This is how a group of students began their work in response to the question 'Do you know anyone who has lived 1000 days?' As they are eight years old, they decided to see if they are 1000 days old by checking 8 times 365. Notice how they just write down the 5 and 6 digits in the solution as "there is nothing above them". They then do eight times 'three' to get 32.
Now these are grade 3 students so they are only just beginning to learn about multiplication and should not be coming across any formal algorithm until Grade 4 at the earliest. But when it does come to the time for them to learn how to compute something like this, I am certain that they will be more succesful by being introduced to the array method first.
The neat thing was that even though they got the calculation wrong, they knew that 8 years was way above 1000 days. So they then tried 6 years, then 5 years, then 4 years and finally 3 years. Each time, the calculation was incorrect but their reasoning based on this calculation was perfect. Not bad for Grade 3!