bodmas.org

Vernier calipers and the venerable screw micrometer allow us to measure small objects with a resolution high enough to see random variation.

Internet use figures tablulated with populations for a list of countries

Nice and clear site on stats for genetics by Jim Deacon from the Biology Teaching Organisation, University of Edinburgh. Useful examples in context and helpful dos and don’ts. There is a section on experimental design as well, and a page that helps people choose the appropriate statistical test.

Freeware stats package for Mac OS X, Linux, Windows

Latest results on new experiments…

A little bit of VBA goes a long way…

Three PowerPoints contain a brief presentation on substituting and a ‘game’ that encourages group work

BBC radio program about history looks at prime numbers

Quiz suite written by esol teacher is at version 6 and getting seriously useful

What would a ‘survival pack’ for science students contain?

Java applets allow exploration of geometrical relationships by dragging

Draft of SD notes for study pack

Draft notes on how to calculate the well-known statistic

Excel on projector helps provide rapidly updated charts to trigger discussion

Read all about it coursework: a useful list

The transit time of a planet can help you find the planet in the sky and can help plan observing trips

fx-83ES defaults to maths mode with surds and fractions

MS Excel or any spreadsheet on a projector with whole class questions

Christopher Alexander was a visionary architect and philosopher. This Web page summarises one of his better known books. Much used by computer scientists.

PhotoShop or similar image editor provides a way of measuring a scanned image accurately, but you need Pythagoras…

50 questions at level 1 and 2 on Number

When photographers include the Moon or Sun in a picture, you can find the angle of view and the focal length of the lens by a simple application of trigonometry.

Mathworld by Eric Weisstein is a huge online reference

Mathsnet is a web site that provides interactive demonstrations of maths topics

Is the hand painted decoration on my Taramundi an accurate logarithmic or equiangular spiral or not?

Looking at things through a simple jeweler’s loup can provide a refreshing ‘take’

I’ll see how gelosia and russian multiplication go down

Use a systematic method to list factors and you get them all

Nice quiz – pity about the feedback

Most people born abroad live in the South of England – especially London. New statistical analysis decouples immigration from ethnicity.

Use the ‘forms’ toolbar in MS Excel to link a slider control with a cell. Then you can make ‘dynamic graphs’. Projected onto a screen, you can ask students to predict what the result of a change is going to be.

Download a spreadsheet that simulates breeding 60 fruit flies
The spreadsheet simulates the results of breeding fruit flies (F2 Generation – Second Filial?) where the expected outcome is a simple 1:3 Mendelian ratio of vestigial winged flies to winged flies
The screen shot above shows an anomalous result – a chi-squared statistic well above 3.84, the critical [...]

What is the smallest number of squares of different sizes that can be joined together to make a square? Answer: 21

Try using 4 colours to colour in some maps – harder than it looks

Controversial replica calculating machine is based on a sketch in a ‘misplaced’ manuscript by Leonardo

Some links to examples of constructions of common shapes and online drafting aids

Analogue synthesisers – a hoot with op amps and noise

Strange geometrical pattern found in 1840s building

Left Hand, Right Hand, Chris McManus, Phoenix, 2003, ISBN 0-75381-355-6

Beware the use of symbols of a graphic nature in maths lessons – you may have students who take the lesson the wrong way

Maths on the Web is a problem – html entities can provide a limited range of symbols – and I like the immediacy of a blogging approach to Maths. Else it is down to PDFs or scans or Whiteboard captures.

A spreadsheet uses simplified low precision formulas to calculate the altitude of the Sun and the Moon for each hour of a given day. Change the latitude to see the effect of moving into the arctic circle. Change the date to see the effect of slipping towards Winter.

How far has your dinner travelled? Perhaps half way round the planet!

Web site aims to motivate keyskills lessons – self test quizzes and practice tests.

Six datasets based on reproduction experiments with fruit flies – used for chi-squared statistics calculations

Probabilities can only be multiplied if events are independent. Sudden child deaths in the same family cannot be regarded as independent.

The Isaac Newton Institute for Mathematical Sciences published a series of 12 monthly posters on tube trains in London during the year 2000. The posters are available at moderate resolution on the Web and can still be purchased as a set from The Mathematical Association’s online shop – a nice tie in.

The posters were designed [...]

By popular request… Remember that a multiplying mixed signs gives a negative answer and multiplying same signs gives a positive answer!

Multiply out the following

2(3x – 2) – 4(2x – 1)
2xy(x + y)
2(4x + 3) + 3(2x – 9)
4(x + y) – 2(x + 2y)
2x(x2 – y3)
2(5x – 4) – 3(2x + 7)
4(10x + 3y) – [...]

The original Online Map Creator Web site provides an online interface to the GMT package
Planiglobe is the new simplified interface – faster but currently has few options

The original OMC has been around for years and will plot contours of ocean depth and continental height. You can pull the plots down as PS files or [...]

