Pouring Problem
What do you think is going to happen in this video clip? Are you surprised?
Age
7 to 11
Challenge level
Maya has two glasses of water:
Image
Watch this short clip to see what she starts to do:
What do you think will happen next?
Click on the 'Show' button to see the full clip and find out.
Are you surprised by the result?
Can you explain what is going on?
Some of this vocabulary might help you to get started:
tall/taller
short/shorter
wide/wider
narrow/narrower
diameter
volume
capacity
Harvey from Hanley Swan Primary wrote:
I thought that it would probably overflow because it didn't look like the water in the first cup could fit in the second as they were the same size. I watched the video and was very surprised about what happened. AMAZING! I think that the reason it managed to fit is that there was a bit of a widening in the top of the cup - the water in the first cup didn't reach this point.
Mimi from Primrose Hill said:
The twist is that both glasses are filled up high and she poured it without the water overflowing. What may be the solution (I am not so sure...) is that the bit in the cup where it grows out near the top, makes the water fill up less (by which I mean it stores more water) and so that makes it stay at the top. Another reason could be that part of the water in the second glass is fake. Therefore, if my reasons are wrong I will not be very surprised.
Nathan from Canberra Grammar School in Australia sent this:
The two glasses Maya has used have an opposite bottleneck. So the volume of the very top of the glass is larger than the volume of the bottom of the glass.
Amy from Luckwell Primary School gave a very clear explanation of what she thinks happened:
Like most people who watched this video, I predicted that the glass which the water was being poured into would overflow. I was a little suspicious, though, as the question 'Were you surprised?' usually means that something unexpected will happen...
What is happening is we are confusing our eyes and assuming that the top half of the glass is smaller than the bottom half. Yes, the top half of the glass is shorter, but it's also wider! On top of this, the bottom half is thinner and we do not pay attention to the shape of the glass as we're
watching Maya pour the water into the right-hand glass. (From now on, pay attention to the shape of your glass!).
When I showed my friends the clips, they were amazed! I was the only one that figured out how it happened though...
Maths Mayhem at North London Collegiate School wrote:
We watched the video as a maths club and were surprised by what happened as we thought it would overflow if you kept pouring.
Kayla thought because the glass is narrower at the bottom and wider at the top, the amount of water in the left-hand glass is the same volume as the space left in the right-hand glass.
Isha thought that both cups were more than half full when she first saw them but now concludes that they have to be half full to start.
We all then speculated that the right-hand glass is slightly wider and taller than the other and maybe the base is slightly larger, however, we couldn't say for sure as we don't have it to measure.
In conclusion, we have decided that because of the shape of the glasses that this is an illusion. The glasses look more than half full but they are only actually half full.
Here's a very different solution from Abdullah who is homeschooled:
I think, in the right glass there is water and that in the left glass there is alcohol.
Because the alcohol particles are smaller than water particles, the alcohol particles go into spaces, which are between the water particles.
When we studied the States of Matter, we did an experiment:
First, we put 10 ml water in a measuring cylinder. And we put 10 ml ethanol in another measuring cylinder. And then we added 10 ml ethanol on the 10 ml water. The reading was 18 ml.
I thought that it would probably overflow because it didn't look like the water in the first cup could fit in the second as they were the same size. I watched the video and was very surprised about what happened. AMAZING! I think that the reason it managed to fit is that there was a bit of a widening in the top of the cup - the water in the first cup didn't reach this point.
Mimi from Primrose Hill said:
The twist is that both glasses are filled up high and she poured it without the water overflowing. What may be the solution (I am not so sure...) is that the bit in the cup where it grows out near the top, makes the water fill up less (by which I mean it stores more water) and so that makes it stay at the top. Another reason could be that part of the water in the second glass is fake. Therefore, if my reasons are wrong I will not be very surprised.
Nathan from Canberra Grammar School in Australia sent this:
The two glasses Maya has used have an opposite bottleneck. So the volume of the very top of the glass is larger than the volume of the bottom of the glass.
Amy from Luckwell Primary School gave a very clear explanation of what she thinks happened:
Like most people who watched this video, I predicted that the glass which the water was being poured into would overflow. I was a little suspicious, though, as the question 'Were you surprised?' usually means that something unexpected will happen...
What is happening is we are confusing our eyes and assuming that the top half of the glass is smaller than the bottom half. Yes, the top half of the glass is shorter, but it's also wider! On top of this, the bottom half is thinner and we do not pay attention to the shape of the glass as we're
watching Maya pour the water into the right-hand glass. (From now on, pay attention to the shape of your glass!).
When I showed my friends the clips, they were amazed! I was the only one that figured out how it happened though...
Maths Mayhem at North London Collegiate School wrote:
We watched the video as a maths club and were surprised by what happened as we thought it would overflow if you kept pouring.
Kayla thought because the glass is narrower at the bottom and wider at the top, the amount of water in the left-hand glass is the same volume as the space left in the right-hand glass.
Isha thought that both cups were more than half full when she first saw them but now concludes that they have to be half full to start.
We all then speculated that the right-hand glass is slightly wider and taller than the other and maybe the base is slightly larger, however, we couldn't say for sure as we don't have it to measure.
In conclusion, we have decided that because of the shape of the glasses that this is an illusion. The glasses look more than half full but they are only actually half full.
Here's a very different solution from Abdullah who is homeschooled:
I think, in the right glass there is water and that in the left glass there is alcohol.
Because the alcohol particles are smaller than water particles, the alcohol particles go into spaces, which are between the water particles.
When we studied the States of Matter, we did an experiment:
First, we put 10 ml water in a measuring cylinder. And we put 10 ml ethanol in another measuring cylinder. And then we added 10 ml ethanol on the 10 ml water. The reading was 18 ml.
Pouring Problem
Maya has two glasses of water:
Image
Watch this short clip to see what she starts to do:
What do you think will happen next?
Click on the 'Show' button to see the full clip and find out.
Are you surprised by the result?
Can you explain what is going on?
Why do this problem?
This task has been designed to stimulate learners' curiosity by presenting them with a surprising outcome. The intention is that the unexpected result will hook students in and encourage them to want to explain the mathematics of the situation using what they know about capacity and volume.Possible approach
You may wish to introduce this task by demonstrating the pouring yourself. (Sherry glasses are ideal!) If you do decide to set up the glasses yourself, the best way to go about it is to fill one glass completely to the brim, then decant into the second glass until the levels are the same.Whether you choose to use the image and video published here or set up a 'live' version, start by showing the class the two glasses both containing water and invite them to talk to a partner about what they see. You could share some of these observations with the whole group, then either start pouring one glass into the other or play the first clip. Give learners a few moments of individual thinking time to consider what might happen next, then encourage them to share their ideas with a partner. Take a wide variety of suggestions from the group. Learners may talk about one glass over-flowing, or there being some left in the glass that is being poured from, for example.
As they view the full video or watch you continue to pour the water, observe their reactions and challenge a few students to share how they are feeling and why. Give them plenty of time to work in pairs to unpick what is happening here. As they discuss, listen out for useful vocabulary and phrases that they are using (for example tall/taller, short/shorter, wide/wider, narrow/narrower, diameter, volume, capacity, "I think... because..." etc.) and write them up on the board for all to see.
You might ask learners to record their conclusions in some way, for example on pre-prepared card shaped like large speech bubbles, which could then be displayed. Draw attention to any pairs who make some generalisations based on the shape of the glasses.
Key questions
What do you think is going to happen next?Are you surprised by what happened? Why?
How would you explain what is going on?