As a parent of young children and former math teacher, yes, we do absolutely memorize those sums. It usually happens at an early enough age that the process of doing so evaporates early in life and becomes part of your base mental code. I spent a significant part of my teaching life teaching high school math for college students (and occasionally grade school math for college students) and there are very much people who never managed to get that memorization step completed. What's really fascinating is that it's an orthogonal skill to higher mathematics. I've seen students who needed to use a calculator to do 6+5 and yet managed to be able to solve algebraic problems. This is, I must add, uncommon, but it's less because one skill depends on the other but rather because the failure to gain the basic math skill leads to an unwillingness to try to gain the more abstract math skill.