**Differentiate by Maths task? Have you checked out Mr Carter Maths yet?**

I have launched a new website and with that comes my first ever blog post! Busy exciting times.

So where to start? www.MrCarterMaths.com is something I have been planning for a while now, I am trying to solve the problem every Mathematics teachers comes across eventually, creating more questions. My site is dedicated to creating sets of questions that all use number generators to allow teachers or students to quickly create new sets of problems to allow practice and development. This is not a new concept and I am aware that there are plenty of number generators around, however I am trying to stand out from the crowd by making my website with the classroom in mind. All of the pages have been made with the intention of the being used on a large interactive whiteboard, with text large enough that even the kids at the back can read it!

Again with the classroom in mind all of the question from my site come in a bronze, silver, gold format allowing teachers to differentiate with ease. Hopefully allowing all of the pupils in the room to be adequately challenged. When they are ready teachers can share the answers with the pupils at the click of a button, in my own classroom I often use this as an opportunity to get the pupils to reflect and decide if the should be moving onto the next section.

When I started the project the obvious place to start was Addition, Subtraction, Multiplication and Division, since then I have managed to add a wide range to my site. Although there are a lot of topics for me to add, I have tried to start by tackling some of the more difficult areas first, for example both the Plotting Equations and Bar Charts pages provided challenges in terms of showing the solutions; nobody wants to see 15 bar charts at once!

Another challenge has been to display some of the more awkward areas of maths such as fractions and indices, in a manner that allows them to appear in a natural state. With the help of MathJax this has been achieved.

I plan to keep adding to my site weekly, until I have covered the content required for GCSE, once this has been done I will be looking to add features such as problem solving to give the site another level. Thanks to everyone who has shown their support so far, follow me on twitter (@MrCarterMaths) if you would like updates!

]]>Take a look at this great resource to develop the understanding of place value, addition, subtraction and number bonds. It took a while to create my own version of the resource but you can make your own if you want.

Create a 10 x 10 hundred grid and create a template scanner with flaps to traverse through the numbers on the hundred grid. Pupils will be able try and solve the calculation highlighted on the flaps and then lift it up to check if they were correct. The tool is great when introducing a 100 number grid and teaching number bonds but I can see many other uses for it. Make sure the flaps match the exact size of each of the cells on the number grid and ensure you use coloured card for maximal impact.

This idea can be extended by investigating n x n grids and would make a great observation lesson. Comments are FREE, please leave one below and let everyone know how you use the idea and resource.

]]>Some of the key buzz words in the educational world at the moment is pupil grit, resilience and perseverance, but how does one develop student mental strength? Below are some ideas to help you to start to think about developing your pupils’ mental strength and in the long term make them mentally strong. Encourage them to do the following;

- Do
**NOT**fear alone time. - Do
**NOT**dwell on the past. - Do
**NOT**feel the world owes you. - Do
**NOT**expect immediate results. - Do
**NOT**worry about pleasing everyone. - Do
**NOT**waste time feeling sorry for yourself. - Do
**NOT** - Do
**NOT**let others influence your emotions. - Do
**NOT**resent other peoples’ success. - Do
**NOT**shy away from your responsibilities. - Do
**NOT**give up after the first failure. - Do
**NOT**fear taking calculated risks.

**Skimming and Scanning**

Skimming and scanning are specific speed-reading techniques, which enable you to read a vast amount of material very rapidly. these two skills can be extremely useful when grasped yet quite tricky to teach.

Skimming and Scanning are two key skills identified in the Programmes of Study for KS2 Reading in the National Curriculum. These skills are important for educators to teach because they help children to read quickly when looking for specific information.They are not, however, skills that should be used all the time; they are not skills to replace reading for understanding but skills to enhance a child’s reading ability and repertoire.

What is Skimming? Skimming tends to be used to read only what is important. It can help you to pick up on main ideas within the text. Although the full meaning can sometimes be lost, it is useful to understand the ‘gist’ of something when reading for general ideas.

