Enriching Mathematically

Part of our challenge as Mathematics teachers is to challenge our more capable students. To be successful teachers we need to impart to students our love of Mathematics. To show how Mathematics can empower us to solve problems.

With these admirable goals in mind I have set myself homework during the January break – to compile a set of enrichment activities to use in my classes.

I don’t intend to reinvent the wheel, but draw together all the great resources available on the web, into one volume. Of course I will acknowledge the source of each activity. What is your favourite enrichment task?

Terrific Tasmania

I have just returned from a fantastic four day holiday in Launceston. We stayed at Alice’s Cottages, which were very comfortable and cute.

We stayed in the “English Cottage” and were frequently visited by Sooty (pictured below). 

Our hosts, Louise and Rob, were the perfect hosts. Very friendly and helpful, they were full of good advice on places to visit, including some great restaurants and pubs. I can really recommend a stay, and please pat and say hello to Sooty for me. I will be returning in the future!

Even while on holiday I was thinking “Maths”. When I saw this winerack in the English cottage I thought of Dan Meyer’s dy/dan blog and his posts WCWDWT (What can we do with this?).

Edublogger Awards

I was very surprised to find that I had been nominated for an edublogger award! (I didn’t even know these existed?)

If you want to vote for my humble blog, left click the image above which will link you to the edublogger voting site. Lots of blogs have been nominated so I am not expecting to win – being nominated was a very nice surprise though!

Roman Sebrle

Three years ago I went on a search of the world wide web for resources that would make my maths courses more interesting (both for myself and my students). I was astounded by the plethora of “stuff” out there. Many teachers are willing to share their worksheets, assignments, learning objects, etc; I was overwhelmed.

Having seen the limitations of purely teaching a skills syllabus (driven by Year 12 final exams and university entrance scores), I wanted to put together a collection of Mathematics investigations. These would be either intrinsically interesting and/or real world applications. The final product had 64 investigations and I named it “Working Mathematically”. An image of the cover is shown at right. For those Maths teachers looking for this type of material, I will post examples at regular intervals on Scribd.

#43 Roman Sebrle

Sport is rich in Mathematics but I must admit that I had never taken much interest in the Decathlon before. I discovered that the formulae used for points scoring system were:

• Points = A*(B-P)^C for Running Events
• Points = A*(P-B)^C     for Field Events

where P is your performance in specified units and A, B, and C are constants.

What a great example of the use of exponential functions! Even more interesting to me was the narrow escape from death that the Czech World Champion, Roman Sebrle, had during training in 2007.

You can see a list of all 64 investigations:  00 contents.doc

Character Strengths

At a recent Professional Development session I was introduced to Dr. Martin Seligman’s theory of Positive Psychology. Rather than explain his theory here, I direct you to the University of Pennsylvania’s Authentic Happiness website.

If you have a spare 10 or 15 minutes try out the VIA Survey of Character Strengths. It may give you some insights into your character strengths and weaknesses! My top 3 strengths were:

1. Love of Learning

You love learning new things, whether in a class or on your own. You have always loved school, reading, and museums-anywhere and everywhere there is an opportunity to learn.

2. Curiosity and interest in the world

You are curious about everything. You are always asking questions, and you find all subjects and topics fascinating. You like exploration and discovery.

3. Zest, enthusiasm, and energy

Regardless of what you do, you approach it with excitement and energy. You never do anything halfway or halfheartedly. For you, life is an adventure.

What are your character strengths?

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.  I 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.