Shifting Times Tables (all of the numbers here are examples so don’t get confused by matching my numbers with yours just follow the formula.)
Level 1 & 2: Consecutive Times Tables: Find the difference between 2 adjacent numbers in the times table eg. 5, 21, 9, 17, 13 you would pick 5 and 9 or 9 and 13 etc. Calculate the difference between the 2 numbers. The difference is the times table. Minus the smallest number by the difference eg. difference of 5 & 9 = 4 so 5 - 4 = 1 which is the shift. So 5, 9, 13, 17 and 21 belong to the 4 times table which is shifted up by 1.
Level 3 & 4: Random numbers in same times table: First find the difference between the 2 closest numbers eg. 112, 125, 151, 177 and 203 you would pick 112 and 125. The difference is 13 (125-112). Now you know the biggest possible times table is 13 and nothing can be bigger than that otherwise 112 and 125 wouldn’t belong in the same times table. Now see if the other numbers are in a 13 times table, adding 13 to the smallest number and working upwards and seeing if the numbers you get include your other numbers. If they do (Like 112, 125, 151, 177 and 203 all get in the 13 times tables starting from 112) Find the closest ACTUAL 13 times tables (13, 26, 39) to the smallest number to make it easier eg. the closest 13 times table to 112 would be 117 so the answer would be 13 times table shifted DOWNWARDS by 5 or you could shift it upwards but then you have to find the highest 13 times table below 112. Now, if any of the numbers don’t match the 13 times table or any times table you have right now you need to make the times table smaller, remember before how I said you can’t make your times table bigger than 13 (or any times table you have now) or your closest 2 numbers won’t be in the same times table? So it has to be smaller than 13, halving it down would be the best option but I don’t think the NRICH web accepts decimals for that particular problem, but if you have an even number try it out. If you do have an odd number, see if any numbers smaller than it could make the numbers you have fit in it’s shifted times table.
Oren Dabbach- Sunnynook School - Year 6