Sets of numbers
How many different sets of numbers with at least four members can you find in the numbers in this box?
Age
7 to 11
Challenge level
Problem
How many different sets of numbers with at least four members can you find in the numbers in this box?
Image
For example, one set could be multiples of $4$ {$8, 36 ...$}, another could be odd numbers {$3, 13 ...$}.
Getting Started
You could list all the properties of each number as a start.
Can you see some numbers which have the same property?
Student Solutions
Children from Beaumaris North Primary School, Melbourne told us:
In our Year 3 Enrichment group we discussed all the possible sets that could be found. Here is what we found!even numbers {$2, 8, 36, 56, 64, 136$}
odd numbers {$3, 13, 17, 27, 39, 49, 51, 91, 119, 121, 125, 143$}
multiples of one {all of them!}
multiples of $2$ {$2, 8, 36, 56, 64, 136$ - the same as even numbers!!}
multiples of $3$ {$3, 27, 36, 39, 51$}
multiples of $4$ {$8, 36, 56, 64, 136$}
multiples of $7$ {$49, 56, 91, 119$}
multiples of $8$ {$8, 56, 64, 136$}
numbers starting with $1$ {$13, 17, 119, 121, 125, 136, 143$}
square numbers {$36, 49, 64, 121$}
numbers containing $2$ {$2, 27, 121, 125$}
square roots {all of them are square roots !}
numbers containing $1$ {$13, 17, 51, 91, 119, 121, 125, 136, 143$}
numbers containing $6$ {$36, 56, 64, 136$}
cube numbers {$8, 27, 64, 125$}
numbers containing $3$ {$3, 13, 36, 39, 136, 143$}
prime numbers {$2, 3, 13, 17$}
numbers containing $9$ {$39, 49, 91, 119$}
numbers that you can subtract one from {all of them again!}
numbers between one and one hundred and forty four {all of them AGAIN!}
numbers between one and one hundred {$2, 8, 13, 17, 27, 36, 39, 49, 51, 56, 64, 91$}
whole numbers {all of them}
triple digit numbers {$119, 121, 125, 136, 143$}
numbers with double digits {$13, 17, 27, 36, 39, 49, 51, 56, 64, 91$}
We enjoyed this because we liked picking out different possibilities and seeing if they worked out. We could have submitted more but the bell rang! Thanks for the great challenge.
Olly from North Molton Primary also found:
multiples of $13$: {$13, 39, 91, 143$}multiples of $17$: {$17, 51, 119, 136$}
... and multiples of $1$ which of course is all of the numbers.
Jin and Anushkawho go to Dubai International Academy had one more set:
digits add to $8${$8,17,125,143$}
Can you find any more? How about triangle numbers and tetrahedral numbers?
Teachers' Resources
Sets of Numbers
How many different sets of numbers with at least four members can you find in the numbers in this box?
Image
For example, one set could be multiples of $4$ {$8, 36 ...$}, another could be odd numbers {$3, 13 ...$}.
Why do this problem?
This problem gives plenty of opportunity for both discussion and exploring patterns, properties and relationships involving numbers. It also helps learners to make general statements about properties of numbers such as squares, factors, multiples, odd and even, and to identify examples for which a statement is true or false.Possible approach
You could also use this interactivity as a starter to this problem where you drag numbers you "like" (i.e. are part of a set) to one side and numbers you "don't like" (i.e. are not in your set) to the other. The children then have to ask questions with yes/no answers to determine the name of your set. You could invite some learners to take the
lead on this themselves, with the rest of the group asking questions.
You could then introduce the problem itself and learners could work in pairs from this sheet so that they are able to talk through their ideas with a partner. (The sheet has two copies of the box of numbers on it.) You could also challenge pairs to find two other
possible members for their sets from the numbers under $150$.
At the end learners could be asked for the titles of the sets they have found and then others could suggest members for these sets. You could make statements such as "$9$ is a member of this set" and ask learners to identify whether the statement is true or false. When sets of multiples of $2$, $4$ and $8$ have been found and discussed, learners could be asked to explain why no other sets of
multiples of even numbers are possible from the numbers in the box.
Key questions
What can you tell me about this number?
Is this odd or even? What else do you know about it?
Which multiplication tables will you find this number in?
Can you see any other multiples of that number?
Can you suggest other numbers that could go together in this set?