It’s been a pretty full on term so far, as it always seems to be, so it was lovely to have a break yesterday evening and do some maths for ourselves! We were fortunate enough to welcome Trevor Starbuck to the first Birmingham and Solihull Further Maths Support Programme network meeting hosted at John Willmott School. The intention of these network meetings is to bring together teachers from across the city who have an interest in meeting with other teachers to explore issues relating to the teaching and learning of mathematics and further mathematics at A Level.

Trevor had spent part of the afternoon talking with some of the higher achieving Year 11s, and then turned his attention after school to a small but very enthusiastic group of willing maths teachers. Not having had the privilege of teaching A Level, and still holding a passion for all the mechanics modules I chose at Uni oh so many years ago, I was really looking forward to this session.

The classroom we were meeting in had been transformed into a den of mechanics experiments. Trevor’s enthusiasm for the subject was radiating from him as he introduced the two experiments we were to undertake. These involved, amongst other things, half pipes, marbles, clamp stands, metre rulers and timers.

The curve shows a quadratic relationship between the distance and the time.

The curve shows a quadratic relationship between the distance and the time.

Firstly, there was timing a marble rolling some given distances. The metre long pipe, marked into 20cm segments, was kept as shallow as possible for the marble to roll. It was then timed 3 times each for rolling each distance from 20cm to 1m and the mean value taken. Results plugged into Autograph and the following graph was produced:

The second experiment involved the the rolling of a marble across a tilted table. Our job was to track its path as accurately as we could, to gather data on its path, distance and time. image  We first set the pipe and clamp stand so the marble could travel a decent path up and across the tilted table. Next was to identify the end point of the path, which crated the x-axis.  This path was timed (at least 5 times, and a mean value taken) and the axis was then split into 8 equal parts.  Rolling the marble as consistently as possible, we tracked when it passed each division (again, 5 times for each, taking the median of the points we had plotted on the division lines).

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We ended up, as you would expect, with a lovely parabola. The final two measurements to take were the height of the middle division – the point where the marble started its downward journey, and, using a bit of trigonometry, the degree of inclination of the table.image

These experiments were reminiscent of those undertook by Galileo in the late 16th Century.  Ofcourse, he didn’t have electronic timers, so we were quite relieved when Trevor didn’t insist on use using a water hour glass timer, similar to what Galileo would have used.  imageAs well as rolling balls across inclined planes and measuring their distance, Galileo also used the Tower of Pisa to give him a vertical height from which to drop objects.  He was able to demonstrate that a body dropped from height starts at zero velocity and increases his speed over time (rather than the constant velocity, that was larger the more the body weighed, assumed by those before him). This also involved his discovery that the velocity of a falling body is independent to its weight and the mathematical expression that, the speed of an object increases as the square of the time, hence our quadratic graph from the results of the first experiment.

Fast forward 100 years and armed with Newton’s Second Law of Motion, we are now able to form some calcualtions from our data.

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And so we have it; practical experiments and calculation enabling us to derive a (very approximate) value of gravity.  There is of course discussion time here for all the aspects not taken into consideration, the main one being air resistence, but our time had come to an end.

The Birmingham and Solihull FMSP network hope to meet at least termly. It was a really enjoyable, practical session; a chance for us teachers to focus on mathematics, from those of us who would like to brush up on our A Level to those who have been teaching it for many moons!  Each meeting will have a specific focus such as this, but there will always be time for discussion of other matters according to teachers’ interests and concerns.  I do encourage any local teachers who are interested in A Level maths (you don’t have to be teaching it) to get involved with the network.  For more information, please contact:

Martyn Quigley
FMSP Coordinator for Birmingham and Solihull
School of Mathematics
University of Birmingham
B15 2TT
0121 414 4800
martynquigley@furthermaths.org.uk

RAG123

image      imageRAG123 Review updated                      RAG123 Review

I’ve been using RAG123 for a year now, after reading about @Benneypenyrheol’s RAG123 marking experiment.  This then led me to @ListerKev, and his selection of posts introducing, explaining and enthusing about the purposes of RAG123.  I decided to trial it in the last few weeks of 2013/2014, and was so impressed with the effect it had on informing my planning to support pupils learning, that it was a given that I’d be using it with all my classes.

From @ListerKev

From @ListerKev

From @_jopayne

From @_jopayne

A quick search on google found that there were several RAG123 posters already created, so it became a fairly easy job to adapt the wordings of these to suit my students and classroom.  As we’ve previously used RAG for pupils understanding of topics, I kept this the same, and 123 became the effort, which linked in with pupils on our reports too.  After using this for a year now, I’ve updated the wordings to the first person, as these will now be going on the first page of pupils exercise books, alongside presentation for learning and our written assessment and feedback system.

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Division PuzzleI came across this idea on superteacherworksheets.com, although I’m sure many others have also used or made something similar.  It’s quite straightforward, pupils complete 9 calculations, find the answers on the puzzle pieces, and put them in the same order as the questions to make a picture! So I made this one for the decimal division that one of my groups is currently working on.

I don’t give the scissors out until the questions have been attempted (as otherwise pupils can easily put the puzzle together!)  The bonus of having the pieces with the answers on is that pupils can self-check as they are working.  There is no reason for the cutting and putting together of the puzzle, other than it is a motivating factor to complete all the questions, giving the pupils well needed practice!

Decimal Division Puzzle

When preparing a resource to take and share at mathsconf4, I wanted to share something which I find valuable and seems to make a difference to pupils learning. So I chose a resource, originally from TES (complex_number) for a topic I find pupils struggle with, yet is a basis for so much mathematics: converting between fractions, decimals and percentages. The resources I use are for groups with little or no understanding of the connections between the three as they start off quite basic.

