With my students, they are introduced to ratios, rates, and proportions. My favorite problem that I pose to them is about a car I bought.
Here is the prompt they would get for this problem.
I was in the market to get a new car. After test driving several different cars, I decided on getting 2001 Buick Century. While driving around after I bought it, I noticed that the gas gauge stays at full until I have about a gallon of gas left and then it goes to empty. So, I went to my mechanic and asked him about it. He told me it would be around $500 to fix it. I did not want to spend the money to fix it so I came up with a solution. What did I do so I would not have to spend the money to fix it?
At this point, students are asked to brainstorm ideas on what to do. Some students say that they would just fix it, but I remind them that I don't want to spend the money. We talk about what information do you know and what type of information could you find out. We eventually get to the gas tank itself and we could find out the mileage that the car gets. So, I give them that I went 300 miles on 15 gallons of gas. I pose this question, how does this help us?
Students point out that we now know how many miles per gallon get. The students will point out that we can find how many gallons the tank is from the owner's manual which is 17 gallons. Then the students set up a proportion to find 340 miles. At this point, I ask the students what does that 340 miles mean. Some students see that this is how far you can go on a tank of gas, but many students still do not see what this information means.
After discussing this problem, we look at how the unit rate could change. I tell the students that I check it once a month and ask why? After discussing that it could change, we talk about what types of things could change the rate.
Many of these students really enjoy this problem. They like that you can come up with a solution to this without spending the money. Some of the students actually have come across this problem with a car they have already encountered. I like this problem for my students because they get to look at different concepts like unit rates and proportions. It's also an excellent real-life example that students may encounter or already have encountered.
