Compare the Cups
1 out of 3
You'll need a collection of cups for this activity.
Problem
Compare the Cups printable sheet
For this challenge, you will need lots of different cups. This picture shows some:
Which might you choose if you wanted a lot to drink? Why?
Which one would you choose if you did not want a lot to drink? Why?
Can you arrange the cups in a line from the one that holds the most liquid to the one that holds the least liquid?
How will you test whether you are right?
Getting Started
Find some cups of your own and use water or sand to try out your ideas.
Student Solutions
Thank you to everybody who sent in their solutions for this activity. Chloe from Mound Elementary School in the USA sent us this picture of some cups to compare:
Chloe said:
In order for me to find out which cup has more water, I need to write down the answer to each cup on a piece of paper.
I wonder what Chloe means by 'the answer'?
Caolan from Knockloughrim in Northern Ireland sent in these ideas:
If I wanted to drink a lot, I would:
Choose the cup which could hold the most capacity, as one might be fatter and one might be taller.
If I didn't want a lot to drink, I would:
Choose the cup that holds the least capacity. I would choose the cup that looks the shortest and slimmest as well as testing the capacity.
How would I arrange the cups from most liquid that could fill it, and how could I prove that I'm right? I wouldn't arrange them by looking at them and roughly judging the biggest, but I would test, using a measuring jug, how much capacity it holds. I would prove this using the measuring jug as it would be accurate.
Caolan makes an interesting point about the different shapes of cup we can find - some cups can be 'fatter' while others can be 'taller'. I wonder how accurately we can tell which cup is bigger just by looking at them?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This practical activity offers a context in which children can develop their conceptual understanding of capacity.
Possible approach
For this activity, have a collection of cups/glasses/mugs available for the children to explore themselves. You may want to offer a context for the activity to link in with a current theme or story.
Pose some questions orally to the group, as in the problem, and encourage them to think about the answers by estimating and by eye at first. You could discuss their thinking and then give them the opportunity to test out their ideas, perhaps with water or sand.
In the plenary, you could pose a final challenge, such as how many of the smallest cup will be needed to fill the largest cup? Again, encourage estimation first before trying it out practically.
Key questions
Tell me about your thinking.
How will you test out your ideas?
Possible extension
You could introduce a much, much smaller container, for example a spoon, and observe what the children do with it.
Possible support
Some learners might need help with awkward pouring.