Ross Isdale, Robert Morrison

Websites for use in Maths. Ross Isdale, Robert Morrison, Chuck Owen & Charley Parsons Firrhill High School 1. www.bbc.co.uk/scotland/education/bitesize/higher / 2. www.bbc.co.uk/scotland/education/bitesize/standard/ 3. www.counton.org/ 4. www.counton.org/gcseandalevel/test/index.html 5. www.mathsrevision.net/gcse/index.php 6. www.mymaths.co.uk/login.asp 7. www.purplemath.com/index.htm 8. www.ies.co.jp/math/java/samples/samples.html 9. www.waldomaths.com/ 10. www.1000problems.org/ 11. www.mathsisfun.com/ 12. www.mathsnet.net 13. www.greylabyrinth.com 14. www.madras.fife.sch.uk/maths/homelearning/ 15. www.nrich.maths.org/ 16. www.coolmath.com 17. www.coolmaths.com /teachers 18. www.cut-the-knot.org/index.html 19. www.easymaths.com 20. www.gcseguide.co.uk/mathsgcseguide.html 21. www.buzzin.net/index.htm 22. www.examstutor.com/maths/ 23. www.bbc.co.uk/skillswise/index.shtml 24. http://puzzle.dse.nl/index_us.html 25. www.lateralpuzzles.com/ 26. www.dotsphinx.com/ 27. www.geocities.com/CapeCanaveral/Lab/4661/ 28. www.highiqsociety.org 29. www.mensa.org.uk/mensa/puzzles.html 30. www.mathsphere.co.uk 31. www.schoolexpress.com 32. www.crocodile-clips.com 33. www.schoolhousetech.com/ 34. www.10ticks.co.uk 35. www.mathsonline.co.uk 36. www.smilemathematics.co.uk/frameset.html 37. www.illuminations.nctm.org/index2.html 38. www.edhelper.com/ 39. www.schoolzone.co.uk 40. www.hereandabove.com/maze/ 41. www.primaryresources.co.uk 42. www.educate.org.uk 43. www.teachingideas.co.uk 44. http://abcteach.com/ 45. http://mathforum.org/ 46. http://meikleriggs.org.uk/ 47. www.motivate.maths.org/ 48. www.exploremath.com 49. www.univie.ac.at/future.media/moe/ 50. www.georgehart.com/virtual-polyhedra/vp.html 51. http://mathworld.wolfram.com/ 52. www.whyslopes.com 53. www.mathacademy.com/pr/index.asp 54. www.amathsdictionaryforkids.com/ 55. www.m-a.org.uk 56. www.worldmathsday.com 57. www.ncetm.org.uk 58. www.censusatschool.ntu.ac.uk/curriculum/scotland 59. www.shodor.org/interactive 60. http://descartes.cnice.mec.es/ingles 61. www.subtangent.com/maths/index.php 62. www.explorelearning.com 63. www.coxhoe.durham.sch.uk/Curriculum/Numeracy.htm 64. www.ilovemaths.com 65. www.cmit.plymouth.ac.uk/resources/topical/default.htm 66. www.puzzles.com 67. http://lgfl.skoool.co.uk 68. www.Calc101.com 69. www.RAFtarget.com 70. www.pbs.org/teachers/math 71. www.teachers.tv 72. www.paperfolding.com/math

1. http://www.bbc.co.uk/scotland/education/bitesize/higher and 2. http://www.bbc.co.uk/scotland/education/bitesize/standard

This is the usual bitesize web site, but for the Scottish market. 1 for all standard grade subjects (maths is in 2 parts) the other for Higher. Both offer the usual revision and test options and are just what we’d expect from bitesize.

3. http://www.counton.org/

On first glance a website for the younger years, however as described below has uses at more senior school level. The home page has various links, one of which is to games and puzzles with a maths theme. Most of these definitely aimed at 1st and 2nd year.

