I have been using Number of the Day (see separate blog here) for some time and found it to be a useful way of regular revisiting a range of basic number skills.

I began wondering whether it would be possible to use a similar resource to practise basic algebra skills. The result is Expression of the Day.

I haven't had the chance to use this very much yet so it may well get adapted in the coming weeks and months. However, the picture below gives an indication of the kind of questions I might pose to students.

As with Number of the Day, the possibilities for differentiation here are almost limitless.

If you'd like to download the PowerPoint slide it's available here.

If you have any suggestions for changes or improvements, please let me know.

# MathsMuggle

## Monday, 1 June 2015

## Thursday, 28 May 2015

### Starter activity - Number of the Day

I should start this post by explaining that this isn't my idea and I'm afraid that I have no clue where the original idea came from. If you know, I'd be interested to hear from you.

My version of Number of the Day has been adapted from something that a colleague showed me about 5 years ago.

I find this to be a very effective starter activity for a Maths lesson. Students are expected to complete a range of different questions using a particular number as their starting point. The questions cover aspects which would probably be considered as 'basic' number skills - the sorts of things that I want my students to be really confident about.

The teacher can choose to include all of the questions or just some by ticking the small boxes.

The teacher also chooses the Number of the Day - I often use the date although the beginning of each month is rather less interesting!

For me, the real strength of this activity is the almost endless differentiation.

For example, students could be asked to add, subtract, multiply or divide integers or decimals or negative numbers. Students may need to make an estimate of the square root if it is not an integer. Students could be asked to find 50% or 35% or 1.5% of the number. Students could be asked to find 1/2 or 3/5 or 8/11 of the number. You get the idea...!

Additionally, the Number of the Day itself can be chosen to make the questions easier or harder.

If you'd like to try this starter out for yourself, you can find the PowerPoint file here.

My version of Number of the Day has been adapted from something that a colleague showed me about 5 years ago.

I find this to be a very effective starter activity for a Maths lesson. Students are expected to complete a range of different questions using a particular number as their starting point. The questions cover aspects which would probably be considered as 'basic' number skills - the sorts of things that I want my students to be really confident about.

The teacher can choose to include all of the questions or just some by ticking the small boxes.

The teacher also chooses the Number of the Day - I often use the date although the beginning of each month is rather less interesting!

For me, the real strength of this activity is the almost endless differentiation.

For example, students could be asked to add, subtract, multiply or divide integers or decimals or negative numbers. Students may need to make an estimate of the square root if it is not an integer. Students could be asked to find 50% or 35% or 1.5% of the number. Students could be asked to find 1/2 or 3/5 or 8/11 of the number. You get the idea...!

Additionally, the Number of the Day itself can be chosen to make the questions easier or harder.

If you'd like to try this starter out for yourself, you can find the PowerPoint file here.

## Saturday, 31 May 2014

### A Lesson: The Capture-Recapture method

I am teaching GCSE Statistics for the first time ever this year. I am lucky to be working with an able group of Year 10 students - all 24 achieved a level 8 on their end of Year 9 assessment - and I expect them to do well in their exam this summer.

I began the year with grand ideas about creating lots of engaging lessons. For example, in one of our first lessons in September, we used Spearman's Rank Correlation Coefficient to test the correlation between the scores given by Strictly Come Dancing judges. We then gave 8 vegetables a score out of 10 and used SRCC to find our perfect vegetable partner within the class!

However, I have not designed and taught as many lessons like this as I had hoped, largely due to the significant time demands of the Controlled Assessment part of the GCSE.

Just before the May half-term holiday I decided it was high time we had a more engaging lesson and I planned the following lesson on the Capture-Recapture method. This was largely inspired by Julie Reulbach's blog about a lesson on the same topic.

I began with this video which is a great introduction to the topic and then explained that students were going to work in pairs to conduct their own capture-recapture experiment. Each pair of students received a lake with fish in and some tags (or a bowl of Weetos plus some Froot Loops on the side!)

Students had the support of the worksheet below but the rest was left up to them.

I was particularly keen to avoid teaching students a particular method for calculating their estimate of the total population. The text book gives the formulas below but as far as I am concerned this topic is just some reasonably straightforward proportion work and the formulas make for unnecessary complications.

I began the year with grand ideas about creating lots of engaging lessons. For example, in one of our first lessons in September, we used Spearman's Rank Correlation Coefficient to test the correlation between the scores given by Strictly Come Dancing judges. We then gave 8 vegetables a score out of 10 and used SRCC to find our perfect vegetable partner within the class!

However, I have not designed and taught as many lessons like this as I had hoped, largely due to the significant time demands of the Controlled Assessment part of the GCSE.

Just before the May half-term holiday I decided it was high time we had a more engaging lesson and I planned the following lesson on the Capture-Recapture method. This was largely inspired by Julie Reulbach's blog about a lesson on the same topic.

