10 Ways to Use and Apply in Maths

I’ve never wrote a ‘Maths’ blog before so this is my first attempt. I’ve spent much of my career in Y6 and one aspect I’ve worked particularly hard at is developing ‘Using and Applying’ (U&A) in maths. There are lots of definitions as to what U&A actually is however; I’m not going to get bogged down in this debate. In my opinion it’s less to do with word problems and more to do with reversing the transactional norm of a maths question. To clarify what I mean here is an ‘shape’ example:


The staple diet of this area of maths is to label a shape with its properties. Nothing wrong with this except it can be a bit ‘dry’ and for the most confident learners presents little challenge. To reverse the process try this; give pupils a list of properties, ask them to choose 5, then to draw a shape to meet the criteria they have set. Immediately pupils have to be creative, they have to USE their knowledge and because the teacher has not given a specific shape, learners have a lot of choice.

10 ways to Use and Apply across the maths spectrum:

  1. Area and Perimeter: Give pupils the answer first and then ask them to draw the shape. For example, draw an ‘L’ shape with a perimeter of 50cm. The same approach can be used for area; draw an ‘L’ shape with an area of 25cm². To extend this further create statements to investigate; for example, Rectangles with a perimeter of 20cm always have the same area.
  1. Measures: Reading scales can be notoriously laborious and often too easy for the best mathematicians. Try this though. Give the pupils a ‘menu;’ create a table with three columns, the first column is the ‘start number,’ the second is the ‘end number’ and the third column is the ‘number of intervals.’ In each column place 5-10 numbers. The pupils now have a menu to create their own scale.
  1. Shape: When the class are learning about different types of shapes or categorising triangles or quadrilaterals the concept is often picked up rapidly. To move the learning on create simple statements for the pupils; the pupils then investigate whether they are true or false (or sometimes a bit of both!) and provide evidence to support their view. For example:
  • An isosceles triangle could have a right angle.
  • A square can only be split in half along a line of symmetry.
  • Two rectangles can never make a square.
  • Two squares always make a rectangle.
  • A rhombus is half of a parallelogram.
  1. Line graphs. This is a simple one to set up; discuss with the pupils how line graphs often tell a story. Give the pupils a range of ‘blank’ line graphs; only draw the X and Y axes and the line. Do not label anything or put values on the axes. Pupils can either tell the story or create a title. This is a great activity done collaboratively. Over years I’ve heard some amazing stories!

  1. Rounding numbers; in my experience this is the archetypal ‘they’ve either got-it or they haven’t’ type lesson and when they’ve ‘got-it’ it doesn’t matter how many decimals places your throw at them it doesn’t get their brains thinking. Instead give the answer and pupils predict what the question could have been; for example. 6.7 has been rounded to the nearest tenth, what could the original number have been?

  1. Multiplication. If pupils learn the ‘grid’ method in your school, you’ll know that some get through the calculations as quite-a-pace. By giving the answer first the thinking begins. For example, A TU x TU calculation gives an answer of 475. What could the numbers have been and what would the completed ‘grid’ look like?
  1. Co-ordinates. This is an effective plenary idea if the pupils have been learning to plot co-ordinates in all four quadrants. Imagine the classroom is a grid and label each corner/area with the numbers 1-4. Give the class a co-ordinate and the pupils move to which quadrant they think the co-ordinate lives!
  1. Time: Calculating differences in time can be quite tricky for most. However, for some pupils it comes quite easily. Instead of asking pupils to find the difference between the start and finish times, give the pupils the answer and either the start or the finish time. For example, the time difference is 3hrs 56mins, the finish time is 06:34 – what is the start time?
  1. Odd one out: This can be used across maths. For this example I’ll use fractions. Write 5 fractions on the board; assign a fraction to each table/group in the class. The challenge of the table is to prove why their fraction is the odd one out. Always ask for evidence to support their argument.
  1. Plan the plenary. Again this can be used for any type or maths. This is a great idea to challenge those pupils who finish in double quick time. Their challenge is to plan a simple game/activity to finish the lesson that MUST help everyone reinforce their learning. The pupils must lead the game/activity. This idea takes some time to embed, but once it does the results are incredible.

If you have any other ideas, let us know – or even better, write them in the comments box below so they can be shared!

The Thought Weavers.


Preparing for Ofsted!

Last year I gave a presentation at the education show entitled ‘Preparing for Ofsted.’ I sifted through lots of Ofsted reports, founds patterns of ‘behaviours’ and looked for things inspectors seemed to be consistently asking for and produced a slide show based on my findings.

