Category Archives: Number

356. Edexcel Shadow Paper

Wow, it’s been a while since my last post. Apologies for that. I’ve been busy with Key Stage 5 things. One of my projects has been creating a shadow paper for the Edexcel AS Maths exam. With so few past papers available and so many papers available online, I wanted an assessment that my students couldn’t find the mark scheme for.

I’ve taken the AS Pure 2018 paper and created a shadow paper, with markscheme. Same level of difficulty, different numbers. I publicised it on Twitter and shared it with over ninety educators in 48 hours. I was stunned by the popularity of this resource. To keep it secure, the lovely Graham Cummings from @mathsemporium has arranged for it to be uploaded onto the Edexcel Maths Emporium. Now I don’t have to directly email people the files.

You can access it with an Edexcel teacher login here. If you don’t have a login, there are instructions on the page on how to obtain one.

I hope this paper saves you some time. I intend to start work on more Pure shadow papers soon, as Pure maths carries the heavier weighting in the AS and A-level exams.

355. Toyota logic

My fabulous colleague, Mr G, has recently been to the local Toyota factory to find out about the Lean model.

The key principles involve efficiency of process. He told me about a school using the Lean model that had tape diagonally along the spines. Students put their folders back in order and the teacher can instantly see if a file is missing. Genius!

Now I happened to be about to cover my textbooks with sticky back plastic. I put duct tape around the spine before covering them. Each book has tape 1cm lower than the previous.

Now you are thinking – that looks nice, but it will never work.

I’ve got news for you – every time I use the textbooks with my class of 34 Year 9 students, they put the books back in order. On the first day I made a big deal of how tidy the books looked and challenged them to put them back tidy. And they did – every lesson!

354. Iced gems

Just a quick idea today. You know the feeling when the multi-pack of sugar paper has dwindled down to just the brown. Great if you want to do trees, bleurgh if you want to do anything else.

I did a tarsia recap with Year 7. There were three different tasks going on and so I photocopied them onto three different colours of paper. The only colour of sugar paper was brown. We went with it. As the class finished their work, we discovered that their work looked like iced biscuits or iced gems. Hence our wall of Algebra Iced Gems:

Some of the cutting and sticking is a bit wobbly, but the class really enjoyed this task and we consolidated a considerable number of skills.

353. Large Data Display

If you teach A-level Maths in the UK, you will know about the prerequisite to know about the large data set for the statistics component. We use Edexcel and so need to know about eight weather locations.

Here is my Key Stage 5 corridor wall display.

I’ve got two maps – one of the World ( a freebie from the Humanities Dept) and one of the UK (¬£2.95 from Amazon).

I’ve included summary information from the CrashMaths booklet.

Of course, you can’t talk about UK weather data from the storm of 1987 – Michael Fish makes a special appearance.

352. Functions refresher

We recently finished teaching the AS Maths syllabus to Year 12. My colleague and I decided how to split up the start of the second year of the course. I’m starting with the modulus function.

I took one look at the skills needed at thought “Uh-oh”. The students are going to be out of practice with this. They are a lovely group, with a wide range of ability, but we’ve been very focussed on Applied Maths recently.

Option A: Go for it and patch up the vocabulary as we go (getting very frustrated – they knew this last October)

Option B: Break them in gently, recap the skills and vocabulary and extend them further

Option C: Reteach the work from last October.

Yes, you guessed it. I went with Option C. I found a brilliant task on piecewise function graphs on the Underground Maths website.

Image credit:

There are four graphs given. The basic task is to interpret the functions relating to each graph, through description or function.

I photocopied the graphs onto card and sliced them up. Each group had a set of cards. One person described a graph and the others had to accurately draw it. Some students went straight onto squared paper, others drafted it out on mini whiteboards. They repeated this until all the graphs were drawn and everyone had had a go at describing (the describer stuck in their card, so that they had a complete set). Whilst they were doing this, I moved around and encouraged the use of mathematical vocabulary.

Note: it was interesting to see how many students had forgotten the significance of open and shaded circles to denote boundaries of inequalities.

The second task was to match up the function cards with the graphs. Once again, accuracy was key as not all graphs had functions and not all functions had graphs. There were also some that nearly, but not quite matched. This activity really brought out the key skills relating to domain, range and function notation that I was looking for. The extension task was to complete the missing pairs.

But, did it work? I can confirm that the following lesson the class made very good progress investing the modulus function and it’s graph, even going as far to solve equations. They knew what the notation meant, how to plot it and how to interpret the graphs.

I really like the Underground Maths website as it has great resources, good support material and always makes students think. Most of the time it gets teachers thinking too!

351. No more glue sticks

Apologies for the infrequent blog posts. Life happens.

I thought I’d share an inspired idea that I saw on Twitter. AJSmith (@MrSmithRE) shared this brilliant video on how to efficiently use hole punched exercise books.

Hole punching exercise books

I converted to using A4 exercise books with Year 11 in September and the improvement was amazing. From low ability students who wanted to bin their Year 10 notes (Do I have to keep them?), to so much pride in their work that they are still using their A4 exercise books for personal study and revision whilst on study leave.

Now I’ve seen this video on tagging notes together, this could be a game changer. Fewer sheets stuck in means fewer pages filled with stuck in sheets, which means the books will last longer. So the Department saves on the cost of both glue sticks and exercise books. Those infuriating students who seem incapable of sorting out their books have got one less excuse now.

I plan on using this with my new Year 10 class in September – they are the exact opposite of my previous GCSE group, so this should make for an interesting comparison. I’ll feedback how it goes.

Now go and watch that video and start saving for an industrial strength hole punch.

345. Practical percentage skills

It’s perfectly obvious that fluency in the use of multiplication tables directly impacts students ability to divide. This grows into confidence with algebra and reverse operations. Students are able to see the links between the concepts. Our understanding of the importance of such skills is part of the success of programmes such as TTRockstars and Numeracy Ninjas.

Why is it then that so many textbooks, websites and resource banks keep the manipulation of percentages as separate skills sets? Percentage increase / Percentage change / Reverse percentages. We know that when concepts overlap, fluency increases when these links are pursued. So that’s what I set out to do.

I have a bright Year 8 class and started working on percentages with them. It didn’t take much to have them confident using equivalent decimal multipliers to find percentages of amounts. Using a multiplier for increase/decrease was a walk in the park. Then finding percentage change came up. Over the years I’ve seen a lot of students get very confused with half remembered methods:

“Which do I take away?”

“What number do I divide by?”

“Is this calculation the right way around?”

I tend to teach new value divided by old value and interpret the answer. It got me thinking – why am I teaching them this? They can increase by a percentage using a multiplier, why can’t they rearrange their working to find the actual¬†percentage? Same goes for reversing a percentage.

After a good discussion, I used this worksheet to recap and develop their skills:

Percentages Linking concepts questions

Percentages Linking concepts answers

Warning: “Original Amount” section, question (d) is a tricky one.

As with all new approaches, it’s always good to see if it worked. I set the following task from Don Steward’s website:

MEDIAN percent problems

I have GCSE students who wouldn’t know where to start on those questions, yet my Year 8 with their ‘have a go’ attitude were absolutely awesome. I’m definitely using this method again!