Here is the my problem: Pam used front-end estimation and adds 345, 311, 418 as 900+(50+10+20) to get the answer 980. Pat rounds the number and adds 350+200+400 to get 950. Who has the better answer? I say Pam because she is only 6 away from the actual answer of 974.
Obviously Pam has the better estimate. I round each to the nearest ten when estimating.
In Pam's problem, where did the 900 come from?
In Pat's problem, where did 200 come from?
Also -- doesn't 345 + 311 + 418 = 1074?
Or is there a typo in your original problem?
It is suppose to be 211 not 311. Sorry.
To determine which answer is closer to the actual answer, let's compare the differences between the estimated answers and the actual answer.
According to the information given, Pam used front-end estimation by adding the first digits of each number. She calculated the estimate as 900 + (50 + 10 + 20) = 900 + 80 = 980. The difference between Pam's estimate and the actual answer is 974 - 980 = -6.
On the other hand, Pat rounded each number individually and added them up. Pat's estimate is 350 + 200 + 400 = 950. The difference between Pat's estimate and the actual answer is 974 - 950 = 24.
Since the differences are determined by how far off the estimated answers are from the actual answer, Pam's estimate is closer as she is only 6 away from the actual answer, whereas Pat is off by 24. Therefore, you are correct in saying that Pam has a better answer.