4. http://www.counton.org/gcseandalevel/test/index.html

An add on to the counton.org site, upon accessing you have two choices A-level and Gcse, obviously this was aimed at those in England but it still has some use. The Gcse side, takes you to test options, one is a random test generator. 50 questions covering the entire standard grade course. It’s a self marking test and provides a comprehensive results table, breaking your marks into topics so you can see at a glance what topics need more work.

The A level side has test facility as well, but also covers tutorials for A-level courses, a lot of which is covered in Higher and Advanced Higher courses in Scotland.

5. http://www.mathsrevision.net/gcse/index.php

This is the Gcse official website for maths. It is full of various revision sheets for all topics of the course. Has a forum where pupils can ask for help and view solutions. It is however not

6. http://www.mymaths.co.uk/login.asp

Very interactive and colourful. Plenty of mathematical games. Unfortunately though, it needs a subscription, but does allow access to some of the site including games and has a selection of tutorials available that change weekly. With subscription, can access a wide range of online tutorials that include interactive demonstrations and questions where the answers are typed in and checked. Also, online homework is available and can be monitored by the teacher giving every pupil a login. 7. http://www.purplemath.com/index.htm

Algebra for all, this has various lessons for just about every algebra related topic.

8. http://www.ies.co.jp/math/java/samples/samples.html

Some interesting Java applets. Might not work in computer rooms but should in class room. It’s a visual program rather than an interactive one so should be ok.

TOP RECOMMENDATIONS The following sites are all highly recommended as sources of mathematical inspiration, enlightenment, ideas and information.

9. www.waldomaths.com/ The main aim of this site is to enable students to investigate mathematical topics and ideas by themselves. Overall, an excellent resource for both pupils and teachers at secondary level (KS 3 to post-16). Lots of Java applets.

10. www.1000problems.org

A source of ‘ready made’ mathematics problems for pupils of all abilities within Key Stage 3 and 4. This site will soon be available on the popular www.counton.org web site that has been so well used at Key Stage 2.

11. www.mathsisfun.com/ A must see web site for S1/2 students and teachers who enjoy imaginatively designed mathematical activities. There are also worksheets and resources available to print.

12. www.mathsnet.net Interactive resources on the mathematics curriculum to help with SATs, GCSE and A-Level (Java may be required). Ideal for teachers interested in experimenting with software. The MathsNet Trail is a fun way to teach pupils how to research and develop a topic.

13. www.greylabyrinth.com/index.htm A puzzle site designed to challenge all abilities. The Grey Labyrinth provides solutions, updates and encourages the usage of these puzzles for education. 14. http://www.madras.fife.sch.uk/maths/homelearning/ The homelearning section of this well-known site is particularly good as it provides access to resources for individuals to learn, practise, test and further develop their mathematical knowledge. Content suitable for pupils from KS 2 to post-16. For access to a World of Mathematical Games try: 15. www.madras.fife.sch.uk/maths/index.html

15. www.nrich.maths.org/ This highly acclaimed site, set up by Toni Beardon, is filled with problems, games and articles that make learning fun. Throughout the site Toni highlights a wealth of material designed to challenge and build curiosity. Incidently, Toni Beardon’s choice of ‘Desert Island Theorems’; The Mid-Edges Theorem, features in the Mathematical Association’s book, The Changing Shape of Geometry edited by Chris Pritchard.

16. www.coolmath.com A colourful web site filled with stimulating material for all age groups and particularly attractive to pupils with learning difficulties. The site divides into 3 main sections: Pupils, Parents and Teachers. www.coolmath.com /teachers is a valuable resource for both teachers and students interested in educational and professional development.

18. www.cut-the-knot.org/index.html ‘Learning starts from wondering’. The purpose of this site is ‘to serve as a resource for things, simple but curious, related to Mathematics’.

27. http://www.geocities.com/capecanaveral/lab/4661/ Olympiad math madness;This is a collection of mathematical problems, invented for mathematical olympiads the world over, and many of them are hard to find in English. Topics include: AnalysisGames and TournamentsGeometryFunctions, Graphs and Equations 28. http://www.highiqsociety.org/puzzles/puzzle1_1.php

The High IQ Society's website – has some very tricky “puzzles” as well as IQ tests etc.

