Oh! Harry!
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Problem
A group of eight children in Class 6 were measuring water using measuring cylinders. They coloured the water to make reading the scales easier.
They lined up the cylinders in two neat rows, each labelled with a child's name and the amount they had measured out.
Then Harry opened the window and the wind blew most of the labels onto the floor! "Oh! Harry!" they all wailed. Can you relabel the cylinders for them using the information below?
Ahmed had measured out just a thousand millilitres and Belinda twice as much as Ahmed.
Grace had measured out three-quarters of the amount that Belinda had done and Freddie had half the amount that Ahmed had measured out.
Which were their cylinders?
Callum had coloured his water blue. How much did he measure out?
Ellie had coloured her water pink and Dan coloured his orange. How much did they measure out?
"Don't drink that!" Harry had laughed earlier, pointing at Dan's cylinder, "It's not orange juice!"
Harry had stretched out his hand, accidentally knocking over his red liquid.
"Oh! Harry!" they had all wailed.
How much was left in Harry's cylinder after the accident?
You can download a resource sheet of the measuring cylinders.
Getting Started
Which cylinder ccould you label first?
Perhaps this helps you label another one?
You might find this resource sheet useful which has pictures of the cylinders and space to write underneath each one. It might help to make a note of the amount of liquid in each one first.
Student Solutions
Thank you for sending in your answers to this problem. Only a few of you explained how you worked it through - particularly clear solutions were sent from Serine, Rukiye from Ashmount School, Rhal and Nikhil at Buckingham College Prep, Oliver and Frederica, Mya and Ciara from Hotwells Primary School. Here is what Serine told us:
Referring to the clues given, the first thing I looked at was Ahmed's because it gives the exact amount which is thousand millilitres. According to that number I can use it to find out the rest of the numbers.
It is said that Belinda's amount is twice as Ahmed's so it equals 2000 millilitres.
Grace measured three quarters of the amount Belinda has. Then the amount will be 1500 millilitres.
The next clue is that Freddie has half of the amount Ahmed has.
There are other clues as well and one says Callum's is blue. There are two blues but because Belinda has the light blue so Callum must have the darker blue. Answer: 1400ml
Another one was that Ellie's is pink and Dan's is orange. Answer: Ellie-1300ml, Dan-700ml - together 2000ml
For the last question I wonder if the picture showed the measure after the accident or not. If it is, the answer would be 100ml, if not it can be zero or other numbers.
Serine sent in a picture with the measuring cylinders labelled:
It's a good point about Harry's cylinder. We don't know whether the picture shows the amount before or after the accident, so your answer will depend on what you assumed.
Teachers' Resources
Oh! Harry
A group of eight children in Class 6 were measuring water using measuring cylinders. They coloured the water to make reading the scales easier.
They lined up the cylinders in two neat rows, each labelled with a child's name and the amount they had measured out.
Then Harry opened the window and the wind blew most of the labels onto the floor! "Oh! Harry!" they all wailed. Can you relabel the cylinders for them?
Ahmed had measured out just a thousand millilitres and Belinda twice as much as Ahmed.
Grace had measured out three-quarters of the amount that Belinda had done and Freddie had half the amount that Ahmed had measured out.
Which were their cylinders?
Callum had coloured his water blue. How much did he measure out?
Ellie had coloured her water pink and Dan coloured his orange. How much did they measure out?
"Don't drink that!" Harry had laughed, pointing at Dan's cylinder, "It's not orange juice!" As his hand stretched out he knocked over his red liquid. "Oh! Harry!" they all wailed again.
How much was left in Harry's cylinder after the accident?
You can download a resource sheet of the measuring cylinders.
Why do this problem?
This problem is a way of practising reading scales in a challenging context. The challenge comes from the reasoning involved.
Possible approach
Key questions
Possible extension
Children could write their own questions using the blank sheet.
Possible support
Children could use the resource sheet and write down the amount in each cylinder. Alternatively, this sheet with the clues and space for noting the amount in each cylinder, might be useful. It might help to have labels of the children's names, for example on pieces of paper or card, which can be moved around underneath each measuring cylinder.