Archive for the ‘Maths’ Category

Mean and standard deviation by stealth

Saturday, February 13th, 2010

Download a set of instructions written in English about how to calculate the mean and standard deviation of a data set.

This has been set to a group of students as homework (old fashioned term, but that is what it was) and I will evaluate the success of the mission in 10 days or so it [...]

Ten Data Sets

Sunday, February 7th, 2010

Download a PDF file with 10 data sets that can be used to illustrate a variety of statistical techniques

Useful pages:
Selected Data-sets from Publications by Martin BlandA stroop effect lap report with actual dataOne for the tree huggers – I always loved that picture of a road tunnel in the trunk of a Giant Redwood as [...]

Five number summary

Friday, February 5th, 2010

10 minutes on the max/min median and quartiles

Five number summary

Thursday, January 28th, 2010

Download a two sided handout on finding the five number summary for a set of data

The five numbers are the maximum, the minimum, the median and the upper and lower quartiles. This set of numbers can tell you about the central tendency of your data, the spread, the extreme values, and provide low order information [...]

Workshop number questions

Tuesday, January 12th, 2010

Download a one side worksheet with some workshop questions on number. Some symbolic questions (equivalent fractions, multiplication) and some word problems (VAT increase).

The main phase of the lesson was about probability. Packs of playing cards, coin tossing, and a discussion about smoking cessation, the National Health, and individual behaviour versus averages. Good stuff, and I’ll [...]

Data module mind map

Monday, January 4th, 2010

I’m using maps to plan lessons more and more. This one is getting a bit out of hand with the links between topics!

More workshop questions

Sunday, January 3rd, 2010

Download a pdf file with 20 questions about number topics.

This will get people back into the groove after the holiday. I allow about 30 minutes for this kind of worksheet. I have back up activities for the more confident students.

More quick number questions

Tuesday, December 15th, 2009

Download a pdf file with 40 (more) quick fire number questions.

Focus on equivalent fractions, rounding, and some questions embedding the four functions including with whole numbers and one or two decimal number questions in familiar contexts. No answers as yet but I might write a set out.

Quick fire number questions

Monday, December 7th, 2009

Download a one side pdf worksheet with 30 quick fire non calculator number questions and numerical answers.

Questions include the four functions with whole numbers and decimal numbers, a few fractions questions including adding related ‘family’ fractions, percentages and fraction conversion, some ratio and rounding and a few problem questions. Designed as a sort of ‘speed [...]

Revision PowerPoint

Sunday, November 29th, 2009

The symbol palette in Microsoft PowerPoint has always included the quarter fractions. Now you get the thirds and the eighths. Handy for quick revision PowerPoint presentations.

You can download a PowerPoint file with 20 slides with quick revision questions for level 1 Maths students. Covers money calculation questions, area and perimeter questions, unit conversion questions, questions [...]

Possibility space worksheet

Sunday, November 8th, 2009

One side on a topic in probability

Lowest terms

Thursday, October 22nd, 2009

6 minutes and 43 seconds on how to cancel down a fraction to its lowest terms. I’d rather describe that as ‘remove all the common factors from a fraction’. Produced using the NCH Debut video capture software, and edited in Windows Movie Maker. Notes on how to do all this coming soon.

Multiplying fractions

Monday, October 19th, 2009

2 minutes and 28 seconds on multiplying fractions. Recorded as a quick reminder for students on a return to study course.

Produced on my College issue laptop using the free version of the NCH Debut screen and Webcam capture software, and using the cheapo USB microphone (Logitech and Belkin sell the same oem device). Attempts to [...]

20 number question quiz

Tuesday, September 29th, 2009

Download a JQZ file with 20 question MCQ on four functions, number words, and place notation.

Link to Web page that displays a random selection of 10 of the 20 questions.

There is a time limit of 20 minutes on the 10 questions just so my Numeracy students can get used to working against the clock. They [...]

Measuring: numeracy introduction

Sunday, September 27th, 2009

Download a PDF version of a presentation on measurements with photos produced especially

Download a pdf with some group activities about measurement. This set of activities is designed to get people actually measuring and moving around the class. Along the way, they will confront skills such as recording data, making tables to show results, working with [...]


Thursday, September 24th, 2009

Download a one side handout with some estimation and BODMAS examples used for homework.