I began with this video which is a great introduction to the topic and then explained that students were going to work in pairs to conduct their own capture-recapture experiment. Each pair of students received a lake with fish in and some tags (or a bowl of Weetos plus some Froot Loops on the side!)

Students had the support of the worksheet below but the rest was left up to them.

I was particularly keen to avoid teaching students a particular method for calculating their estimate of the total population. The text book gives the formulas below but as far as I am concerned this topic is just some reasonably straightforward proportion work and the formulas make for unnecessary complications.

Students seemed to enjoy the lesson, certainly understood the method and, most importantly of all, I had plenty of spare Froot Loops to take home for my 3 year old daughter!

About to start |

'Fish' now 'tagged' |

## Tuesday, 1 April 2014

### Showdown - a revision activity

Although Revision Races remain my favourite revision activity in the Maths classroom, Showdowns are just behind them in second place. I first discovered Showdowns when, Linda Masters, a colleague of mine introduced the Maths Department to a range of Kagan Structures. A number of these structures are now used regularly within the department although some adaptations to them have been made. This is how I use a Showdown for revision in Maths.

Students work in small teams of about 4 students to answer a range of Maths questions.

These questions are displayed on the whiteboard one at a time. (I use Smart Notebook software). You can make up your own questions but old examination papers are a good source of questions too.

For each question, every group nominates a leader. At my school, we make the leader wear a silly hat to identify themselves and most students seem to enjoy this!

The teacher then awards points for correct answers or even for good working out on a difficult question. These points are then recorded on a score board.

After each question, all leaders need to be prepared to be chosen by the teacher to offer further explanation about their answer or the method used. A good explanation will receive a bonus point.

Before the next question, new leaders are appointed (and the silly hats move round).

Then the Showdown continues as described above.

I usually find that I need about 15 questions for a 50 minute lesson but this can vary depending on the difficulty of the questions posed.

At the end of the Showdown, the team(s) with the most points will win prizes.

You can download an example showdown by clicking here.

If you'd like to know more about how I use Showdowns, please let me know.

And if you're using interesting and engaging revision activities, I'd love to find out more from you.

Cue Ennio Morricone! |

These questions are displayed on the whiteboard one at a time. (I use Smart Notebook software). You can make up your own questions but old examination papers are a good source of questions too.

For each question, every group nominates a leader. At my school, we make the leader wear a silly hat to identify themselves and most students seem to enjoy this!

**Initially all students must work on the question individually**for a period of time - mini-whiteboards are an excellent resource for this. When an appropriate amount of time has passed - enough for all student to have a good go at the question - the team are allowed to discuss and compare their methods and their answers. The leader then has responsibility for deciding on the correct answer (if there is any disagreement) and showing this answer to the teacher.An example question. |

After each question, all leaders need to be prepared to be chosen by the teacher to offer further explanation about their answer or the method used. A good explanation will receive a bonus point.

A Showdown scoreboard. |

Before the next question, new leaders are appointed (and the silly hats move round).

Then the Showdown continues as described above.

I usually find that I need about 15 questions for a 50 minute lesson but this can vary depending on the difficulty of the questions posed.

At the end of the Showdown, the team(s) with the most points will win prizes.

You can download an example showdown by clicking here.

If you'd like to know more about how I use Showdowns, please let me know.

And if you're using interesting and engaging revision activities, I'd love to find out more from you.

## Thursday, 28 November 2013

### Revision Races

My all-time favourite activity for an engaging Maths revision lesson is a Revision Race.

I first introduced these to my colleagues in 2011 having found the idea via TES Resources. A quick internet search tells me that there are a few Revision Races around including those in the Bits and Bobs section of the 'Number Loving' website. I have also seen these activities called Revision Relays.

However, during the last two years my colleagues and I have developed an approach to Revision Races which seems a bit different from the way other people use them. In this post, I will describe how I run a Revision Race and how this differs from what appears to be the norm.

The standard version of a Revision Race usually involves students answering a series of questions as quickly as they can. They are given an initial question and must bring the correct answer to the teacher before they are given the next question. The winner would be the student, or group of students, who answer the most questions in the allotted time. I did try running a Revision Race in this way a couple of times but I had a key concern: what should I do if a group of students got completely stuck on one question even after multiple attempts?

I believe that my adapted version of a Revision Race addresses this issue and also has a number of other added aspects which teachers may find useful.

Firstly, in my Revision Races, students have access to all of the questions right from the start. These are printed on a single piece of A4 paper, a copy of which is given to each student. (This remains far more cost effective than having lots of copies of different questions all on separate sheets of paper). Questions might focus on one particular topic area as in the example below or could be more of a mixture. The rules can vary slightly depending on the class but this format allows me to let students answer the questions in any order they wish and/or allow them to attempt to answer more than one question at a time before bringing me the answers. This can be particularly useful with a larger class when long queues of students wanting their answers marked can form all too quickly.