29. http://www.mensa.org.uk/cgi-bin/item.cgi? id=849&u=pg_dtl_art_news&m=pg_hdr_art

Not regular maths problems – but lots of lateral thinking required to solve these kind of puzzles. These kind of puzzles encourage pupils to think “out of the box” yet in a logical fashion.

30. http://www.mathsphere.co.uk/resources/

Site for primary age pupils and their parents. Includes some free resources such as worksheets, dictionary, board games, etc.

30. www.mathsphere.co.uk

Appears to be merely a website selling resources. Nothing much on offer here that can't be got for free elsewhere.

32. www.crocodile-clips.com

Website selling Crocodile Clips software inc. Crocodile Maths. Free demo is advertised but link doesn't seem to work.

33. www.schoolhousetech.com

“Printable Worksheets, Activities, and Tests for the Differentiated Classroom”

Website selling worksheets and other resources. Has some downloadable samples and demos.

34. www.10ticks.co.uk

Well-known Maths website with loads of resources. Registration is required (but free) in order to get much out of the site e.g. the many sample packs each of which contain 40 free worksheets. These claim to give a minimum of 30-45 minutes work. Also has lots of resources on sale. 35. www.mathsonline.co.uk

E-learning and teaching resource designed for English Key Stages 3 & 4. Sells a number of resources – mainly ICT-based – that “enable ICT to facilitate students' understanding of important maths concepts. These range from interactive teaching tools, whiteboard tools, games and worksheets”

36. www.smilemathematics.co.uk

Google-powered search engine for Maths sites – has a number of links already listed under headings.

37. http://illuminations.nctm.org

(note there is no www at the start of this web address) website of the (American) National Council of Teachers of Mathemetics lots of online “activities”

38. www.edhelper.com

American site – lots of “daily practice” available. Needs registration.

39. www.schoolzone.co.uk

The main use of this website looks to be the huge guide to other websites. Results of searches list whether online lesson plans and / or interactive whiteboard content is included, as well as age / stage any given site is suited to. Registration required to make use of search results.

40. www.hereandabove.com/maze

This site does what it says on the tin – i.e. it makes mazes, within specified parameters.

41. www.primaryresources.co.uk

Loads and loads of free stuff such as “follow me” cards. Ideal for S1. REVISION As examinations approach and pupils begin to get anxious, there is an increasing demand for revision materials. The internet has proven to be useful tool for learning and students are becoming more confident when working with computers. In addition, the internet is an information and communication medium many have access to.

The following sites have been described as useful study aids by many pupils studying mathematics.

19. www.easymaths.com This site approaches mathematics from a pupil’s point of view. It aims to overcome the difficulties of the topic by first addressing ‘What’s the point of it all?’ and developing the subject in a way that is easy to understand, turning it into more of an enjoyable challenge than a chore. The site has access to GCSE tutorials, practice exam questions and study aids.

20. http://www.gcseguide.co.uk/mathsgcseguide.htm Direct access to study notes, practice test material and coursework. The site is divided into 6 main sections to encourage a structured approach to revising.

21. http://www.buzzin.net/index.htm A fun and educational web site offering advice and revision at Key Stages 2, 3 and 4. The animated web design is a great idea and may be a helpful start for individuals new to using the internet as a source for revision.

22. http://www.examstutor.com/maths/ The complete A Level exam revision solution. A database of exam questions and answers. The Site of the Week is an excellent feature that can provide excellent access to further related topics. FUN & PUZZLES Many years ago, Cockcroft argued that ‘the appeal of problem solving and puzzles is widespread; attempts to find solutions can provide both enjoyment and increased understanding’. The skills developed through discovery, reasoning and enquiry are transferable and long remembered..

I have included the following web sites to fuel some curiosity and challenge even the most able mind.

