bodmas blog

Concord centre mural in Sparkbrook. Nice work.

The Angel needs renovating or demolishing. Used to be a rough but tolerable pub before the drugs started…

Current views from the city centre: little that is old in some places.

Writing on the wall – taggers run supreme in parts – shades of the Sinclair essay

The students will be sleeping above the graves of early Victorian members of the hebrew congregation of Birmingham. They will be surrounded and cradled on three sides by canal, railway and ring-road; three forms of mass transport.

I have made a pdf file with 14 practice readings copied from Web sources for use in a Need to Know lesson.

As part of the English Speaking Board qualification, students need to read a text aloud. This activity is designed to give students practice at reading aloud – how often do any of us read text aloud to see how it flows? – and to give each other feedback.

I will then increase the pressure a bit by asking the students to record their text using simple sound recorders. The resulting compilation will induce cringes no doubt, and will not be published here!

I have mixed journalistic writing with more academic or ‘reference’ sources. I’m guessing that students will find the news articles easier to read aloud than the more formal writing. This should prompt some discussion of the general idea of writing to read.

Godin has encapsulated the key message of the last four weeks of enrolment.

“Every person who encounters your organization for the first time comes with beginner’s mind. She knows nothing about yesterday or how hard you worked or your financing or what it took to build it. She’s here now, she’s first, let’s go.”

This is going to get printed in 24pt and put on the notice board. It means we can’t make assumptions about what adult students know about the educational process. It also means that I have to explain the learning process. Otherwise they fall back on the last model they had – and that didn’t work too well, otherwise adult students would not be taking level 2 qualifications.

Download an audio MP3 that explains prime factors in 5 minutes, with one example. [1.6 Mb, 48Kb/sec mono]. Students are given terms to look up in a textbook and to search the Web for at the end of the recording. Most people will need a visual cue for the repeated division calculation.

The speech was recorded in the kitchen, with better results than the ‘market maths’ audio file, although the echo is obvious. Two takes and it was finished, I do stumble over a list of factors at one point, but it is a minor glitch and not worth the time to re-record or edit out. The 48Kb/sec bitrate gives reasonable quality in return for a file size of around 1.6 Mb for just over 5 minutes of time.

The script

Prime factors

This fountain sounds regular but the water does not repeat exactly each cycle, there is some change. A lot of processes in nature sort of repeat but not exactly. Prime numbers give us some insight into systems like that. Large prime numbers multiplied together also protect the security of your bank account using public key encryption.

Most Maths textbooks will define a prime number as ‘a number with exactly two factors, itself and one’. Six has factors of one, two, three and six and it can’t be a prime number. The number seven has factors of one and seven only so it is a prime number.

A more visual way of looking at the factors of a number is to imagine arranging small stones in different shapes, so six can be arranged as one row of six stones or as two rows of three stones. Twelve can be arranged as one row of twelve stones, two rows of six stones or three rows of four stones. Some numbers, like seven, can only be arranged as one row of stones, and these are the prime numbers.

The first few prime numbers are two, three, five, seven, eleven, thirteen and seventeen. One isn’t a prime number as one has only one factor. Two is the only even prime number.

Numbers that are not prime are called composite numbers. Any composite number is made by multiplying together a certain list of prime numbers. For example, twelve is made from two times two times three, so the prime numbers two, two and three are the ‘signature’ of twelve. We call two, two and three the ‘prime factors’ of twelve. This is confusing as the prime factors are very different to the factors of twelve like four and six. You just have to keep the two ideas separate.

To find the prime factors of a composite number, you try to divide the number by each of the prime numbers in turn starting with two. If a prime number can divide the number with no remainder then it is a prime factor.

An example will help. Remember that the first few prime numbers are two, three, five, seven, eleven. Suppose I want to find the prime factors of ninety. Ninety is an even number, so I divide ninety by two to get forty-five. Two is a prime factor of ninety so I make a note of it, and then I try to divide forty five by a prime number. Three goes into forty-five fifteen times, so I have three as a prime factor to add to my list. Fifteen divided by three again gives five, itself a prime number, so these are my last two prime factors.

Ninety is given by multiplying two by three by three again and then by five. As three appears twice, we can say that the list is two times three squared times five, using index notation for the repeated multiplication by three.

Your turn: find the prime factors of 300. [ 15 seconds ]. I get two squared times three times five squared.

Look up prime factors in the index of any gcse textbook to find more examples. You will also see ways of setting out the calculations on the page. Look for a section on ‘factor trees’ if you have a visual orientation.

Search the Web for the phrase ‘the music of the primes’, this is the title of a book, if you are interested in the uses of prime numbers.

Download a 3 minute MP3 on the unitary method [1.3 Mb ] for solving simple problems.

