Archimedes' Principle: Volumes using Water

Every so often I like to look at the videos on the TED web site, and this one stayed with me a long time before I realised what I might be able to do with it...

The basics of the idea remained the same throughout, but I came across some blocks to what I wanted to do. The major one was that I was fixated on getting some 10cm x 10cm x 10cm perspex cubes for measuring (easily fixed with measuring jugs... I couldn't see the forest for the trees).

The main 'objective' of the lesson was to calculate the volume of irregular solids. I then carried this through to density, using the same video and concept, but this blog is about the volume lesson.

I went to the local pound shop on the weekend prior to our lesson, and purchased an assortment of fine goods. In all, I wanted 9 pairs of things to 'dip' and calculate the volume of.

I spent just under £10 and did get a few things I had lying around the house. We finished with a scented candle, a yo-yo, a plastic wrestler, a Noddy figure, a gun-shaped eraser, light bulbs, [forgotten object], a golf ball and a tennis ball (we haven't yet done volume of spheres).

In six groups of five, pupils dunked, measured water displacement and recorded the volume of three of these objects. In their groups they then created a net, and solid, for a prism of the same volume. This gave pupils an opportunity to discuss and consolidate their understanding for the volume of a prism through creating their net.

To finish up, we collected the created solids and compared them against their measured objects. This allows for a discussion regarding the comparison between them (unexpected outcomes, perhaps) and also for a discussion regarding whether our calculated volume would actually be that value for the yo-yo, the light bulb and the tennis ball (of course not, given the empty space).

And finally, we looked at a clip from Parks & Recreation in which a local fast food restaurant have started selling a 'child' size drink. The clip shows a discussion taking place over a table in which one person explains that the 'child' size label refers to the drink being the size of an average 'liquefied 4-year-old'. I explained that this is essentially what we had done - melted our solids down and refrozen them in the shape of our prisms.

The following lesson introduced density and gives a nod to Dan Pearcy's blog post as well as using - the same principle as that final video, with the use of my weight to calculate my volume.

The lesson I have just described didn't all occur within one lesson. I intended to be observed using this lesson, but a GCSE English exam was moved in to my room, meaning that my lesson started 20 minutes late, with my tables rearranged to an exam-friendly layout. We finished up the following day, because of 'school life' taking over, it seems. The above is the way that the lesson will run with year 10 in the coming weeks, though!

Stretching the Top End

I work in an inner city school in Leeds. I have worked in the same post for 2 and a bit years now and I'm really enjoying working there. I have a good rapport with the vast (vast) majority of pupils and I'm getting more and more praise from senior members of staff. In the last two years our GCSE results in Maths have increased by about 20%... I'm not saying it's all me, but I'm saying that my input has a sizeable effect.

Myself and another colleague (who also joined at the same time from my previous school) take the D/E pupils from modular and we enter them for linear exams. We hammer them in class and organise extended revision sessions after school, into the evenings, at weekends and during holidays. Some of the pupils who attend these sessions are not the kind of kids you expect to turn up to do maths revision until 7pm (and then walk home in the rain, cold and pitch black of night - choosing to do it again two days later) and it's very humbling to have that kind of impact on some difficult pupils. I leave every session drained, but so full of optimism and positivity after spending 3 hours with kids who are working so hard and making it so apparent that I made the right career choice.

I love the effect that I have had on our results and our C/D and D/E borderline pupils, but I'd like to make more of an impact on stretching our top end. At the moment we have about 5-6% of our Year 11s achieving A/A* and this fact depresses me a little.