This one side homework was produced by copying and pasting from other worksheets I have written over the last few years. Definitely a 20 minute task. We use estimation questions as a way for students to show understanding of the sequence of [...]

Number questions

Wednesday, September 16th, 2009

Just a PDF with 40 four function questions with numerical answers. You can never have enough examples. This was used as a class exercise as individual work, and I had useful conversations with individual students about concrete examples. Issues around columns, place notation &c as usual.

A little bit of subtraction, some short and long multiplication [...]

Accuracy (Google Earth and sundials)

Friday, July 24th, 2009

A colleague draws a short line at the edge of the whiteboard recording the image of the window frame when the Sun shines in the classroom window and then carries on. As he is an enthusiastic and engaging teacher, the students’ attention is drawn away from the mark. The students are always amazed at how [...]

Foreign currency

Sunday, July 19th, 2009

Download one side on foreign currency conversion. It explains converting from Sterling to foreign currency and back again, and has a few questions of each kind. The worksheet assumes that students will use calculators.

I was searching for Web pages with simple explanations of the topics in the Number unit of an access maths module so [...]

48 Numeracy Questions

Tuesday, June 23rd, 2009

Download a PDF with 48 Numeracy Level 1 questions broken down into 4 ‘days’ worth of homework.

Gaussian distribution

Sunday, May 31st, 2009

Ruth’s been clearing out and found an old 10 Mark note. I could not resist scanning the detail with the Normal distribution on the front face next to the portrait of Gauss.

Graph questions for revision

Wednesday, May 27th, 2009

Download a PDF file containing a four page worksheet with graph plotting questions.

Trigonometry question on reader survey

Saturday, May 23rd, 2009

A tale of two solutions.

Wolfram Alpha

Friday, May 22nd, 2009

A search engine for Maths. You can type things like “y = (x+1)(x-1)x” or “weather Birmingham UK 2008” and get graphs and data. You can type a search term like “x^3 – 2x = 10” and the system will solve the equation exactly or approximately and draw graphs.

Metric Units starter

Thursday, May 14th, 2009

Download a metric units quiz. One side of A4 with a question where students match a measurement of an object (weight of new born baby, height of typical door) with the corresponding value (3Kg, 2 metres). Then the students have to find objects in the room that are various sizes. Finally some questions involving simple [...]

Algebra: simplifying expressions

Wednesday, May 13th, 2009

Algebra The BasicsView more presentations from keithpeter.

Click on Full Screen View on the player above (bottom right of the player, icon looks like a projector screen) to use on your interactive whiteboard.

Just one side of A4 on simplifying expressions, including collecting terms, multiplying terms, cancelling down algebraic fractions, and multiplying out brackets. Needs directed [...]

10 numeracy questions

Friday, May 8th, 2009

Just 10 questions a bit like the Level 1 numeracy test with answers.

Questions on areas and circles

Thursday, April 30th, 2009

Download a single sided worksheet with 14 mixed area and circle questions with numerical answers.

Nothing amazing, just some practice questions for Level 2 Access Maths students. Covers areas of rectangles, triangles and composite shapes, together with circumference of a circle, and area of a circle. The worksheet also has a couple of those problems like [...]

Adding Fractions: ‘traditional’ presentation

Thursday, April 30th, 2009

Adding Fractions: traditional approachView more presentations from keithpeter.

The slideshare presentation above is my attempt at explaining how to add fractions to a group of students taking the Level 1 Adult Numeracy Certificate. This particular group is aiming at joining an Access to Higher Education course next year, and so I’m using a more ‘academic’ style [...]

Introduction to Fractions using Smarties

Thursday, April 23rd, 2009

Introduction to Fractions using SweetsView more presentations from keithpeter.

Slideshare from an OpenOffice Impress presentation on the basics of fractions. Based on an idea from Malcolm C. It worked for his students so I’ll try it out with my Level 1 Adult Numeracy students.

A couple of worksheets coming as well…. You can download a PDF of [...]

Number questions: four functions

Saturday, April 4th, 2009

Download PDF file containing a one side worksheet with 28 questions covering the four functions, writing numbers from words and rounding. Numerical answers on the sheet.

The graphic above (taken on my little Fuji compact digital camera in macro mode) shows my check answer for the long multiplication. I had to actually calculate the answer as [...]

