...and we put them end to end, how far would they reach?
This was a bit of a "Christmas" problem I put to my class as we were one day away from finishing school for the year. Thought we might as well see if they have learnt any problem solving skills this year...
And what did they do?1. Reach for a calculator
"The answer is 6.4429235." came a confident and speedy reply.
Really? What type of units are we talking here.
2. Give up
Checking on a website (www.worldometers.info) that showed real-time statistics, we quickly found that the population of the world is constantly changing?
"The numbers keep changing! It's impossible to work out!"
3. Make some "assumptions"
All good maths is based on assumptions and we sometimes need to rely on approximation.
For example, we decided to take the world's population as
7 084 224 052 people
which is what it was at about 10.00am Australian EDST on 10th December 2012.
Also, we recognised that not all candy canes are the same - so we agreed to measure the one I had been given earlier by a generous student, that was about 9cm long - the candy cane, not the student.
4. Some calculations
Now we had some numbers to work with, we could play!
Number of people x length of candy cane =
63 758 016 468 cm
or 637 580 164.68 m
or 637 580.16468 km
So how far is that???
Not content with just having a number like that, the cruel and demanding teacher asked for a real-life example of how far the line of candy canes would reach.
"Can we get to the moon?"
After much googling and discussing...
"The moon is about 357 000 kms away from the Earth at its closest point."
"Yes - we can get to the moon!"
"But can we get back???"
More googling and discussing...
"Well, we're going to be short of the Earth by about 76 417 kms."
"So we can get there and then get 3/4 of the way back to Earth."
"What if we stretched it around the equator?" asked the unsatisfied teacher.
Well, more calculating and googling ensued.
Soon we knew that the distance around the equator is about 40 000 kms.
Brains were starting to flag now so I suggested we try a few of the problem strategies we had sung about in our class play - "Mastering Math" - like draw a picture, make a table etc.
"Can we act it out?" asked one enthusiastic student.
"Sure!" I replied. "This group of desks can be the earth. How far around is the equator again? Oh - 40 000 kms! Right, so each time we walk around the desks, that's going to be 40 000kms. Let's go!"
And off we went. A group of 5 or 6 students and me walking around "the earth", counting by 40 000 for each lap.
I paused at the end of 5 laps - 200 000 kms - to see if anyone was going to make the intuitive leap to 600 000 ( 3 x 200 000) but no-one did so we kept walking.
I stopped again at the end of 10 laps (400 000 kms) but again no spontaneous flash of recognition.
We ended lap 15 (600 000 kms) and the students realised that we couldn't do any more laps - we only had 37 580 kms of candy cane left - it wouldn't stretch to a 16th lap.
Using this as our remainder, we used a calculator to work out that this was about 0.9395 of a lap.
So our line of candy canes would go around the world 15.9395 times.
I asked the students to come up with some questions of their own - how would they like to extend the inquiry?
Here's what they came up with:
- How many more candy canes would we need to complete the trip back from the moon?
- How many candy canes would you need to go to the moon 7 times?
- How many candy canes would you need to get to Pluto and back?
- How much sugar would you need to make all these candy canes?
- How many candy canes are made every year?
I think this was a great thing to do on the second last day of the school year.
Which leads me to say that my blogging may slow down a little over the Christmas break as we take our summer holiday in Australia. Thanks for reading this far and for following the blog.
Normal service will resume sometime in late January.
Have a great holiday season.