Tuesday was year 9 parents evening. I teach our top set and the talents that these pupils come in with impress me every day. I spent 4 hours without breaking from conversations informing parents of their kids' potential and having wonderfully positive conversations about their potential GCSE grades, rarely having a negative word to say. I told each parent (24 out of 29 possible attendees) that their kid has my attention between 3pm and 4pm for the next 2 and a half years - with two stipulations: (i) I receive 24 hours notice (mainly so that lifts are arranged and there's no confusion, but also because I may be busy with revision classes, needing to get home or year 11 football) and (ii) the pupil brings the work or finds it in the textbook (this isn't an extra lesson for me, but a chance to help out with pupils who are taking responsibility for their own work). (There is a third, which is just that they have the option to bring me sweets or a chocolate bar to say 'Thanks!'... I stressed the optional part, but did suggest that I would have a negative view of them for the rest of eternity if they didn't and wasn't sure if they'd be able to live with this!). At the time, one pupil booked Thursday to work on circles and a bit of standard form and brought a mate to do some area work from a lower set and in class three of the girls have asked if they can come on Thursdays to get some extra work done.

I'm planning to extend our foundation linear revision sessions to B to A and A to A* sessions taking place in evenings, at weekends and through holidays closer to exam time and I'm looking into offering the Free Standing Maths Qualification to selected students next year. We're taking some of our current year 11s to a maths inspiration workshop at West Yorkshire Playhouse in March and intending to book Rob Eastaway for a session and invite some of our local 'partnership' schools to get involved.

Further down the school, I'm assigning our Numeracy Leaders to year 8 pupils as mentors and they're also starting a Maths Computer Club for pupils to come and complete any MyMaths homework or play maths games every Thursday.

I'm so busy at the moment, but I'm loving every moment of it (until I teach year 7 or 8 and I start to get a bit disheartened with their approach to schooling). Because I'm doing all of this, Mr. Gove, do I get paid more from September? I only ask because, to be honest, I'd love some more money. Regardless of your (expectantly-absent) response, I'll do it anyway, because I want our kids to have all the opportunities they need to succeed at our school.

Gangster Squad: The Four Measures of Average

On Friday evening I went to the cinema with my old man, my brother, his partner and mine to see the new Ryan Gosling film 'Gangster Squad'. I do this, and it annoys me - there was one point in the film where the 'Gangster Squad leader's wife is looking over some information about who he can recruit. I thought I could do something with it, and here is my effort...

I'll start with a 'teaser' clip. I wanted the trailer, but there's bad language and references to sexual behaviour, so I eventually came to this:

There are four tasks available here, for two different sets of data. The tasks are to work out who to recruit from the data you are given, using the mean, median, mode and range. I hope (since this has taken me a decent amount of time) that each one gives you a different squad with (possibly) a few repeats across the tasks.

Tell them that they're putting a squad together and they're to choose five police officers from the choices given. At the end of the task, you can check their work by asking who they'd pick and why...

I chose fictional police officers from, firstly, TV and film, and secondly, cartoons.

I'm quite proud of this one. I hope you can get some use from it and if you find any errors or improvements, please do let me know.

Revision Activity: Pass The Parcel

I teach a lovely year 10 group this year. Intelligent and polite and a generally nice bunch of kids to chat to and teach. Every week, they're invited to join me after school for 'Warty Wednesday' - a revision session so-called because this is the day that one boy in the class has his warts removed. Typically, about 10 kids turn up and we do some relaxed revision on topics we've already covered.

This week was 'Area and Perimeter' - up to and including parts of circles and compound shapes involving them. I don't like to prepare too much for it, so I made an A3 sheet with shapes on it and arrows where I wanted them to write dimensions. When they came in, I asked them to write a dimension on every arrow - this would be their sheet. We then passed this clockwise to the next person who found the area and perimeter of the shape with 'my' dimensions. After a short while, we passed them on and I asked the next person to receive the worksheet to check the work of the previous person before moving on.

At the end of the session every pupil should have had a sheet with a variety of area and perimeter questions and other people's work for them to look over and revise from.


I'm sure there's a lot of mileage in this - either with small groups, or in class having tables pass them around (if the seating plan suits) or along rows (if your seats are like this) - and can be extended to basic probability (colouring in dots instead of writing measurements), calculating averages (writing a given amount of numbers for those around them to calculate) or even setting each other different questions for basic number work.