Arrange the digits

Monday, March 9th, 2009

Download a jqz file with 8 questions about rearranging digits to make the largest and smallest numbers. You can also save a Web page with the questions about rearranging digits and use that with students.

As usual, I have set the HotPotatoes options to remove all the buttons (the quizzes open in new windows in Moodle), [...]

Nutrition Information Tables

Sunday, March 1st, 2009

Numeracy teaching with a healthy eating message.

Numeracy: Quiz on rounding

Monday, February 23rd, 2009

Download a JQZ quiz file with 10 questions on rounding whole numbers of various sizes. You can also download a Web page with the quiz ready for use.

Part of the 20 minutes project, written on the way in on the train.

Number: place value quiz

Monday, February 16th, 2009

Hot Potatoes quiz on place value in whole numbers up to the tens of millions

Numeracy: words to figures

Tuesday, February 10th, 2009

Download a HotPotatoes quiz JQZ file for writing numbers in figures and back again. You can also save a copy of the Web page export of the words to figures and back again quiz.

An example of 20 minutes a day e-learning but actually took 35 minutes because of the need to help a colleague switch [...]

Example frequency distribution

Monday, February 9th, 2009

Download a two page PDF file [ 10 Mb file ] with scans of the histogram and cumulative curve drawn from a frequency distribution of adult male weights (made up data!). The frequency distribution has a moderate skew and shows the way the mean, median and mode spread out under those circumstances. The frequencies and [...]

Tree diagram build

Sunday, February 8th, 2009

Just a tree diagram that builds, based on a with replacement problem

Average and spread

Saturday, February 7th, 2009

Central tendency and dispersion PowerPoint on Slide Share

Data handling introduction

Friday, February 6th, 2009

PowerPoint presentation sets the scene for a new topic and includes a mind map

Avoiding common mistakes

Sunday, December 7th, 2008

Students mark incorrect answers: they avoid making the same mistakes

Reverse percentages slide deck…

Tuesday, November 18th, 2008

I’m trying a visual way of introducing those reverse percentage story problems that go like this: “Fred has had a pay rise of 10% and now earns £22000. What were his wages before the pay rise”.

Ratio and Proportion slide deck

Sunday, November 16th, 2008

Ratio and proportion problems introduced visually

Maps of US election results

Thursday, November 6th, 2008

areas of the states projected so that they are proportional to the number of seats in the electoral college. By Mark Newman

Fractions addition: slideshare

Thursday, October 16th, 2008

Quick And Dirty Fractions MethodView SlideShare presentation or Upload your own. (tags: fractions maths)

I use this quick method for adding two fractions of moderate size with Science students who need to revise basic numeracy quickly. The method is less efficient with large numerators and denominators and with denominators that have large highest common factors.

Most ‘everyday’ [...]


Friday, October 10th, 2008

Free geometry software

Keillor Distribution

Thursday, October 2nd, 2008

More than once on internet mailing lists I have encountered people who ridiculed others for asserting that “nearly all x are above [or below] average”. This is a recurring joke on Prairie Home Companion, broadcast from the fictional town of Lake Wobegon, where “all the women are strong, all the men are good looking, and [...]

Lattice multiplication

Wednesday, September 24th, 2008

Download a sheet of lattice multiplication blanks. Lattice or Gelosia multiplication has gone down very well this year with Access Maths students. The blanks save a bit of drawing in the sessions.

I’ve noticed that the YouTube above and some of the step by step explanations of lattice multiplication handle the carries in a slightly different [...]

BODMAS quick quiz

Sunday, September 21st, 2008

Download a PDF of a BODMAS quick quiz. Print it out and use in the first ten minutes of the lesson to test how much was absorbed in the last lesson!

The reverse questions help understanding I find. Adult students want to know the reasoning behind the methods.

Of All The People In All The World

Saturday, September 13th, 2008

A touring exhibition by Stan’s Cafe is a gift to Maths teachers. Statistics suggested by viewers, people represented by rice grains.

Spreadsheets to talk about

Saturday, June 21st, 2008

The humble spreadsheet can encourage students to talk about doing mathematics. Ideas and investigations you develop are futureproof. The ‘small laptops’ that are becoming more common allow more flexible use of class based pair and group work.

