# Make a square with one cut

This is one of those amazing sheets which keep them going for quite a while!  I’ve tried this with a lower set Yr10, an extension class in Yr8 and even a few teachers!  It’s hugely differentiated all on one sheet and the way it’s laid out encourages students to wander to another shape if they get stuck – some of these are really hard.

I quite often offer scissors but most people quickly realise that they prefer just to do it with a pencil and visualising it – which of course is the whole point!

Make a square with one cut

# Think of a number, but how does it work?

This is a nice development of the classic “Think of a Number” problems that are a good way of introducing algebraic equations.  Nrich covers this introductory activity with Your Number Is… and other linked activities.

This one takes it a stage further.  Proving algebraically why this works would be a nice extension activity. Note that with the numbers below, this will only work in 2015.  I’ll leave you to work out what you need to change for subsequent years!

Work this out as you read.

Be sure you don’t read to the bottom until you’ve worked it out.

First, pick a number 1 to 7

Multiply this number by 2.

Multiply it by 50.  (Come on, you can do that without a calculator).

Now, subtract the four digit year that you were born.  e.g. 1984

You should have a 3 digit number:

The first digit of this was your original number.

The next two numbers are your age.

# Uncovering Fraction Misconceptions through True and False cards

Having been inspired by some ideas from Resourceaholic and also from Robert Wilne @NCETMsecondary here, I thought I’d create these True or False cards for use with Year 7.  We have covered fraction of an amount, equivalent fractions, adding fractions, and top heavy / mixed numbers so far, but you could easily adapt these if you want to include, for example, multiplying and dividing fractions. I designed the false ones first which really got me thinking about misconceptions that I think could be occurring.  The true ones were relatively straightforward after that.  Enjoy!

Here they are as a Word doc: Fractions True False cards And if the formatting looks a bit weird, as a pdf doc: Fractions True False cards

# Initial reflections on #mathsconf2015

I signed up to MathsConf in a rash moment during Feb half term when giving up my Saturday to hang out with 800 maths teachers seemed like a good idea. It turned out it was. I knew nothing about the event nor the organiser, La Salle but the programme looked interesting and I recognised some names from blogs I follow. And it was free.

This event in Aston University was the 3rd in a series of 6 and essentially part of La Salle’s “mission” to help teachers build a professional learning network underpinned by their product “Complete Mathematics”. So the event was essentially a marketing exercise for the product. Not to do them a disservice by saying that – it was an extremely useful event.

The bulk of the day involved workshops. I’m sure they were all great, but I can’t help feeling that I picked well!   The 3 I attended were excellent and very varied in their nature.

A recurring theme of many of the discussions was deeper understanding amongst learners and I certainly came away from the day feeling vindicated in my instinct that a mastery approach is a “good thing”.

Another reflection: only once did I hear anyone mention Ofsted. It was refreshing to be with a bunch of professionals who have the conviction of their own experience to not just blindly follow what they are told to do. Having said that, these 800 teachers were hardly representative of the 350,000 Maths teachers in the UK, the vast majority of who would, quite rightly, not have given up their Saturday. We have to be realistic about teacher workload and any reforms, new ideas or changes to pedagogy have to be set in the context of a profession already under considerable strain.

Finally, it was great to make new contacts. Somewhat daunting and random with so many people there, but it was great to actually meet some of my contacts on Twitter and blogs that I follow.

Here are my rough notes from the session which probably won’t make much sense to anyone else. (Things in italics are my reflections, not what the speakers said). If I feel the urge, I may write more on individual sessions once I have had chance to digest them a bit more. But for now, my family needs me back!

# Spending time on Proportional Reasoning

This week saw 4 lessons with Year 9 on “Proportional Reasoning”.  It’s a skill that pervades lots of topics, obviously ratio but also underlies algebra, fractions, shape, measures, statistics, everything really!

Our school has been trialling some resources developed by the ICCAMS project. I liked the look of some of them for example, this one:

However, I was a bit nervous as it seemed like there were lots of examples that would involve whole class, teacher-led discussion and not enough for students to do. So I had these from Don Steward’s Median, ready on a slide.

It also seemed to me that all the various examples and contexts used fundamentally the same skills and that students (as I had a fairly high achieving class) would “get it” and then quickly get bored.

I was wrong. As we looked at the different examples it became clear that the change of context was not straightforward.  In the example above many students initially added 10cm to the 6cm and 7cm to get 16cm and 17cm.  Once we had examined it further and introduced the concept of a Double Number Line, they fully appreciated why this was wrong.   So then we looked at this one:

Again, many fell into the trap of adding 2 to the 30m to get 32m rather than 35m by taking a multiplicative reasoning approach.

