I feel it’s time the site gets developed a little further and so have now moved it to:

**If you would like to continue to receive email updates from the new site please enter you email address in the subscription box on the right hand side in the new site.**

I really hope you like the look of the newly revamped Great Maths Teaching Ideas website and I look forward to continuing sharing the ideas and resources with you all in the future!

Thanks for your continued support!

Filed under: Uncategorized ]]>

I bet you’ve not seen this one before…

There is a linear relationship between air temperature and the number of times a cricket ‘chirps’ per minute. What an interesting idea for a lesson on plotting straight line graphs!

After putting across the idea of the relationship, and motivating the pupils by explaining how the next time they are out and about in the countryside and want to know what the temperature is they can work it out by listening to crickets, give them this worksheet which gets them plotting the linear relationship between degrees fahrenheit and chirps per minute. The worksheet is quite scaffolded and I took some artistic (mathematician’s) license to adjust the coefficients of the equation so that it was more appropriate for secondary school pupils to work with. After working out their table of values and plotting the straight line graph they are given questions that assess their ability to interpret the graph.

If degrees Fahrenheit means nothing to you (because like me, you are English) then you can move the lesson on by giving the pupils this worksheet that gets them plotting the degrees Fahrenheit to degrees Celcius temperature conversion chart. Note the slight increase in pitch with the decimal number coefficient and the negative axes. There are some more interpretation questions to follow once they have completed plotting the graph.

A really nice plenary to this lesson is to get a pupil up at the front and get them to do cricket chirping noises with the rest of the class counting how many they made in a minute. The class then have to use the graphs they have plotted to work out the ‘temperature’ in both degrees Fahrenheit and Celcius.

Great fun and a bit different than teaching this topic from a dry textbook…

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Filed under: Algebra, Using and Applying Tagged: Celsius, chirp, coefficient, conversion, crickets, Fahrenheit, graph, interpretation, linear relationship, minute, straight line, Temperature ]]>

How many times have you marked a GCSE paper which is a two-pointer where the question asks “find the size of angle x” and then “explain how you worked this out” to find that the pupil got the size of the angle correct but wrote an explanation that didn’t get the second mark? You kind of knew what they meant in their explanation, but the mark scheme was looking for “interior angles in parallel lines are supplementary” rather than “the angles next to the lines add up to 180”.

Here’s a very simple worksheet that I made to teach a lesson on using the correct language to describe angle facts. The idea is that you run through them with the pupils filling in the explanations on the worksheet which they can then use as a reference sheet when attempting questions later in the lesson.

I found a great way to start this lesson off is to ask the pupils to solve a typical angle fact question with an explanation of how they worked out the angle. The plenary is then exactly the same question followed by them comparing their answer at the end of the lesson with the answer they wrote in the starter to see how much they learned during the lesson.

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Filed under: Shape, Space and Measure Tagged: angle, angle facts, complimentary angles, Supplementary angles, vocabulary ]]>

I’ve found getting some pupils to understand the concept of equality to be surprisingly difficult. The problem seems to limit pupils’ ability in many other topics such as equivalent fractions, solving equations and changing the subject of a formula. I stumbled upon an article the other day that gave me some insight into why pupils struggle with it. When you do a calculation on a calculator, what button do you press to get the answer? The equals button. The article argued that kids think of the equals sign as an ** operator**. Kids see the equals sign as something you press to get an answer.

Enlightened with this possible explanation for kids’ misconceptions, by fortune I then came across an interesting blog post by the excellent Keeping Mathematics Simple blog called “How to teach the properties of equality through problems solving“. The author puts forward a way of teaching the topic of solving linear equations. Her method, of focussing on developing the concept of equality first, before moving on to solving the equations later is logical and well thought through, ensuring there is no misconception about the properties of equality before teaching how to solve the equations.

When teaching solving linear equations (or similar) in the future I think I’ll experiment first with giving them something like 2x = 10 and ask them to come up with 5 equations based manipulating the first one (do the same to both sides etc…) e.g. 4x = 20, 2x + 2 = 12 and so on. They could produce a spider diagram with the starting equation in the middle and alternatives off on legs. Once they solve for x they can then subsitute it back into all of their equations and they’ll see that the statements of equality still hold true. Hopefully this will help develop an understanding of the properties of equality which is so important if their learning of solving equations is going to be anything less than procedural.

