In our tuning in and unpacking our central idea a few days ago (Tuning into Our Unit ) we wondered about different ways we use negative numbers in real life situations.

To help with our wondering, we began with this:

Lausanne's elevation is 495 metres.

What does this mean?

With your partner draw an explanation of your theory.

We use the word 'theory' all the time.

It's a word of safety that allows us to try and share ideas and possible answers we might have without being made to feel wrong.

I think this is an important strategy to establish at the beginning of the year for enquiry-based learning to really manifest. We examined what theories are in depth and reviewed this often until I could gage that students felt really comfortable sharing any idea they had by saying 'my theory is.....'.

Now we have a culture where the children feel safe to take risks without the risk of ridicule because theories are great to create regardless of their right/wrongness.

Quite often when we are reflecting in maths or exploring new concepts or skills, the children readily want to add theories they are formulating and wanting to test without me suggesting they record it.

Theory making is a key component of our classroom language. It allows us to take risks without fear of 'failure'.

With that simple instruction, a lot of knowledge was shared and build amongst the pairs. The word 'theory' popped up a lot as I listened in.

After sometime, we gathered in a circle and shared our explanations at the same time in a circle. We looked at the other ideas displayed and then pointed to an explanation we felt clearly communicated what we mean by Lausanne's elevation is 495 metres.

We then discussed some of the ideas shown.

Some samples:

This was a great way to assess our understandings and to also assess ways to visually communicate more effectively.

We then looked at some images on the data screen: Images Link

After half a minute viewing one, partners then discussed what the image tells us about elevation.

This helped us to gain a deeper understanding of sea level, elevation and altitudes and how we use positive and negative numbers for these.

Some of us knew that seas can be below sea level, so why is it sea level?

But the oceans go up and down with tides, so are we just estimating sea levels? Is it the average?

With climate change and oceans rising, does that mean we have to change the elevation of Lausanne?

How do we actually know what the sea level measurement actually is? How do people measure it?

These were just some of the great wonderings and theory-sharings we had from these images.

We then researched things we find above and below sea level on the Internet and found their depth (negative numbers) or elevation, height or altitude (positive numbers).

For below sea level, children found the depth of things like:

° the depth a blue whale can dive down to

° where the Titanic is

° the deepest known part of the ocean - Challenger Deep

° how far down is oil, diamonds or gold found

° depth submarines travel

° underwater cave depths

For above sea level, children found the elevation, height or altitude of:

° the Burj Khalifa

° the Eiffel Tower

° Mt. Everest

° Uluru

° the Great Barrier Reef

° the deepest part of the Bermuda Triangle

° Mt Vesuvius

° the altitude A380s fly

etc

Some took their thinking further by deciding that to find the elevation of the Eiffel Tower, first they should find the elevation of Paris and then add the height of the Eiffel Tower. You've got to love it when kids think like this without prompting.

Other types of mathematical thinking in their research often involved appreciating the need for averages. Eg, Some children find the deepest part of the Great Barrier Reef and wondered whether they should use that figure or the average figure provided. Reasoning and logical skills were needed in a lot of these fact findings. Should we use the elevation of the top or the bottom of Angel Falls? etc

Either individually or on pairs, we then created a scaled diagram that showed their measurement from zero (sea level).

Some samples:

In sharing, children then posed questions to each other such as:

° What's The difference in distance between the average depth of the Great Barrier Reef and the height of Uluru?

° If I climbed up from a gold mine to the top of St Helens, how far had I travelled?

etc

The questions posed needed to include both positive and negative numbers to help us understand what we are doing when we add or subtract those types of numbers.

In reflecting, we felt this helped us to gain a deeper appreciation of needing negative numbers.

One student proposed we should try to create a new measuring system whereby we get rid of sea levels and negative numbers and instead create a new elevation /altitude system by starting at the deepest known level of the ocean and working up. Thus, eliminating the need for negative numbers.

It sounded like a great investigation. Two other students were interested in investigating that too so in our next maths time they will be working on that whilst we do other enquiries.

It's great when children pose their own problems to solve and as teachers, we need to value that and that real engagement and wondering to be explored.

Hi Graeme, seriously your blog is like my Maths bible!! Are your recording sheets available to download and print anywhere? Thanks :)

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