What Is Scanning? When scanning, a child looks for a word, specific fact or piece of information without reading everything. This tends to be used when you are looking for something specific.

These skills can be taught in the classroom through a variety of ways. They are great skills to have for life (and not just for doing well in School tests).

A few ways to teach this are listed here.

1. Give children a text and a short amount of time. Ask them to skim the text then report back to what it is about.

2. Similarly to above, explain to the children that a word, phrase or punctuation mark is used throughout the text. The child to find out how many times it is used in the quickest amount of time is the winner.

3. Ask children to find a specific word in a wordsearch. Explain how they could scan for the first letter of that word then look around the letter to see if the second letter connects etc

4. Using images such as the one below to spot words can help children scan and pick up on lines etc that are unusual compared to the rest of the picture. This encourages children to look carefully for a specific thing whilst ‘reading’ the picture. As the children get quicker at doing this a timer could be introduced. (Have a go at the one below. How long does it take you to find all 6 words?).

5. Similar to the idea above would be using books such as ‘Where’s Wally?’ This will really encourage children to scan quickly as it is all about training the eye to spot something the mind wants to find! Let your eyes work for you when searching for information and encourage children to use their finger to help focus their gaze.

By teaching children how to skim and scan in fun ways (and by helping them to do so in timed conditions) will ensure that they are are able to retrieve information quickly and have the skills needed to answer questions such as ‘find the word that means….’ or ‘What sentence shows that…’

For more information on testing, assessment and on how to make English lessons more engaging for children please follow Literacy Consultant on Twitter @jo_c_gray

Please see below for some more skimming and scanning pictures;

]]>Now these hidden word puzzles have been a massive hit on the web and people have enjoyed finding the missing words in these pictures and sharing them on their social networks.

Therefore, why not share 1 the 6 images below to your pupils as a starter to a lesson to get them focussed and engaged. The find the hidden word challenge makes a great literacy task in any lesson and could be projected on the interactive whiteboard with pupils coming up to the board to show their solutions. You have to admit these image words searches are so much better than the conventional word searches that some teachers use.

Comments are FREE, please let others know how you end up using these images in your lessons.

]]>**Lego Math in the classroom. Did you know that you can use Lego to teach Maths?**

Recently I have become very interested in conceptual variation – different representations of the same concept. It has become particularly important this year as I have inherited a class who has a poor understanding of key mathematical concepts, so I have been researching ways of developing depth in understanding. I am ashamed to say that as a Year 5/6 teacher I haven’t in the past used as much concrete and pictorial representation as I should have, it hasn’t seemed necessary. However, it definitely seems the way forward for my current class, so the children have been investigating a whole range of images and models. During the latest unit of work we have been exploring fractions, specifically equivalent fractions.

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Whilst trawling the Internet for ideas, I came across a photo showing the use of Lego to teach Math. The word Lego originates from the Danish ‘leg godt’ meaning ‘play well’, so imagine my pupils’ delight when the box of Lego arrived from Year 1 and they discovered that instead of drawing fractions of the usual cakes, chocolate bars and pizzas, we were going to use plastic bricks to learn. I began by letting the children represent some simple fractions so that they understood how different sized pieces could represent different ‘wholes’. For challenge, some of them were encouraged to use multi layers rather than a flat shape. Pupils then started to show non-unit fractions and, as a result there was some quality talk produced about the relationships between different pieces. In addition, some children independently started to make their own fraction addition calculations.

We then focused on the equivalence that I wanted to develop so, with some careful questioning, pupils investigated the relationships between fractions, using the Lego pieces for reference. To help less able learners I encouraged the children to use the same colour piece each time so that they could relate the colour to the fraction, as some seemed to find it difficult when the colour was different. I allowed pupils to record their work on the iPad so that they had a photo of their work which they had annotated.

Using the Lego gave a different context and it was amazing how some of the children who had a good understanding of fractions found it a challenge. Spatial issues were highlighted from those clearly not used to using construction toys much. Some found it quite difficult to find corresponding pieces that fitted patterns, and said they found it difficult to think in 3D.