The power of presenting different contexts for the same basic skills both provides interesting ways to practise that skill as well as giving the student (and teacher) an assessment of whether they have mastered it or not yet.  Sometimes misconceptions can be strongly engrained, maybe even more so in top set kids who are used to being right most of the time!  It takes time to develop the right instincts when approaching these problems and gain that depth of understanding.  With topics as fundamental as Proportional Reasoning, that is time well spent.

# A little something for Pi day

The Story of Pi

I created this a few years ago and it now adorns our maths corridor.  It started by having a Pi number line.  There are lots readily available to download. We used one containing the first 1000 digits, I think our corridor was long enough to fit the first 600-700 or so.  The idea being that the number of digits discovered relates to a point in history.

I never quite got round to finishing this.  If anyone fancies doing some of their own research on the history of pi, and filling in the blanks, then please do so by editing this document. Otherwise, just use what is there – it’s still an interesting story!

# Multiplying Fractions

It’s a more straightforward operation than adding. I ultimately end up saying “top times top, bottom times bottom”.  That works, but why does it work, when it doesn’t work for adding fractions?

This might help a bit…  Reinforces the notion that of means times, i.e. when I buy 4 bags of crisps at 30p each, they cost 4 x 30p.  Same for fractions, e.g. 1/5 of 2/3

Multiplying fractions

There is so much out there, it is sometimes hard to know where to start.  I have compiled a personal Top 10 Maths Teaching Resources page.  Following blogs is great as it gives you a drip feed of ideas.  It may not feed directly into the next lesson you are about to teach but plants a seed for later. Again, here is my personal Top 10 Maths Blogs.  And finally Twitter, which I am very much a novice at (I am @mhorley), so I refer you to Michael Fenton’s post on tips for how to get set up. Also, this post by ICTEvangelist.

With all of these things, there is the risk that you feel deluged with new information.   Remember, it’s not like responding to e-mail from your boss! You don’t have to look at anything if you don’t have time.  And you really don’t have to spend more than a few minutes a day looking at any of it for it to be really valuable. After a while you develop a sense of want you want to read and what you can skim over.  It does take a bit of investment up front to get things like Twitter set up (maybe 30mins – 1hour), but it is really worth it, believe me!

# Sometimes you just need to write your own worksheet.

Adding fractions with year 7 today. We’ve spent a bit of time examining equivalent fractions so I felt we were ready. I used an idea that was developed as part of a Lesson Study that I worked on with 2 other teachers a couple of years ago. In the lesson itself we used fraction walls to reinforce the idea of equivalents. After over an hour, we were there, with most being able to find equivalents and successfully add fractions, some no longer using the fraction wall.

So, on to the next lesson. I feel like I have a good sense of how they need to develop this and how I need to scaffold it for them. It’s one of those occasions where I could hunt around online and in text books to find a set of questions that might be OK. Or, if I sit down and think deeply about this, in 10 minutes I have the perfect set. For my class. At this point in their learning.

So here they are. You never know they might be perfect for your class too. But it’s not very likely!

# Making marking maths books meaningful (and manageable)

I’m lucky to work in a maths department with many wonderfully collaborative and creative teachers. But something that we have all acknowledged we need to get better at is marking students’ books.

School policy is that we are supposed to mark books every 2 weeks. This is meant to take the form of a marking “dialogue” where we pose questions and set challenges, extension questions, etc. Some staff manage this, but most (including me) don’t. When I do, I feel a faint warm glow that I have done it, but actually on reflection, the students get little benefit from the 2-3 hours it takes me to mark a class set of books. I think about what I could achieve by researching and planning better lessons in that time and I’m convinced this would have a lot more impact on learning.

However, student feedback and formative evaluation is critically important – it’s right at the top of Hattie’s list of effects (here, here and here)

We had a great department meeting today where we discussed some ideas. I will share those here once they are more fully developed (I promise!), but in the meantime, can you share good practice you have seen? Or do you know of any good articles with ideas.  In particular, I’m thinking:

What’s the focus of your book marking? Asking questions? setting targets? Providing feedback – what sort of feedback?

Any particular templates that are good? e.g. stickers / slips to stick in books.

What policies work? i.e. they are realistic and are stuck to consistently by teachers.

Please comment below or tweet me @mhorley or e-mail me mark.horley@gmail.com