Round the Two Dice
Problem
Round the Two Dice printable sheet
There are two dice, each of them with faces labelled from 1 to 6.
When the dice are rolled they can be combined in two different ways to make a 2-digit number.
For example, if I roll a 2 and a 3 I can combine them to make 23 or 32.
Now round each of these numbers to the nearest 10. 23 rounds to 20 and 32 rounds to 30.
Repeat for other rolls of the dice.
Do both of the numbers you make ever round to the same multiple of 10?
There are some interactive dice that you can use for this problem.
Getting Started
You could record your results in a table like this one:
| Numbers rolled | 1st two-digit number | Rounds to | 2nd two-digit number | Rounds to |
| 2 and 3 | 23 | 20 | 32 | 30 |
| 2 and 6 | 26 | 30 | 62 | 60 |
Student Solutions
When looking at this problem, we found that it is impossible to round each of the numbers to the same whole number. We think this is because when you roll different digits you will always get a range of whole numbers that round either up or down.
Srieyohme from Woodend School wrote:
I rolled the dice over and got 36 different combinations. There were six combinations that give the same nearest 10 on rounding. They are 1 and 1, 2 and 2, 3 and 3, 4 and 4, 5 and 5, 6 and 6.
Woodmansterne Primary School would like to offer a solution
We found that when one die showed 4 and another showed 5, we could make 54 and 45, both of which round to 50.
Kind regards,
Hawthorn Class
Thank you for those submissions. If you can build further on any of these solutions, do get in touch with us.
Teachers' Resources
Round the Two Dice
Round the Two Dice printable sheet
There are two dice, each of them with faces labelled from 1 to 6.
When the dice are rolled they can be combined in two different ways to make a 2-digit number.
For example, if I roll a 2 and a 3 I can combine them to make 23 or 32.
Now round each of these numbers to the nearest 10: 23 rounds to 20 and 32 rounds to 30.
Repeat for other rolls of the dice.
Do both of the numbers you make ever round to the same multiple of 10?
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 two-digit numbers to the nearest multiple of 10. 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:
| Numbers rolled | 1st two-digit number | Rounds to | 2nd two-digit number | Rounds to |
|---|---|---|---|---|
|
2 and 3 |
23 |
20 |
32 |
30 |
|
2 and 6 |
26 |
30 |
62 |
60 |
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This organisation of results will support the children to notice patterns and conjecture about when numbers will round to different multiples of 10.
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 10? Why? When will this happen?
Possible extensions
Extension 1: Did the class find examples where both two-digit numbers round to the same multiple of 10? Can they then come up with a rule about when both of the two-digit numbers will round to the same multiple of 10?
Extension 2: 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, whether the two-digit numbers made will round up or down?
Extension 3: What if you change the numbers on the faces of the dice?
Extension 4: What happens if you introduce a third dice and make six different two-digit numbers? Can they ever all round to the same multiple of 10?
Extension 5: Have a go at the activity Round the Three Dice and practise rounding numbers to the nearest multiple of 100.
Possible support
Copies of the table for children to write the numbers into would be useful.
A number line would also be helpful to support children in reasoning about which multiple of 10 is closest to a given number.