Mathematics Alive! Real Life Maths

@ Clementi Town Secondary School (by Venkataraman Swaminathan)

Activity 1: Your Age by Chocolate Math

• Click HERE to see activity
• This is similar to the Ghost Whisperer!

1. First of all, pick the number of times a week that you would like to have chocolate (more than once but less than 10) (i.e. n)

2. Multiply this number by 2 (just to be bold) (i.e. 2n)
   
3. Add 5 (i.e. 2n+5)
   
4. Multiply it by 50 -- I'll wait while you get the calculator (i.e. 50(2n + 5))
   
5. If you have already had your birthday this year add 1759.If you haven't, add 1758.
   
6. Now subtract the four digit year that you were born.
   
7. You should have a three digit number
8. The first digit of this was your original number (i.e., how many times you want to have chocolate each week).
9. The next two numbers are
   YOUR AGE! (Oh YES, it is!!!!!)
   THIS IS THE ONLY YEAR (2009) IT WILL EVER WORK, SOSPREAD IT AROUND WHILE IT LASTS.

Example: Connectedness for right-angled triangles

• cos, sin, tan
• one angle is equal to 90 degrees. 2 remaining angles not necessary equal.

Real Life Activities

1. Marina's Fish Shop [Quadratic Equations]

The task: The re-size the square and the isceleous triangle gives the least area (minimise lighting)

• Using Geogebra, students explore the sizes of the square & triangle that will result the minimum area.
• http://wzcoemathsctss.net/geogebra/marina_fish_problem.html

2. World Population Study [Exponential]

• Using different "Family" configuration to prompt students to think

Others in the handout:

3. A Real Problem [Scaffolding worksheet]

4. Taxi Taxi [Coordinate Geometry]

5. Linear Equations in the Real World

6. A real scenario [Coordinate Geometry]

Using Geogebra to investigate the various possibilities
The 3 points are: BSS (4, 6); FTSS (-5, 1), BHSS (-2, -5)
To find the point which is equi-distant from the 3 locations.

1st exploration: When the perpendicular lines of all the sides of the triangles intersect



In the next investigation, draw Pink lines which are angle bisectors. And eventually dark blue lines which are just perpendicular lines joining the point to the line opposite.

Finally... The solution...

Along the way, mathematical languages come in: For example

• Describe a perpendicular bisector. Perpendicular bisector of a line? No, line is ofnfinite length. So, it has to be a line segment.

Indeed, I like this activity! We can incorporate more ICT use in this particular activity. Instead of providing them the map, we could actually task the students to gather the information from GoogleMap! On the other hand, more scaffold could be provided to guide the students to pen down their thoughts while they explore the various possibilities using Geogebra.

7. Why Venus is a Morning & Evening Star?

• AU: Units of Measure Distance between the sun and a planet
• AU> Astronomical Unit, a measure of distance, based on the mean sun-Earth distance. The International Astronomical Union defines the AU as the distance from the Sun at which a particle of negligible mass, in an unperturbed orbit, would have an orbital period of 365.2568983 days (a Gaussian year). The AU is thus defined as 1.4959787066E+11m (149,597,870.66 km). [source: http://www2.jpl.nasa.gov/basics/units.php]
• Examples: Mercury 0.3871; Earth 1.000 AU
• Distance bewteen sun and venus:

Solving the problem

• Assumption 1: Earth, Venus and Sun lie on the same plane
• Assumption 2: Venus and Earth rotate around the sun (in circles) as students have not learn about ellipses yet

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June Holiday Projects - TLLM iGnite ProjectSecondary 3 - 2009

• http://dsstllmproject.net/sec3projects/igniteprojects.htm

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Other useful sites:

• The Mathematical Association (UK) http://www.m-a.org.uk/
• http://wzcoemathsctss.net/
• http://wzcoemathsctss.net/geogebra
• Resources: http://wzcoemathsctss.net/workshop/ws4.zip

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One of the biggest takeaway is the introduction to Geogebra! Well, compared to the version I saw last time, it's more user-friendly! Certainly, it's possible for us to use in our classrooms! Good news - it could run in both Windows and Mac platforms!

20090529 Tan Kah Kee Awards

It's just a coincidence - to come across the exhibition of the award winning entries of the Tan Kah Kee Awards this year. It also happens to be the last day of the exhibition.

First time view the exhibitions. Well, one learning point, drawn from the observations - nothing is too small to be small! Innovation could be carried out in varying scales - big or small - sophiscated or just simple!

Look at the shoes for rainy days! Look at the spoon with thermometer!
Run out of ideas? Just need to be observant - there exists lots of areas for improvement.

20090529 Visit to Singapore Science Centre

Went to the Science Centre, just wanted to visit the iSpace.
Am excited to have a hand in most of the hands-on activities available. Like a few of them:

• Google Earth on a circular plane surface - by tilting it up and down, left and right we are able to navigate the globe. I guess nothing beats when we find where our homeland is! Found Singapore!!! While doing so, it reminded me the latitude and longtitude values of the Singapore island :D
• The Diorama Table - That combines technology and art! So gracefully done... so beautiful :D
• The Talking Mirror - which reads and shows the pictorial representation when the word card flashes before it. Wah! It makes learning so much more visual and fun :D

Sharing on Leadership... (by Eunice)

* In blue are some lines captured from Eunice's slides...

1. Do you get self-satisifed with your victory? How will you push yourself to a greater height while adhering to your moral compass?
My thoughts
Personally, I think, as human beings, we naturally enjoy the moment of victory, which is the satisfaction that we wanted to have after putting efforts into the task (into the process). That moment of "self-satisfaction" - yes, I do. And I indulge, and I enjoy indulging in it for a while, to enjoy the sweetness. It's like a comfortable cushion that we could always 'fall back' on especially when we experience set-back. However, it doesn't mean indulge and never get back to reality and move on!

The victory is an affirmation of our efforts, our choice - a milestone in a long journey. When we reach the signpost, there's where we take stock, reflect and plan how to move on. Yes, reflection is very important, and certainly our moral compass will provide another check of our process. Have how we live and what we do guided by our values. Have we arrived at where we are through rightful means? Have our action lead to some undesireable impact, etc... directly or indirectly to people around us (or even those beyond)...

2. What response do you often have when people tell you that you can do better?
My thoughts
Unfortunately, I would not interpret this as an encouragement to do better. My natural response would be, "huh? You mean, you think I've not put in my best effort despite that I've put in my best?" Of course, that's when I've put in my best effort at that instance! and next, I could further interpret that as an insult!!!

I'm more receptive if it comes from myself, through my truthful self-assessment, "I can do better"... That's to inform others that I'm capable of doing better than what you see now. Of course, if I've already reached "the point", I would say, "That's the best I could give now".