When asked about favorite sport, 15 students like to play soccer and 19 students like to play tee-ball. How many students are there in all?

The correct answer is: 34

15 students like to play soccer and 19 students like to play tee-ball. 
Total number of students = 15 + 19
To find partial sums add the digits in tens place and ones place seperately.
Partial sum of 15 + 19
Step 1 : Add digits in tens and ones place seperately:
10                                    05
+ 10                   and        + 09

_____                             ______
20                                        14
Thus, the sum of 15 + 19 are 20 + 14 = 34.

So, there are 34 students in all.