We have moved to www.greatmathsteachingideas.com

The site has been an amazing success since the launch in June this year. We’ve had over 1000 visitors from all over the world to the site since it started. Thank you to everyone who has supported the site since day one and I hope that you have found it a really useful place for getting lesson ideas, resources and a place that makes you think. I’m really enjoying developing the site and continuing sharing everything I find with you all.

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

www.greatmathsteachingideas.com

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!

An unusual way to teach plotting straight line graphs…

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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…

Angle facts- getting the language right

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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.

Teaching the properties of equality through problem solving- repost from Keeping Mathematics Simple

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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.

Draw me a rocket! SSS, ASA, SAS constructions task

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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!

4 great resources for teaching collecting like terms in algebra

Ever been teaching collecting like terms (simplifying) and just needed 20 questions you could put up on your interactive white board to set the pupils off on? Looking for the questions to be differentiated according to ability and for the answers to be on the next slide? If so, check out this pdf slideshow!

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!

Probably the best blogs by maths teachers around the world

Image by DavidErickson via Flickr

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: Read more of this post

Idea for ICT based homeworks; your thoughts and suggestions welcomed…

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Why do we set homeworks?

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.

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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: Read more of this post

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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.

How fast are the planets?

Which planet is travelling the fastest in its orbit? Which is slowest? Is there a link between distance from the sun and how fast the planets travel?

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!

The Fibonacci Sequence in nature

Image by lucapost via Flickr

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.

Thoughts on why kids struggle to understand fractions and proportion

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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. Read more of this post

What does the cube look like?

I created this worksheet based on a problem on the excellent NRich Maths website.

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.

New ‘Pedagogy’ topic- sharing thoughts, ideas and good practice

First of all let me say a HUGE thanks to everyone who has been following this website in the short two weeks that it has been running. As of today we have had 179 different visitors to the site from 14 different countries including 1 visitor from Brunei! People have been downloading the resources non-stop. In the first fortnight it seems as though the site is already helping maths teachers improve their practice and save time by sharing ideas and resources which was the mission from the start.

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.

Going through the praise withdrawal

Is giving lots of praise counter-productive?

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. Read more of this post

Giving rotational symmetry the ‘wow’ factor

This video is taken from the iTunes Visualiser called Jelly that makes pretty patterns that react in real time to the music that is playing. The patterns produced show rotational symmetry and could be used as an excellent resource in a starter or plenary on the topic.

Marathon Man Bearings

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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! Read more of this post

Pure inspiration- nature by numbers

This has to be one of the very best videos I have ever seen to show the beauty and power of maths. Just imagine all the ways you could use this to inspire the kids.

Rotational symmetry- synchronised swimming

Further to our post “Symmetry the fun way: B-boy dancing“, Mr Williams suggested a great idea of using synchronised swimming as inspiration for a lesson about rotational symmetry.

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.

Making 100

Pupils write out the digits 1 to 10 like this:

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!