In February 2013, Ofsted paid my school a visit. As a result I’ve recently updated the slide show and below is the new updated version. I hope it will help you when your visit is due!

Preparing for Ofsted! 2013

<div style=”width:425px” id=”__ss_12069324″> <strong style=”display:block;margin:12px 0 4px”><a href=”http://www.slideshare.net/paceanderson/preparing-for-ofsted-nec-2012&#8243; title=”Preparing for ofsted! nec 2012″ target=”_blank”>Preparing for ofsted! nec 2012</a></strong>

<div style=”padding:5px 0 12px”> View more <a href=”http://www.slideshare.net/thecroaker/death-by-powerpoint&#8221; target=”_blank”>PowerPoint</a> from <a href=”http://www.slideshare.net/paceanderson&#8221; target=”_blank”>paceanderson</a> </div> </div>

Lee of the ‘Thought Weavers.’

Knowing me, knowing you! Building Positive Learning Relationships with Children

Knowing me, knowing you!
Building Learning Relationships with Children
Is there one child in your class who gets to you for all the wrong reasons? That one child who pushes all the wrong buttons. The one that makes all your behaviour modification strategies look futile. My friend Katy once described such a child.
She said “He just takes me to a place where I don’t want to go!”
We’ve all met the little terrors! They come in all shapes and sizes from 7 to 17. However, despite their differences many of them share very similar features.
The similar features/traits means they are:
Usually boys
Usually bored
Usually on the SEN register
Usually come from the same area/estate /neighbourhood
Usually have siblings with similar traits
Usually from dysfunctional families.
Right! We all know the sort of child we are talking about by now – don’t we?
Think about their behaviour in your lessons. How do they make you feel? What is it that they do that makes you feel so hostile toward them? Usually if you could have one wish it would be for them to move far, far away (this is totally natural as we have felt this way many, many times ourselves) However, the Likelihood of them moving away is about as likely you winning the national Lottery three weeks in a row. So what is the answer? Picture this little angel in your head and ask yourself some of the following questions:

What makes them happy? Scared?
Where do they go on holiday?
Who is their hero?
Who do they look up to?
What do they want to be when they are older?
What’s their favourite colour?
What’s their favourite drink? Food?
Do they have any pets?
If they had a super power what would it be?
If they ruled the world what would they change?
What do they think of your lessons?
What do they think if you?

If you can answer ‘I don’t know!’ to more than three of the questions above, then you are doing that child a disservice! You’ve almost written them off before you have even got to know them. We know that it’s very difficult, at times, to find something endearing about the disruptive little whirlwinds, who attempt to sabotage your entire lesson every week. But if we give up on them – who will believe in them?

The key to getting them on your side is building positive, appropriate relationships. It’s truly amazing what you find out about them once you start asking. The trump card you have up your sleeve is yourself and your life outside of the classroom! They love to know all about you! It’s a brave thing to do but done correctly it can move mountains.

You don’t have to share you home address, credit card details or the names of your first ever boy/girl friends. But let them know the name of your dog, your favourite food, football team, where you like to go on holiday, what you wanted to be when you were their age.

For the bravest amongst you; you could (God forbid) tell them your first name; the names of you family members; where you went to school. It goes without saying if the information you share is going to compromise yourself or close friends then keep it to yourself.

Once they know you a little better you become more three dimensional. You become a real person not just a 2D image of a name on an exercise book or on their timetable.

When they enter your classroom next time hit them with:

“How did your game go this weekend Jake?” or “Sarah did you go your aunties’s party last night?”
It’s way better than “Jake stop that and sit down!” or “Sarah did you write up that experiment like I asked you to?”

Don’t get me wrong they still have to be accountable and ‘write up the things like you asked them to…’ but the odd friendly ‘humanistic’ comment does break the ice.

“Where do I get the time to ask all these questions?” We hear you cry: the answer is direct and simple ‘make time’ think about the wasted minutes some of us use trying to redirect negative behaviour. You can create chances walking along the corridor, whist on playground duty, on the bus during school trips, diary entries, play scripts in literacy, planning and budgeting a day out (Maths), circle time or the 3 minutes packing up time at the end of the day. Say to yourself I’m going to find out one thing new about ‘x’ today and I will impart one piece of information about me. Try it the results are astounding!

Lee and David (The Thought Weavers)

“Education is the most powerful weapon you can use to change the world.” Nelson Mandela

The dancer in the classroom!