Filed under: Algebra, Pedagogy Tagged: equality, Equals sign, Linear equation, misconceptions, problem solving ]]>

If you’ve just taught SSS, ASA and SAS triangle constructions and you are looking for a consolidation activity, checkout this ‘draw me a rocket’ compound construction activity. As far as rockets go it’s quite basic but if they get it done first I’m sure they could add some modifications!

Filed under: Shape, Space and Measure Tagged: asa, compound constructions, constructions, rocket, sas, sss, triangles ]]>

Instead of a list of questions, how about giving the pupils a ‘collecting like terms pyramid’ to climb! The worksheets work in the conventional manner where the bricks above are made by collecting the like terms from the two below. The worksheets are differentiated as easy and a bit harder.

Alternatively, just looking for a conventional worksheet, but one that has lots of scaffolding with worked examples and an explanation of the process? If so then check out this worksheet!

Hope you find these resources handy!

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Filed under: Algebra Tagged: algebra, collecting like terms, simplifying, slideshow, worksheets ]]>

There are some really great blogs out there written by maths teachers who really care about their practice. I enjoy reading their posts as they share their insight and ideas and think about how it could improve my own teaching.

There is wheat and there is chaff out there. To save you time in separating the two, I have compiled this list of the best blogs I have found so far:

Written by the highly witty and entertaining Kate Nowak, I love this blog for lots of reasons. I find Kate’s perspective on things quite different to my own and I usually come away from reading one of her posts with lots of new ideas in my mind. Her recent post “Union” looked at the similarities between teaching maths and performing yoga of which there are more than you might think!

I find her blog a useful way of ‘keeping the big picture in mind’ rather than becoming obsessed with the details all the time. A definite must read.

One of the best blogs I have found discussing pedagogy in maths teaching. Based in the Phillipines, Erlina Ronda blogs regularly in pursuit of her mission:

“This blog isn’t about making math easy because it isn’t. It’s about making it make sense because it does. This blog is my contribution to narrowing the gap between theory and practice in mathematics teaching and learning”.

There are regular blogs about using Geogebra effectively in teaching maths. Her most recent post, “Geogebra and Mathematics” provides a useful oversight of the potential for using Geogebra in high-quality maths teaching and learning.

Typical of the quality and thought provoking posts on this blog is “Teaching algebraic thinking without the x’s“. A great read for anyone thinking about how to introduce algebra.

An insightful blog, regularly updated that is well worth your attention.

A highly entertaining and informative podcasting maths blog. You could point interested high-attaining pupils to this site or listen to the podcasts yourself if you are looking for ways to jazz up your lessons with interesting ideas.

Their most recent podcast, “Infinity and Beyond!” explores the ideas behind infinity in lots of ways including Zeno’s Paradox and thinking about about different sizes of infinity. There is even an infinity joke too!

There is a link to where you can download their podcast from iTunes which you could direct your pupils to if there were interested in listening to it on their iPods.

Definitely add this site to your favourites.

As the name suggests, this blog, written by a colleague of the Keeping Math Simple blogger Erlina Ronda, is about the pedagogy of teaching mathematics and how we can enrich our teaching with multimedia. The author of this blog, Guillermo Bautista is an expert in using Geogebra within his teaching and has written numerous tutorials for the beginner-intermediate and advanced users. Over 30 tutorials are online currently and he is adding more all the time.

There are links to free online e-textbooks that you can distribute to your pupils if you so wish, links and reviews of many different pieces of software that you can use to enhance your teaching.

His recent post “Mathematics and Multimedia Blog Carnival #2” showcases a compilation of fun and inspiring maths teaching ideas that is certainly worth a look.

Together with Keeping Math Simple, this blog provides useful instruction and many interesting ideas.

This well established, excellent blog is written by American maths teacher Dan Meyer. He has strong views on pedagogy, particularly on how textbooks serve to restrict independent mathematical thought. Dan has appeared on TV and been a guest speaker for TED. Check out his TED talk below.

