I changed my strategy for teaching proportions this year. Instead of teaching how to solve for the variable in proportions first, I taught how to build a proportion from a word problem then solved for the variable. The word problem featured a unit rate which nicely tied in what was taught before.
I used a foldable featured below.
First I asked what are the two units being compared in the problem. I made sure everyone knew what I meant by unit. I would either get blank stares or examples. If I got blank stares I would give them examples such as pounds, joules, miles, hours…. Make sure to explain that a unit provides a description for a quantity. When it comes to what goes on top and what goes on bottom, I explained that time usually goes on the bottom. However, the most important thing is to make sure the units match on the top and match on the bottom.
When they worked on activities the next day I made sure to remind them to include the word ratio because it helped them stay organized. This is an easily forgotten step.
Next, I asked for the known ratio from the problem. A known ratio are two quantities being compared. The ratio also has to match the word ratio. The word problem had a tricky component that I would make sure to point out. Students had to double the miles since the problem said it was one way and they needed to know the commute both ways. I reminded them they need to make sure they read the whole problem because they may be tricked if they don’t.
Finally I went over the unknown ratio. I first asked, what do we use for an unknown number (variable). Then we read the question and figured out what the variable was. I explained usually the variable is found in the question, in the form of, “how many miles or how much…” Then we wrote the unknown ratio with the other given quantity and variable.
Finally we set up the proportion and set the two ratios equal to each other. I made sure to take time explaining why these two ratios are proportional.
I believe this was helpful because it gave them context with proportions. Proportions, unit rates and ratios are hard concepts to understand if you don’t tie it in to word problems (real life situations).