50 Mathematical Ideas

Friday, May 30th, 2008

Useful book for when students ask ‘do you like mathematics?’

GCSE Maths revision

Sunday, May 18th, 2008

GCSE maths web site sees increase in hits.

Correlation Coefficient

Tuesday, March 4th, 2008

Access students get a taste of what is coming next year in statistics

Spearman Ranks

Friday, February 8th, 2008

Ranking data simplifies the calculation

Apple pie

Saturday, January 12th, 2008

Food labelling – traffic lights or the full data?

Data vocabulary crossword

Monday, January 7th, 2008

Quick quiz for students to check their understanding of the words used in the book

Radioactive decay simulation

Friday, December 7th, 2007

48 quiet dice used to model half life

Why Algebra?

Sunday, November 4th, 2007

Where do you cut the map?

The number zoo

Sunday, October 14th, 2007

Naming the parts of the real number line and sneaking Venn diagrams back onto the syllabus…


Tuesday, October 9th, 2007

Don Norman has it wrong for adult students

Excel 97 arithmetic

Thursday, September 27th, 2007

Microsoft foobar

Bodmas quiz

Tuesday, September 25th, 2007

10 questions in hot potatoes

Maths tables

Sunday, September 16th, 2007

Maths tables produced using MS Excel

Mean, median and mode

Thursday, August 30th, 2007

Single sided worksheet on the three averages and probability

Percentage questions

Wednesday, August 29th, 2007

Calculator based exercises

Fractions and decimals

Tuesday, August 28th, 2007

More questions to keep the learning going


Monday, August 27th, 2007

Quick worksheet on an abstract topic

Whole number questions

Sunday, August 26th, 2007

Quiz sheet with answers

Dynamic graphs

Saturday, August 25th, 2007

Scatter diagram with draggable data points demonstrates line of best fit issues

Decimal multiplication

Tuesday, July 24th, 2007

More Hot Potatoes quiz questions with feedback

Decimal subtraction

Monday, July 23rd, 2007

Another 10 multiple choice quiz questions

Adding decimals

Sunday, July 22nd, 2007

Hot Potatoes quiz for decimal addition

Learning Patterns

Saturday, June 30th, 2007

Are there patterns to learning in Maths? Are these different in different subjects?

Equations slideshow

Tuesday, May 15th, 2007

Slideshare deck shows step by step solutions.

Trig summary sheet

Sunday, April 29th, 2007

Trig problems bring together a lot of skills

Blood Stain Analysis

Wednesday, April 25th, 2007

Some notes from a new blog


Sunday, April 22nd, 2007

PowerPoint gets a sound track and is published to YouTube and TeacherTube. TeacherTube has problems with sound on MOVs made with iShowU version 1.33

Dimensions and typography

Friday, April 20th, 2007

Volume and area are not the same!

Area and volume quick quiz

Friday, April 20th, 2007

More questions about area and volume of easy shapes.

Perimeter, area, volume questions

Thursday, March 29th, 2007

32 old chestnuts with answers on two sides of A4. Easter exercise.

Area formulas

Sunday, March 18th, 2007

YouTubes on rectangle, parallelogram and triangle, and on circles and composite shapes

The plan

Friday, March 16th, 2007

A record of a negotiation; the start of a week of whiteboards


Sunday, March 11th, 2007

Multiplying out practice with feedback in hot potatoes

Binomial probabilities

Saturday, March 3rd, 2007

Chi-squared test viewed another way…

Digital literacy

Saturday, March 3rd, 2007

What do we need to teach people about computers?

Directed numbers

Thursday, February 22nd, 2007

A small note for the top of the whiteboard…

Divided by a common…

Wednesday, February 21st, 2007


Access Maths

Monday, February 12th, 2007

Equivalence is different to identity

Directed numbers.

Sunday, February 4th, 2007

Adding and multiplying requires a ‘rules switch’.

One use of the inclined plane

Wednesday, January 24th, 2007

Blood stain measurement as a motivation for maths and error analysis.

Algebra podcast

Thursday, January 18th, 2007

Multiplying terms helps students to revise indices and directed numbers.