A BBC News article reports a survey by the Institute of Advanced Motorists into perceived driving risks based on a sample of 700 drivers. The survey finds differences based on gender and age regarding the risks.

60% of women drivers in the sample cited ‘tailgating’ as a major risk compared with 47% of male drivers in [...]

Thanks to Jeremy for this Web site…

Print Free Graph Paper

Seems to have a good range of patterns including polar and log-lin. The metric rulings are on the right, and seem short of smaller divisions (i.e. 20mm/2mm isn’t there). The isometric papers could come in handy for 3-d drawing!

“The mistake made by the nurses was a mathematical miscalculation which in other working environments might not have been quite so catastrophic”

The quote is from the coroner in a case of a 15 day old baby given 10 times the prescribed dose of Digoxin to slow a fast heart rate and appears on the BBC [...]

Why A4 paper is the shape it is?

I’m doing some numeracy sessions for HND Chemistry students. I needed lots of specific examples and exercises within the area of Chemistry.

Basics with an emphasis on converting from everyday to metric units – US origin. Good stuff on density. PDF file, part of a comprehensive set of lecture notes
Stuff on standard form part of a [...]

Timetabling (that three dimensional jigsaw puzzle) is occuring and it looks like I’ll be teaching a GCSE Maths course next year. Expect a week by week puzzle page. Hot Potatoes looks like the way to go with quizzes and puzzles delivered through a blog like WordPress with ‘future posting’. Animated formulas (see below) might be [...]

Napier’s Bones were a 16th century calculating device based on lattice multiplication, from the inventor of logarithms.

The Natioanl Library of Virtual Manipulatives for Interactive Mathematics is a Web site with a large number of Java applets that invite students to explore Mathematics problems. ‘Manipulatives’ is the US term for things like Cuisenaire rods and Dienes blocks.

The Java applets are mapped to the US curriculum based on ‘grades’. I have used [...]

Java game speeds up estimation with three digit whole numbers.

An alternate formula and why it might be easier to just use the standard one!

There is a simple graphical construction that you can add to estimate a more accurate value for the mode of a grouped frequency distribution (see the red lines on the sketch graph below).

Can you write a formula for the value of the mode estimate in terms of the locations of the bar boundaries and the [...]

Edward Lorenz was using a primitive computer (it was 1963) to numerically integrate an apparently simple set of coupled differential equations. The computer worked to 6 decimal places and printed out each line to 3 places. Restarting a run, he noticed that the trace started looking similar but became slowly different to a previous run [...]

Planetqhe is a site by David Kay Harris dealing with probability. There are Excel spreadsheets that present problems in probability in a novel way, including two stage tree diagrams.

The presentation is different to the usual one in UK GCSE textbooks – Harris is head of Maths at the International School of Toulouse and the site [...]

David E Joyce of the Clarke University has provided a set of Java classes that allow complex geometrical constructions too be built using parameters passed to a Java applet.

The Geometry Applet
Euclid’s elements with dynamic diagrams

The geometry applet looks as if it could be used to provide dynamic graphics to help students explore locii and circle [...]

rLogo is a Java based implementation of the Logo programming language. I used a simple ‘starter’ in a recent Maths lesson where students had to learn about the exterior and interior angles of a polygon and learn to solve problems along the lines of ‘can a regular polygon have an interior angle of 125 degrees?’.

On [...]

The starting square has side 1. Another side 1 square appears, and then a side 2 square is added across the top of them. Then a square of side 3 appears to the left, and a sqare of side 5 appears underneath.

The sequence of the sides of the squares is like this…
1, 1, 2, 3, [...]

recipe: 300ml of milk and three tablespoons of treacle – warm milk over electric hotplate in milk pan. Spoon treacle in and stir well.
looks lumpy but dries (in a few days) really convincingly
Students set up a dissection board or similar with some wall paper afixed – set the board at known angles
drop the simulated blood [...]

The NFER has a long term project (started in 2002) tracking students’ experience of citizenship education. The most recent report is referenced as follows….CLEAVER, E., IRELAND, E., KERR, D. and LOPES, J. (2005). Citizenship Education Longitudinal Study: Second Cross-Sectional Survey 2004 Listening to Young People: Citizenship Education in England (DfES Research Report 626). London: DfES

The [...]

The Centre for Innovation in Maths Teaching based at the University of Exeter provides a range of materials for free download on their Web pages. In particular, there is the Mathematics Enhancement Programme for key stage 4 that provides GCSE maths materials as PDF downloads. There are 20 units available, and the units are provided [...]

A series of Java based statistics simulations provides covarage of most aspects of statistics at level 3 and 4 (Normal distribution, skew, sampling, tests of significance)
These are part of the Rice Virtual Lab in Statistics and you can download the lot as a ZIP file (or as JBuilder source code)
The site also includes a stats [...]

