Sorting the Numbers
1 out of 3
Can you put the numbers in the correct place in this Carroll diagram?
Problem
Can you put the numbers in the correct place in this Carroll diagram?
You could print off this sheet to complete.
Getting Started
What do you know about the number $1$, for example? So where would you put it in the diagram?
You could look at each number in turn in this way.
In the second Carroll diagram, what do all the numbers in the top left box have in common?
How are they different to the numbers in the bottom left box, for example?
Student Solutions
Rowena from Christ Church Primary Schoolexplained how she filled in the first diagram:
I first looked at the two columns. Between $5$ and $15$ you don't use $5$ and $15$. So I started at $6$ for the right hand column, it went in the top row, $7$ in the bottom etc. When you count up it goes from bottom to top and back again until you reach a multiple of $10$, then it stays in the box you just put a number in. After I did this for $6$ up to $14$, I moved to the left hand column and repeated the same process for $1-5$ and $15-30$.
Well explained, Rowena, thank you. Here is the picture Rowena sent of her completed diagram:
Thank you also to Cong from St Peter's Roman Catholic Primary School and Callum and Katie from Eynesbury CE(C) School for their solutions. Callum and Katie, you were so close in the second Carroll diagram, there was just one heading which you had slipped up on. Perhaps you can see why Cong's works? Here is Cong's completed diagram for the second challenge:
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 children a way of sorting numbers according to different properties and also forces them consider more than one aspect at once. It also provides opportunities for children to explain their placing of the numbers, using appropriate language.
Possible approach
Key questions
What can you say about the numbers is this box that is different from the numbers in that box?
Possible extension
Learners could go on to using these sheets given above as a follow-up, especially that last four questions.
Possible support
Children could start with the simpler Carroll Diagrams problem.