Sir Ken Robinson tells a great story about girl whose parents were terribly worried about her lack of concentration in class;

I also have a very similar story. (I have kindly been given permission by Lucy’s mom to use her real name and share this story)

Two years ago Lucy came into my class as an enthusiastic Y5 girl. However, there was a problem, or to put it more precisely, a reputation that came with her. Lucy couldn’t concentrate in class.

Lucy couldn’t ‘sit still’, she was ‘noisy’ and her energy levels never seemed to wane. I thought carefully about this, as her teacher I became concerned. I wrote to her parents to request a meeting. At the meeting her mom informed me that this was ‘Just Lucy’. At the time I felt a little unsupported, however, I look back now and realise her mom was spot on. Lucy was just Lucy. She can’t sit still, she likes being vocal and she loves moving around the classroom; it was my duty to adjust to Lucy, not Lucy’s job to adjust to school! I therefore went about thinking of strategies to help Lucy and her learning.

I first ensured there was plenty of movement. I facilitated lots of talk (P4C was wonderful for Lucy) and sitting at a table became a choice not an order. At home Lucy’s mom decided to see if Lucy would enjoy ice-dancing…She loved it! In fact two weeks ago she won her first competition!

In the words of Sir Ken Robinson, Lucy didn’t have a problem; she wasn’t ‘naughty’ – she was in fact ‘a dancer’, someone who loved moving! Even more importantly Lucy can still be ‘just Lucy’

Last week I took two classes, Lucy included, on a residential trip. It was a tiring but wonderful week, the children gained invaluable and immeasurable experiences and collaborated on a range of tasks. It quickly dawned on me that all of the tasks had something very much in common:

  • No activities were preceded with a learning objective.
  • Differentiation was decided by the youngsters themselves
  • No-one got things wrong and everyone made mistakes
  • Every pupil was challenged but not compared with each other
  • Adults allowed children to explore possible solutions
  • Nothing was neatly recorded in  books
  • Children were encouraged to set their own targets
  • There were no walls (Except for bed time!)
  • Children were smiling – lots!

Taking ideas from outdoor education centres is not just about asking children to identify trees in the wooded areas and having a camp fire. It’s also about using ideas like those above; where children were challenged but had choice, where they built their self esteem by making mistakes. When youngsters didn’t always have to sit still and be quiet.

Talk to any teacher and they’ll tell you the value of an outdoor educational experience. So what bigger hint do we need that classrooms (In their traditional sense) are not always the best places to learn, they’re just a small part of the wider picture.
On Monday morning the children walked into my classroom. It felt different though. Unnatural. Odd that these young people were forced to congregate in a room within a building called a school after hugely successful week in an environment very different from a school.

For the past five years I’ve researched, experimented and applied many theories to my pedagogical approach, taking every opportunity to tap into children’s natural way of thinking and learning. It follows that perhaps over the next five years my emphasis should be on the physical learning environment and how it can be used to help all children succeed.

I will make lots of mistakes, but after last week I feel confident that it’ll work out for the best!

Remember when children are ‘fidgety’ it’s because they don’t want to be still, when they’re not concentrating it’s because they’re bored and when they’re noisy perhaps they want to perform! Whatever the reason, it is our jobs to adjust to the needs of the children, not the other way round. I no longer worry about Lucy, she’s just fine!

The Thought Weavers

Praise and Motivation within the Classroom


The answer is No!

Ian Gilbert (Independent Thinking Company) says:

Be aware that we cannot really raise someone’s self-esteem for them, as it is not yours to raise in the first place, hence the word ‘self.’  All you can do is to work to create an environment in which their capability and lovability starts to come through. [1]

So what are you doing within your class/school to promote lovability and capability?

The answer is all in the ‘praise’ that we give the children.   Almost everyone enjoys praise; whether you are 7 or 70.  It’s a pleasant experience to hear you have done something well; but praise should come with a health warning:  If too much is used or it’s not targeted correctly it can be ineffective.   Some practitioners give out praise like confetti but as you have no doubt guessed four fifths of it is wasted and falls by the wayside.  Therefore (In keeping with the wedding theme) effective praise should be issued like the bouquet: directed and caught by just the one person.  However, it goes without saying that we don’t face away from the children and throw praise over our shoulder.

When issuing PRAISE think:

P = PERSONAL: Aimed at just one individual

R = REFLECTIVE:  The learner should be able understand they’ve received it.

A = ASSESSED: You, the teacher, should know why you are giving it.

I = IMMEDIATE:  Catch them doing the right thing and praise immediately.

S = SENSITIVE: Not all children like being praised in front of others.

E = EFECTIVE:  It should have a lasting impact on the learner.