I personally subscribe to Dan’s blog, reading his posts with interest. I must admit, I don’t always agree with his methods which promote removal of lots of scaffolding and the use of open ended tasks. We’ve all been infront of a class that we’ve given an open ended task to to see them freeze and not be able to show any form of independent thought or intuition. In a world where we have to show near continual progress I think it would be a brave teacher who’d go with these methods wholeheartedly. Nonetheless there is a nagging voice deep in my mind that says that, whilst he is perhaps quite idealistic, he could be totally right, and by persevering with these methods, kids might perform better. They may be starting from a low level, but if we don’t give kids the chance to use independent thinking then they may never in their school careers.

A great blog with lots of quality content to get you questioning the way we teach.

Everytime I find a good maths blog I add a link to it on my ‘blogroll’ which can be found on the right hand side of this page. I’ll also send out a post letting you all know.

I hope you’ve found this post useful and if you have any thoughts or suggestions of other great maths blogs feel free to get in touch in the comments section below.

Cheers!

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Filed under: Algebra, ICT, Pedagogy Tagged: algebra, Best maths blogs, Blog, blogging, Dan Meyer, Education, Geogebra, ICT, independent thinking, independent thought, multimedia, podcast, TED, textbooks, tutorials, useful blogs ]]>

What is the point of homework? What are we trying to achieve by setting the kids homework?

Consolidation and practice of what was learnt in class? Promoting self-study skills and independent thought? Learning of new concepts?

I’d like to think we set homework for all these reasons. It is well known that getting the kids doing homework improves their attainment in maths. Colleagues I have discussed the topic of homework with have commented that they find that lagging the topic of the homework approximately one week behind when the topic was studied in class leads to better attainment. This is perhaps unsurprising as it promotes the revisiting of previous learning to secure long-term memory retention. If you haven’t seen the Ebbinghaus Forgetting Curve before then you really must look at it now! It doesn’t tell a good teacher anything new or surprising, but does answer the question that perpetuates through every staff room: “why can’t the kids remember what they learned last week?”. Revisiting concepts is the key to long-term memory rentention. Repetition, repetition, repetition.

We use the brilliant MyMaths software for some of our homeworks. Student voice surveys we have conducted suggest that on the whole, pupils enjoy doing the online homeworks more than conventional book-based ones. This isn’t surprising since most modern pupils feel more comfortable infront of a computer than a textbook. The big bug-bare we have as teachers about the online MyMaths homeworks is that the kids type their answers into the software and don’t have to record their workings. As teachers we are more interested in their route taken to the solution rather than the final destination itself as this shows up misconceptions in understanding.

Our pupils must never lose the skills of putting pen to paper to show workings through maths problems. I do wonder sometimes how we can combine the engaging ICT format that seems to motivate kids so well with the traditional skills learned through textbook homeworks. In short, I haven’t any perfect answers, only ideas. I’m not sure whether the ideas have value and are worth trying so would really appreciate your thoughts in the comments section below!!! Here are a couple of ideas I have been pondering on recently:

I may experiment with printing out (and photocopying) the online MyMaths homeworks for the pupils this year, getting them to stick the page in their exercise books and making them do their workings in their books before they then type the answers into MyMaths. The kids could then do self-assessment using the automatic marking MyMaths provides. The impact of this strategy on the photocopying budget might have to be investigated though!

Imagine setting your pupils a homework on adding fractions with different denominators. Imagine you send them to a Youtube video that features the following:

- Explains the learning objective (to add fractions with different denominators)
- Explains the concepts involved, emphasising on understanding rather than methodological processes.
- Worked examples of some questions.
- Presentation of questions that the pupils must complete for their homework. The kids pause the video here and do the questions.
- Answers to the questions (without workings shown so they can’t cheat and just skip to this bit).
- Encouragement of the pupils to self assess on how they did on the questions and what they have learned.

My idea is that the videos would not be like the conventional ‘how to add fractions’ videos you find online. Nearly all of them just use demonstrating and modelling as teaching strategies and rely upon the viewer to absorb what is being presented rather than engaging them in the learning of the concepts. My videos would be much more focussed on ** active learning** techniques using strategies like “pause the video now and think about what comes next” or “pause the video and try to work out a rule for describing what we have just seen”. Getting the pupils actively thinking and engaging during the conceptual explanation stage is rarely ever done on ‘how to’ maths videos.