Secondly, students have a maximum of three attempts at each question.

Each team has an answer grid (see below) which must be completed for each question.

If an answer is incorrect, students can choose either to make another attempt or to move on to another question.

Students generally use mini-whiteboards to do their working out and, if they get really stuck, they can bring these to me for a hint or to find out where they have gone wrong.

I have also devised a scoring system for my Revision Races. If the first answer is correct, six points are scored, four points are scored if the answer is correct at the second attempt while only two points are scored if the third attempt is right. If the third attempt is incorrect, students score no points for that question and must move on to another question.

Finally, I record the all of the points on an Excel spreadsheet as they are gained during the Revision Race. This means that students are able to keep track of their progress during the lesson on a live scoreboard.

A bit of conditional formatting means that the cells of the spreadsheet change colour depending on the number of points scored. I find that this use of colour also serves as excellent Assessment for Learning for me as a teacher. For example, on the spreadsheet below, I can see that Question 4 caused lots of problems which indicates that I need to revisit this topic.

In order to try to reward different approaches to a Revision Race, I usually award prizes to the team with the most points but also to the team with the longest run of green answers.

I have made some resources available to get you started. They are downloadable by clicking on the links below.

Revision Race score board

Revision Race answer grid

Revision Race - algebra questions

If you'd like to know more about how I use Revision Races, please let me know. And if you're using Revision Races in a different way that is really successful, I'd love to find out more from you.

I first introduced these to my colleagues in 2011 having found the idea via TES Resources. A quick internet search tells me that there are a few Revision Races around including those in the Bits and Bobs section of the 'Number Loving' website. I have also seen these activities called Revision Relays.

However, during the last two years my colleagues and I have developed an approach to Revision Races which seems a bit different from the way other people use them. In this post, I will describe how I run a Revision Race and how this differs from what appears to be the norm.

The standard version of a Revision Race usually involves students answering a series of questions as quickly as they can. They are given an initial question and must bring the correct answer to the teacher before they are given the next question. The winner would be the student, or group of students, who answer the most questions in the allotted time. I did try running a Revision Race in this way a couple of times but I had a key concern: what should I do if a group of students got completely stuck on one question even after multiple attempts?

I believe that my adapted version of a Revision Race addresses this issue and also has a number of other added aspects which teachers may find useful.

Firstly, in my Revision Races, students have access to all of the questions right from the start. These are printed on a single piece of A4 paper, a copy of which is given to each student. (This remains far more cost effective than having lots of copies of different questions all on separate sheets of paper). Questions might focus on one particular topic area as in the example below or could be more of a mixture. The rules can vary slightly depending on the class but this format allows me to let students answer the questions in any order they wish and/or allow them to attempt to answer more than one question at a time before bringing me the answers. This can be particularly useful with a larger class when long queues of students wanting their answers marked can form all too quickly.

An example of a Revision Race focusing on algebra. |

Secondly, students have a maximum of three attempts at each question.

Each team has an answer grid (see below) which must be completed for each question.

If an answer is incorrect, students can choose either to make another attempt or to move on to another question.

Students generally use mini-whiteboards to do their working out and, if they get really stuck, they can bring these to me for a hint or to find out where they have gone wrong.

I have also devised a scoring system for my Revision Races. If the first answer is correct, six points are scored, four points are scored if the answer is correct at the second attempt while only two points are scored if the third attempt is right. If the third attempt is incorrect, students score no points for that question and must move on to another question.

Revision Race answer grid |

Finally, I record the all of the points on an Excel spreadsheet as they are gained during the Revision Race. This means that students are able to keep track of their progress during the lesson on a live scoreboard.

A bit of conditional formatting means that the cells of the spreadsheet change colour depending on the number of points scored. I find that this use of colour also serves as excellent Assessment for Learning for me as a teacher. For example, on the spreadsheet below, I can see that Question 4 caused lots of problems which indicates that I need to revisit this topic.

Revision Race score board |

I have made some resources available to get you started. They are downloadable by clicking on the links below.

Revision Race score board

Revision Race answer grid

Revision Race - algebra questions

If you'd like to know more about how I use Revision Races, please let me know. And if you're using Revision Races in a different way that is really successful, I'd love to find out more from you.

## Tuesday, 5 November 2013

### Improving students' collaboration using acrylic sheets

I use mini (A4 size) whiteboards very frequently in my classroom. They are great for Assessment for Learning of course but I also find that students are happier to have a go at a tricky problem, safe in the knowledge that they can rub it out if something goes wrong.

