resource missing

Something old, something new…

Thoughts and Ideas, Website /

I’ll admit to having to cheat a little bit on this challenge; this post is one of the few I had to write ahead of time and schedule to post later. I have a good excuse – I’m getting married today, and I imagine that, even though my fiance is very understanding about the amount of time and energy I put into teaching, even he would object if I blogged during our wedding day.

​While I’ve been organising over the summer, I realised that my resource collection has grown exponentially again this year. I made the move to storing resources electronically this year, which has meant I’m drowning in far fewer bits of paper and it’s much easier to find the worksheet I want than rifling through folders. Despite this, I still have my entire cupboard under the stairs full of bits and pieces that need transferring or updating – I think it’s going to be an endless task.

Finding, developing and trying new resources is one of my favourite parts of teaching, which is one of the reasons I started the resources pages on my site- it’s far easier to link to a page at home, then find that again at school, rather than email things to myself, which I then forget about the following year. As above, this project is still unfinished, but I hope to put a big dent in it over the next few weeks. But what makes a good resource?

Something old…

Anyone who knows me is aware that I have a hoarding problem. I struggle to throw anything away – this extends to all aspects of my life, not just teaching resources, and our (fairly small) house is filled with my “junk”. However, some of my favourite and best lessons or resources are those that I’ve had the longest, and I still use them every time I teach a topic. 

For example, I wrote a worksheet for interior angles in polygons for my first observation for my GTP, which makes it about six or seven years old. It was originally designed for a group of Year 9s with high literacy needs, so it’s a write-on sheet with plenty of step-by-step guidance and help to structure answers, but it works every single time I use it, so I continue to do so.

Sometimes you have to be careful though – due to my magpie-like tendencies to keep everything, I do keep some stuff that, quite frankly, is either rubbish or needs serious adapting. I look at resources and think “oh, I’ll adapt that at some point” – I’ve just checked the dumping folder on my computer and there are currently 462 files in there waiting to be updated or changed. With the huge wealth of resources available on the Internet now, it’s easier to just delete or bin a sub-standard resource and find something better.

While I’ve been writing and updating our KS3 and KS4 curricula this year, I’ve been pulling in a lot of “old” resources. Tidying up my storeroom at school, I found a load of pre 1990s textbooks (which makes some of them older than me!). Before I binned them, I had a flick through – lo and behold, lots of Venn diagram questions! They’ve joined the shelf marked “resources useful for new GCSE”, along with a purple box with some superb-looking investigations from Maths O’Level during the 80s sometime. I’m hearing SMILE maths cards being mentioned an awful lot too – they’re all available from the National Stem Centre, and well worth a look.

Something new…

Teaching the same sequence of lessons with no change each year would bore me to death. Even if a lesson works really well, I never teach exactly the same lesson twice. When planning a lesson now, I look at what I used last year, keep the good stuff, strip out the rubbish, then go looking for interesting stuff to fill its place.

I’ve discovered a few fantastic resource websites this year, mostly through Twitter. These are:

  • Resourceaholic (@mathsjem): Jo does a frequent “Maths Gems” post, which picks out some lovely ideas from Twitter and makes sure they don’t get lost in the digital mire. She also has some great resources uploaded and linked – I’ve particularly enjoyed her A Level ones this year.
  • Solve My Maths (@solvemymaths): A great source for stretching problems (for pupils and teachers!) – I’ve now heard this site mentioned on three separate training days.
  • Miss Brookes Maths (@Stacy_Maths): Stacy and I seem to share a common goal, which is to catalogue all the resources on the Internet. It’s been interesting as both our sites have developed this year that she and I have very little overlap in the things we post, which just goes to show what a diverse world of resources we now have to pick from. A massive time-saver with planning.
  • Educating Mr Mattock (@MrMattock): Peter has written some brilliant blog posts with creative lesson ideas to try. Bearings in the hall might get an outing next year…

(I feel the need to add that this is not A LIST… well, it is, but I’ve only listed stuff that’s new to me this year and is primarily about resources rather than general blogs – I may do a longer post about all the other fab stuff out there at some point).

Something borrowed…

As a quick estimate, I reckon about 60-70% of my best or favourite lessons, activities and resources have been pinched from other teachers. I was lucky enough to have a brilliant mentor during my NQT year, who used to start off our mentoring meeting every week by going to his filing cabinet and pulling out a (beautifully) hand-written sheet with a great investigation on to try with a particular class. I’ve still got them in a stack somewhere, and I’m slowly transferring them over to electronic versions to share with more people. This Growing Squares investigation is one of them. The way I introduce Pythagoras’ theorem with most groups was similarly pilfered from an inspirational teacher I worked with on the Student Associates Scheme while I was still at university.

My biggest tip for student teachers and NQTs has to be “borrow what you can” – often, the most experienced teachers have taught their lessons hundreds of times in their careers, and know what works and what doesn’t. Adapt where necessary, but don’t be afraid to use someone else’s stuff (with their permission, of course!).