There is nothing wrong with the Jim Bowen school of thought: lovely, smashing, super, great but if you want to promote effective sustainable learning you have to be concise with your choice and use of praise.

There’s a subtle but massive difference between:

 “Well done Sally super writing.”


“Sally the adjectives you have used to describe your character are super.”

 Sally will feel happy and contented with the first statement.  However, in the latter statement she knows exactly what she needs to do next time if she wants to receive that sort of praise.

The giving out of ‘stickers’ to reward children for the learning is also beneficial but remember that gratification I child receives from a sticker lasts about as long as the adhesive on the back.

Knowing the difference between ‘Intrinsic’ and ‘Extrinsic’ motivation was our starting point for issuing praise.

Dealing with children who were extrinsic learners, I soon came to understand that they were mostly motivated by external factors: stickers, certificates, house/table points, postcards home or the weekly mention in assembly.  Nevertheless, if (God forbid) they went a week without any recognition, this would have a major impact on their motivation and their ability to grasp new concepts within their learning.

On the other hand the intrinsically motivated learners sought their motivation from within – enjoying learning for learning’s sake.  They got their excitement or ‘buzz’ from learning a new piece of information, a new skill or after successfully revisiting an item with which they previously struggled.

To summarise we have found it most beneficial to be more succinct and to the point with our praise.   I’m not saying that we don’t, slip into the Jim Bowen role,  you may still hear the odd well done, great answer, lovely explanation within our classroom.

But we now have a greater awareness and you are more likely to hear:

“Thank you Harvinder for that great question, you really got me thinking then.”

“Super Idea Joel, I can see you’ve used the text that we’ve read earlier.”

“James that’s the second time you’ve used that strategy to solve that divisional problem well done,”

How do you praise and the reward the children in your class?  We would love to hear from you.

Lee & David (The Thought Weavers)

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[1] Source of Quote:  Gilbert, Ian, Essential Motivation in the Classroom.  (Routledge, Farmer,London) 2002. p.136

Letting Go – Letting Children Learn.

Giving Them The Wings To Fly – Letting Go And Letting Children Learn.

I can remember a few years ago I was complaining to a friend how tired I was with all the effort I was putting into my planning and the difficulty I was experiencing planning exciting lessons.  I began to moan about how time consuming the whole process was.  He smiled and casually asked,

“Are you busy planning for teaching or learning?”

The question hit me like a brick:  What was I actually doing?  Was I just actively keeping myself busy to justify my Local Authority salary or was I facilitating challenging, exciting, thought provoking learning?    His comments caused me to question my whole existence as a teacher.  I had to ask myself the question:

‘Within my classroom was I the fountain of all knowledge or was I the lead learner modelling the skills of how to seek knowledge?’

Was I the proverbial ‘Sage on the Stage?’ or was I endeavouring to be the ‘Guide on the side?’

I realised immediately that all I had done since I became a teacher was to act out the role of the teacher; in exactly the same way I had experienced it as a child.  As Ian Gilbert(Independent Thinking Company) says “I had learned to do as I was told and do it well.”   I had taken on the mantle of the expert – a role where the children had not only to guess what was in my head but more importantly what was contained within my planning folder.

The dilemma I then had was: How do I plan for learning?

I had sailed through a history degree and a PGCE in Primary Education and during this time  no-one had told me the difference between teaching and learning.  I must have also missed the seminar where they explained how exciting learning could be when the teacher ‘lets go’ and allows the children to become the co-authors of their own learning journey, of their own identity.

So how does one “Let go, so to speak?”

Firstly you have to remember that as the adult in the learning relationship we are naturally the ones with the knowledge and indeed most of the answers.  However, its not our job to dish the facts out willy-nilly – our job is to empower the children to develop skills so as they can seek the knowledge and facts for themselves.

A few practical tips that I suggest in helping practitioners to ‘let go’ is to immediately hand the lesson over to the children within minutes of starting. There is nothing as boring as hearing a teacher harp on and labour the point for 25-35 minutes of a lesson.  Let the learners know where the following lesson fits into the big picture and what they need to be looking out for throughout the lesson. Then explain the lesson objective: ‘We are learning how to…’   I am learning how to ….’

I usually start with “Today your going to learn something that’s going to transform your life!”

Whether is does or not; I guarantee you’ve got their attention.  Then throw the lesson open!

“Right two minutes with a partner; tell each other everything there is to know about 2D shapes…!”

You have engaged the children instantly and also assessed their prior knowledge.

Once you have them back; ask them to think of a few ‘High Order Questions’ (see our Blog from the 22nd May 2011 – Using Bloom’s Taxonomy in the Classroom.)  Again this is another speaking and listening; collaborative learning exercise.

