A student reported to our schools math lab where I reside. He had a handout on proportions shown in the photo below and stated that he didn’t know what to do.
I find that in the vast majority of situations like this the student lacks the conceptual understanding of the topic. As is typically the case, I started my sessions with the student by focusing on something he more intuitively understood. Teens know money, phones, games, music and food.
In this case I started by showing him a photo on my phone shrunk then enlarged the photo and talked about how I could double the size of the photo. We talk about what doubling means then I show him a handout with the photo in two sizes (below).
I explained that the small photo was 3×2 inches and that I wanted to enlarge it. The bottom of the big photo is 6″ but I needed to figure out the height (vertical length) which is marked with an X.
I had him figure out the height (4). Then I explained that proportional means the shape is the same but bigger or smaller. In this case both the side and bottom were multiplied by 2. Then I showed him the “mathy” way of doing the problems. This progressed towards the handout he brought into math lab. By the end he was doing the proportions independently.