pupil who calculates your pin code first will get to keep the card (Obviously it is fake printed card). This normally increases the engagement and desire to hack the credit card pin code. Have fun!
Do not forget to check out all the other Magical Maths lesson starters available on the site.
Comments are FREE so please leave on below! So, what is my pin code? Answers below!
Financial Math lesson starter
]]>As an educator good grammar is paramount! The irony is most teachers, including me, will sometimes overlook this fundamental concept. It is worth noting that it should be the responsibility of teachers of all subjects to promote good grammar in their lessons and not just the role of your English faculties. I would advise all schools to have a common methodology across all subjects to deal with grammar mistakes. This could be in the form of a common marking sheet or CPD promoting correct grammar and highlighting common grammar mistakes.
Below is a selection of funny grammar mistakes that you can browse through and share with your fellow educators. They are pretty funny but really promote the message that good grammar is needed throughout society and not just in education.
Comments are FREE, please leave one below. If you have a funny grammar mistake that you would like added to the list then please let us know.
Funny Grammar Mistakes
]]>I am sure you have heard “Let it go” from Disney’s Frozen many times before but this is a must watch for any of the great mums out there. This is a version that you would hear if Elsa was a mum and not the ice queen. Play it to your class and watch them scream with laughter!
This parody of Elsa’s Let it go is a must share, especially to a great mum or mums that you know out there. I guarantee it will definitely brighten up their day!
Comments are FREE, So please leave one below.
]]>Are you looking to challenge the most able in your class or want to develop mathematical confidence of your learners? This is a great Maths trick to easily remember your times tables from 13 to 20. You might have come across the hints and tips to remember your standard times tables and found this very effective but I find when I show learners this method to learning your 13 to 20 times tables, it just simply blows them away!
It is very important to note that learners should not write anything down when using this method to learn their 13 to 20 times table. Try to get them to this in their heads to help develop mental Maths skills. Go through the example below with them and then get them to practice loads of questions from the 13 to 20 times table in their heads. Practice Practice Practice, this is KEY!!!
This makes an amazing lesson starter and I remember the first time I showed a learner the ability to remember their 13 times table, it was truly heart warming. I could see it, in their eyes the happiness that it gave them. The process shows to the “not so confident” Mathematician that a bit of resilience and few Maths tricks that anyone can be great at Maths!
Comments are FREE, Please leave one below about how you used the resource.
Example of quick method to Learn your 13, 14, 15, 16,17,18,19,20 times table
This is how easy and effective this process is and you can apply it to any numbers between 10 and 20!
Let’s try 18 x 16.
Get Learners to practice practice practice!!! Try these;
18 x 13
13 x 16
17 x 18
17 x 15
12 x 19
Another method of learning your 13 times table
]]>A times table chart is a resource that should be up in any Mathematics classroom or child’s bedroom. This resource will ensure that learners can refer to the appropriate times table when practising and assessing themselves.
There are also many ways in which to help you memorise your times tables but having a times table chart just make sure that pupils will have “maths on the mind”. The times table chart will always be there, just in case there want to spend a quick couple of minutes revising them or referring to them as part of a bigger Maths problem.
In the classroom I tend to allow learners to have a copy of the times table on their desk or stuck in their exercise books. This is so that they can check or refer to a time table when solving Maths problems. This makes sure that learners can go on to solve larger Maths problems even if they have forgotten one of their Maths times tables. I have also found times table games are a very effective resource to help aid the practice and memory of times tables. Also for your high ability learners check out the secret to learning your 13 to 20 tables.
Times Table Chart Resources
There are hundreds of times tables resources available online. I have found that anything that is colourful and interactive helps a great deal. However, why not get your child or learner to make their own resource. This will give them a sense of pride when it is up on the wall or stuck into their exercise books. It also helps in the memory retention of their times tables.
Comments are FREE, please leave one below.
Top 10 Maths Times table chart
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Are you looking to develop your mental maths skills? If so, then you have come to the right place! Dividing integers can be tricky but the following rules will help you decide whether a number can be divisible by another single digit number. This is a great set of mental maths tricks to help you do this and one that should be shown to all budding mathematicians. Do not forget to take a look at another set of mental maths tricks about ways in which to learn your times tables.
Developing mental maths is very important in Mathematics and it is a skill that is gradually being neglected in schools across the globe. Learners are getting more and more dependent on technology and struggle to even do the most simple mental Maths.
Comments are FREE, please leave one below.
Dividing Integers Hint and Tricks
Divisible by 2
Divisible by 3
Divisible by 4
Divisible by 5
Divisible by 6
Divisible by 8
Divisible by 9
Why Teaching Needs You – Teacher, YOU Matter! Advice on Becoming a Teacher!
Teachers are some of the most amazing people on the planet. After our parents, our teachers have the most impact on us, one so profound that we are almost certainly a product of what they have taught us. I would like to thank all the teachers I have ever known.
Can The Last Person To Leave Turn Out The Light?
And my favourite:
“I sort of just… fell into it.”
So many of the teachers that I have worked with don’t have a logical progression on how they came to do what they do. I too fall into this category. Yes, teaching does give me a steady income, it does have some opportunities for progression into management, if that’s what you want to do, and sometimes I get job satisfaction from imparting knowledge to my pupils… but none of those things are the reason i’m a teacher.
Very often teaching seems to happen to teachers. It is as though we are stumbling through our lives when a giant piano drops from the third floor window and slaps us with a shiny certificate of Education. Before we know it we are elbowdeep in marking, student targets and lesson plans.
