Estimate the first digit of the quotient. Multiply it by the dividend. Subtract the product of your estimate from the divisor. If the answer is lower than the number you are to subtract it from, and yields a number that the divisor can still divide into, your estimate is too low. Go back and estimate again but with a higher number.
Round the divisor and dividend before dividing. If it does not go into the dividend easily, then your estimate is too low. Pick another number that can be easily divided into the dividend. For example, 157 divided by 34 will force the student to estimate 160 divided by 30. An attempt to divide these estimated numbers will produced an estimates quotient with a remainder. Instead, round the 30 up to 40 and you get 4 as the estimated quotient. The real quotient is 4 with a remainder of 21. The first estimated quotient would have been 5 with 3 as a remainder --- too high for this problem, but yielded from and estimate that was too low.
Perform the quotient estimate and then complete the real problem. You estimate is too low if the real quotient is higher than the estimated quotient by more than three.
Check by multiplying. Multiply the quotient and the divisor to get the quotient number as the product of the check problem. If the product is less than the dividend, the estimate is too low.