A better way of planning – my first attempt

I was blown away by the post by @leadinglearner yesterday (which can be found here – and if you haven’t read it yet, it might be a better use of your time in the short term than continuing reading this). One of the reasons, I think, is that I can see how it links to things I have been trying to do (see my series of posts from last summer) but takes it to a completely higher level – but in a way that is easy to see. I was dead keen to try this out for myself, and so….I did!

Attached below you will find a document for a series of lessons I have designed for my year 7 bottom set. I am sure it can be improved (not least in terms of the SOLO learning intentions), but you have to start somewhere. I do wonder if it is a little repetitive in places, but I do wonder if that is sometimes the nature of the beast in maths, not least at such a low level.

Anyway, have a look, and if you think it can be improved, please let me know! I will continue using this model for my planning of all classes and so may end up sharing more on here, and any feedback will be most useful and helpful. Thanks

New SoW 7.3 – Adding and subtracting!

Half term report (or simply: breathe!)

As I alluded to previously, Christmas 2014 saw me change jobs after 4 and a half years. Having reached the end of 6 hectic weeks, I thought it might be a good time to document my experience, thoughts and fears, not least because hopefully putting my thoughts down in print will allow me to mentally declutter!

  • Change is difficult at any time, but especially part way through the year – I guess this is obvious, but even now I still don’t think I am fully ‘there’. I was so comfortable at my old school – too comfortable, in fact, which was one of my reasons for leaving – and the first week in particular was a huge shock to the system. In fact, it became a simple case of survival at times. But a rough plan of what I was doing, and supportive colleagues who helped me bed in quickly, got me through to the weekend, where I could regroup.
  • Schools which appear quite similar can be very different in practice – both my old and new schools serve predominantly white, working class intakes from ex-mining communities. But that is pretty much where the similarities end. The ethos of my new school, the behaviour management systems, and the aspirations are all very different (in a good way). I know this was a great move for me. I can’t wait for that day when I finally feel like I’ve arrived and am fully comfortable in the post.
  • Expectations on all levels need raising  – both in terms of behaviour and in work ethic, it’s clear standards for some of my students were a little low. My year 8 class admitted earlier in the week that the previous teacher was soft on them in terms of the BM system in place – which all staff are required to follow religiously. I feel like I’ve made some progress here, although there is still a way to go.
  • I have a large/scary amount of control over my class AND my environment – the freedom I have is something I have found difficult to cope with at times, and has led to me having crises of confidence on many occasions. We have no scheme of work at all, so I decide what to teach and for how long. This can be quite a daunting prospect, although I also recognise the huge opportunity it provides. Similarly, the fact I now have my own room is a great opportunity for me to impress my values and expectations on students – it had been my aim to get a display put up this week, but the replacement of windows and the associated removal of asbestos prevents this from happening.
  • I just need to focus on the process and not worry (too much) about the outcomes: like George Michael, I gotta have faith – in my running, I’m all about the process – running consistently, through all weathers and good and bad runs alike, will deliver the outcomes I want. Similarly, I need to be confident in my methods and strategies of teaching, and know that if I am producing the goods day in, day out, students will make the desired progress.

Although half term hasn’t really started yet, I’m looking forward greatly to the second half of the spring term. I feel in a much happier place, and feel this is the time to start kicking on and making big inroads on student progress. I look forward to catching up with old blogs to inspire me as ever!

A potential epiphany….

“Jaws isn’t about a shark, and Tinker Tailor’s not about spying” – Mark Kermode (paraphrased)

This quote from one of my favourite podcasts struck me as I began planning for next week this morning. I was creating my objectives/SO THATs/success criteria, when I began to wonder whether SO THATs were actually pretty indistinguishable from success criteria. A quick glimpse at few of my ‘go to’ blogs in this area (here by Dan Brinton, and here and here by Zoe Elder) convinced me that there was sufficient difference to continue treating them as separate parts. So I began planning. But two different lessons, for two different groups, brought about the same observation in mind – “it’s not about that, it’s about something else!”

Example 1: Year 11 – WAL about estimating the mean SO THAT we can achieve full marks on estimating the mean questions.

Success criteria: a) we can calculate an estimate for the mean from a set of grouped data; b) we can calculate proportions from a set of grouped data

Example 2: Year 7 – WAL about area and perimeter SO THAT we can calculate area and perimeter of squares and rectangles.

