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March 01, 2014

Cartesian divers

I had quite some fun with a couple of Cartesian Divers.

Cartesian divers: The couple I got were plastic hollow vials with a weight on the cap of the vial. They are not very well done (tubes that the plastic was not that well stuck on, but they work). The weight is such that they barely float on water (upside down). The air is trapped inside the vial.
If you close the cap of the bottle and press the bottle the divers sink to the bottom and return when you release the pressure.
I got an opening with introducing density (math class) to the 6th graders when they visited a science fair and felt that the kerosene and water layers was something that they understood because they knew density. We did a few measurements but I quickly realized that they didn't feel ready to do multiplication and division with fractional/decimal quantities. A detailed quantitative learning of the subject seemed out of question and I had to switch to will this float or sink exercise.

The children gave 7 objects they had (eraser, stone, pencil sharpener, magnet, etc) and I added three - a (Jodo Gyan) density 1 g/ml ones plastic block, a 10g/10ml tens plastic block and a cartesian diver to take the total to 10 things. I talked about the density and the idea of comparing an object's weight in gm vs the same object's volume in ml is what determines if an object floats or sinks.
Before each guess I weighed the object and talked about what it would mean if it floated or sank.

It seemed that the additional step of weighing was starting to feel a little boring so along with the third measuremnt I casually dropped the cartesian divers into the bottle and started their dives (you develop showmanship). We spent some time playing with them and trying to explain them, luckily we failed and this gave motivation to do the other tests and learn things well.

It was interesting to see their reactions to things they found counter intuitive
- one sharpener (enclosed air gap) floated and another sank (open to allow water to flow in)
- light objects can sink!

Then it got even more interesting when I dropped the density 1 blocks from a height they both sank. The children were apparently pleased as this was what they claimed to have written. A note: 6th graders are young kids and sometimes they quietly 'correct' their guesses while writing the observation alongside (I had asked them to maintain columns for object, mass, guess, actual). My purpose of getting them engaged, having some expectation before a measurement but correctly recording the observation was satisfied, so I am ok with this (my fun starts later).
As they were looking all smug (they had all got all the answers right) I gently inserted the ones block. This time it floated comfortably. This was, of course, an unacceptable development. Next the tens block floated when slowly inserted into water. A student suggested that I only needed to tap it a bit on its head, but this didn't make it sink. I gently tapped it and it recovered.

I asked the children to add the volume of each object given its mass and whether it sinks or floats. This now gave me a chance to see if the kids had been able to connect the relationship between mass, density and volume.

With the 7th graders who had done a bunch of experiments with density before I just showed the cartesian divers and asked them how it worked. We then went over the stories of multiplication and division of the relationships between mass, volume and density and this time around they were able to introduce these stories to the 5th graders as well.

They also tried to explain why the phenomenon works and only when they finally noticed the water raising in the vials due to pressure did they get why it sinks.

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