1. The difference between the consecutive numbers are 3 so that’s the times table.
2.a) We know that the times table is the difference of the consecutive terms, so if you find out 13 – 8 = 5 you can tell the times table is 5. Now that we know the times table is we can figure out the shift by doing 8 – 3 = 5, so the shift is 5
TIMES TABLE: 5 SHIFT: 3
2.b) To find out the times table we will do 41 – 27 = 14 and from that the times table is 14. To find out the shift you do 27 – 14 = 13 so the shift is 13.
TIMES TABLE: 14 SHIFT: 13
2.c) Because they are randomised you need to estimate the closest 2 terms, which in this case is 51 and 37. So you need to do 51 -37 = 14 so the times table might be 14. To make sure it’s 14 you check it with another number. If you do 51 – 23 = 28 and 28 is a multiple of 14 so 14 is the times table and the shift is.
TIMES TABLE: 14 SHIFT: 23
2.d) They all end in 4 so from that we can tell the shift is 4 and the times table is a multiple of 10. If you replace the 4s with 0s you can notice they’re all multiples of 50 and 10.
TIMES TABLE: 50 (OR 10) SHIFT:4
2.e) You find the difference of the two closest terms which are 332, 373 and 373, 414, they’re both the closest because the difference of the two pairs are both 41 therefore the times table is 41. If you find out 41 * 3 = 123 and 123 is 4 below 127, and if you do 41 * 8 you get 328 which is 4 below 332 so the shift is 4.
TIMES TABLE:41 SHIFT: 4
3. If the terms are all odd the times table would be even and the shift would be odd.
4. They’ll all be even if the times table and shift are both even.
5. They’ll be odd and even the times table is odd
6. If the units are all identical then the times table is a multiple of 10
7. If there’re are only 2 different unit digits the times table then the times table ends in a 5.
8. My method will always work because the difference of the consecutive terms is always the times table.