Slideshare – half way there

Sunday, January 14th, 2007 lets you share slides. Imagine if you could record sound and time transitions…

Cumulative frequency screencast

Thursday, December 14th, 2006

Plot the curve and find the median and IQR

Averages from frequency tables

Thursday, December 7th, 2006

I guess this is a podcast with visuals.

Tree diagrams screencast

Sunday, November 26th, 2006

YouTube video about tree diagrams in GCSE Probability. Me talking with illustrations provided by a PowerPoint presentation. I scripted the speech but then extemporised at various points – and managed this in two complete takes.

Probability questions

Thursday, November 23rd, 2006

A maths quick quiz for the first 15 minutes of the lesson. I usually kick off the data handling module with the probability topic as it sits on its own and links back to fractions so nicely.

Tree diagram script

Sunday, November 19th, 2006

Script for an explanation of tree diagrams suitable for GCSE Intermediate maths; there is (nearly) always a tree diagram question for students on the data handling paper. I’ll add a problem sheet before recording the screencast.

Probability screencast

Sunday, November 19th, 2006

9 minutes and 46 seconds on basic probability, including the probability scale, expected frequencies, mutually exclusive and independent events, possibility space diagrams and even a without replacement problem. All aimed at a GCSE Intermediate group. The .mov file was produced by ‘presenting’ a PowerPoint while speaking a commentary recorded using iShowU screen cam software. YouTube provide the hosting and convert the .mov to a Flash movie.


Friday, November 17th, 2006

Wooden toy found at the Frankfurt Christmas Market that is in Birmingham UK at present.

bodmas for calculators

Wednesday, November 8th, 2006

The formula above has to be written as a single line with brackets to ensure that the top line is calculated before the division, and that the square root function applies to the result.

√(((5.51 – 6)x2 + (5.89 – 6)x2 + (6.51 – 6)x2)/3) =

We spent an hour working over examples with recent Casio calculators [...]

Plotting scientific data with MS Excel

Tuesday, October 31st, 2006

MS Excel has powerful data plotting functions but the default settings are for illustrative graphs for presentations rather than printed graphs of scientific data. This handout suggests some settings that might produce better quality graphs.

How much can you remember?

Sunday, October 29th, 2006

Half term break provides a gap long enough to forget some bits of Maths, and this worksheet is designed to jog memories.

Leverage fractions

Saturday, October 14th, 2006

By spending extra lesson time on fractions – front loading in the jargon – I can save time on percentages and ratios. This kind of teaching needs trust from students; as I teach adults, I’m upfront about what I am doing.

Flash fractions

Thursday, October 5th, 2006

Very handy web site has flash animations of basic fractions processes complete with fla files for further customisation.

Fractions, tables

Tuesday, October 3rd, 2006

‘Spot the common factors’ approach works well for equivalent fractions puzzles. The kind of puzzle with unknowns on the bottom provokes thought!

Prime factors

Sunday, September 24th, 2006

More audio learning: five minutes on prime numbers and finding prime factors. Students need something to write on and with unless they have excellent short term memory!

Market maths

Saturday, September 23rd, 2006

If 5 kilos of potatoes cost £2.60, how much will 7 kilos cost? These are simple everyday problems but spending a little time on them lays the foundation for percentages and ratios nicely. This podcast works through some easy examples.

Numeracy blog and scientific calculator

Wednesday, September 6th, 2006

Numeracy blog for teachers from Scotland, and a Flash animation Scientific Calculator

Quick Quiz 5: Fractions

Tuesday, September 5th, 2006

Word file with fractions quiz. I use a 10 minute quiz at the start of each lesson to soak up later arrivals and to consolidate the work from the last session. The students get used to working under test conditions

Maths Quiz on decimals

Friday, August 25th, 2006

The last one before I have to start using PDFs because of fractions

A quiz a day helps the grades…

Friday, August 25th, 2006

...boost the mark by 5 or 10 and that could mean a whole grade

Another maths quiz

Thursday, August 24th, 2006

Just 10 minutes at the start of each lesson

Quick maths quizzes

Wednesday, August 23rd, 2006

Quick quiz (on paper) at the start of each lesson…

Formulas in text

Friday, July 21st, 2006

Ambiguous descriptions of formulas in newspapers

GCSE Map finished (well, begun)

