Sets of Numbers
How many different sets of numbers with at least four members can you find in the numbers in this box?
Problem
How many different sets of numbers with at least four members can you find in the numbers in this box?
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?
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
Key questions
Possible extension
Learners could make their own list of numbers to make into as many sets as possible. You could suggest using triangular and cube numbers as well as various multiples.
Possible support
Some children might find it useful to list all the properties of each number in the box.