Oh! Harry!
2 out of 3
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Problem
A group of eight children were measuring coloured water using measuring cylinders.
The cylinders were labelled with a child's name and the amount they had measured out.
Then Harry opened the window and the wind blew 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 a thousand millilitres and Belinda twice as much as Ahmed.
Grace had measured out three-quarters of the amount that Belinda had, 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 peach and Dan coloured his orange. How much did they measure out?
Harry had knocked over his red liquid at the beginning of the lesson! 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
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
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
This activity could form part of a lesson on reading scales or one on capacity.
You could have the image of the cylinders on the board as an introduction, and begin by reading the clues together. (You may find this SMART notebook file useful. It contains the images from the problem, and the text which can be revealed gradually. Thank you to Mark Dawes for allowing us to share this file.) Ask learners to think on their own about which clue they could use first, then encourage them to talk to a partner. Invite suggestions from the whole group about where to start and why. Children could then work in pairs on the problem.
As the children work, listen to their discussions and in particular listen out for those who are justifying their choices clearly. Warn a few of these pairs that you would like to hear from them during the plenary, asking them to focus on their reasoning and explanations.
Key questions
Which cylinder do you think holds 1000 ml?
Which would be another easy one to try?
Which clue could we use next?
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.