Passport to a C

– A more active approach in Maths

Passport to a C is a program of work developed in response to students’ requests to make maths revision lessons more active. There is no underestimating the importance of good exam preparation. Preparation is a key factor in success at GCSE. Traditionally revision lessons leading up to a maths exam contain a teacher input followed by exam questions.

Imagine a different type of lesson where students are given a set of cards and asked to sort them. Card sorts are used widely in most subject areas. However, I have seen little use of them in secondary mathematics’ classrooms. This approach is based on Malcolm Swan’s research ‘Towards more active approaches’.

Each revision lesson includes a sorting activity, some key words and a collection of images or numbers connected in a variety of different ways. Students are encouraged to discuss and search for links. In doing so, they display their current level of language and understanding of a given topic. This encourages students to apply pre-existing knowledge. It also allows teachers the chance to assess students and decide on the best way to develop the lesson. Student response to the approach is generally positive. Comments include I like to sort the cards my way. I can look for connections. I feel good when I can explain my ideas to someone else.

Having used this material with a variety of groups the level to which the students are able to sort the cards changes depending on the topic. Initially students make quite superficial connections then another student sees a different way of sorting. Thus a snowballing effect occurs as the students thinking gets HOTTER.

This resource is going to be launched to parents at the forthcoming parentinformation evenings. It is already available through the VLE. These resources used in conjunction with other revision materials such as Bitesize will provide the students at CCHS [Cramlington Community High School, CLV’s previous incarnation! –Ed.] with a very powerful revision programme and a passport to a C.

Michael Smith & Graham MacPhail



Sequential questions and self correcting worksheets

– Two ideas to ideas to help students construct knowledge

After nearly 6 months on a stodgy diet of 21st century science for the hard of thinking, my year 10 students were experiencing some distress at the higher fibre content of additional science. They were being weaned on some proper chemistry, and some weren’t sure they liked it.

First up was a starter size portion of atomic structure (reviewed from a previous lesson), followed by a main course looking at formation of ions and the formulae of ionic compounds, with a bit of equation balancing for pudding.

Explaining how to solve the problems would have been relatively simple, but as this was a top set class I wanted students to work out for themselves how each piece of information related to the next from first principles.

My usual strategy for doing this would have been to ask the class a series of sequential questions, using each to tease out another piece of information until the group as a whole had constructed a set of rules for writing formulae. I was discouraged from teaching this way in this instance because this would involve a lengthy bit of chat about the topic before I began and guessed (correctly) that I’d be sick of the sound of myself before any questioning started. I was also worried that if any individuals got lost it would become impossible to help them catch up if the whole class was involved.

Strategy 1: sequential question cards

I wrote down an idealised version of the dialogue I had hoped to have with the class, then chopped it up into individual questions and chunks of information which I put on numbered question cards. Students were asked to work through the questions collaboratively in groups, finishing each question before they moved on. The answers to previous questions were not given directly, but they were referred to. I worried that students would peek forward to get hints, but in fact none thought to do this.

Student response

Student groups worked through the questions at a slower pace than they might have been expected to as a whole class, but they made steady progress and were generally successful at making links between one question and the next without any external support materials such as textbooks.

Having each question on a new card encouraged students to consider them independently rather than giving them a worksheet which they might have rushed forward without completely understanding each stage. Without me having explained why elements formed particular ions, by the end of the lesson some could work out why this must be the case from first principles, which was exactly the goal I had in mind. Most did not get this far however, and there were some problems specific to this approach. My attention was spread thinly over 10 student groups, and some made early errors which I did not spot until their later efforts had dissolved into a muddy puddle of mis-comprehension.

There were also some weaker students who hid behind brighter group members, and it was hard to spot and support these individuals – although this problem would have been worse in a whole class teaching environment.

Strategy 2: Using self-correcting worksheets to highlight early misunderstandings

In the subsequent lesson, I used an idea I’d been introduced to through some collaborative work with the maths department to help students selfassess whether they had understood a step well enough to move on. Excel worksheets can be made which check students’ answers for you (returning a smiley face for a correct answer).