6. www.mymaths.co.uk/login.asp Select Games then Millionaire. Based on the popular TV show, the mathematical version of Who wants to be a millionaire? A fun way to revise and test able pupils to 16+.

23. www.bbc.co.uk/skillswise/index.shtml Designed to improve numeracy skills through lively games, quizzes and factsheets. Teachers resources are also available on-line.

24. http://puzzle.dse.nl/index_us.html ‘The Ultimate Puzzle Site’, well, not actually the ultimate but it does offer a number of challenging puzzles for a variety of abilities. Please note the apparent space in this web address is in fact an underscore.

25. www.lateralpuzzles.com/ Filled with situational and lateral thinking puzzles. A top site for a mind- bending experience!

26. www.dotsphinx.com/ Click on Rubik’s Puzzle Collection to experience the challenges we once held in our hand, now at the click of a finger on-line.

27. www.geocities.com/CapeCanaveral/Lab/4661/ ‘Olympiad Maths Madness’. Welcome to the hardest mathematics problems on the web (apparently!). Choose a challenge and select your favourite musical composer to aid enlightenment or to at least soothe the mind.

28. http://www.highiqsociety.org For those who simply love the challenge. You may wish to subscribe to enjoy the full experience. 29. http://www.mensa.org.uk/mensa/puzzles.html The only requirement for joining Mensa is that an individual’s IQ falls within the top 2% of the population. But lesser mortals can try the brainteasers here.

SECONDARY RESOURCES The following web sites provide an excellent resource bank of learning support materials, worksheets and activities to improve learning and teaching:

30. www.mathsphere.co.uk A top site for numeracy. Literally thousands of worksheets available to download.

31. www.schoolexpress.com In addition to free worksheets, this site offers hundreds of educational software programs.

32. www.crocodile-clips.com Free GCSE software.

33. www.schoolhousetech.com/ A worksheet factory. Some packages are free to download.

34. www.10ticks.co.uk Mathematics worksheets for both teachers and pupils but you will have to register first.

35. www.mathsonline.co.uk A subscription web site that provides innovative, high quality teaching materials for all stages of secondary education.

Also check out: 36. www.smilemathematics.co.uk/frameset.html 37. www.illuminations.nctm.org/index2.html 38. www.edhelper.com/ 39. www.schoolzone.co.uk PRIMARY RESOURCES 40. www.hereandabove.com/maze/ An addictive maze-maker web site filled with imaginative ideas and resources.

Additional recommendations: 41. www.primaryresources.co.uk 42. www.educate.org.uk 43. www.teachingideas.co.uk 44. http://abcteach.com/ 45. http://mathforum.org/

46. http://meikleriggs.org.uk/

Click Other links then Sites for teachers. This site provides access to 675 web pages of teaching ideas, materials and resources. The content of each web site is clearly detailed to save you time when searching for a topic.

MULTIMEDIA MATHEMATICS

47. www.motivate.maths.org/ is a video-conferencing project for schools designed for students to experience the magic of mathematics first hand through interaction with professional mathematicians. Anyone wishing to introduce multimedia activities in the classroom can access 48. www.exploremath.com and for a gallery of multimedia learning material refer to 49. www.univie.ac.at/future.media/moe/

THE BEAUTY OF MATHEMATICS We don’t always need a reason to research mathematics, sometimes it’s good to be curious, to look and see and enjoy the beauty of mathematics. Here are a few web sites that caught my eye.

50. www.georgehart.com/virtual-polyhedra/vp.html Virtual reality polyhedra – simply stunning. An Encyclopaedia of Polyhedra by George Hart. He highlights the enormous aesthetic appeal and relates this to investigation and learning.

51. http://mathworld.wolfram.com/ Eric Weisstein’s World of Mathematics. A site described as ‘the Web’s most extensive mathematics resource’.

52. www.whyslopes.com ‘Tasty appetizers’ from arithmetic to calculus, with a clear focus on critical thinking and reasoning. 53. www.mathacademy.com/pr/index.asp Platonic Realms is filled with interesting facts, quotes, challenges and articles. Take a look at the PRIME Encyclopedia.