Success criteria: a) we can calculate area and perimeter by counting squares; b) we can find area and perimeter of shapes not drawn on squared paper; c) we can explain the formulae for area and perimeter

Now you are probably ahead of me already reading that, and know what I’m about to say, but I can honestly say this is a bit of a Eureka moment for me which will change my planning from this day forward. I was using Zoe’s approach of the WAL as the ‘what’ of learning and the SO THAT as the ‘why’ of learning, with the success criteria being a ‘how will I know I have learned it?’ check. But a brief glimpse of my plans for year 11 would suggest the lesson isn’t about estimating the mean, it’s about grouped data, with estimating the mean providing a context for that learning. It’s what I believe Dan Brinton writes about in his blog (citing Shirley Clarke) which I have linked above. Similarly, if we look at my plans for the year 7 lesson, I’m not sure that is a lesson about area and perimeter; rather, I think it’s a lesson about formulae using the context of area and perimeter. And actually, that’s not what I want that lesson to be about.

So I made refinements. My year 11 lesson became:

WAL about grouped data SO THAT we can accurately answer questions on estimating the mean and cumulative frequency.

Success criteria: a) we can estimate the mean from a set of grouped data; b) we can draw an accurate cumulative frequency diagram and derive quartiles and the median from it; c) we can calculate proportions satisfying a condition from both types of representations of data

and my year 7 lesson became:

WAL about shapes SO THAT we can find the area and perimeter of squares and rectangles.

Success criteria: a) we can find area/perimeter by counting; b) we can find area/perimeter of shapes not drawn on squared paper; c) we can explain how to find area/perimeter for a shape where we don’t know the measurements

I think, particularly with the year 7 lesson, there is still an implicit tendency towards formulae at the end, but the lesson is now much more clearly focused towards area and perimeter. What are we learning about? Shapes. Why? So we can find the area and perimeter of squares and rectangles. How will we know we have been successful?….. and so on.

Having thought closely about this area this morning, I think there will be occasions where the WAL, SO THAT and success criteria may need to be closely linked, particularly towards the knowledge acquisition end of things. But equally, most of the time it will be appropriate to redraft the plans, even before the content of the lesson in considered.

What do you think? Have I got the wrong end of the stick, or does it seem like I’m on the right track? I’d love any feedback you may have, either here in the comments section or on Twitter via @Still_Improving. Thanks for reading!

Day 2 reflections – Don’t worry about a thing….

….’cos every (little) thing is gonna be alright!’

Well, day 2 seemed to begin with a bit of internal contrived panic – I had a last minute revision session with my year 11s despite not having seen them yet – but once that had passed, things seemed to become clearer in my mind. I ran around less, people came to find me less, and I taught a few lessons, too!

It just takes a bit of getting used to. All of it. Having my own room again (I still keep thinking somebody’s going to come and take it off me any time now!), split lunches, and the quiet on the corridors at break and lunch (it’s out of bounds for students). I love the PD system the school has – instantaneous and with no follow up or paperwork required! As a result, my lessons need tightening up a bit, but I’ll get there soon enough.

There are still of course SOME issues, but it is still early days. I have noticed I am slouching at the board, and in fact I’m doing too much at the board full stop. A balance that needs redressing. Overall, though, today was a much happier day than yesterday, and I suspect tomorrow will be even calmer still. My books are neatly filed, my seating plans written up neatly and printed out, my desk is tidy. My inbox is virtually empty. I’m feeling much more organised, and once again my new colleagues have been amazingly supportive. And I’m even smiling, more so than I ever did at my last school (again, new year, new habit!)

And best of all, it’s nearly Friday…..!

Day 1 reflections

New year, new term…..NEW JOB?!?!?

Finally, after much waiting, I took up my new post. I felt I’d had a decent break, I slept well and woke at the time I’d planned. I was in school early, eager to get cracking….until stuff got in the way. Like not being able to get in the building (note to self: if the school has a keypad entry, find out the code BEFORE the first day), not being able to connect to the school wifi, finding out my year 9 class have 6 lessons a week, not 5, and therefore one lesson a week with another member of staff, who teaches them on a Monday, and………

Yes, it was busy. No, I still don’t have a clue what I’m doing. But yes, it WILL get better. I am sure of it. Not least because I have my own room (although I haven’t really even begun to think about what I’m going to do with it), lots of TAs to help me, a very understanding HoD, and a corridor full of colleagues willing to listen, and help.