Using a maths template sheet, I created a workbook with 5 worksheets, one for each step in understanding I wanted students to develop. Each worksheet had 3 problems, and once all 3 were done correctly, students had to write a worked example in their books before they started the next sheet.

While students worked on these sheets in pairs or independently, I gave microteaching sessions on each stage for students who identified (based on the worksheets) that they needed it.

By the end of this lesson, many students had constructed a method for writing balanced equations for reactions where ions are formed based only on information they could get from the periodic table and their knowledge of electron structure. Others had at least consolidated their knowledge of atomic structure and how ions form.

“Through working corroboratively, Maths and Science have been able to share and reflect on good practical teaching and learning strategies. Through conversations with each other and students, we have been able to critically analyse and adapt a resource which could be used commercially across departments.

Through lesson observations we have been able to see how this resource is viewed through the eyes of a student at Cramlington. This has been such a powerful experience and would encourage teaching staff to observe lessons outside of their own department. You will be amazed at what you might find and hopefully be brimming with ideas. ”  – David Gray


Student feedback was that they enjoyed using the worksheets. They were familiar (as used so often in maths) so needed no introduction, and they felt encouraged by the instant gratification of a smiley when they got something right. Students worked very independently, so I could really focus on microteaching rather than keeping half an eye on the rest of the class.

I’m a rubbish multi-tasker, and for this reason I struggle with microteaching in a normal rambunctious classroom, but this wasn’t a problem here. Interestingly, many of the students who came forward for microteaching were those who rarely ask for help in normal lessons, and I managed to have a reasonable dialogue with one student about his learning for the first time this year. I think the fact that the smiley feedback made their misunderstandings so obvious may have helped them approach me for this.

An obvious downside of the worksheets is that they can only be used to correct questions which have a defined answer which can only be expressed in a limited number of ways. I would not use them regularly, but as a tool for helping students develop a methodology in a logic-based topic I found them very helpful. I suspect there are many other subjects where this kind of instant student feedback could be useful in making discovery learning a little bit more palatable and easier to digest.

Katherine Shorrock & David Gray

Maths for Breakfast Anyone? (Issue 7, Conference June 2010))

– Flexible intervention inspires year 11

The maths intervention program is specifically aimed at year 11 pupils who were not achieving that important, life changing, grade C. The intervention program allows students to get one-to-one tutoring, something which many parents do not have the luxury to afford, often costing £20 a pop.

A few ideas were tried out to find out how intervention would be the most effective. Originally starting with the idea of one-to-one sessions, we soon realised that three-to-one sessions were the way forward with more willingness to come from the students if they were not on their own. It also meant that there could be more contact time with the maths coach as with one-to-one sessions the time slots soon filled up and they would only be seen once a week, but the group sessions allowed them to have two or three sessions a week.

Having small groups gave the students more confidence to ask questions or say that they did not understand things as there was not the pressure of a whole class watching them, and allowing them to learn things at their own pace.

This new found confidence was often reflected in the classroom setting, with them attempting questions in class that they maybe previously avoided.

The small group setting also meant they could not shy away when they were asked questions, so always had to be thinking.

Another issue that the program helped us to overcome was that students did not revise or did not do enough revision, or left revision too late, a common finding in many C/D borderline students. Therefore, the intervention program put in the extra revision time.

As time went on the program progressed with new additions to it. One of these being morning maths revision. This involved the students coming in early for morning registration and getting 30 minutes of maths everyday before school. We began by doing 5 minutes or so of teaching into a topic and then set challenges so that students had something to work towards.

For example obtaining 100% on the mymaths C’s to B’ booster packs, and rewarded those that achieved this with Haribo! We found that this encouraged many of the pupils to do some work at home. As if they had not been able to complete the challenge during morning registration, they often worked on it at home.

We also did whole days of maths. Although this was originally greeted with grunts, it proved to be very successful with almost all of the students saying they were pleased they had done it.

On these days we carried on the Haribo challenge but with slightly different rules. Everyone did a test in the morning when they came in, all aiming to get a grade C. Anyone that managed it got some haribo! Following on from their results in the morning exam pupils were givena lesson to improve their mark. In this lesson they worked independently using custom designed ICT resources focusing on all the topics they had been unable to do on the test, or had got wrong. In addition they could also utilise revision guides or, if they preferred there were a number of teachers available to speak with.