However, I think that the spontaneity is part of the magic of the profession. There is method in the madness of becoming a teacher and it is a curious sort of madness indeed.
When a teacher takes that first leap into the unknown and embarks on a career of sharing knowledge, they are taking on a mammoth emotionally and intellectually demanding task which is not for the fainthearted. This is why…
Teacher, YOU Matter!
It may sound trite or preachy… but it is most certainly true. Imagine every school, college, academy and University without its teachers. What would they be but empty buildings filled with milling leaderless minds, hungry for knowledge and thirsting for intellectual fulfilment?
The truth is that we human beings, although great at being taught are not so great at learning on our own. Even that wonderful skill, of being an ‘independent learner’ needs to be taught.
But why should you listen to anything I have to say?
Well, like you, I am a teacher.
I have been teaching in the postcompulsory sector in the United Kingdom for the last five years. I’m not a professional selfhelp guru, neither am I a psychiatrist. I am just a teacher sharing my own firsthand experiences in my field.
I started out wanting to be a writer, to entertain young adults with sciencefiction and fantasy novels. However, I realised pretty early on that it wasn’t going to be easy to make a living from writing full time. After being turned down for a dozen studentships and receiving up to a hundred rejections from agents and publishers, I decided to do a teaching qualification. It couldn’t do any harm, I thought to myself, and besides, the government is going to give me a bursary to do it.
Teaching was never supposed to become ‘a real job’. However, quite soon after I began my teacher training I suffered through a series of setbacks: a death in the family, a chronic and debilitating illness and relationship troubles. These all combined to stop me writing for a number of years.
Suddenly my backup job had become my only job.
It was then that I had to sit up and ask myself some pretty serious questions:
In answer to the first question I love the experience of creating. Most importantly, I enjoy interacting with readers and enjoying their feedback and the debate that can create. The answer to the second question was quite simply, to tell stories. I have always believed that stories are what make us human. They are vital for us. We use them to explain our most difficult concepts. In essence, they are what make us human.
The answer to the last question: ‘How Can I Make Myself Matter?’ was a little trickier. Working in the state sector has been certainly an education for me and I can’t deny that I do often feel like I matter.
A teacher is a person who has a massive impact on a young adult’s life. Whenever a student tells me that they enjoyed our lessons so much that they are doing English at University I am always a little taken aback. I think wow! Isn’t that wonderful? This lesson has given a student the impetus for their future career path.
A MILLION LITTLE PATHS
I imagine students wandering down a million little paths. Their teachers a sign posts pointing towards different directions.
But then there are LOT of times when I feel like I positively don’t matter; even though my teaching role is no longer my only role. I write fiction and nonfiction; I teach a range of subjects but there are a lot of things about the teaching profession which drag teachers down and make them feel unimportant, demotivated, deflated, and worthless.
Often, in Teaching, trying to protect teachers is seen as being an ‘enemy of change’. It is clear that some people are worried that in focusing on teachers, we may be losing focus on students. But that just isn’t true. A happy teacher has always meant happy students. So have no fear because by trying to take back some of your own selfbelief, you will become a better teacher and your students will feel the benefits too.
The National Union of Teachers put together a pretty alarming collection of quotations made by the British government about teachers on their website (www.teachers.org.uk). A few choice examples are here:
You may have heard quotes along these lines in the past few years, quotes which have contributed to a culture where teachers often feel like they don’t matter. And if they don’t matter then why should they bother? Why should they bother with the long hours, the daily attrition of classroom and staffroom politics, behaviour management and continually feeling like secondclass citizens where they have to tiptoe around their students and managers?
Why should they stay at all? Wouldn’t they be happier if they left? They’re smart people; they can retrain and do something else…
And as quick as magic, another teacher leaves the profession forever.
This introduction is called ‘Can the Last Person to Leave Turn out the Light?’ because the rate at which teachers are leaving the profession altogether is the saddest predicament currently befalling students in the current education system.
Secondmost disheartening is the fact that all these teachers have no clue how important they are or how much they matter. And they do. They are invaluable, they are brilliant, and they are the glue holding the entire system together: all their extra hours, their goodwill, their optimism and their selfreflection.
When I told my teacherfriends that I was writing this book and proceeded to ‘test it out’ on them, I was taken aback by how important they felt this message was, how much they needed to hear it. So it is now full of the advice that I have given and been given, on how to cope with a stressful working environment, while at the same time maintaining my sense of self and confidence.
For all of you who are reading this guide and have realised that you are struggling emotionally with your teaching career, you know that you need to make a change. Until now you may have been unsure as to how to go about making that happen, but you are ready to start taking charge of your teaching life.
I’m not promising that the change will happen overnight. Perhaps you will have to make some pretty radical changes to how you approach your career and where and how you work. Rest assured there will probably be a whole series of physical and mental snags to deter you. In your journey through this series of miniguides you will become familiar with many exercises that will encourage you to think of teaching in a very different way.
You will learn to:
As you read, highlight, underline, photocopy and printout sections which really ‘help’. This way you can find them and use them easily when stressful, ‘real life’ situations arise and put the exercises into practice. The more you do this, the more you will benefit from the guides and the more the exercises will become habitual.
Whether you have been teaching for twentyfive months or twentyfive days, it is natural for YOU to need support and the wonderful thing is that YOU have found an affirmation of how much YOU MATTER, how much the teaching profession NEEDS YOU and ultimately, what a wonderful resource YOU are for your students and colleagues.
In fact, I’m quite sure that you already know how remarkable YOU are. Everyone needs a little reminder once in a while. There is so much more of your potential waiting to be released and set in motion.