54. www.amathsdictionaryforkids.com/ ‘An animated, interactive dictionary for students which explains over 400 mathematical terms in simple language’. Just take a flick through the dictionary – it’s an interactive lesson. There are definitions, examples, activities and opportunities to practice ideas.

55. www.m-a.org.uk The Mathematical Association website – you can find the various Maths Challenge past papers and solutions here.

56. www.worldmathsday.com Practice mental arithmetic in timed competitions with pupils of similar ages all around the world! (Runs from February to mid-March). Check site for annual date.

57. www.ncetm.org.uk

A fantastic English site that contains good discussions and research for teachers as well as links to resources, a “Mathepedia” and ideas for using the interactive whiteboard in class.

58. www.censusatschool.ntu.ac.uk/curriculum/scotland

A great resource for teaching statistics. Ready-made worksheets and data that you can select based on topic and year group. For the really keen, you can even get your class or school to fill in the “Census at School” questionnaire online and then use your own data in class.

59. www.shodor.org/interactive

Good American resource featuring interactive online resources and lesson plans on a variety of topics organised by grade.

60. http://descartes.cnice.mec.es/ingles

Online “lessons” from a Spanish site organised by year group. Good scope for interaction in class or revision at home. Some displays are a little messy but most are great. Also includes investigation work under the “maths workshop” heading.

61. www.subtangent.com/maths/index.htm

A nicely-organised, highly visual maths website providing investigations, games, quizzes, revision and teacher resources. Games need to be downloaded so make sure to do this prior to using in a lesson.

62. www.explorelearning.com

Some nice interactive “gizmos” for teaching maths and science. Very clear and visual and easy to navigate. Unfortunately requires subscription but allows 5 minutes for free on each gizmo or a 30-day free trial.

63. www.coxhoe.durham.sch.uk/Curriculum/Numeracy.htm

A primary resource providing links to interactive activities organised by topic. Would be very useful in S1 classes and low-ability classes.

64. www.ilovemaths.com An Indian website containing puzzles, ideas, jokes and information about Indian mathematicians, pi and zero. Solutions to puzzles available but site is not interactive e.g. to do matchstick puzzles you need matchsticks!!

65. www.cimt.plymouth.ac.uk/resources/topical/default.htm

Nice collection of two dozen maths investigations and activities, each with pupil resources, overhead slides and lesson plans that relate to real-life e.g. lottery, earthquakes, fair-trade.

66. www.puzzles.com

A great collection of aesthetically-pleasing puzzles. Puzzles that can be played online are under “Puzzle Playground” whereas the “Puzzle of the Week” requires Print n’ Play.

67. http://lgfl.skool.co.uk

Online lessons with audio tracks that pupils can use to revise topics at home. “Mathematical Toolkit” can be downloaded by teachers for a variety of software and resources for interactive boards. 68. www.Calc101.com

An automated service for doing maths questions using the Mathematica program. Gives step-by-step solutions for derivatives, integrals, matrices and more of the topics that come up in Advanced Higher.

69. www.RAFtarget.com

Great for the “What use is maths in the real world?” crowd. Online activities and tests on various parts of the curriculum (mainly S1/2) with differentiation built in. Would advise against doing tests however as they contain one question on the recruitment aspect of the RAF! Can make log-ins and monitor class progress. Can also be used in science.

70. www.pbs.org/teachers/math

Ideas for teachers looking to make lessons more relevant to other areas of life. Provides lesson plans and resources. Organised in American system.

71. www.teachers.tv

The website for the TV channel allows you to view any programme, any time and also to access the resources that go along with it. Most of the Channel 4 “Maths 4 Real” series is also there.

72. www.paperfolding.com/math

A fun site showing how origami relates to maths!

I hope you have seen something here that you may wish to follow up. There is a wealth of information available on the World Wide Web useful for bringing mathematics lessons alive.