The concluding part to the topic was an art session where we used the work of Mondrian to investigate equivalent fractions. The children related the Lego work to the art, and could describe the equivalence between different squares and rectangles. The children then planned and produced their own ‘Mondrian’ out of pastels and some did the same with Lego.

We certainly ‘played well’.

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**Casio Calculator – An explanation to that 2 different Casio calculator answer debate**

It’s Saturday. I’m out with Garstang Cycling Club, enjoying the lumpy roads that traverse the Forest of Bowland and waiting for the promised torrential rain which is supposed to stop us overheating on this cool March morning. We stop for a coffee at a fine Waddington café and I see this on Facebook from my friend Karen as I tuck into my bacon and Stilton panini:

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Well, this is easy. The one on the left is obviously right and the one on the right is obviously not right. I give it almost exactly no more thought and continue the bike ride up towards Pendle Hill, beginning to worry that we might be about to go all the way to the summit, then across the Ribble and past Stonyhurst College. Then my left crank falls off and I cycle four miles with just one pedal. You should try it. Mostly for the pleasure that arrives when you stop doing it. I call my wife to ask for a lift home and notice she’s come to the same conclusion about the two calculators as I. She’s also a maths teacher. She even has a degree in the subject and everything.

Someone else, another teacher, then disagrees. We dismiss her as obviously wrong but there’s something thoroughly logical about her explanation. It just doesn’t sit right with me however. I wonder, where is BODMAS/BIDMAS/PEDMAS/PIDMAS actually defined? It certainly wasn’t Euclid’s doing.

A video is posted. The apparently knowledgeable chap in the video (and I’ve not listened to it all the way through, I was busy watching the Tour of Catalonia on the tellybox) disagrees with my thinking. Further research brings up another video in which Professor Stein joins the 1 camp but then, two weeks later, changes his mind.

Let’s summarise my thinking:

6÷2(1+2) requires us first to work out 2 times (1+2). Why? Aren’t division and multiplication equal in precedence? Certainly. But 2 is fixed to (1+2) due to the absence of any multiplication sign. In the same way, 4n÷2n is 2. Rejecting that thought would lead to 4n÷2n being 2n². Another way of viewing this: we are commanded by BODMAS to dispose of the brackets first. If I have 6÷2(3) then the brackets are still there. I cannot yet divide 6 by 2. I can only rid myself of the brackets by multiplying 2 by 3. 6÷6=1.

However, I can find no evidence anywhere to suggest that this implicit multiplication should be dealt with differently from explicit multiplication. This page at StackExchange gave me some food for thought, in particular Greg Martin’s comment about spacing and scope, still however I saw nothing definite.

Then, while trying to answer my question about implicit multiplication and BODMAS, I found the now retired maths professor George Bergman of the University of California, Berkeley discussing the order of arithmetic operations. Revelatory to me was the following (my emphasis):

From correspondence with people on the the 48/2(9+3) problem, I have learned that in many schools today, students are taught a mnemonic “PEMDAS” for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If this is taken to mean, say, that addition should be done before subtraction, it will lead to the wrong answer for

a−b+c. Presumably, teachers explain that it means “Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction”, with the proviso that in the “Addition and Subtraction” step, and likewise in the “Multiplication and Division” step, one calculates from left to right. This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation fora/bc, namely, (a/b)c.But so far as I know, it is a creation of some educator, who has taken conventions in real use, and extended them to cover cases where there is no accepted convention.So it misleads students; and moreover, if students are taught PEMDAS by rote without the proviso mentioned above, they will not even get the standard interpretation ofa−b+c.

Also, from PurpleMath.com (a website written by Elizabeth Stapel, formerly of Western International University, Phoenix, Arizona) ’The general consensus among math people is that “multiplication by juxtaposition” (that is, multiplying by just putting things next to each other, rather than using the “×” sign) indicates that the juxtaposed values must be multiplied together before processing other operations.’

So, what have I learnt today?

Firstly, this problem almost certainly only exists because someone wrote it to create discussion.

