Smelly Jocks?

I often scan the daily newspapers for good, bad or funny examples of the use of statistics. Today in papers such as the Courier Mail and the Herald-Sun, we find the breaking story “Over half of men wear same undies for 3 days”.

The stats are claimed to be from “a Galaxy study of 1100 men released today”. Here are some of the statistics quoted:

 *  46 per cent of men followed their mother’s advice and were never caught out and about without clean undies on

*   3 in 4 men would prefer to spend the money on beer or a burger

*  7 per cent of men admitting to wearing women’s underwear at some time

*  The average man has 11.7 pairs of undies

This statistic amused me. I had to go and check how many pairs I had. 10 pairs. Oh Oh, I am below average? I also showed this statistic to a male collegue. His comment: “Yeh, that would be about right. I have 12 pair but some of them have holes – that would account for the missing 0.3! And the following statistic backs this up:

*  About half say their underpants have holes or bad elastic

So to sum up have you got any good examples of statistics or mathematics in the news?

Of course one of the best bloggers online – Kerry Cue – has a blog titled Mathspigs, which specialises in such news articles.

10 Clues

WHO AM I ?

1.  Some consider me to be the most famous Mathematician of all time. Others scoff at this suggestion.

2.  My middle name was “Lutwidge”.

3.  I discovered that there are 30 different ways to paint the faces of a cube with 6 different colours. If some faces can have repeated colours then this increases to 2226 ways!

4.  I lived in the nineteenth century.

5.  I discovered an algorithm to calculate what day of the week any date would be.

6.  I lectured in Mathematics at Oxford University.

7.  I created logic problems where you had to make a conclusion from the clues given.

Here is an example:

All puddings are nice.
This dish is a pudding.
No nice things are wholesome.

8.  In invented “Doublets” or “Word Ladder Puzzles”, where you change one word into another by changing one letter at a time. For example, change MICE into RATS:

MICE

MITE

MATE

MATS

RATS

Now can you change FOUR into FIVE?

9.  I wrote a 6 x 6 square poem:

I	OFTEN	WONDERED	WHEN	I	CURSED
OFTEN	FEARED	WHERE	I	WOULD	BE
WONDERED	WHERE	SHE’D	YIELD	HER	LOVE
WHEN	I	YIELD	SO	WILL	SHE
I	WOULD	HER	WILL	BE	PITIED
CURSED	BE	LOVE	SHE	PITIED	ME

10.  I wrote a novel that became very famous. “At the start of the book I sent my heroine down a rabbit hole….without the least idea about what would happen afterwards“.

I am Charles ………………….

[If you know, don't give the answer away, but perhaps leave another clue]

Blog Images

I have taken a big dose of truth serum and here are the results:

1. I LOVE IMAGES! If I browse a blog and it doesn’t have any images, videos, slide shows, etc, then I usually don’t add it to diigo, delicious or only2clicks. An exception to this is Math Tales from the Spring. This delightful Maths blog is all text, but Mrs. H tells such charming and interesting stories, that you can’t help but keep reading! Her lasted article is about using IWB’s, which reminded me that I must do a post about using IWB’s in Mathematics classes.

Whenever I need to manipulate images I use the free but excellent program Irfanview. For example, the image below was made using the “create panorama” command. Can you work out its meaning?

2. I have “wasted” a lot of time today browsing the world wide web, instead of mowing lawns, cleaning gutters, etc. I discovered The Newspaper Clipping Generator:

The above text from The Lazy Bloggers Post Generator.

and Create an Animated Cat:

or MagicWidgets T-Shirt Maker:

So, like some of my students, I have been “off task”. I am determined though to get back on track this coming week, and post some good solid Mathematical content. Stay tuned……

Choose your topic

Had a bit of fun with my Year 9 Maths class this week (MATHS = FUN)!

I challenged each student to choose a Maths topic and then I would give them an impromptu question to answer. They could not use a calculator (or mobile device), and could not use pen or paper. As well, the same topic could not be repeated.

The first chose Pythagoras’ Theorem and then successfully answered “hypotenuse” to the question “What is the longest side of a right angled triangled triangle”. I then wrote on the board – Students (1) v. Teacher (0).

The next student tried for an easy question: adding whole numbers from 1 to 100. They did not specify how many numbers so I gave: 87 + 39 + 62 + 79. After 10 seconds of intense concentration they gave an incorrect answer. Yeh the teacher strikes back! One all.

Third student: “3D Solids”. Question: “What is the name of the 12 sided regular polyhedron”? I could have launched into a lesson on Platonic Solids here. But the student quickly came back with “Dodecahedron” – he could even spell it!

Fourth student: “Numbers multiplied by one”. I’ve got to give it to these Year 9’s they can be tricky. Not to be outdone, I remembered from my Psychology teaching that people can, on average, retain 7 +/-  2 didits in their short term memory. Question: “839701524 x 1″. Student got one digit wrong in answer, aha teacher strikes back.

Fifth student: “Counting by whole numbers from 1 to 10″. Damn, should have excluded a few easy topics like this. Students get a point.

Sixth student: “2D shapes”. Question: “What is the name of a triangle that has all its side lengths different. Long pause…… Aha – Students (3) v. Teacher (3).

Then the bell went and we packed up and went to lunch.

I was happy with this activity – it was a good opportunity to use Mathematical language, and the format gave the students a good chance to beat the teacher. What do you think?