However, these whiteboards are generally used on an individual basis and I wanted to find a way to increase collaboration without losing students' willingness to 'give it a go'.

For some time, I had been admiring the 'group whiteboards' that I had seen in blog posts by US teachers such as Fawn Nguyen but I could not find a source of these in the UK. (If you know of one, please let me know).

Then, one day last academic year, a colleague of mine suggested using sheets of acrylic (clear plastic) instead and this has turned out to be an idea of great genius!

We initially experimented with a single sheet of acrylic - cut to fit a standard classroom desk. We quickly confirmed that dry-wipe pens could be used to write on them and that they would also wipe clean again (although I advise you to avoid using red pen which is strangely stubborn!).

The 'eureka moment' was the realisation that, since the acrylic sheet is clear, we could place paper

__underneath__it. This opened up a whole world of possibilities. The opportunity to place diagrams, pictures, sets of axes etc. underneath and to be able to write or draw on them while still being able to make changes or corrections seemed really powerful. Another bonus is that the paper resource remains clean so is reusable, saving money too!

We now have 16 acrylic sheets in the Maths Department which is enough for even our largest teaching groups to work in pairs and these are proving popular with both staff and students.

They have already been used for a variety of topics including:

- Angles in parallel lines (see photo)
- Circle theorems
- Loci (to get the general idea without the precision of a pair of compasses)
- Plotting graphs of various types
- Solving simultaneous equations graphically
- Graphing inequalities and regions

Using an acrylic sheet to work on the topic of angles in parallel lines. |

I'm certain there are many more possibilities for using these acrylic sheets in Maths and colleagues from other subject areas have also seen ways that they could use these in their lessons. I hope to share more ideas about how to use these acrylic sheets in future blog posts.

If you'd like to know more or if you have any further suggestions or comments, please let me know.

## Thursday, 31 October 2013

### Consistently Good CAN BE Outstanding

This is my first blog post - thank you for reading.

Firstly a bit of background: I'm in the 16th year of a varied teaching career and I'm now in my 4th year as Head of Maths at a non-selective converter Academy which has a significantly better than average intake.

I am fortunate that the vast majority of students at my school are able and motivated. I am also fortunate to have a full team of 'specialist' Maths teachers. They're all qualified too!

When I took over the department, Maths GCSE results were below expectations. 69% of students had achieved A*-C grades in Maths in the summer of 2010 compared to over 90% in English.

In subsequent years, the Maths GCSE A*-C figures have been 82% (2011), 86% (2012) and 88% (2013). Progress is also good now with over 90% of students making at least 3 levels of progress and more than 60% of students making 4 or more levels of progress. This year we hope to break the 90% mark for A*-C and a figure of 50% A*/A is not out of the question.

In this blog post I want to focus on one particular aspect of what we have done to achieve this recent success.

As a department we aim to

I can think of no greater compliment to my colleagues than when we heard students say, during our Ofsted inspection earlier this year, that the Maths Department were just teaching normally. (Clearly others were not!)

I believe that our experiences demonstrate that consistently 'Good' lessons can lead to 'Outstanding' outcomes for students.

Firstly a bit of background: I'm in the 16th year of a varied teaching career and I'm now in my 4th year as Head of Maths at a non-selective converter Academy which has a significantly better than average intake.

I am fortunate that the vast majority of students at my school are able and motivated. I am also fortunate to have a full team of 'specialist' Maths teachers. They're all qualified too!

When I took over the department, Maths GCSE results were below expectations. 69% of students had achieved A*-C grades in Maths in the summer of 2010 compared to over 90% in English.

In subsequent years, the Maths GCSE A*-C figures have been 82% (2011), 86% (2012) and 88% (2013). Progress is also good now with over 90% of students making at least 3 levels of progress and more than 60% of students making 4 or more levels of progress. This year we hope to break the 90% mark for A*-C and a figure of 50% A*/A is not out of the question.

In this blog post I want to focus on one particular aspect of what we have done to achieve this recent success.

As a department we aim to

__teach 'Good' lessons all of the time__and I am confident that on the whole we achieve this. We have been brave enough to ignore the pressure from SLT (especially when Ofsted was looming) to teach 'Outstanding' lessons. We are far from convinced that it's possible (or important to try) to do this day in day out. As Tom Sherrington says "It is the 99% of lessons that are never observed that really matter. So, we need to focus on things that we do every day." To the best of my knowledge, in the last three years, nobody in the Maths Department has had an internal observation of any kind graded as 'Outstanding'. I'm sure that I find this fact far more pleasing than I should!I can think of no greater compliment to my colleagues than when we heard students say, during our Ofsted inspection earlier this year, that the Maths Department were just teaching normally. (Clearly others were not!)

I believe that our experiences demonstrate that consistently 'Good' lessons can lead to 'Outstanding' outcomes for students.

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