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September 01, 2013

Will this float? : 7th grade exploration on math and science

One of the areas we covered in the science/math classes was density. Here is a video of the experiments that the kids remember doing in class.

Remembering Archimedis
We started with toying with the idea of volume of an irregular shape and thinking of a way to measure it. We followed Archimedis story of having to figure out whether a crown which weighed the same as some amount of gold was in fact entirely made up of gold or not.
We spent some time thinking about it, or whatever it is that each child does when it wants to indicate that apparently he/she is thinking. It usually involves staring at a speck of paint on the ceiling. I insisted that what we were about to do they already knew, which was followed by even more intense staring.
Once we put it in water and I indicated that the displaced water has the same volume as the stone I immediately connected it to the crow story that everyone hears from when they are young. Our experiments were a bit of little kludge when we used the milkman's jars, the smallest being 100 ml to try to measure the volume of a small irregular stone. Luckly, it is also a math class and we measured that the height of the water was only around 1/4 the height of the cup (go fractions).
I looked around the house to find something that would make the measurements easier and found Ani's measuring jar and weighing scale. I also found some cups Arham has that fit into each other.
Does it float or sink?
I used the iron blots that I had collected for the pendulum experiments and we did a session of how much it takes to drown a small plastic cup. Shi mentioned that given iron sinks its surprising that ships that are made of iron float. I asked him to hold the thought. On placing the mass that sunk the smaller cup in the larger cup it would float. On loading this cup further...before doing each of these steps we would try to predict if this time the cup would float or sink.
Shi concluded that with the same mass if the volume is bigger things float, hence, ships float because their volume is so big.
Density of water
Since we had now encountered the impact of mass and volume I introduced the concept of density of an object being the mass per unit volume. We measured the density of water and confirmed that it was indeed close to one.
How much water is displaced when an object floats
Now things get interesting, I asked how much water is displaced when an object floats. Given the experience of a sinking object the children said it depends on the volume of the object. We tried putting the same mass in gradually increasing volumes and found that they were all displacing the same amount of water.
We then measured the weight of the cup and the objects in it and found that the number we get (in gms) is the same as the volume that is displaced (in ml).

Note 1: This would not be true if a liquid other than water is used (or if I added say copious amounts of salt to the water changing its density)
Note 2: Actually, the volume displaced is not 'exactly' the same. The larger cup has a slightly larger mass, but given the larger mass of the object placed in it the delta mass is not significant to alter our measurements given the accuracy we could do them with.
They had to think and tell me:
1) Why it is that if an object sinks its volume matters and when it floats its mass matters?
2) Why does a solid like ice floats on water?
My head is going to explode
There are many interesting idioms in Tamil, one of them meaning I thought so much that my head is going to explode. Ok, we didn't get it, can you tell us now?
I think its these moments that teachers enjoy, when any word said is waited in anticipation and when what you don't say is going to have a bigger impact than anything you say. "Did you discuss your ideas? No, you should." After a minute or two of we really don't know followed by silence one kid finally says, the whole object doesn't go into the water so its whole volume can't matter. Now the kids start catching on, oh yeah, the amount of water displaced is only as much as the shape the object goes into water and this must depend on the weight (I haven't gotten around to differentiating weight from mass).
The second question is more of an opening for me to talk a bit about how we view solids and liquids in their atomic structure and the open lattice structure of ice.
Things to see
When I am short in time then instead of doing stuff we just watch some vides - one that showed hot water was less dense than cold water, that egg sinks in water, floats on salty water. How do you make it float mid way in water? Multi layered liquids (based on density). There was also a very nice animation of objects with different densities, masses and shapes that captured how the water in the tub increased when an object is dropped in as well.
Assessment Videos 
A couple of the kids had made the Bartons pendulum and coupled pendulum experiments for a friday teachers meeting. The kids were keen on making another video for the many things they had learnt over the week. I decided to use this as an assessment technique to see how they work alone and with others. The whole operation was done within 35 mins.
The kids had to discuss what they had liked and come up with what each wanted to talk about while giving the others also something to talk about. There was very little prep time, but mentioned what I found was missing the last time they made videos (mentioning the things that are used in their experiments). I tried not to interfere and even had to walk off in the middle of a video, I did prompt the youngest to say (ml) for the volume she found.
It also gave an opportunity for children think through and make a presentation logically, breaking down all they want to say in a step-by-step manner ( I should take the weight of the measuring jar before I fill water in it). This process is useful in their life no matter what they end up doing.

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