Year 5 spot patterns and investigate puzzles in Maths

Spotting patterns and investigating puzzles is an important part of our Year 5 mathematics curriculum, not least because these activities highlight the fun and intrigue of maths.  Year 5 have been putting their column subtraction skills to good use this week whilst investigating a pattern first discovered by an Indian mathematician - Kaprekar - just after the Second World War.  He found that if you take any three (different) digits, rearrange them to make both the largest and smallest numbers possible, subtract the smaller from the bigger, then repeat the process with your answer, then you will reach a number which keeps repeating - 495.  After first double-checking that this did, in fact, work with any number, Year 5 were interested in the patterns they spotted with their results. Several noted that the middle digit of every answer was 9; others spotted that the numbers either side of the 9 always added up to 9.  It took a while for them to work out why this might be so, until they thought about what was happening in the tens column with each subtraction.

Next they wanted to know what would happen with 4 digit numbers.  Painstakingly, they tried lots of combinations of digits. Another important part of being a mathematician is resilience - trying a large number of combinations takes time and effort.  Eventually they found, yet again, a mysterious number which the calculations kept returning to - take a look at the photo for the answer...