If your student will enter eighth or ninth grade in the autumn, then it’s likely she will be enrolled in Algebra I in one of those grades or the other. Often students first encountering algebra find themselves abruptly thrown off stride by the change from a focus on numbers and arithmetic operations to relationships between quantities.

Here’s a typical problem of the sort your student will likely see, along with an answer and explanation. This might help to provide a preview of the new form of mathematical thinking your student will be asked to practice.

Problem:

During your family vacation to a lake this past summer, you and your mom asked about a boat rental. The owner of the business said that the rate for the first two hours was $350 and that each additional half-hour would cost $50. Your mom and dad agreed to spend no more than $600 to rent the boat. For how many additional half-hours can you rent the boat?

Answer and Discussion:

What we need to do here is write an equation that shows how the price for the first two hours plus the number of additional half-hours adds up to what can be spent – $600.

1. We know that the first two hours are $350.
2. We know that each subsequent half-hour is $50.
3. We know we can spend no more than $600.

We’re going to use the letter “x” to represent the number of half-hour segments we can buy.

Here’s the equation:

350 + 50x = 600

Now we can solve for x. To do that, we need to remember that our goal is going to be to get x alone on one side of the equal symbol.

50x = 250

x = 5