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Learning Targets

• I can ask questions about a situation to determine whether two quantities are in a proportional relationship.
• I can solve all kinds of problem involving proportional relationships.

Whenever we have a situation involving constant rates, we are likely to have a proportional relationship between quantities of interest.

• When a bird is flying at a constant speed, then there is a proportional relationship between the flying time and distance flown.
• If water is filling a tub at a constant rate, then there is a proportional relationship between the amount of water in the tub and the time the tub has been filling up.
• If an aardvark is eating termites at a constant rate, then there is proportional relationship between the number of termites the aardvark has eaten and the time since it started eating.

Sometimes we are presented with a situation, and it is not so clear whether a proportional relationship is a good model. How can we decide if a proportional relationship is a good representation of a particular situation?

• If you aren’t sure where to start, look at the quotients of corresponding values. If they are not always the same, then the relationship is definitely not a proportional relationship.
• If you can see that there is a single value that we always multiply one quantity by to get the other quantity, it is definitely a proportional relationship.

After establishing that it is a proportional relationship, setting up an equation is often the most efficient way to solve problems related to the situation.

Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?

• What information would you need to be able to solve the problem?

A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.

1. Order the people from greatest to least in terms of total number of comments checked.
2. Order the people from greatest to least in terms of how fast they checked the comments.