Thursday, July 20th, 2006

Now I have the topics mapped, it is time to start adding bits of content

Geometry Applet: Triangle

Saturday, July 15th, 2006

Draggable triangle with perpendicular height

Geometry Applet: Parallelogram

Friday, July 14th, 2006

Simple use of David Joyce’s Geometry Applet to animate diagrams

GCSE: Algebra map

Friday, July 14th, 2006

Time to start putting some content in soon

Flash: Consolidation

Wednesday, July 5th, 2006

This timeline is all my own work and I didn’t look at the textbook… Lesson 2 and 3 applied to an animation showing how the area of a parallelogram is calculated…

Tinderbox: GCSE map

Thursday, June 29th, 2006

Tinderbox from Eastgate systems allows rapid development of complex web sites and a visual map of ‘emergent structure’ of a teaching task

Teaching rate of change

Sunday, June 11th, 2006

Use a guitar to explain rates of change of various variables

GCSE Maths paper 1

Tuesday, June 6th, 2006

Feedback from the first paper

Phase angle spreadsheet VBA

Wednesday, May 31st, 2006

Use VBA for smooth dynamically updating scroll bars

GCSE topics

Monday, May 29th, 2006

Last minute favorites for the non-calculator Module 5 paper


Tuesday, May 23rd, 2006

When is a crime rate valid?

Triangle in a triangle problem

Friday, May 19th, 2006

Why do some students find this problem so hard?

Tuesday Whiteboard: reflections and edges

Tuesday, May 16th, 2006

We were looking at finding a value for the intercept of a straight line graph when the scale of the graph made it difficult to have an X axis that started at zero – we were setting up and solving a simple equation within a context.

This second whiteboard processed using ScanR was taken in [...]

Unusual mould

Wednesday, May 3rd, 2006

Black rust form mould grows in concentric circles


Thursday, April 27th, 2006

Convection cells in a round bottomed flask

Areas by Audio: Podcast

Sunday, April 23rd, 2006

An audio lesson on easy areas with a single one side sheet of diagrams. This will be used by at least one student who can’t make the lesson because of shift pattern change.

Pythagoras animation

Tuesday, April 18th, 2006

MS PowerPoint on Pythagoras converted to Flash animation using OpenOffice 2

Circle Area and composite shape animation

Monday, April 17th, 2006

Flash animation generated by Open Office 2.0 from an MS PowerPoint presentation

Basic areas animation

Sunday, April 16th, 2006

Flash animation about basic Area formulas produced using OpenOffice

1600 watts

Wednesday, April 5th, 2006

1600 watts is (apparently) the rating of a modest 35mm film projector in an arthouse cinema…

Flash: Perimeter

Wednesday, April 5th, 2006

Flash from PowerPoint on a perimeter presentation with mini-exercises

Chi squared spreadsheet

Tuesday, April 4th, 2006

Calculates chi-square for a two number table, and applies Yates’ continuity correction

Flash from PowerPoint

Monday, April 3rd, 2006

Open Office 2.0 can export PowerPoint presentations as rudimentary flash animations

Preview in Mac OS X

Tuesday, March 28th, 2006

Preview allows you to cut diagrams out of PDF files and save them as PNG or JPG files

Superposition of two sine waves

Monday, March 27th, 2006

Spreadsheet shows effect of adding two phase shifted sine waves

Straight line graphs

Sunday, March 26th, 2006

Pop some graphs on the gcse blog and ask for the equations by e-mail?


Saturday, March 25th, 2006

“Gestures that complement rather than simply illustrate verbal instructions can boost children’s ability to complete problems in mathematics, researchers report.”

Complementary gestures are illustrated as…

“When using complementary gestures, however, the teachers pointed to each of the numbers on the left and then signalled the subtraction of the five on the right side by scooping their hand [...]

GCSE Mind Map

Tuesday, March 14th, 2006

Put the whole of GCSE Maths where you can see it

Migraine and hole in heart

Monday, March 13th, 2006

According to the BBC News quoting research by doctors in London and Shrewsbury, there may be a link between migraine with aura and a hole in the heart. Their figures (quoted from the BBC article) are as follows…
“The latest study screened 432 migraine with aura patients, and found 24% had a moderate [or] large PFO [...]

Central England Temperature series

Monday, March 13th, 2006

Notice any trend? Upwards? Downwards? Part of a sine wave of longish period? Scribble an idea now, then compare with the full series.

