15 February 2015

Stretching Practice

I currently teach at a girls' grammar school. This means all of my students are on track for an A or A* at GCSE. It's a bit like teaching top set all the time, but without the confidence levels you would expect from such bright students. They learn new concepts very quickly but are often unwilling to take risks.

Finding suitable resources for such smart and hardworking students can be difficult. If I choose exercises that are too easy, they'll feel patronised and get bored with maths. Besides, it's not a good use of their time to do practice that's too easy. But if I choose exercises that are too difficult, they'll be frustrated and it won't help them develop fluency. So I put a lot of effort into ensuring my resources are the appropriate level of challenge.

It can be hard to find stretching practice questions. I often have to make my own worksheets by piecing together questions from a variety of sources, which can be really time-consuming. In this post I recommend good places to look for challenging questions. I'm focussing on topic specific practice here, not general problem solving questions like those from UKMT.

Finding challenge in recap
Last week I was planning a lesson on ratio for my Year 10s. My school's schemes of work are the very definition of a 'spiral curriculum' (mastery people, look away now!). My students study ratio and proportion in Year 7, and again in Year 8, and again in Year 9. The Year 10 scheme of work includes one lesson recapping ratio. I need to make this lesson suitably challenging or it will be a waste of time, but I can't find a single GCSE question on ratio that this class would find in the slightest bit difficult. Thankfully my department has some copies of the textbooks from the series 'Extension Mathematics' which contain excellent stretching questions. Some examples of their ratio questions are shown below - they're harder than the standard ratio questions in other textbooks.

1. Paula finished a cross country race in 20 minutes. When Paula finished, Sonia had only completed 5/8 of the total distance. Sonia’s average speed was 75 metres per minute less than Paula’s. Find the length of the race and Sonia’s speed (in metres per minute).

2. Two numbers are such that their difference, their sum and their product are in the ratio 1:4:15. What are the two numbers?

3. Find x if  2 + x : 4 + x = 6 + x : 9 + x

Questions like this will probably become more commonplace over the next few years as we prepare students for the 'new' GCSEs which will have a increased focus on problem solving.

Online sources of practice questions
1. CIMT - The Mathematics Enhancement Programme from CIMT offers an extensive collection of exercises for all Key Stages. I was using their website so much in my NQT year that I bought a set of their textbooks to flick through (order form here). Since then, Craig Barton has very helpfully provided links to CIMT's material on his website (via TES) - it's organised by topic instead of by book, making it easier to locate what you're looking for. For example if you're teaching angles then you can access all the material through this link, including worksheets, activities and assessments.
2. Brilliant.org - I've mentioned this website before but it deserves another recommendation because I'm now using it on a daily basis to find extension questions. Two examples are shown below for the topic of linear graphs. The questions on brilliant.org are brilliant(!) and there's enough to pull together a challenging worksheet on most topics.

3. Median Don Steward - This is usually my first port of call when I'm looking for resources. Often I find the right level of stretch for my students. Don Steward provides a variety of resources including rich tasks, practice questions and revision worksheets. The extract below is from a surds extension task.

4. Maths Malakiss - Written by an experienced maths teacher based in Dubai, this website provides a range of worksheets which include a good level of challenge. A circle theorem example is shown below.

I recently made a homework on angles for my top set Year 9 using questions from this website. I recommend the Windows snipping tool to make the process of collating questions as quick and painless as possible.

5. Exam Questions - If you're looking for GCSE practice questions then there's some excellent sources of questions by topic, including:
6. Resourceaholic.com! I feature a range of recommendations in my resource libraries (many - but not all - are aimed at 'high ability' students). In three months I'm moving to a comprehensive school so I may teach Foundation GCSE for the first time - expect my resource libraries to grow accordingly.

Questions to make students think
I want to end this post with an example of a question my top set Year 9 students recently encountered in a test. They'd studied indices (including fractional and negative indices) and most students found it pretty straightforward, so it was hard to find a way to really make them think. The question below worked well - the vast majority of students got it wrong. In the example answer shown, at least the student attempted to evaluate each expression, although some clear misconceptions have emerged. When I went through the question in class we wrote the decimals as fractions and it all became clear. It was definitely a question worth looking at. This is the sort of thing I should ensure I include in my lessons - questions that require proper thinking rather than just following a standard procedure.
I'd love to hear where you get your most challenging questions from - have I missed any good sources? What do you use to keep your best mathematicians on their toes? Please comment below or tweet me.

1. You mentioned UKMT, do you also use the mentoring questions? Also you might like Canada maths challenges.

1. I'm not familiar with either but will check them out, thank you!

2. My comment became a rambling mess, so I've blogged about my use of the FAM papers instead! https://sxpmaths.wordpress.com/2015/02/18/year-10-revision-competition/

1. Thanks Stuart, I love your idea. Will borrow that!

3. Thank you! I'm teaching in a grammar for the first time this year, with very few resources in the department and am struggling to extend. Some new ideas there. I think I'll be coming back to this blog entry regularly!

1. That's great! I've put a lot of effort into developing my school's resources because I think this is a big challenge at a grammar school. Also, the volume of work students get through in lessons is huge - I find it can be at least double the amount at other schools - so you need to prepare a lot for each lesson. Even if I take along a substantial worksheet and an extension activity, there's likely to be some students who just plough through it all and need more. It's hard work! Good luck with your new job. It's great teaching at a grammar school from the perspective of getting to teach lots and lots of mathematics day in day out. Enjoy!

4. If you're looking for problem solving resources, see this post: http://www.resourceaholic.com/2015/06/problems.html