Something blue!

I apologise for the tenuousness of this link…

About halfway through this year, my classroom was awash with paper. This seems to happen every year, and it’s down to having Year 11, I reckon. At some point, you have to start giving them practice worksheets and booklets tailored to their specific needs, and organising these can be a pain. Something I found very helpful to combat this was copying paper resources onto coloured paper depending on strand – so all of the “Number” resources got copied onto blue paper (similarly, Shape is green, Algebra is yellow and Data is red/pink – I have no idea where these colour associations have come from, but that’s how I see them mentally). This meant that pupils could narrow down which pile of worksheets they needed to look in, and made it much easier for me to put everything away again at the end of the lesson, as all the blue sheets went in one box, yellow in another, and so on.

Similarly, I’ve previously copied non-calculator and calculator papers with different-coloured front pages, so pupils could find these more easily and see links or similarities between papers and questions.

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LOTW 10/05/15 Comparing and ordering fractions and decimals

Lesson, Resource missing /

In the spirit of encouraging personal positive thinking, I’ve decided to start a new Sunday blog series on the best lesson I’ve taught the previous week.

This week my pick actually covers two lessons of work, and was delivered to my Year 9s on Thursday and Friday. To provide a bit of context, we’re trialling the Mastery Pathway with KS3 this year, and pupils sat the Elementary 4 test on Tuesday, covering negative numbers, substitution and lots of fractions and decimals work. They passed the previous three tests pretty well, but this one caused some difficulties, with marks ranging from 30% to 70%. After doing a bit of analysis on the results, I decided that my first topic for re-teaching would be working with fractions and decimals, particularly ordering and converting between the two representations.

I’d tried the Standards Unit card sort with them a couple of weeks ago, and that didn’t really work for them – although they had a good go, it was too overwhelming for them. I decided to adapt it slightly, removing the percentage cards (we’ve not covered percentages at all yet in the Mastery Pathway), and changing the denominators to something slightly more friendly. I also added significantly more structure to the activity, interleaving skills practice with the card sort. The adapted version worked really well, and I’m pretty confident that I’ve plugged most of the gaps with most of them now – I’m planning a quick test next week to check.

1. Ordering fractions using a common denominator

We started with a “which is bigger” problem – I’ve previously blogged about how much I love this activity, and we did a lot of work at the start of the year with problems like these.

It was really positive to see that their mathematical explanations have come on leaps and bounds since the start of Year 9. We discussed the ideas of using a common denominator and pros and cons of bar and pizza modelling again. 

I then gave them four fairly standard problems to do. We discussed the importance of showing working out – on the test, many of them hadn’t shown their working, and had lost method marks. I asked them all to show clearly which common denominator they had used and how they converted the fractions.

I deliberately picked the fourth problem with a common denominator of 100, to lead us into the next bit on converting fractions to decimals.

Next, I handed out a set of fractions cards from the card sort I planned to use. I asked what they would pick as a common denominator for the nine fractions highlighted, and got the pupil who said “twentieths” to explain why. 

We also discussed what they would use as a common denominator for the whole set, and how they could find this. However, I wanted to focus on the twentieths to start with, so I got them to convert those, writing their answers on the cards.

2. Converting fractions to decimals

I then quickly retaught conversion of fractions to decimals with “easy” denominators. I was confident that they understood the concept and links with place value, as we spent quite a bit of time on this when I initially taught the topic, but they clearly hadn’t mastered it as many of them made errors with this on their assessment. We discussed a few examples, then I set them off with ten to do for themselves.

We spent a couple of minutes discussing different strategies for the final question, and I got two pupils to the board to demonstrate their alternative approaches: converting to a mixed number, then dealing with the fraction part, or converting to a denominator of 100 first, then converting to a mixed number.

The pupils then changed the first nine fractions into decimals using a denominator of 10 or 100. We discussed why the eighths might cause problems, and suggested that we could use a denominator of 1000. However, as I wanted them to try these using division, we didn’t change these too at this stage.

Next, we did a quick refresher on dealing with more difficult denominators using division. On their tests, many pupils had confused the numerator and denominator, with many instinctively putting the larger number under the “bus stop” and then getting in a mess. 

We talked about the fact that order matters with division – as an aside, I’ve stopped automatically correcting pupils when they say this the wrong way round, and instead asking them if they’re sure they mean “9 shared by 45” instead of “45 shared by 9”. I also reinforced correct use of recurring notation.

Finally, I got them to change the eighths cards using division. By this point, we’d reached the end of the first hour, so we quickly summarised to pick up where we’d finished off the previous lesson.

3. Converting decimals to fractions

We sped through this bit, as we covered this in lots of depth during Elementary 1. My main focus here was getting pupils to simplify their answers, particularly with a factor of 5 in the numerator and denominator, so I included plenty of examples of this type.