The ‘unitary method’ just means ‘find the cost of a unit’. Typical problems include

1. 5 lemons cost 95 pence, how much will 8 lemons cost?
2. 2 lb of sprouts cost 80p, how much will 5 lb cost?

These problems are simple and students can solve them quickly. 4 minutes plus a worksheet is about as much lesson time as I would spend on this topic. Full understanding provides a basis or ‘hook’ for percentages, ratios and even fractions.

The podcast has some sound recorded in Birmingham Market mixed in at the beginning and end just to lighten things up – I just walked up and down the stalls with an external mic on the digital voice recorder, and I was surprised how good the resulting track was. I recorded the speech outdoors; not such a good idea as the microphone picks up the always present traffic rumble from a main road, although there is definitely no echo.

The script

Birmingham food market sells fruit and veg of all kinds, and each stall holder has their own way of pricing their wares. You need to use your mental arithmetic skills to get the best deal.

In GCSE Maths, we have problems like this; three kilos of peaches cost two pounds forty pence. How much will five kilos cost?

To answer this kind of question you always start by finding the cost per kilo. In this example, you divide two pounds forty pence by three to get eighty pence per kilo for the peaches. Once you know the cost per kilo, you multiply by the number of kilos you want to buy, in this case five kilos. I get eighty pence multiplied by five to be four pounds.

To summarise: divide the cost by the weight to find the cost per unit. Then multiply by the weight you want to buy.

Try this example: Two pounds of tomatoes cost seventy pence. How much will three pounds cost? [ a few seconds ]. I got one pound and five pence. I divided seventy by two to get thirty five pence per pound and then I multiplied the thirty five pence by three to get one pound five pence. I multiplied the thirty five pence by three mentally; three thirties are ninety pence and three five pences make fifteen and then I just added.

Now you try these – answers are at the end.

Question one. Seven oranges cost eighty four pence. How much will ten oranges cost?

Question two. Three kilos of potatoes cost one pound twenty pence. How much will seven kilos cost?

Question three. Twelve eggs cost one pound eighty pence. How much will eight eggs cost?

Question four. Two pounds of sprouts cost ninety six pence. How much will five pounds cost?

Answers: Question one, one pound twenty. Question 2, two pounds eighty. Question 3, one pound twenty. Question four, Two pounds forty pence.

This method is called the unitary method as it is based on finding the cost per unit. Look up unitary method in a textbook and practice some more examples. Now back to Birmingham Market.

“I’ve been using 960 for some time now, as it’s slightly smaller than full width, and it’s divisible by 3, 4, 5, 6, 8, 10, 12, 15, and 16 (imagine the grid possibilities). I’d love to hear what all of you are wrestling with.”

Cameron Moll has adopted 960px as his design width for fixed layouts (article via Zeldman’s blog). Moll has picked this width as it has a larger number of factors and allows a wider range of grid possibilities than the more ‘exact’ 974px. I personally tend to use the browser at around 800px wide on my iBook anyway, but Mac OS X tends to encourage non-maximised windows as a result of the drag and drop functionality. I know Windows users tend to maximise their windows (I do too at work, although my CRT monitor is on 800 by 600 so I can keep the refresh rate around 100Hz).

I shall be sticking with liquid layouts on this page – I’m currently using a hacked version of the Minimalist Fever theme on this WordPress site. I’m also using a definition list on the home page in an attempt to get 4 or 5 posts ‘above the fold’ on a typical page. Log analysis has already shown that the ‘posts before the current one’ are getting more exposure through this; the clicks on the ‘old’ posts were very low while using Kubrick and similar themes where the current post was all that was visible above the fold. I suppose using the definition list with title and excerpt is prolonging the eyeball time for each post.

Nielsen has sensible advice on window size assumptions for current Web browsers viewed on PC monitors. Optimise for 1024 by 768 but allow for smaller sizes.

• Colleges have rules about students publishing on college servers and so they should
• Many journalists have their own blogs (Jeff Jarvis’ Buzzmachine”, and Kieren McCarthy as two examples)
• Is it time to encourage our students to branch out and set up their own blogs?

I would probably suggest that the students should adopt a nickname for now as the Way Back Machine can be unforgiving if you are trying to live down things you wrote years ago.

A simple blogger account would introduce students to the joys of self-publishing, and would encourage the students to get friends and relatives to read the pages and leave quotes. As the students are not publishing on College servers, there would be no editorial role needed. It transpires that sub-editors may be a dying breed anyway, and student journalists may need to get used to editing their own copy.

Judging by the Telegraph experiments, journalists may soon need to podcast and produce short videos as well, so perhaps a single podcast per student and some collective video on YouTube might round off an online CV.

I’ll be checking this one out with the Powers-That-Be. We’ll get that Social Web thing going soon, I’m sure. It will be interesting to see who develops their blog into a permanent project.