The four fastest 8th graders at Sun Prairie Middle School raced each other in a fifty-yard dash. You couldn't see the finish, but you overheard the following comments:

List two possible orders for the runners at the finish of the race. Explain how there can be more than one correct answer.

For this question, a 4 point response is needed. In order to receive all 4 points, you need to list 2 correct possible orders the runners could have finished in and then provide a complete explanation of your answer.

There are actually 3 possible correct orders to this problem. They are:

Along with listing at least two possible orders for finishing the race, you need a complete explanation.

Your explanation must indicate that Lisa is the only person who has a fixed position which is last place. It does tell you that Wendy must come in first or second because Wendy finished ahead of Ron. The comments don't tell you if Ron came in ahead of Lowell or not. There are other possible orders to the finish because the other than Lisa, no one has a fixed position in the order finishing the race. With your explanation you would want to include how you arrived at the solutions you did. What problem solving strategy did you use? You could show a simple drawing if that was the strategy you used along with your explanation.

Be sure your response to a question like this is complete, specific, and clear. The less complete your explanation the fewer points you will receive. Go for all 4!

A 4 point response could look like this:

1. Wendy was first, Ron was second, Lowell was third, and Lisa was fourth. 2. Wendy was first, Lowell was second, Ron was third, and Lisa was fourth again. There could be more than one correct answer because the comments didn't say if Ron finished ahead of Lowell or if Lowell was ahead of Wendy.

A 3 point response could look like this:

There are two ways I could think of the places people got in the race. The first one is Wendy would finish first, then Ron, then Lowell, then Lisa. The next way I could think of is Lowell would finish first, then Wendy, then Ron, and finally Lisa.

In this response, you will notice there is no explanation which prevents this answer from earning full credit.

A 2 point response could look like this:

Wendy could have won but Lowell could have won the race. There can be more than one correct answer because Wendy finished ahead of someone and Lowell finished ahead of someone.

You will notice that this response doesn't provide any correct orders, but does explain why there could be more than one order.

A 1 point response could look like this:

Wendy finished ahead of Ron and Lowell finished ahead of Lisa. There can be more than one correct answer because you need to figure out who was first.

In this response the explanation to answer the question is not complete and there is no correct list of possible orders.