Academically speaking, I was a late developer and my maths understanding didn’t really blossom until I was at university. I owe a great deal to a single book, or should I say tome, called *Engineering Mathematics* written by K. A. Stroud. The book starts literally by teaching you how to count and ends up with you manipulating functions with complex variables! What is so special about the book is that it is set out unlike any other textbook I have ever seen. The format is based around ‘frames’ which are small nuggets of learning that build off what was covered in the previous frame. Many frames end in a question that you have to work through with the answer shown at the start of the next frame. By using this format, not only is the learning well structured, progressive and planned, it is also based on active learning techniques that requires you to engage with it at each and every stage, barely reading five sentences without you having to challenge your understanding to answer a question. I would see my videos as a visualised format of similar learning techniques used in *Engineering Mathematics*.

Production of the videos would take a while but I wouldn’t see each one lasting more than 10 minutes. The Jing software is an excellent resource for producing short videos which just screen capture your PC. You can just record your giving of the lesson on your interactive white board and it will produce the video for you (and upload it to Youtube if you have the Pro version). It would be an ongoing project that would mature over a period of years if it was shown to have value in improving learning.

I ponder ideas like these all the time yet don’t always have the experience or confidence to choose which ones are worth thinking about further. I’d love to hear your thoughts and ideas about what I’ve discussed above to get another perspective on them. If you think you can contribute something please feel free in the comments section below. Many thanks and let the discussion begin!

Filed under: ICT, Pedagogy Tagged: Active learning, homework, Jing, Learning, MyMaths, student voice, video, Youtube ]]>

There are some excellent resources on the TES website and Properties of Quadrilaterals Dominoes is one of them. Not much explanation needed; just match the shapes to their names and properties in a game of dominoes… The resource was created and published by the www.notjustsums.com website.

Filed under: Shape, Space and Measure Tagged: angles, dominoes, game, parallel, properties, quadrilaterals, shape, sides, Tile Games ]]>

Start by asking the students to come up with what information they would need to work this out. You can then take their ideas and if necessary lead them to working out each planet’s speed by doing the distance travelled in it’s orbit (assume circular orbits) and the time taken for one complete orbit (a planetary year).

You can Google the orbit radii and planetary year times in the lesson. Get them to convert the units; if the distance is in km, get them to convert to m; if the planetary year is in earth years, get them to convert to seconds etc. They could even use standard form to work with the large numbers involved.

This idea came from watching Mr S teach a lesson which was based on using pi in real applications. In fact, the task uses many areas of maths including speed = distance / time, units conversion, compound units and standard form.

An engaging using-and-applying investigation for a high-attaining group. Cheers Mr S!

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Filed under: Number, Shape, Space and Measure, Using and Applying Tagged: circular, circumference, compound units, distance, orbits, pi, planetary year, planets, radii, seconds, solar system, speed, standard form, time, unit conversion, units, years ]]>

As the end of term draws near we are all looking for lessons to inject a bit of fun into the last two weeks of term. I need some display work for my classroom so am getting the pupils to create posters about the famous mathematician Fibonacci.

After introducing the Fibonacci Sequence, I then showed the pupils this presentation which shows where it turns up in nature. We also talked about Fibonacci and how he was actually called “Leonardo of Pisa” and how he brought the base ten number system to Europe. We also drew some Fibonacci spirals and then looked at the shape of a Nautilus.

The pupils were astounded by the presentation and it really inspired them. One of them even asked me “did God use the Fibonacci Sequence when he built all the universe?”! One of them then said “Sir, we are made up of Fibonacci numbers too; we’ve got 1 nose, 2 hands, 5 fingers etc…”. He then said he was going away to look at animals and see if they have numbers of limbs and features that were Fibonacci numbers. Isn’t this what we are aiming for in our pupils? Initiative, enquiry, curiosity, questioning. Great!

They have all gone away super keen to find out more about the great man and to gather things to put on their posters next week.