On the next few pages I have listed the websites that I feel are appropriate for each subject year group. Obviously most websites could be used with various years and abilities; the most widespread have been included in “useful for all classes” heading. All websites are easily navigated and are user friendly. Happy surfing!. Useful sites for use with 1 st year. http://www.counton.org/ (3) http://www.mymaths.co.uk/login.asp (5) www.mathsisfun.com/ (11) http://www.madras.fife.sch.uk/maths/homelearning/ (14) www.coolmath.com (16) http://www.buzzin.net/index.htm (21) www.hereandabove.com/maze/ (44) www.primaryresources.co.uk (45) www.educate.org.uk (46) www.teachingideas.co.uk (47) http://abcteach.com/ (48) http://mathforum.org/ (49)

Useful sites for use with 2 nd year http://www.counton.org/ (3) http://www.mymaths.co.uk/login.asp (5) www.mathsisfun.com/ (11) http://www.madras.fife.sch.uk/maths/homelearning/ (14) www.coolmath.com (16) http://www.buzzin.net/index.htm (21)

Useful sites for use with Standard grade / Intermediate course http://www.bbc.co.uk/scotland/education/bitesize/standard (2) http://www.counton.org/gcseandalevel/test/index.html (4) http://www.mathsrevision.net/gcse/index.php (5) http://www.ies.co.jp/math/java/samples/samples.html (8) www.waldomaths.com/ (9) www.1000problems.org (top end) (10) www.mathsnet.net (12) http://www.madras.fife.sch.uk/maths/homelearning/ (14) http://www.buzzin.net/index.htm (21) www.coolmath.com (16) www.easymaths.com (19) http://www.gcseguide.co.uk/mathsgcseguide.htm (20) www.mymaths.co.uk/login.asp (5) www.lateralpuzzles.com/ (26) www.crocodile-clips.com (32) www.schoolhousetech.com/ (33)

Useful sites for Higher http://www.bbc.co.uk/scotland/education/bitesize/higher (1) http://www.counton.org/gcseandalevel/test/index.html (4) http://www.ies.co.jp/math/java/samples/samples.html (8) www.mathsnet.net (12) www.greylabyrinth.com/index.htm (For higher and beyond) (13) http://www.examstutor.com/maths/ (22) www.lateralpuzzles.com/ (25) www.geocities.com/CapeCanaveral/Lab/4661/ (27)

Sites for teacher use. www.coolmath4teachers.com (17) www.bbc.co.uk/skillswise/index.shtml (23) www.geocities.com/CapeCanaveral/Lab/4661/ (27) www.mathsphere.co.uk (For use with 1st – 4th years) (30) www.schoolexpress.com (31) www.crocodile-clips.com (32) www.schoolhousetech.com/ (33) www.10ticks.co.uk (34) www.illuminations.nctm.org/index2.html (37) http://meikleriggs.org.uk/ (46) www.motivate.maths.org/ (47) www.exploremath.com (48) www.univie.ac.at/future.media/moe/ (49) www.georgehart.com/virtual-polyhedra/vp.html (50) http://mathworld.wolfram.com/ (51) www.whyslopes.com (52) www.mathacademy.com/pr/index.asp (53) www.amathsdictionaryforkids.com/ (54)

Sites for all classes http://www.purplemath.com/index.htm (7) www.madras.fife.sch.uk/maths/index.html (14) www.bbc.co.uk/skillswise/index.shtml (23) www.nrich.maths.org/ (15) www.cut-the-knot.com/ (18) http://puzzle.dse.nl/index_us.html (24) www.dotsphinx.com/ (26) http://www.highiqsociety.org (28) http://www.mensa.org.uk/mensa/puzzles.html (29) www.10ticks.co.uk (34) www.mathsonline.co.uk (35) www.motivate.maths.org/ (47) www.edhelper.com/ (38) www.schoolzone.co.uk (39) www.exploremath.com (48) www.univie.ac.at/future.media/moe/ (49) www.amathsdictionaryforkids.com/ (54)