I’ll be fine. It’s just going to take a while to get up to speed.

I can’t wait for that day….!

And another one….

Triangles and rectangles

 

I saw this just as I was settling down in bed last night. 1 1/2 hours later, and after double, treble and quadruple checking, my solution is as follows*. Another fab puzzle, putting into practice a variety of skills. And I even managed to find two routes to the answer!

IMG_0400

 

*Upon further inspection last night, I had made a mistake and posted a slightly different solution on Twitter. Still a bit rusty!

The rectangle puzzle

Today began with me reading through some tweets I’d favourited, including the latest from @mathsjem (who if, for some ridiculous reason, you’re not already following, you should follow immediately). In the section on problem solving, she remarked the following:

“It’s a good idea for maths teachers to try to solve unfamiliar problems every now and then (like the example below from ‏@dannytybrown) to remind ourselves that mathematical problem solving often requires patience, creativity and multiple attempts. We all experience frustration in problem solving, just like our students do, but we know that the satisfaction of eventually finding the solution is well worth it.”

I wholeheartedly endorse this view. It is something I have become acutely aware of recently and, as I will be teaching top set for the first time in my career from next week, I find this an excellent way of testing my rustier skills. I blogged previously about the looped polygons puzzle, and today I decided to tackle another of @dannytybrown’s puzzles, namely this one:

rectangle puzzle

I must admit I huffed and puffed for a while on this, but in actual fact I was only really able to solve it once I’d had a look at another of Danny’s puzzles which was mentioned in @mathsjem’s post:

rectangle problem

This had me confused for ages. I just couldn’t find a way into it. So I looked at solutions proposed by others and tried to understand them. Eventually, and after a lot of confusion on my part, I got there (although I am awaiting a reply from Danny based on what I regard as a key aspect of the solution with which I am not overly happy at present). In the end, the solution boils down to using trigonometric ratios to make finding the answer much easier.

So back I went to the paper folding puzzle. I had already jotted down what I knew and had deduced – the length is rt 3 x w, the width is w. This means that the base of the right angled triangle can be written as (rt 3 x w)/w. During my first attempt at the problem I had calculated the hypotenuse at being w + ((rt 3 x w)/3). When I went back to it and tried again from scratch, however, my curiosity was stirred, and I worked through it slightly differently.

We know that hyp^2 = w^2 + ((rt 3 x w)/3)^2. Working this out leaves hyp^2 = w^2 + 3w^2/9. This adds up to 4/3w^2, which when you root it gives a hypotenuse equal to 2w^2/rt 3. And if we rationalise the denominator? Well then the hypotenuse of the triangle equals (2 x rt 3 x w)/2 – twice the length of the base. This then means that the angle between the base and the hypotenuse must be 60 degrees.

On my first look at the problem, I really struggled with identifying how much of the folded section would fall outside the rest of the sheet. In fact, I couldn’t comprehend how I would even begin to calculate this. Having gone away and come back to it, however, I realised the thing I was trying to grasp earlier was that the fold line acts as a line of symmetry. So if I doubled the angle, that would allow me to calculate how far the sheet would fold across the existing section. Except that it was now quite straightforward. The angle being 60 degrees, added to the original 60 degrees, creates an equilateral triangle. The section that will fold over neatly onto the existing paper can be shown by drawing a diagonal from the bottom line (where the diagonal already ends) to the top left corner. The length of the diagonal is (2 x  rt 3 x w)/2 which, believe it or not, is the same as the length of the sheet from the left hand corner to the point the diagonal meets it. This means that there is half of a small rectangle (or 1/6 of the total shape) that will overhang when folded.

The original question asks for the ratio of the area of the new shape : the area of the original shape. The shape is 1/2 + 1/6 of the original (1/3 is folded over), leaving 2/3 of the original, meaning the ratio is 2:3.

I loved doing this problem, and I think it also helped having a break and focusing on another problem….particularly when that problem and this shared a key, common, but overlooked (in my eyes at least) bit of mathematics!