The final part of the day was the students taking the same test again but with the numbers altered to see how much progress they had made through the day.

Most pupils went up one or two grades which was a great confidence booster and also showed them that if they just did a little bit of work they could improve their grades.

Results in January showed that so far the intervention program has been a success with 70% of the cohort achieving their grade C. Many of the students commented that they may not have passed if it had not been for the extra time and help they had received in maths intervention.

The intervention program was not only about teaching the pupils how to do things, but also about giving them the confidence to have a go at everything!

Kayleigh Rainbow

Setting an expert’s challenge in 3D (Issue 8, January 2011)

– Stepping outside the comfort zone with ‘launch assemblies’, 3D experiences and project learning.

Any teacher knows that getting students engaged in their subject is one of the most vital parts of education; in maths we are constantly searching for new ways to hook students in to the topics being taught in class.

When David Price and David Jackson visited the school earlier this term to discuss our involvement in the new Learning Futures project, I was inspired to turn what was an enquiry module of work into a project learning opportunity through which students could learn the importance of using data presentation to form an argument.

Project-based learning is an approach to enquiry in which students explore real-world problems and challenges, with any challenges being set by an expert in the field. The students engage in design, problem solving, decision making, and investigative activities. It allows students to work in groups or by themselves and allows them to come up with ideas and realistic solutions or presentations.

Our new module of work covering data handling is organized around the question of ‘Can we save the Planet?’ and was originally planned to involve a series of small tasks based on the effects of pollution. Having heard from the two visitors, I re-evaluated this and decided to be brave, step out of my comfort zone and try to develop our first real maths project.

Jackie Stent was able to put me in touch with Phil Tomlinson, the Divisional Energy Specialist for a large company in Ashington. I arranged a meeting with him to discuss the ways in which he could support the module of work. He was full of ideas to help; agreeing to launch the project through a letter to the students, and to view the work the students created to give them a real audience. We agreed to base the module around the recent Cancun meeting, where governments will meet to try to create a new Kyoto agreement, with each group of students being assigned a country’s data to work with.

I then had to decide how to launch the project to year eight in a way that would engage them. I decided to hold the first ‘Maths Assembly’ and booked the hub for the first lesson of the half term; but had to solve the problem of how to give it a hook! Having already identified a series of video clips to introduce students to the dangers of global warming, I tried to think of a way to go even further. Having seen the 3D screen in action for the school production of ‘Return to the Forbidden Planet’, when a dancing alien joined in with the cast, I thought about making use of the 3D facilities to get the students thinking about the context of the project.

Graham Quince and I designed a 3D true or false quiz, which students would answer by showing hands in assembly. A variety of facts, designed to emphasise the severity of the problems our planet is facing, would fly out in front of students as they were flown around the planet we were discussing. Graham built this and agreed to help out on the day in making sure everything went to plan; a vital help, which I couldn’t have done without!

And so the day finally arrived. Having never led a school assembly before, I was more nervous than I had been since my NQT year! The students filed in, the excitement growing as they were handed 3D glasses upon their arrival.

Students were a little unsettled in the first assembly, but with small adaptations made to the running order the second assembly went much more smoothly and effectively. Students were desperate to wear the glasses; asking whether they should wear them for each bit of video. The enthusiasm they had for the task can be clearly seen and feedback from students has been extremely positive.

“I think that the 3D was amazing. I think we should do projects like this more often. ” – Luke, Year 8

There are still, however, further improvements to be made. I found it difficult to discuss the answers to questions during the excitement of 3D viewing; staff have suggested that they would like more time to discuss the questions and ideas promoted in the assembly when back in the classroom, which we will implement when the module next runs.

Only time will tell how the remainder of the project based learning goes, as we will be working on it for the remainder of this half term. The launch assembly brought this new maths project and the global issues it concerns, to the forefront of students’ attention; hopefully making all of the nerves worthwhile!

Ruth Christopher