This year I produced our end of year assessments for Year 8 and 9. We have a few basic principles that we follow when we create our Key Stage 3 assessments:

**Single Tier Key Stage 3 Assessments.**I know this one is controversial, but I want every student in the year group to take the same assessment. I've never been happy with prematurely allocating students to tiers in Key Stage 3. When we've done that in the past, I've found that students end up getting 'stuck' in certain sets. So now, although our regular end-of-topic tests are tailored to each class, our big assessments (twice a year) are one-size-fits-all. This makes the assessments more difficult to write, but helps us get a better sense of relative attainment across the whole year group.**Testing All Taught Content.**We know it's frustrating for students to spend ages learning and revising topics that are then not tested. So we try to include questions from every topic taught during the year. And we would never test on topics not yet taught - this is counterproductive (it damages confidence and tells us nothing). This is why we don't give full higher tier GCSE papers at the end of Year 10 - I'm strongly opposed to it.**Testing Knowledge, Skill and Reasoning.**We want to test procedural fluency and reasoning skills, but we don't believe there's a strict separation between these things. Well-written questions test both, so we try to find as many of those as we can.**Challenge.**It's so important to include a good level of challenge. I can't stand it when students finish a 60 minute assessment in 20 minutes and then sit there looking bored because they found it easy. There should be plenty of questions that make them think. And given that the outcomes of these assessments help us determine the groups we'll put students in next year, we need our assessments to provide us with enough information to get these decisions right. If half the year group get 90%+, it's not helping us identify our strongest mathematicians.

**Question Style**

I don't have time to write many of the questions myself. Thankfully there are plenty of good questions around, and tools like Dr Frost mean they are easily accessible. Here's an example of a question that is well suited to a single tier Key Stage 3 assessment:

This is from a WJEC Foundation paper. What I like about this is that Part

*a*is very accessible to all students with a calculator. So the vast majority of students can get a mark here. Part*b*requires an understanding of inverse operations. Some of our lower attaining students found that more difficult than we expected them to.Here's a similar one. I adapted this from an old AQA GCSE question. The majority of students got Part

*a*correct. But Part*b*required a bit more thinking, and it surprised me that many students got it wrong, suggesting we need to work on their proportional reasoning.Questions with multiple parts where the first part is highly accessible and the parts get increasingly difficult are perfect for single tier assessments. Ideally every paper would full of these, then you don't end up with the situation where some students can only do the first four questions and can't access the rest of the paper. Here's another example of a question that has both accessible and challenging parts:

Perhaps this ramps up in difficulty too quickly. There could be an additional part between

*b*and*c*with moderate difficultly.If a paper is full of questions like this then it's both accessible and challenging. Next year I want to include more of this. This year my paper ended up with the classic format 'easier questions at the start, harder questions at the end', which doesn't create a nice experience for the lower attaining students.

In the remainder of this post I want to share some of the more difficult questions I included in my Year 8 assessments. Some of our high attainers said they found the mid-year assessment too easy, and I didn't want a repeat of that.

**Circles**

In Year 8 our students are introduced to pi, and they learn how to find the circumference and area of a circle. We go into depth by exploring questions involving semi circles and quarter circles, which takes a lot of reasoning. MathsPad has some great tasks for this:

And for even more challenge, there are problems like this:

There's absolutely no need to accelerate onto the formulaic

^{θ}/_{360}πr^{2 }when there's so much reasoning to be done in Year 8 with semi circles and quarter circles.To test these reasoning skills I included this question in the non-calculator assessment (taken from OCR's sample GCSE questions):

And this question in the calculator assessment (I can't remember the source of this one - I think it might be Edexcel?):

Even our very best Year 8 mathematicians found these questions challenging. In my very bright Set 2, no student got more than one mark on either question. This suggests we still have work to do on developing their reasoning.

**Fractions**

Although this wasn't one of the most challenging questions on my Year 8 assessment, I decided to give this question a mention here because it surprised me. Fractions questions are often so procedural, I wanted to include a fractions question that took a bit more thinking. Even though the vast majority of students in my class have no trouble adding, subtracting, multiplying and dividing fractions, this question was answered very badly. Even halving five eighths proved conceptually challenging.

**Volume**

There are lots of 'high tariff' volume questions to choose from. These are good for a single-tier assessments because most students should be able to pick up

*some*of the four or five marks available even if they can't complete the whole question.This cylinder question (adapted from AQA) stumped most of my students. They all correctly worked out the volume of water in the Cylinder A, but then found the volume of the whole of Cylinder B and divided one volume by the other. This is a classic example of students following a formulaic approach to answering a question, rather than stopping to think about what the question actually says.

**Interweaving**

As much as possible I tried to find questions which combined more than one topic they'd studied this year. This is particularly easy to do for Pythagoras and ratio, which both come up all over the place. For example, this question combined ratio and percentages:

*Joseph’s flock has 55% more sheep than goats.*

*What is the ratio of goats to sheep in the flock? Leave your ratio in its simplest form.*

This was originally an IMC question. Can you guess what went wrong? Most students in my class simplified 45:55 instead of simplifying 100:155 (or equivalent). They have the knowledge they need to answer this question correctly. They just didn't think.

They had much more success on this 'problem solving' style question on the non-calculator paper which also involved ratio and percentages.

*Andrew is paid £250 a week.*

*Each week, he:*

*- shares his pay with his sister in the ratio 3 : 2*

*- saves 12% of his share.*

*How many weeks will it take Andrew to save £360?*

This is an AQA GCSE question from 2014. It was done pretty well.

And even though we'd spent time on questions just like this back in December, not a single student in my class picked up any marks on this non-calculator question:

This is a SQA specimen question but I added the requirement to answer without indices to add extra challenge. It interweaves index laws, fractions and expanding brackets. All three topics were on our Year 8 curriculum.

Although we do a lot of work on fractional and negative indices in Year 10, we do look briefly at negative indices in Year 8. So the higher attaining students should know that

*x*^{-1}=^{1}/_{x}and*x*^{0}= 1. They didn't get this far though. A few students realised that they should be adding the indices, but they seemed to panic at the thought of adding 1/2 to -3/2. Now I think about it, I remember A level students finding this kind of thing difficult when we used to teach C1 too. Perhaps this is something to spend more time on when we do fractions, instead of skipping over fractions with common denominators.*****

I've featured a number of GCSE questions here, but I should emphasise that our Key Stage 3 assessments draw on numerous sources, including old Key Stage 2 SATs questions and old Key Stage 3 questions. Anything that's right for our students goes in, we're not precious about what it was originally written for. I wish I had more time to write my own questions.

I'd love to see some of the questions that most challenged your Key Stage 3 students in their assessments this year, so do tweet me some examples.

I'll write a similar post soon about some of the questions I used to challenge Year 9.

*****

*For context, I work at a comprehensive school in the London Borough of Sutton. There are five grammar schools in our borough, which slightly reduces our intake of high attainers. We are proudly non-selective. It's a fairly affluent area so only 14% of our students are pupil premium. We are quite ethnically diverse (41% White British compared to 66% nationally). We have 22 students with EHCPs. We are a new school with around 200 students per year group and we currently only have Years 7 - 10 (we'll have Year 11 next year). In general, most of our students have excellent attitudes to learning and want to do well. The average score on our end of Year 8 assessment was 57% and the highest score was 95%.*

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