While they were doing these ten problems, I circulated to check they were cancelling down their final answers – often, all that was needed was a quick “point” at their page to prompt them to check again!

4. Putting it all together

For the remainder of the lesson, I got pupils to make a summary poster of all the work we’d done, using the cards we’d worked on in the previous lesson. They drew a number line on a sheet of A3 paper, and ordered the twentieths cards, then matched up the decimal equivalents. We used the decimal equivalents of eighths to position these on the number line, then I demonstrated checking this by converting all the fractions to eightieths.  

I’ll add some pictures of the finished posters tomorrow.

Evaluation and final thoughts

This lesson is a lot more “I do, then you do” than most of my lessons, but it seemed to work really well for the pupils. Most of them found it a real confidence booster, and enjoyed the opportunity to just reinforce skills they were shaky on. They found the card sort much more accessible with a step-by-step approach. I’d use this again next year with a similar group, possibly adding a few extra cards for fractions greater than 1.

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How I teach trigonometry in right-angled triangles

How I Teach..., Resource missing /

I’ve been teaching trigonometry from scratch with Year 10 this week, so thought it would be a good opportunity to blog about the way I introduce sine, cosine and tangent. This is another sequence of lessons I love teaching, because it’s one of my tried and tested approaches and seems to work well each year.

​We started the lesson with a few quick questions on Pythagoras’ theorem (I used these ones). I taught them Pythagoras’ theorem way back in November, but most of them remembered how to solve the problems with a bit of prompting. I was aiming to refresh identification and use of the word “hypotenuse” and also provide a link from something they’d previously learned about right-angled triangles. After we’d done this, it was on to the first bit of the trigonometry introduction!

1. The relationship between lengths and angles
After trying a few different approaches in my first few years of teaching, I’ve settled on introducing trigonometry by drawing and measuring triangles. When I taught this initially, I used three nested similar triangles, but I found that this caused confusion for some pupils, as they couldn’t see the three separate triangles clearly. I adapted this to look at the triangles separately last year (see this video on YouTube if you’re interested in a tutorial for pupils to follow), but I decided to try two similar and one different this year. 

I asked the pupils to draw the three triangles in their exercise books, measure the length of the hypotenuse and angle theta and record their results. Next I introduced “opposite” and “adjacent” terminology and we added those column headings to their table. I then got them to calculate opp/hyp, adj/hyp and opp/adj using calculators and add their results to the table.

We discussed what we saw from the results; why were the results for triangles A and B identical, but the results for C were different? We got to the idea that there was a link between the side measurements and the angle we’d measured, and that if the triangle was enlarged, both the angle and the ratio of the measurements would stay the same.

2. Using trig tables
When I first tried this way of introducing trigonometry, I got pupils to then work out sine, cosine and tangent of the angles on their calculators, and spot that these came out with the same results, moving quite quickly on to missing angle problems the same lesson. However, in the last couple of years, I’ve avoided calculators altogether for the first lesson or two, and got pupils using trig tables instead. 

So after the activity above, I handed out a set of trig tables (download a copy here) and got them to look at the rows corresponding to the angles in their triangles. We spotted that our results matched fairly well with the values in the tables, and discussed how inaccuracy in measurements could have contributed to our results being slightly out.

By this point we were reaching the end of the lesson, so to finish off, I taught them the names of the three ratios, emphasising that these are just relationships between two sides on a right-angled triangle (for now!).

3. Writing sine, cosine and tangent ratios
After a few more Pythagoras problems to kick the lesson off, I set the pupils off on a task focused on labeling sides and writing trigonometric ratios correctly. I gave them a set of triangles with all three side lengths shown and asked them to write down the ratios for sine, cosine and tangent for each triangle. Once they’d done this, they worked out the decimal values of each one on their calculators, then it was back to the trig tables to work out an approximate value for the angle.

4. Traditional GCSE problems
By this time, they were getting a bit fed up with the tables; a couple of them were complaining that their eyes were going funny from squinting at the values, and one pupil said “but surely we don’t get this in the exam?”. So at this point I showed them three examples of some more traditional exam-type problems (with two sides and a missing angle), and also demonstrated how they could use the inverse sine, cosine and tangent buttons on their calculators rather than struggling with the tables, explaining that the inverse buttons were just working backwards from the trigonometric ratio to the angle. The rest of the lesson was spent practising these new skills using questions from a textbook.

(I almost felt the need to write an apology there for referring to textbook use, then stopped myself. I think it’s absolutely vital that time is built into maths lessons for skills practice, and sometimes the best way to do that is to get them to work through some carefully selected problems independently).

I’ll blog next week about where we go from here. I’m in two minds about continuing to finding missing sides (which is what I’d usually do), or alternatively doing more in-depth problem solving using angles first – but I’ve got a few days to think about it!

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