Tuesday, 19 April 2016

Key Concepts Enquiry into the Cubic Centimetre

Using the PYP Key Concepts is an enquiry-based maths classroom's best friend. They help students have ownership and gives them the tools to ponder deeply about concepts or skills they are enquiring into.

Beginning to explore our new unit's central idea into volume & capacity:

I thought it could be interesting for us to really dig deep into the cubic centimetre.

With the key concepts displayed, I asked the students which concept we should use first.  A few suggested function, one suggested connection but most felt form would be best so we used that first.

With each student having a cubic centimetre, we used the think-pair-share strategy to think about what a cubic centimetre is like.  They jotted down their understandings and observations individually and then shared with the partner.

Then as a whole class we thought the following:

FORM: What is a cubic centimetre like?

- it's 3 dimensional because it has 3 dimensions: length height width
- it takes up space
- doesn't have to be a cube

During this sharing and discussion, we compared the cubic cm with a square cm. It's important that we can understand why the symbols for them have a 2 or 3. Children fully know what a 2D or 3D shape is by the time they get to Year 6, but many don't realise what that actually means.  many haven't connected with the concept of what the two dimensions or three dimensions actually are which gives them their names. So, whenever opportunities arise we discuss that in review throughout the year.

An interesting question came up from this:  Can shapes be 1 dimensional?

We thought about that and some of us suggested a line could be 1D because it only has 1 dimension- length?

A few of us debated this idea- surely a line still has height as well as length.

Mathematically, the concept of a line is 1D even though we can measure its height.  We then wondered if we could see a line under a microscope then would be see it being 3 dimensional because of the raised ink.

An interesting idea!

This last sharing also made us wonder a lot.  Does a cubic cm have to be a cubic shape?

Surely if it is cubic it must be a cubed shape!

Some debate began in our room.  

Not having planned this, but since it had generated such a great wondering, 
I gave partners an estimated blob of bluetack each. 

I then displayed the key concept change and suggested we first try to make an identical cubic centimetre using the blutack.

Some ingenious and creative ideas emerged.

Children estimated the volumes and interesting discussions took place.

- Does it matter if that chunk is taken out of the corner?
- Do the sides have to be flat?
- Is it taking up more volume?

Some chose to use rulers:

I loved this idea:

Another group saw that idea and took it a step further. We often discuss how ideas can and should help others to spark and so the partners above were happy that helped create this amazing idea:

Isn't it so fantastically creative?

Having made our identical cubic centimetres, we went make to the student's idea that a cubic centimetre doesn't need to be cubic in shape.

Had any of our original thoughts on this changed?

Using the key concept change I wrote the question beside it: Does the shape have to be a cube to have a volume of 1 cubic centimetre?

Using their bluetack cubic cm, we explored that idea and discussed with our partners.

We then placed our bluetack cubic cm under either YES or NO.

Looking at our thoughts, we discussed our reasons why we either thought YES or NO.

We still couldn't come to a consensus and I didn't want to tell them the answer. As enquiry-based teachers, we should help students build their own understandings, so we have left this on a table and during our unit we will continue coming back to think about it to see whether our understandings change or not.  It's also powerful, I think, to keep these type of learning tensions floating in our minds to mull over rather than always getting an answer right away.

We then had time to select one more key concept to help us think about cubic centimetres.

Some chose connection, some chose function and one student chose perspective.

After investigating the cubic cm with those chosen key concepts the partners shared their ideas and discoveries with the whole class.


- it is used to measure volume or capacity of smaller objects
- it is a formal unit to help give precise measurements
- we can stack them beside each to make shapes and measure their volume

This was a really interesting investigation done too:


- it is connected to cubic metres equals 1 million cubic metres
- 1 cubic cm equals 1 millilitre
- 1 cubic cm connects with cubic mm and cubic km
- cubic centimetres are connected with square cm because you need to use that to help find a cubic cm

Using the key concepts helps guide children into deeper thinking and when they are given a choice of concept to use, it allows student-driven learning to take place. 

Some really deep thinking took place today- all from the humble little cubic centimetre- which I think would have been difficult to achieve if we weren't a PYP school and had the key concepts as a learning tool. 

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