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Filed under: Number, Using and Applying Tagged: base ten, Fibonacci, Fibonacci number, Fibonacci Numbers, Fibonacci Sequence, Fibonacci spirals, Golden Ratio, Leonardo of Pisa, Number Theory, petals, phylotaxis, pineapple, pinecone ]]>

I’m at the very beginning of my teaching career. Amongst the day-to-day business of teaching, whilst on my PGCE I spent quite a lot of time thinking about how to break down mathematical ideas into key concepts that the kids could understand and thought about how best to communicate them. I found this time valuable and illuminating as it challenged my own deep understanding of concepts that I’d taken for granted. The area of maths that I have so far found most interesting to think through in this way has been proportion and the link with fractions.

Why do so many kids really struggle to understand the idea of proportion and also how you can represent it as a fraction? I’m not sure for certain but I think one explanation is that** *** they don’t understand division*.

I remember sitting in a dingy, damp mobile classroom about 15 years ago, when I was in Year 8.This building did not inspire learning with it’s bouncy, rotten, squeaky floor boards and noisy, single electric heater that occasionally emitted a puff of luke warm air that kept the frost bite at bay during those period 6, dark lessons at the start of the spring term. Fortunately the inadequacies of the learning environment were counterbalanced by the inspirational, eccentric maths teacher, Mr M. He rode the boundary between challenging us and making us feel totally stupid but had a sense of humour sharper than iced lemon juice that endeared us all to him. Mr M flat out refused to teach procedures. We spent many lessons focussing on concepts alone, talking them through as a class endlessly with Mr M steering the conversation like a helmsman in a yacht race, keeping it moving towards the goal despite us zig-zagging off on conversational tangents.

Despite the time we locked Mr M in the store cupboard, the most vivid lesson I remember was about proportion. Mr M asked us “somebody explain to us what division is”. What seemed like a minute later, but what was probably 20 seconds, he asked us again. After another deathly silence he finally relented and went into an explanation of what we would today call chunking. He explained the idea of separating things up into groups of a certain size and then counting how many groups you have. In hindsight I feel ashamed to not have understood this in Year 8 but in my defence would say I remember learning division procedurally at primary school rather than by chunking.

Division is a double-edged sword. There are two ways of looking at it and I personally wonder whether we need to show kids both ways, rather the one way most teachers convey it.

The first way of looking at division is through the chunking method. If I want to do 10 divided by 5 I imagine I have 10 of something, split them into groups of 5 and the answer is how many groups I have. This is the method now commonly taught in primary schools and the kids seem to really understand it (on the most part). 20 divided by 5 becomes the question “how many 5s in 20?” and the kids are happy answering it. It’s a nice visual method that link to the times tables, showing how division is the opposite of multiplication. The idea of remainders is also tangible and consistent.

The second way of thinking about division is precisely the opposite of the first way. When doing 10 divided by 5 we said split into groups of 5, how many groups do we have? **We could equally have said split 10 into 5 equally sized groups, how many in each group? **Think hard about this last sentence and really get it clear in your mind. Division is a double-edged sword because you get the same answer whichever conceptual model you use for *x* divided by *y*:

- Split x into groups of size y, how many groups do you have? or,
- Split x into y number of equally sized groups, how many in each group?

The first conceptual model, which for ease I’m going to call * the chunking model*, is useful when you use division in arithmetic. I put forward that we should consider actively teaching the second conceptual model for division, which I’m going to call

If we were teaching fractions and wanted to show 2/6, many of us would draw a shape, lets say a circle, split it into six equal sized sectors and colour in two of them. This conceptual model of showing fractions is simple to understand and shows the idea of proportion very clearly but is, I would put forward for your consideration, a poor model. It communicates the idea of proportion well but that is it. In another lesson we would then teach the kids that to turn 2/6 into a decimal they do the division sum 2 divided by 6. We tear our hair out trying to enlighten them with the fact that 2/6 and 0.3 recurring are the same thing but many of them don’t see it.