Seasonal Variation

As I’m writing this post, I notice that the number of “hits” on my blog, since I started it in February this year is 6666! More important blog statistics are shown on my Webmaths dashboard. The graph shows how many hits my site gets each day as shown below.

This graph seems to me to be a good example of seasonal variation. It could be used as data in the Core Data & Statistics unit of VCE Further Mathematics. The graph could be “smoothed”, the seasonal indices computed, and a seasonal adjustment performed.

For the last two saturdays their has been a plunge in the graph, with the peaks coming on mid-week. Could the Saturday plunge be explained by less web browsing due to sport and other weekend activities?

Another question worth analysing is:

“Do the peaks occur immediately after a post; or is their a time lag; or are the peaks independant of posts?” Note that I had posts on the 2, 7, 11, 14 and 19th of October.

Origami and Mathematics

 

My interest in origami was initiated by Yuki and Reiko, two Japanese exchange students we hosted. The photo below shows two beautiful hexagonal boxes and their lids they presented to us - excellent examples of modular origami.

I then set out to find as many books and websites on paper folding that I could. I gathered together many models and activities into one book (its cover is shown below). I found that paper folding was an intriniscally motivating activity for many students. Now I would not dream of teaching a geometry unit without some paper folding. There are some very obvious applications such as:

1. Polygons – triangles, rhombus, pentagon, hexagon, octagon, etc.

2. Angle Properties – eg. 180 degrees in a triangle, trisection, etc.

3. Polyhedra – cube, rectangular prism, tetrahedron, octagon, etc.

4. Symmetry

5. Powers of 2

6. Algebra and Problem Solving

Any serious study of Origami should include the story of Sadako Sasaki. This heart rending story of a young Japanese girl who has Leukaemia results in Sadako trying to fold 1000 paper cranes. I highly recommend that you read “Sadako and the Thousand Paper Cranes” by Eleanor Coerr. My Origami Self Assessment rubric covers a unit of work that starts with reading this book and finishes with the student having to teach someone else to fold their chosen model.

Origami is such a vast topic that I cannot begin to do it justice in this short blog post. But take my advice and go on a jouney of self discovery – you and your students will love it!

Check out my origami web links on Diigo.

You can print various origami paper here or here. 

Karen Bass’ students listed the following things they had learned/experienced through her “mathagami” projects. Patience, precision, “don’t give up”, creativity, geometric concepts, and that math class is fun.

My favourite origami model’s are: shirt, sonobe cube, fancy box and modular swan (pictured). Their is no doubt in my mind however, that the richest mathematical origami task is folding a circle into a truncated triangular pyramid. But that is material for another future blog post.

Have fun folding and let me know what your favourite model is.

Expanding horizons

Sometimes it is too easy for teachers to have blinkers on. Since I have discovered the wonderful world of blogging, I have spent many hours searching for and, evaluating other teachers math blogs. You can see the results (36 math blogs) of my searching and evaluating on my Only2clicks page.

Recently, I have taken the blinkers off, and started to expand my horizons. For example, I recently discovered Kathleen McGeady’s “Integrating Technology into the Primary Classroom“. This great blog taught me that I have to get off my butt and start using more web2.0 tools in my blog. Perhaps the odd video? Kathleen’s post on Origami reminded me that I must post on this much loved topic of mine. Thanks Kathleen!

While browsing amongst Kathleen’s great posts, I discovered that one of her students has started his own blog. So I navigated over to Riley’s Blog and left a comment. Thanks Riley for reminding me that I must get my students blogging!

 Next, I discovered Andrew McDonald. He is an author, writer and biped from Melbourne, Australia. His first novel for children is about Charlie Ridge, who has one small goal in life – to be the Greatest Blogger in the World.

Andrew’s Blog makes very interesting reading, which makes you think his book might be pretty good too. I’ll do a review after I’ve read it [watch this space]. His blog post dated 19 Sep, 2009, made me laugh. It is about Kevin Rudd’s Youth Blog. Andrew thinks Kevin should make his blog more interesting. For example, have a countdown flash object to Malcolm Turnbull’s birthday!

So, all these blogs show me that I’ve still got a lot to learn. Luckily I love learning, so I will continue to expand my horizons.

The point

During a 100 minute maths lesson, a good teacher should be able to sense at a certain point, when the students concentration is wavering. Even adults have trouble concentrating on the one task for this long!

At this point, the teacher needs to intervene and change something. In many cases this may be a new activity. In some cases though, the students just need a quick break before they are ready to refocus. I like David Cox’s “What’s the Point?” activity.

What strategies do you use to keep students on task?

My favourite flash games

Here are a few of my favourite Shockwave Flash (swf) games. Warning! they are highly addictive and you may lose many hours of your life. They all require problem solving skills and perseverance. Nearly all students and teachers who have tried them have been highly motivated by them. Mathematical content? I will leave that up to you to judge.

1.  Click Drag Type

2.  Bloxorz

3.  Coffee Shop

4.  Leapfrog

5.  Light Bot

6.  Broken Calculator

7.  Higher or Lower?

8.   Ray Ray

9.  Algebra Puzzle

Rotations

When teaching about rotations it is easy to rotate polygons, letters or numerals. To have your students investigate the degree of rotational symmetry, guide them to the “Learning MATH” lesson on Rotation Symmetry  and its associated flash learning object.

Alternatively (or in addition) you can download my Number Rotations worksheet to set for your class.

For example the triskelion on the Isle of Man flag (see image below), has three fold symmetry, that is it requires a rotation of 120 degrees to rotate back upon itself.