Wednesday, 18 November 2015

The concept of Infinity!

We read Kate Hosford's fabulous book titled 'Infinity and Me' as a means of exploring the concept infinity and to encompass how it looks mathematically. 

The story tells of a girl enquiring into what infinity is by asking different people's perspectives.  

Prior to reading, we jotted down our thoughts of what we thought infinity was, how we could portray it visually, things we felt might be infinite etc. We did a turn-n-talk and then discussed as a whole class some really amazing theories.

Some sample thoughts:


Together, we wondered whether the following were infinite or not as suggested by some of us:

° imagination

° time
(but we wondered whether time really did begin with the Big Bang or not; if it did begin at that point in time then time cannot be infinite because as one student theorised something infinite has no beginning nor an end)

° the universe
(we discussed recent theories that there are multiple universes so according to those theories, our universe might not necessarily be infinite, bit there IS a possibility that there are infinite universes.  This blew our minds away!)

° both positive and negative numbers
(Our first maths unit this year explored how numbers extend infinitely in both directions, so I'm glad this was suggested)

° religious beliefs / God- Buddha-Allah

° the human race
(Again, we tested this theory with the notion that something cannot be infinite if it had a beginning)

° a circle
(One student questioned this saying that a circle is made up of connected dots so those spaces between the dots - even though we can't see them with our eyes - means a circle isn't infinite. Interesting idea!)
° a pine trees' life cycle

° the future

° people's thoughts

° life - we expanded this to mean life in the universe

° death

and a funny idea popped up that peanuts are the same shape as an infinity symbol so therefore we must conclude that peanuts must be infinite. 

All of these deep discussions involved expanding upon our preconceived theories and evaluating others.   

We then examined and discussed these infinity symbols:


We then started reading the book and stopped after the girl had thought about what she might or might not want to do for infinity.  We jotted down our own thoughts of what we might like to do for infinity and shared these.

In the next part of the story, the girl asked a chef how he imagines infinity. He holds up a noodle and asks how many times do you think you could cut this in half.  I then gave partners a 48cm line which we imagined was a noodle.  We halved and halved again as much as we could and that same time thought about the fraction patterns we were making.  

Could we halve the fractions again and again for infinity?!?

Student sample of halving and halving again the 'noodle'.  This pair decided to go further by drawing a square and then smaller square on the table:

We then reflected on the fraction patterns we found and how we discovered them. 

Some samples:

In sharing how far we had got with our fraction patterns, one student shared he had got to 1 out of infinity! 

We felt this was an amazing thought and at the same time we wondered where it was possible or not.......and if so, what did that really mean?!?

We then had some time creating our own symbols for infinity and explained why:

                     This made us wonder if change is also infinite? 

After our break, we used the Connect-Extend-Challenge thinking routine as a whole class:

To make a 3D connection with infinity we explored Mobius strips and tested our hypotheses of whether we thought it had one or two sides.  There was a quite a lot of interesting debate about this until someone came up with the idea of drawing a line in the centre that connects.  This testing changed a lot of our thoughts about it. 

A sample:

We then did a think-pair-share of how this connects with the concept of infinity.

After this we then explored fractals and discussed what they were and they they might be created.

Finally, we started experimenting with different types of graph /drawing paper to create fractals of our own or to design images that could represent infinity.  We will continue thinking about different designs till we find one we are proud of and want to publish.

Some initial experiments: 

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