Is there any wonder? Think back to the conceptual model we used to explain 2/6 as a fraction. We ‘divided’ a shape into six equal pieces and coloured in two of them. If you are going to look at fractions as division sums, which I think we have to if we are going to try to explain that they are equivalent to decimal numbers, then to explain 2/6, why are we taking one of something, splitting it into six pieces and colouring in two of them? The conceptual model is neither the chunking model or the proportional model. The problem is that we are thinking of the ‘whole’ as being unity rather than the numerator. If it were the chunking model we would say we start with **two** circles and split them into ‘groups of six’, how many groups do we have? We obviously don’t even have one whole group but we do have part of a group, two out of six of one group of six. This gets across the idea of proportion as well as providing a conceptual model for representing fractions that is consistent with thinking of them as division sums, which should make the link between fractions and decimals clearer. If we use the chunking model the “whole” is taken as the number of things in one group (the denominator).

Alternatively we could teach 2/6 using the proportional model which would take **two** circles and split them into six equal sized pieces and asking the question “how much of a circle is in each piece?” which also conveys the same fractional part which is less than unity, the idea of proportion and a model that is consistent with division. If we use the proportional model the “whole” is taken as unity.

To sum this up, when we are explaining fractions and the idea of proportion, shouldn’t we use a conceptual model that incorporates the idea of division which we then teach them is necessary to convert them into decimal numbers? The link between fractions and decimals is much clearer and they still learn proportion. If students learn fractions are actually just division sums then this will dispel the common misconception that fractions are pictures showing proportion rather than actually also being numbers themselves.

This is all quite higher-order thinking and something that should definitely not be taught to your average year 7. It would blow their mind and they would never want to set foot into your classroom again! What about discussing the different approaches with your level 8-10 pupils though? Rather than teaching them the procedural routines those kinds of kids absorb and replicate so freely, why not also show them (if time allowed) the different conceptual models and see what links they can make to other parts of maths. Let them see why a fraction is equivalent to a decimal number rather than them just accepting it because you said so. If they understand why 12 divided by 4 is the same as 6 divided by 2 using the chunking model and they looked at fractions as division sums, wouldn’t they get a whole new perspective and understanding of equivalent fractions? Wouldn’t this make their understanding of algebraic fractions where they need to change the denominators to match by using equivalent fractions so much better?

No one model is perfect for all topics. If you think about it the chunking model is totally inappropriate for explaining how to calculate sector angles in a pie chart, the proportional model is much better. I don’t intend to stray far from the traditional path early on in my teaching career. Much smarter people than me have been teaching the traditional conceptual models for a long time. Nonetheless, I will keep thinking about when it might be appropriate to dip into alternative conceptual models if they have the potential to boost understanding.

Your thoughts on any of my mumblings above would be appreciated. Please add to them in the comments section below and fuel the debate!

If Mr M is still around he should feel proud for asking that question “what is division?”. It is about 15 years too late but I think I might now just about have a reasonable answer. Sorry Sir…

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Filed under: Pedagogy Tagged: concepts, division, fractions, proportion, whole ]]>

The pupils have to use their skills of visualising 3D shapes to draw patterns on the faces of a cube net after deciphering where they should go by looking at 3D views of the cube. To scaffold the task an actual cube net is also included so they can build what they think is the right solution. There is a nice extension for the future engineers who have excellent visualisation skills.

I found this to work well with medium-to-high attaining year 7 and 8 classes.

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Filed under: Shape, Space and Measure, Using and Applying Tagged: 2D, 3D, cube, net, nets, patterns, puzzle, visualisation, visualising ]]>

To build on the great early success of the site I’ve introduced a new topic of blog posts called ‘Pedagogy’. You’ll see it in the menu at the top of the page. The idea is to blog about pedagogy: *the method and practice of teaching *sharing things that I have learned, experimented with or good practice other people have written about. Will it be subjective? Of course. Will I change my mind about things as I become more experienced? Undoubtedly. Is it still worth blogging about? Definitely because healthy debate and reflection is always a good thing, for beginners just as much as for experienced pros.

This area of the blog will be much more interesting if people get involved in the debate, sharing their thoughts and experiences. You can do this by simply submiting them in the ‘comments’ section at the end of blog posts. Let me know what you think of my first pedagogy blog post Going through the praise withdrawal.

Thanks again and I hope you keep finding the site useful and thought-provoking.

Filed under: Pedagogy Tagged: pedagogy ]]>

It seems as though recent research is suggesting so. Too much praise apparently can send the message that you are surprised the kids can solve the problems you set them and actually leads to them becoming demotivated. The idea is simple: *give strong praise less frequently as it will have more effect*. Praise, like any verbal or physical action, gets less effective the more frequently that you use it.

