Round the Three Dice
What happens when you round these three-digit numbers to the nearest 100?
Round the Three Dice printable sheet
There are three dice, each of them with faces labelled from 1 to 6.
When the dice are rolled they can be combined in six different ways to make a three-digit number.
For example, if I roll a 2 and a 4 and a 5, I can combine them to make 245, 254, 425, 452, 524 or 542.
Now round each of these numbers to the nearest 100:
245 rounds to 200, 254 rounds to 300, 425 rounds to 400, 452 rounds to 500, 524 rounds to 500 and 542 rounds to 500.
Repeat for other rolls of the dice.
Can each of the six numbers round to the same multiple of 100?
Can each of the six numbers round to a different multiple of 100?
There are some interactive dice that you can use for this problem.
Begin by rolling the dice and making the different three-digit numbers. Then round each of them to the nearest 100. Remember that sometimes you round up and sometimes you round down.
You could record your results in a table like this one:
Round the Three Dice
Round the Three Dice printable sheet
There are three dice, each of them with faces labelled from 1 to 6.
When the dice are rolled they can be combined in six different ways to make a three-digit number.
For example, if I roll a 2 and a 4 and a 5, I can combine them to make 245, 254, 425, 452, 524 or 542.
Now round each of these numbers to the nearest 100:
245 rounds to 200, 254 rounds to 300, 425 rounds to 400, 452 rounds to 500, 524 rounds to 500 and 542 rounds to 500.
Repeat for other rolls of the dice.
Can each of the six numbers round to the same multiple of 100?
Can each of the six numbers round to a different multiple of 100?
There are some interactive dice that you can use for this problem.
Why do this activity?
This activity provides a meaningful task for practising rounding three-digit numbers to the nearest multiple of 100. It encourages children to record their results, notice patterns and make predictions.
Possible approach
A possible starting point is using a number line to remind the class what is meant by rounding.
The interactive dice can be used to model the activity on an interactive whiteboard or can be used by the children as they engage with the task. You may also find that individual dice are useful.
As the task is being modelled, the results should be recorded in a table, perhaps like the one below:
This organisation of results will support the children to notice patterns and conjecture about when numbers will round to different multiples of 100.
Some children may move onto the extension tasks (below).
Key questions
Which numbers can we make?
What will they round to? Will they round up or down? Why?
Do they round to the same multiple of 100? Why? When will this happen?
Does it make a difference if the digits rolled are unique?
Possible extensions
Extension 1: Did the class find examples where some of the three-digit numbers round to the same multiple of 100? Can they then come up with a rule about when this will happen? When will two round to the same? Or three? Or four? Or five? Or all six?
Extension 2: Did the class find examples where each of the three-digit numbers round to a different multiple of 100? Why? Why not?
Extension 3: Having completed the original task, ask the children to add a column to the right hand side of their table to note when numbers round up or down. Can they predict from the initial dice roll, how many of the three-digit numbers made will round up or down?
Extension 4: What if you change the numbers on the faces of the dice? Can you pick numbers so that all of the six three-digit numbers round to the same multiple of 100? Can you pick numbers so that all of the six three-digit numbers round to a different multiple of 100?
Extension 5: What happens if you round to the nearest multiple of 10 instead of the nearest multiple of 100?
Extension 6: Have a go at the activity Round the Four Dice and practise rounding numbers to the nearest multiple of 1000.
Possible support
Copies of the table for children to write the numbers into would be useful.
A number line might also be useful to support children in reasoning about which multiple of 100 is closest to a given number.
Children may like to try Round the Two Dice before tackling this task.
What we like to see
We have written an article on what we are looking for when we decide which solutions to publish.
Explain your methods clearly for other school students to read.
Give reasons and convincing arguments or proofs where you can.
You can share your work with us by typing into the form or uploading a file (must be less than 10MB.)
What can I upload?
- Word documents
- PDF files
- Images - any format
- Screenshots
- Photos of written work
If your work is on another app
You can also send us a link to your work on:
- Youtube/Vimeo
- Google Docs
- Sharepoint/Office 365
- Anywhere sensible on the internet!
How we use your information
By uploading your solution here you are giving us permission to publish your work, either as a whole or edited extracts, on the NRICH website and in associated educational materials for students and teachers, at our discretion.
For our full terms of use regarding submitted solutions and user contributions please see https://nrich.maths.org/terms
Your information (first name, school name etc) is optional. If supplied, it may be used for attribution purposes only if your work is published on the website. Data that you supply on this form (e.g. age if supplied, location if supplied) may also be anonymised and used for evaluation and reporting.
For more information about the University's policies and procedures on handling personal information, and your rights under data protection legislation, please see https://www.information-compliance.admin.cam.ac.uk/data-protection/general-data.