It starts with a slideshow of artwork where proportions could be viewed as a theme. IMG_0337This includes works from Piet Mondrian, Victor Vasarely, Ellsworth Kelly and Frank Stella. With a quick review of what fraction, percentage and decimal (based on a 100 square, so using £s and p to support the decimals) mean, pupils then create their own artwork on their 100 square.  They then use their art work to write the fraction, percentage and decimal of each colour used.   The advantage of using this resource has been to consolidate the connection between the fraction out of 100 to the percentage. IMG_0339 The next step is to move onto a 50 grid, 25 grid, 20 grid and 10 grid, and hence the need to change the fraction to out of 100 in order to write the percentage.   Accompanying the grids are some fraction, percentage and decimal tables, with an extra column for the fraction out of 100, for pupils to practise their conversions. IMG_0342 IMG_0343 A similar resource I’ve used is a skittle pie charts. I’ve done this by giving out skittles (20, 25 or 40) and pupils to make their own circles, grouping the colours, section ing them off and writing the fraction, percentage and decimal for each section. I’ve also given out a template for pupils to colour in given skittles (this was actually to help with interpreting pie charts, but linked in nicely to the fractions, percentages and decimals work the pupils had completed previously. IMG_2292 IMG_2293  IMG_0338 All the files are linked below to use and adapt as wished! 1. Equivalent FDP Mosaic 2014 1. Mosaic Art 1. Mosaic Fractions Sheet 2. FDP Calculation Foldable 2. FDP Starter 2. Interpreting pie charts 2. Interpreting Pie Charts 3. FDP The original idea and basis for these came from TES (complex_number) and an American website, all freely available.  I’ve adapted into my own documents and made them to suit my groups.  Thanks, as always, to the originators of the ideas to sharing so freely, allowing me to use your ideas in teaching my groups.

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Being an avid reader of @mathsjem’s resourceaholic blog, especially her maths gems, I’m often inspired to try something out.  This time, from gems 30, was the homework expectations. I still get frustrated by pupils lack of presentation skills, despite reminding them of our school’s presentation for learning rules (which are in a bullet point list).  It’s not just following the rules, but the attitude it reflects in their learning, and therefore the expectation of achievement they give themselves.  I hope that if I expect excellence, then pupils can achieve excellence!

So for me to expect excellence in their presentation, I don’t just want a list of rules, but a model to what excellence looks like.  I will start trialling using this model in the next few weeks (with a tweak or two to the design and colours) with the aim of launching it with my classes in September, and a focus on presentation for learning in those first few lessons and home learning.

Presentation for Maths Learning

2nd August: Attached below now is the updated version, which includes presentation target codes for the pupils, as presented by @letsgetmathing at mathsconf4.

Presentation for Maths Learning

Presentation for maths learning

Failing and Sailing

Having read the blog post from Meolscop High School: Shuffling Sums, about First Attempt In Learning and Second Attempt In Learning, and then meeting the lovely @missfilson at mathsconf15 and hearing more about her department’s work on growth mindset, I was inspired to give it a go with students at my school.

The first introduction was with a year 7 group who had been constructing triangles using ASA. I gave them the following problem asking whether students would construct identical triangles if they were gien only angles.

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Some students were thinking about it straight away and were happy to write down their opinions, but there was a significant amount of students who were reluctant to write anything down because they didn’t know the right answer. It was important to spend time explaining to the students that I was interested in their thoughts and not whether ther answer was right or wrong. At this point I also said that they may want to write a sentence or try constructions to help them come to an answer. For this first attempt, I wrote individual hints in their books to give the students support towards their second attempt. I also wanted to help students feel ok with not getting the right answer the first time, and to share with each other their “FAILs” and hints.

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I also tried this with a year 9 group working through ratio and proportion. Students were gven the miles/km conversion lines and asked to complete any missing values they could. Again, students found it difficult to attempt anything to begin with as they wanted to know the right way to calculate the amounts, but after some encouragement, most students made their first attempt.

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Looking through students first attempts, they’d all had a go at a valid method, so with support would be able to continue along their line of thinking. This time, instead of giving individual hints, I grouped the feedback into the three methods they’d attempted:

1. Putting values against each step on the double number line

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2. Recognising where the miles value had doubled, so doing the same to the km

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3. Finding the relationship from miles to km

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I reviewed these methods with them as a whole class, and gave them the option of continuing with the method they started with, or changing to a different method. Some results are below (the final student being keen to make corrections corrected her first attempt before rewriting onto the second!)

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From this work, it is evident to me that students find it difficult to grasp the mindset of attempting something without knowing if they are “doing it right”. This won’t change overnight, but the failing and sailing is another step towards developing growth mindset within my maths classroom.

Mock Exam Follow up

Our year 11s have completed another mock paper, and I wanted a more robust way of each pupil working on a topic which they shouldn’t have lost marks on, along the idea of @just_maths oops sheets.  I knew which topics I wanted to target, and whilst looking at the PRET homework that @mathsjem and @DIRT_expert collated, I put together worksheets with a model solution to the target question, the memory box for revision, skills practice and exam question practice.  I’m so grateful to the resources that fellow maths teachers put online, as I was able to quickly find appropriate questions from the PRET homeworks (thanks to @_rhi_rhi, @AdamGoodridge18)

The worksheets are all below, remembering the credit going to the above folks.

Mar13 2H 05Circl

Mar13 2H 11ExpandFactorise

Mar13 2H 13Pythagoras

Mar13 2H 13Trigonometry

Mar13 2H 15SimilarShapes