Sorting Numbers
Can you sort numbers into sets? Can you give each set a name?
Age
5 to 7
Challenge level
Problem
Numbers can be sorted in many different ways. We are just going to be using the numbers from 0 to 50.
In this box there is a set of numbers:
Image
They are the odd numbers between 20 and 40.
In this box there is a different set of numbers:
Image
They are multiples of five.
Now you can make your own sets. Think of a good title for each of your sets.
Getting Started
Try choosing two numbers which "go together" to start with. What is the same about them?
What other numbers would go with the first two?
Student Solutions
Samantha from Kaleen Primary School wrote:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49My group is all odd numbers from 1 to 50
Molly from Worfield Primary sent in some different sets:
Odd Numbers between 0 and 25 (half of 50):1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 and 25.
And Even Numbers between 25 and 50:
26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 and 50.
I wonder if "between" is the right word to use here? What do you think?
Alex from Sprowston Juniors and Yale from Randwick Public School offered similar sets. Here is Alex's:
Prime Numbers up to twenty: 2, 3, 5, 7, 11, 13, 17, 19And Yale's:
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 - they are all prime numbers between 1 and 50
Again, perhaps "between" isn't quite right?
Finally, Roxy from Burrowmore Primary found a different way of sorting the numbers. She says:
We think you should have 2 boxes.
1. Numbers with a curve in them: 0, 2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 45, 46, 48, 49, 50
2. Numbers without a curve: 1, 4, 7, 11, 14, 17, 41, 44, 47
You could link this to venn diagrams and even have numbers with both curvy and straight lines!
What a good idea, Roxy!
Teachers' Resources
Sorting Numbers
Numbers can be sorted in many different ways. We are just going to be using the numbers from 0 to 50.
In this box there is a set of numbers:
Image
They are the odd numbers between 20 and 40.
In this box there is a different set of numbers:
Image
They are multiples of five.
Now you can make your own sets. Think of a good title for each of your sets.
Why do this problem?
This problem provides an opportunity for children to sort and categorise, both of which are important mathematical processes. This open activity challenges children to find their own categories and then name them, which might mean it is a good way to introduce specific vocabulary.
Possible approach
You could begin by putting some numbers into a box on the board yourself and asking the children to describe the set. Encourage learners to find different ways of naming a particular group of numbers or introduce them to new vocabulary as appropriate. Pairs of children could come to the board to create their own set in a similar way.
Children could work in pairs, perhaps using digit cards/number cards, and pencil and paper. As they work, it is a great opportunity for you to listen to their justifications and how well they are able to use mathematical language.
As a plenary you could write several numbers on the board and ask pupils to say which one doesn't belong and why. Encourage creative responses to this - in fact any could be chosen if we give an appropriate reason.
Key questions
What is the same about these two numbers?
Can we find others that could go with them?
What could we call this set?
Is there another way we could describe the set?
Possible extension
Encourage learners to increase the range of numbers from which they are selecting examples.
Possible support
Some children might want to use just the numbers up to 20, for example, to start with. You could get them started by suggesting categories to make.