If you are looking for an open-ended activity to spark thinking and stoke conversation then try this Big Brother-style balloon trick. For example, six numbers are crowded in the basket of a hot air balloon which is quickly losing height.
To save the balloon from crashing, children in twos or threes have to decide which number should be evicted, and more importantly, why that number should leave? This scenario motivates children to think of a specific reason which they then justify and defend to the rest of the class. So, imagine the numbers in the basket are 5, 10, 15, 20, 25 and 30.
You could argue that 5 should go because it is the only single digit number. Then again it could be 25 because that's the only square number.
What about the number with the most factors? Number 30 has 8 factors and so that makes it heavier than the others so 30 may be evicted. 15 is the only teen number. Twenty has the same number of letters as factors. 10 has the smallest digital root. Repeat the process until there is one number left.
You could try the balloon debate with shapes too
John Dabell is a numeracy consultant and teacher trainer