How do you give less praise yet still convey enthusiasm for the subject? Apparently the answer lies in distinguishing between praise and feedback; understanding the difference between “you’re right” and “that’s truly awesome, well done!”. It is important that when you cut back on praise that you don’t cut back on feedback.

Rebecca Zook has written a blog post (I wanted to say an awesome and thought-provoking blog post but had to restrain myself) called Toning down the praise which explains where this idea has come from and her reflections on how moderating her use of praise is going. She points out how giving lots of praise to right answers can actually discourage the kids from taking risks and sends out the message that wrong answers are of no use which is of course totally the wrong message to be broadcasting!

If we want to encourage an environment of creativity, enquiry and learning shouldn’t we be giving praise to thoughtful, logical, albeit wrong answers as much as (if not more than) correct answers based on recall rather than understanding?

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Filed under: Pedagogy Tagged: cutting back on praise, feedback, less praise, more feedback, praise, Rebecca Zook ]]>

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Filed under: Shape, Space and Measure Tagged: iTunes, jelly, patterns, rotational symmetry, video, visualiser ]]>

In 2009, comedian Eddie Izzard ran 43 marathons in 51 days around the UK. He endured blisters, losing a toenail and damaging an ankle ligament. He also had daily ice baths which, in his own words, were “to stop your legs inflating to the size of an elephant”! After running over 1100 miles he returned to Trafalgar Square on 15th September 2010.

This is a fascinating story and one that you can use to inspire your pupils! The idea is that pupils have to use bearings and scale measurements to describe his route. This is a nice task that you can get the pupils to do to test their knowledge after they have some familiarity with bearings.The BBC made a great series of programmes following him during his run and the first five minutes of the first episode sets the scene quite nicely:

You can then give the pupils this worksheet which explains the task. You may find it appropriate to model on the board how they can approximate the route as a series of straight lines and then how to take the bearings. In addition to taking the bearings they can use scale measurements to estimate the distance of each part of the journey they are describing. You may find it useful to print the worksheets on A3 paper to make them a bit bigger and easier to take the measurements from.

To finish up this task you can show them the video of Eddie crossing the finishing line:

In addition to making bearings a bit more interesting, it gives the pupils an extra opportunity to develop their literacy skills.

Enjoy!

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Filed under: Shape, Space and Measure, Using and Applying Tagged: BBC, bearings, Comedian, Eddie Izzard, marathon, measurement, scale, story ]]>

No further comments needed!

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Filed under: Algebra, Number, Shape, Space and Measure, Using and Applying Tagged: Fibonacci Sequence, Golden Angle, Golden Ratio, Insect wings, nature, number patterns, Phi, sequences, Spiral, Sunflower ]]>

Here is the Japanese Team in full flow at the Sydney Olympics:

There is an excellent routine at about 2 mins into the video which has some fantastic rotational symmetry in it. You could freeze frame the video here and use it to demonstrate the concept.

There are endless possibilities you could go on with from here: could they design their own synchronised swimming pattern/ routine and draw it or act it out on land, get them in the pool for a cross-curricular link if you have one or could they do some research for a homework to find as many pictures showing rotational symmetry in sports and other applications as they can? Great fun.

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Filed under: Shape, Space and Measure, Using and Applying Tagged: rotational symmetry, symmetry, synchronised swimming, using and applying ]]>

1 2 3 4 5 6 7 8 9 10

The aim is to create an expression that equals 100 by putting as many + – X and / signs between the digits as they like. You might like to demo one like this:

1 2 3 + 4 5 6 X 7 / 8 – 9 = 123 + 456 X 7 / 8 – 9 = 513

Obviously this one is too high but it does illustrate the method. You can decide whether the pupils must use BODMAS or not (I’d suggest they do!) and whether they are allowed to put brackets in as well.

There are many solutions and you might like to post them in the comments section below when you find them!

Thanks to Cat for this engaging little starter. It might make a brilliant homework too!

Have fun!

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Filed under: Number, Using and Applying Tagged: addition, arithmetic, bodmas, division, homework, multiplication, problem solving, puzzle, starter, subtraction, using and applying ]]>