The chart above (shown without axes on purpose) is a plot of the yearly mean temperature from 1800 to 2005 taken from the Central England Temperature series. The series extends from 1659, as [...]

Beaufort Scale

Saturday, March 4th, 2006

I once heard the Beaufort Scale rendered as epic poetry. The reader started in a quiet conversational tone, speaking fairly quickly. As he ascended the scale, the voice grew louder and the pace slowed. The word ‘HURRICANE’ was bellowed at considerable volume.

The table below was copied from a notebook entry made one foul day in [...]

200 cubic kilometres of ice every year

Thursday, March 2nd, 2006

A recent post to the Real Climate blog details recent work on satellite images of Greenland showing the volume of ice flow into the sea from the glaciers that surround the coast.

The numbers are large – 220 cubic km of ice per year is currently flowing from the glaciers into the sea. That apparently corresponds [...]

Aperiodic tiling

Sunday, February 26th, 2006

I think I understand what labyrinth tiling might be, but I’ll need to check… It looks nice anyway, especially the labyrinth produced by just looking at the horizontal or vertical edges.

Calculating with large positive integers

Sunday, February 26th, 2006

The demonstration version of Reduce for Windows (scroll down page when it loads) – a computer algebra package – can be used to factorise large prime numbers (and polynomials!) as a way of demonstrating the properties of large numbers. Interactive sessions on a projector (the fonts are a bit small but there is no [...]

Of hammers and singers

Tuesday, February 21st, 2006

“Until the 19th century, there was no concerted effort to standardize musical pitch and the levels across Europe varied widely. Even within one church, the pitch used could vary over time because of the way organs were tuned. Generally, the end of an organ pipe would be hammered inwards to a cone, or flared outwards [...]

Fruit fly results

Friday, February 17th, 2006

Gender differences in the mendelian ratio?

A new Hogben?

Tuesday, February 14th, 2006

Maths for the Million – what new chapters would you add?

Mendeleyev’s Dream

Monday, February 13th, 2006

Original periodic table had gaps and forced re-measurement of many atomic weights and other properties.


Saturday, February 11th, 2006

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

Active Internet Users…

Monday, February 6th, 2006

Internet use figures tablulated with populations for a list of countries

Statistics for genetics

Saturday, January 28th, 2006

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.

R Project

Tuesday, January 24th, 2006

Freeware stats package for Mac OS X, Linux, Windows

Simulated blood stains

Saturday, January 21st, 2006

Latest results on new experiments…

Mystic rose Excel macro

Thursday, January 19th, 2006

A little bit of VBA goes a long way…

Algebra substitution game

Wednesday, January 18th, 2006

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

Prime number podcast

Monday, January 16th, 2006

BBC radio program about history looks at prime numbers

Hot Potatoes

Wednesday, January 11th, 2006

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

Maths for science

Tuesday, January 10th, 2006

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

Circle theorems

Monday, January 9th, 2006

Java applets allow exploration of geometrical relationships by dragging

Standard deviation recipe

Saturday, December 24th, 2005

Draft of SD notes for study pack

Chi-square statistic and test

Friday, December 23rd, 2005

Draft notes on how to calculate the well-known statistic

Writing about charts

Friday, December 16th, 2005

Excel on projector helps provide rapidly updated charts to trigger discussion

100 words

Sunday, December 11th, 2005

Read all about it coursework: a useful list

Planet transit times 2006

Sunday, December 11th, 2005

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

Casio calculator

Wednesday, December 7th, 2005

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

Pie charts

Sunday, December 4th, 2005

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

A city is not a tree

Wednesday, November 30th, 2005

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

Measuring bloodstains with Photoshop

Saturday, November 26th, 2005

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

Number questions

Friday, November 11th, 2005

50 questions at level 1 and 2 on Number

Finding the focal length

Sunday, October 30th, 2005

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.

Maths handbook

Sunday, October 9th, 2005

Mathworld by Eric Weisstein is a huge online reference


Saturday, October 1st, 2005

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

Logarithmic Spiral

Thursday, September 29th, 2005

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

Macro World

Wednesday, September 28th, 2005

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

Multiplication: different methods

Monday, September 26th, 2005

I’ll see how gelosia and russian multiplication go down

Finding factors

Friday, September 23rd, 2005

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

BBC Maths quiz

Tuesday, September 20th, 2005

Nice quiz – pity about the feedback

Born abroad

Wednesday, September 7th, 2005

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

MS Excel dynamic graphs

Sunday, August 28th, 2005

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.

