A day after I had worked with the sixth grades (Udavi) with Cartesian divers I went over their guesses of what the volume of an object should be based on its mass (in g) and whether it floats or sinks.

Given that they claimed to know density and knew the density of water was 1 g/ml. I wanted to see if the kids could guess if the number for the volume (in ml) would be greater or less than the mass that we measured in the class (in gm) based on if it floated or rank.

Most sat on the fence and put the same number for mass and volume. At this point a child shared her insight - Anna, mass and volume are the same.

I must mention that this moment showed me how far I had come as a teacher. I did not blow up.

I did have a 2 second shut down and moved on. I inquired if there were others who could help answer her question.

A few hands went up and the children said mass is measured in kg/g and gave examples of

potatoes & tomatoes and volume is measured in ml/L water, oil, diesel, petrol. I wondered if the problem was that the unit of volume is always used with liquids. I inquired if they thought solids have volume and liquids have mass...this question made them uncomfortable. Their thinking was liquids were measured in L so if another thing that is not measured is needed, you can take this number, similarly solids have mass ('weight') that is measured in kg/g and since that is all that is measured (reinforced by my 'clever' experiment) the other quantity is what we got from measurement.

There was also a question of why we bothered with the measuring scale. I gave her the battery and eraser that we measured before (one in each hand) and asked her to tell me how many erasers would be needed to weigh the same as the battery. She said 2 to 3. I asked her to look up their weights. The battery was 18g and eraser 3g. She said she understood that we do it to compare accurately.

Another child pointed out that the battery was also much bigger than the eraser and so naturally its weight was more...

We then did an exercise I asked children to close their eyes and placed different objects in their open palms (in two cases I was also supporting some of their weight) and asked them to guess how big the object was based on its weight, we used pencils, magnets and a large cardboard box. I had to pause when one child lifted his desk for the volunteer to weigh. All the estimates were significantly off (and none of the children cheated).

At some point a child came up with the following distinction - '

I also clarified that it might be confusing that we seemed to have been comparing two different quantities ml with g. I reminded them that we were doing was finding the density g/ml and then comparing it to 1 g/ml which was the density of water. If the calculated fraction was a proper fraction it would float and if it was an improper fraction it would sink.

I asked if they could think of an object whose volume can increase significantly, but the mass changes only by a bit or even fall. It needed the hint of a 'party' to get to a balloon. We then talked about how to distinguish a balloon that is filled by a helium cylinder and that filled with their mouths.

In the next class, I asked them if they remembered the difference between mass and volume. The children said mass is weight and volume is space. But, what was more interesting is how they said it mass is weight (both hands down palms facing upwards), volume is space (both hands moving away from the body).

I shared the distinction of the child, '

Given that they claimed to know density and knew the density of water was 1 g/ml. I wanted to see if the kids could guess if the number for the volume (in ml) would be greater or less than the mass that we measured in the class (in gm) based on if it floated or rank.

Most sat on the fence and put the same number for mass and volume. At this point a child shared her insight - Anna, mass and volume are the same.

I must mention that this moment showed me how far I had come as a teacher. I did not blow up.

I did have a 2 second shut down and moved on. I inquired if there were others who could help answer her question.

A few hands went up and the children said mass is measured in kg/g and gave examples of

potatoes & tomatoes and volume is measured in ml/L water, oil, diesel, petrol. I wondered if the problem was that the unit of volume is always used with liquids. I inquired if they thought solids have volume and liquids have mass...this question made them uncomfortable. Their thinking was liquids were measured in L so if another thing that is not measured is needed, you can take this number, similarly solids have mass ('weight') that is measured in kg/g and since that is all that is measured (reinforced by my 'clever' experiment) the other quantity is what we got from measurement.

There was also a question of why we bothered with the measuring scale. I gave her the battery and eraser that we measured before (one in each hand) and asked her to tell me how many erasers would be needed to weigh the same as the battery. She said 2 to 3. I asked her to look up their weights. The battery was 18g and eraser 3g. She said she understood that we do it to compare accurately.

Another child pointed out that the battery was also much bigger than the eraser and so naturally its weight was more...

We then did an exercise I asked children to close their eyes and placed different objects in their open palms (in two cases I was also supporting some of their weight) and asked them to guess how big the object was based on its weight, we used pencils, magnets and a large cardboard box. I had to pause when one child lifted his desk for the volunteer to weigh. All the estimates were significantly off (and none of the children cheated).

At some point a child came up with the following distinction - '

*w**hat I can feel is mass and what I can see is volume*'. This seemed an aha moment for everyone and there were smiles all around.I also clarified that it might be confusing that we seemed to have been comparing two different quantities ml with g. I reminded them that we were doing was finding the density g/ml and then comparing it to 1 g/ml which was the density of water. If the calculated fraction was a proper fraction it would float and if it was an improper fraction it would sink.

I asked if they could think of an object whose volume can increase significantly, but the mass changes only by a bit or even fall. It needed the hint of a 'party' to get to a balloon. We then talked about how to distinguish a balloon that is filled by a helium cylinder and that filled with their mouths.

In the next class, I asked them if they remembered the difference between mass and volume. The children said mass is weight and volume is space. But, what was more interesting is how they said it mass is weight (both hands down palms facing upwards), volume is space (both hands moving away from the body).

I shared the distinction of the child, '

*what I feel is mass and what I see is volume*'; with the 5th graders who had trouble with the multiplication/division stories for density and they seemed to get it too.
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