Secondly, nobody seems to know where BODMAS (or whatever you choose to call it) came from. In all honesty, this is key to the debate!

Thirdly, this means whatever the author wishes it to mean and, frankly, without knowing exactly what problem the author was trying to solve, we cannot know a firm answer.

But the answer’s 1.

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This is definitely an example of when calculators get it very wrong and would make a great starter for discussion and debate in any Maths lesson. It appears that one of the calculators has not been taught the order of operations, can you tell which one? : )

Can you explain why this is the case? The original tweet caused a twitter storm and generated some interesting discussions. Comments are free, please leave one below.

]]>Can anyone explain why this is the case?https://t.co/HHGy47D3Sq pic.twitter.com/mUBKOgHuRq

— Magicalmaths.org (@magicalmaths) March 25, 2016

**Maths in a Multi Academy Trust (MAT)**

If you follow me on twitter you will know that I have not been positive regarding the White Paper published recently. Continuing tweets led me to clarify that I am not opposed to academies or MATs as such, but rather the wider issues surrounding academisation and wider issues included in the White Paper such as land, teacher training routes and curriculum requirements.

I have had a positive experience in my one term in a MAT. There are significant advantages in being one of a group of schools. I’d like to pick out a few of the highlights of this term.

I am a maths specialist and part of my role has been to work within a primary school. This has supported the primary staff but I have benefited by deepening my understanding of different key stages. Coaching staff in a different school has been a good experience and I will be encouraging teaching staff, where possible, to take part in a similar activity.

Students in primaries have visited the secondary school to use specialist Science facilities. This has wider benefits beyond the curriculum in that students are seeing the “big” school and this may reduce anxiety in transition.

Discussing schemes of work develops a through curriculum and one intended outcome is increased progress in Year 7. The increased knowledge in KS1 and KS2 outcomes can only benefit the KS3 curriculum.

Where used effectively schools can share resources such as minibuses and specialist staff. Having a subject specialist who can be consulted for support within a network is beneficial as they know the schools, the students and have existing relationships with staff. A fresh pair of eyes is always useful but a long term position allows for long term development; issues are identified and the solutions are supported.

These are the highlights of working within a MAT. I am fortunate to work in a setting where the students’ needs come first, demonstrated by a rich curriculum and freedom of choice. I am genuinely excited about the future and seeing how we can further develop cooperative working to improve the outcomes of children.

**Maths Teaching In My Classroom – a perspective from downunder**

In Australia we have a bird called a Bowerbird. One of its characteristics is that the male of the species builds a nest of bright shiny articles in order to attract a mate and will frequently spend hours re-arranging these objects to form an attractive display. Like the bowerbird, I amass a bright array of objects thus forming a hook which reels my students in to overcome the negative perceptions of Maths in the primary classroom. In vain I have told my students that maths is all around us: nature; music; shopping, to name a few; so now I use variations of three elements.

Firstly I use humour. The Murderous Maths series of books and website are an excellent source of humour and challenges which I find particularly useful in gaining student attitude. As I read the books aloud with students following, we stop at each problem or challenge and work it out in the classroom. This teaches students that Maths is not the dull irrelevant subject that many seem to think it is.

Patterns in Maths is another tool I use. This can be as simple as origami models – covers symmetry nicely; or even showing that knowing your 12 x 12 Multiplication Grid can help you find equivalent fractions (Thank you Magical Maths org for that tip!).

However, my best hook has to be knitting. Knitting covers so many different areas (pun intended)! It entails numbers, working mathematically and problem solving – dropped stitches anyone? Knitting also encompasses other key learning areas. History; fine motor skills; talking and listening; collaboration; mindfulness spring to mind immediately. At the moment, my year 6 class (all 29 students) are knitting either a scarf or a teddy bear. The boys in my class were more enthusiastic about knitting than the girls and I am asked on a daily basis if we will be knitting that day.

Admittedly, I am waiting until next term before explaining to them all just how much Maths they have covered! Perhaps I will wait till report time.

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