The headmap sphaeric web page has a simple geometrical method for finding rough positions of the planets based on using concentric circles to represent the orbit of the planet and of the earth.

I’ll re-work this a little minus the ideology.

Note added 27th Feb : errors prove large for Mars. The smaller signal is the declination [...]

Cumulative frequency curve summary from the Teacher Training Agency!
The TTA material covers the syllabus for the Numeracy test that newly qualified teachers must take
The material is presented as Web pages that are also available in a plain form for printing out
Areas of numeracy covered
There are interactive practice tests available as well as written questions
Could be [...]

The Centre for Innovation in Mathematics Teaching has a range of simple Web pages that set up a problem in a context using GCSE level Maths.

Chance of false matches in DNA matching (genetic fingerprinting) is a useful leader for a lesson on combined probabilities – and directly useful to Forensic science students!
Mistaken DNA Identification has [...]

The diagram above is re-drawn from Mike Ollerton’s book Getting the buggers to add up published by Continuum. Most of the issues he raises for engaging children and teenagers are alive and well for adults…

Take away aspects of ‘behaviour’ – less challenging anyway
Add in a big set of built in hangups and partial constructs about [...]

Central Limit Theorem – you can roll up to 5 dice up to 10000 times and plot the frequency distribution of the total score. As you ‘roll the dice’ a second and third time, the cumulative score is shown so that the Normal distribution can emerge through repeated samples. Nice touch – imagine using this [...]

” The distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal “.

“Thus, the Central Limit theorem is the foundation for many statistical procedures, including Quality Control Charts, because the distribution of the phenomenon under study does not have to be [...]

Histograms are meaningless for datasets smaller than about 500 items – you will be better off using a dotplot. I think that the ‘error bar’ for each bar of the histogram can be approximated by the square root of the frequency so that a bar with a frequency of 36 could have a standard deviation [...]

The MathsWorks Project has a series of laboratory projects on different aspects of Maths in Biotechnology. One of the projects is about blood spatter pattern analysis and has a very usable practical using milk to calibrate the relationship between drop stain shape and angle of surface.

There is also a good treatment of the mathematical assumptions [...]

The Genetics Laboratory Manual from the University of South Florida has plenty of detail on Drosophilia Melanogaster and the various genetic manipulations available.

You can simulate the Mendelian inheritance of a simple trait using a couple of coins and some patience – and a Chi-Squared statistic can be calculated from a table of observed and expected [...]

These are mostly first year University level but the datasets, examples and general approaches might be useful for Unit 6 on the BTEC Applied Sciences

Darren Wilkinson is making his Statistics teaching notes, PowerPoint slides and homework exercises freely downloadable as PDFs
John Matthews distributes his Biomedical Science Statistics module notes as PDFs

Professor Matthews’ Summary Measures and [...]

Filippo Brunelleschi was the mathematician and artist who designed the dome of S. Maria Novella in Florence. How much maths did Brunelleschi know? Did he know about astronomy, and could he use an Astrolabe ?

I was able to find a paper mapping his friendships with local mathematicians and astronomers and astrolabe dealers using the new [...]

Numeracy support material for nursing is based on a numeracy course in the department of Health Studies at York University.

There is a lot of useful vocational context here and some nice examples, alas hampered by dated Web design (frames based site, flash animations used to convey material, assumptions made about screen size and so on).

The [...]

The mathscentre Web site has a growing collection of resources in a variety of formats – short leaflets on key numeracy skills (all of fractions on two sides) to longer packs of materials.

The student portal maps leaflets and revision books by vocational subject but often the leaflets are generic. The Web site does not appear [...]

James Brennan is providing his Understanding Algebra book free for online access. This algebra text is geared to US educational requirements and styles but there is a lot here that Access students doing science modules could use.

The book is pure exposition of the basics – few worked examples and no problem sets. I found it [...]

Download a 6 page worksheet

Following the TROL example, I am adding some PDFs of worksheets here. The first is 40 short questions for revision for students taking an Access course – this first test is non-calculator. Topics covered include

Whole numbers, fractions and decimals
Percentage and simple percentage problems
Basic Unit conversion
Ratios (including foreign currency)
Basic probability

Students will get [...]

Teacher Resources On Line has a lot of downloadable PDF files with quizzes, problems and mini-investigations. Could be useful. The arithmetic practice PDF file has 12 pages of puzzles around tables and simple arithmetic operations but presented in a puzzly way with number squares and other visual shapes. Could be handy for use with Access [...]

A big thankyou to the University of Hull Study Advice Services crew for making their worksheets and leaflets available online without password protection.

I’ll be using the excellent Mathematics Practice for Nursing and Midwifery (a PDF file) available to my access students over the half term as revision and a bit of a challenge for the [...]