MS Excel simulation

Saturday, August 27th, 2005

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 [...]

Perfect Square Dissection

Friday, August 26th, 2005

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

4 colour theorem

Thursday, August 25th, 2005

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

Leonardo’s adding machine?

Wednesday, August 24th, 2005

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

Ruler and compass constructions

Tuesday, August 23rd, 2005

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


Monday, August 22nd, 2005

Analogue synthesisers – a hoot with op amps and noise

Bradford Wool Exchange windows

Saturday, August 13th, 2005

Strange geometrical pattern found in 1840s building

Right Hand, Left Hand

Saturday, August 13th, 2005

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

Symbols – a cautionary tale

Wednesday, July 20th, 2005

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

HTML entities

Wednesday, July 20th, 2005

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.

Altitude of the Sun and Moon

Sunday, July 17th, 2005

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.

Food miles

Friday, July 15th, 2005

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

Key Skills 4 u

Thursday, July 7th, 2005

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

Chi-squared data: flies

Tuesday, July 5th, 2005

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

Independent events

Tuesday, June 21st, 2005

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

Maths Posters

Wednesday, June 15th, 2005

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 [...]

Algebra practice

Tuesday, June 14th, 2005

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) – [...]

Online map creator

Saturday, June 11th, 2005

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 [...]

Stats on driving risks

Monday, May 30th, 2005

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 [...]

Special graph papers

Saturday, May 21st, 2005

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!

Decimal point kills baby?

Friday, May 20th, 2005

“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 [...]

A4 paper ratio

Monday, May 16th, 2005

Why A4 paper is the shape it is?

Chemistry Numeracy

Thursday, May 12th, 2005

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 [...]

GCSE Maths

Wednesday, May 11th, 2005

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

Tuesday, May 10th, 2005

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

Virtual Manipulatives

Saturday, May 7th, 2005

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 [...]

Estimation Game

Friday, May 6th, 2005

Java game speeds up estimation with three digit whole numbers.

Standard deviation

Thursday, May 5th, 2005

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

Formula for mode

Tuesday, May 3rd, 2005

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 [...]

Lorenz attractor

Sunday, May 1st, 2005

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 [...]

Probability simulations

Thursday, April 28th, 2005

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 [...]

Geometry applet

Tuesday, April 26th, 2005

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 puzzle

Monday, April 25th, 2005

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 [...]


Friday, April 22nd, 2005

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, [...]

(simulated) blood stains

Wednesday, April 20th, 2005

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 [...]

Children using the Web…

Monday, April 18th, 2005

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 [...]

CIMT GCSE Materials

Saturday, April 9th, 2005

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 [...]

Statistics simulations

Sunday, March 13th, 2005

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 [...]

Finding planets

Wednesday, February 23rd, 2005

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 curves from the TTA

Wednesday, February 23rd, 2005

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 [...]

Genetic fingerprinting – probability of false match?

Wednesday, February 23rd, 2005

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 [...]

Maths for adults

Sunday, February 20th, 2005

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 [...]

Some stats simulations

Sunday, February 13th, 2005

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 [...]

Central Limit Theorem

Sunday, February 6th, 2005

” 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 [...]

Normal distribution sample simulation

Saturday, January 15th, 2005

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 [...]

Blood spatter pattern analysis

Saturday, January 1st, 2005

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 [...]

Fruit Fly Genetics

Monday, December 20th, 2004

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 [...]

Statistics notes

Friday, December 17th, 2004

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 [...]

“From the Vault of the Heavens”

Friday, December 10th, 2004

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 [...]

Nursing numeracy support material

Sunday, November 21st, 2004

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 [...]

From College to University

Sunday, November 21st, 2004

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 [...]

Algebra book online

Sunday, November 21st, 2004

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 [...]

40 questions…

Thursday, October 28th, 2004

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 (TROL)

Saturday, October 23rd, 2004

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 [...]

Maths in vocational context

Tuesday, October 19th, 2004

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 [...]