First problem I have is having students come in prepared. Most don't bring paper or pencil. Luckily, my classes work well together so they help each other out. Second problem is having them stay on task. I tried to integrate more partner work in but oftentimes it came down to one student doing the work and one watching. I hope they learned by watching. Third is the fact that many of my students just struggle with basic number sense. So applying it to the 'bigger picture' sometimes is just too much.
Many students are also low readers, so attempting story problems isn't very fun.
I do like teaching functions. I often illustrate it by "buying things a store".
So if I go to Store A and buy a soda, it's $1. If I buy 2 sodas, it's $1. If I buy 3 sodas, it's $1. They figure out the rule.
Next, if I go to Store B and buy a soda, it's $1 If I buy 2 sodas, it's $2. If I buy 3 sodas, it's $#. They figure out the rule.
Next, if I go to Store C and buy a soda, it's $1. When John walks in and buys a soda, it's $2. Suddenly it's not fair and we talk about functions giving one answer (price) for each set amount (soda). Different stores can have different prices but they have to be "fair" with a rule.