Our Numbers
1 out of 3
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
Problem
For this game you will need a 1 to 6 and a 0 to 9 spinner. The 1 to 6 spinner will give us the tens digit and the 0 to 9 spinner will give us the ones digit. (You could use our interactive spinners, or make your own.)
You will also need two cards which each have six boxes drawn on them, as well as twelve counters.
Each player chooses the special types of numbers that they will collect.
For example, Sara chooses numbers you can share equally among 3 (e.g. 3, 9, 21, 39 ... ).
Nala chooses even numbers (e.g. 4, 10, 20, 44 ... ).
Each of them spins a spinner and then when it rests they read out the number (tens and ones).
If it's 21, then Sara places a counter in one of the boxes on her card. If it is a 10 then Nala gets a counter for her card. If it's a 30 then both of them get a counter.
Have a go at this game. When you've tried it a few times, decide which types of numbers are best to choose so that you fill all the boxes on both cards as quickly as you can.
Spinners description
For accessibility. The link shows a sheet containing more spinners. The first spinner has numbers from 1 to 9. The second spinner has numbers from 1 to 8. The third spinner has numbers from 1 to 7. The fourth spinner has the numbers 1, 2, 3, 4, 1, 2, 3, 4.
Getting Started
What could you try first?
How will you know whether the spinners' number fits in your set?
Student Solutions
Jacob and James from Fishergate Primary School played this game using our interactive spinners.
Using spinners $1-6$ and $0-9$ we tried to see who would win if one was even and one was odd. The odds won as we got these numbers.
| Numbers |
| 25 |
| 32 |
| 29 |
| 35 |
| 54 |
| 52 |
| 55 |
| 22 |
| 35 |
| 51 |
| 11 |
Then we found out the $3$ times table beat the $5$ times table.
| Numbers |
| 29 |
| 51 |
| 22 |
| 36 |
| 26 |
| 51 |
| 11 |
| 54 |
| 23 |
| 26 |
| 37 |
| 10 |
| 69 |
| 24 |
Someone else wrote in to tell us that they found that broad sets work well if you have to get one but narrower sets work better if you want to get them all. Jacob and James then tried different spinners.
We did numbers more than $20$ and numbers less than $20$. Numbers more than $20$ won because there are four tens on the left spinner that would work but there are only two tens that would work for less than $20$.
| Numbers |
| 37 |
| 24 |
| 38 |
| 14 |
| 14 |
| 28 |
| 11 |
| 30 |
| 23 |
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 gives pupils the opportunity to use all their number knowledge and expand their number awareness. There is a chance to experience an element of scientific exploration as they choose the properties of the two groups and test to see what happens.
Possible approach
Have two spinners ready to generate the tens and units figures, and then with the class decide on two different groups (sets) of numbers to look out for. (You could make your own spinners or use our interactive versions.) When a number is generated this gives an opportunity for discussion about which group the number belongs to - if any.
When this introduction has been repeated a number of times with different sets being chosen, discuss with the pupils about what affects the choices of sets so as to get six of each set in as few spins as possible. Give them chance to try out their own combinations in pairs.
Allow time for the whole group to come together to talk about the combinations they tried and to report on their findings. This might also be a good time for children to pose further questions which they would like to investigate.
Key questions
Tell me about the group you've chosen.
Can you say something about why you made this choice.
How do you decide whether the spinners' number belongs to your choice?
Possible extension
Some children could make hundreds, tens and units spinners.
For a further challenge, learners could design some different spinners - what about ones that contain just some of the numbers twice? How does this affect the children's choice of numbers?
Possible support
The children may need some adult support to physically spin the spinners. Some may need help in remembering how to check whether the number belongs to their group.