Following this your teaching input could then last for approximately 10 minutes – This is where you demonstrate a concept or introduce and new piece of learning.  Once you have completed this its back ‘letting go.’

“Okay on your wipe boards create a few irregular heptagons; but they must have at least one set of parallel lines and one perpendicular line containing within them – off you go!”

After 10 minutes convene and share your ideas!  Address any misconceptions or misunderstandings – at this point you’ll know who is flying or who is struggling to take off.

Encourage the children to ask questions to devise a new set of criteria for the next shape (AGAIN IT’S THEM! AND NOT YOU!)   Trust me they will come out with some gems.

“Thank you Sophie – Sophie would like to see how many octagonal shapes you can create that are symmetrical and have no more than two obtuse angles – okay off you go!”

Finally the plenary can be used to sum up the learning; iron out any problems that are still arising; ask questions about how you can apply the learning into an everyday life situation.    Another superb way to achieve a quick assessment of a child’s learning is to say:

“Hamzah you are at a bus stop and the bus is coming and you’ve got thirty seconds to explain to Sheeva what you have learned today.”    The children love this and ninety five percent of the time if they can articulate it;  they can apply it using pen and paper.

I hope that has helped some of you!  If you are thinking you cheeky toad I knew all this already. However, so many times I have seen teachers with the best will in the world helping children to such a degree they actually protect them from failure and stifle all learning. So, whilst this blog may not be for you, the ideas may help colleagues within your setting.

There is a beautiful analogy about a small child helping a butterfly that was struggling to escape from its cocoon – click on the link below.

Remember all we do is help the children to develop their own wings so they too can fly.

Cheers David & Lee (The Thought Weavers)

There is a lovely story of a butterfly struggling to get out of a cocoon – check the link below:  http://www.brianchong.net/2011/04/the-butterfly/


I get knocked down…

Imagine the scene: You’ve at last got your interview for that Deputy Head post the one you’ve always wanted. You sit there in your brand new suit and tie, wriggling uncomfortably; is it the new shirt digging in? Or is it the fact that the suit lies dormant on your Visa account still waiting to be paid for; lying there unloved like a tube of after sun in Cold November. Hands are clasped, tight, sweating, slightly trembling – you casually but cautiously look around at the assembled panel of seven! Yes seven of them!

The lead assassin from the Local Authority stares at you with steely, slate grey eyes. Uncannily he looks a little bit like Bill Oddie but has the compassion and tenderness of Hannibal Lecter – he makes his move and unceremoniously, unsmilingly, unsympathetically draws the first blood. No soft sweetener to put you at ease; No! He goes straight for the jugular; asking a question so alien from the ones you have practised in your head previously; the ones that you have practised with your colleagues; with your family; even the dog had to go through the benefits of collaborative group work, safeguarding; rigorous monitoring and pupil assessment. The question! Oh the question – it still has to be answered! The neurons are screaming frantically in terror as they race around your head looking for the opening line, that ‘Obama slickness’ that will have them eating out the palm of your hand within seconds.

But nothing occurs! The line you are searching for refuses to materialise – that one precious line that could, so easily, save you from the degradation that lies ahead. What happened next is unforgivable and beyond reproach; the elastic band that attaches the brain to you lower jaw suddenly snaps! You’re now the proverbial rabbit in the headlights, in career free fall; falling faster and faster into the abyss. Into the cesspool of self doubt and uncertainty.

The opening question (still insufficiently unanswered) is followed by question after relentless question; each ones picks you up and slams you against the ‘metaphoric’ wall that has just been self erected within your psyche. You once again scan the room looking for a friendly glimpse of humanity, of empathy – but you know you are alone! Alone with only the two evil horsemen of humiliation and indignity for company.

Suddenly from behind the heads of the malevolent septet of distaste gathered before you; a glimmer of hope can be seen – a lifeline. Outside the window a small blue tit hangs upside on a branch, he pecks away nonchalantly at a lush green leaf completely unaware of the torture that he is witnessing through the window. I close my eyes for a brief second and wish we could change places; as I slowly open them again I look for him but alas – he has gone. Left me! Left me alone to be savaged by the baying crowd. Hungry for blood; hungry to stamp out the very last crumb of hope that is contained within my poor, dilapidated, decrepit ego.

Well that was the experience I had of my first ever interview for a Deputy Head post. Can you beat that? If so. I’d love to hear from you.

Oh by the way; ‘On this particular occasion I was unsuccessful’ – And the blue tit? Never saw him again!