ALP Math
Index Assessments Lessons Vocabulary Rubrics Home
Federal Way Public Schools  
Makes Connections
Lesson 29		 Connect with Mathematics

Practice 2:

Use the information from the picture to answer this question.

Since the slide has been so popular, the owner of the carnival wants to decrease the chances of winning a free ticket for this ride. On the dartboard, the triangle shape has two sides that are each 8 units long. He wants to decrease the length of each of these sides to 4 units.

Compare the chances of winning a free ticket for the slide on the old dartboard versus the new dartboard. Use words, numbers, and/or pictures to explain your answer.

This question requires a short answer response for a possible 2 points. You have the opportunity to score some student responses below. First, look over the requirements or rubric for scoring this problem.

2 points - Response makes clear connections between conceptual areas by doing the following:

  • Indicates that the chance of winning a free ticket with the old dartboard was 4 times greater than winning a free ticket with the new dartboard (or equivalent, such as; the chance of winning with the new dartboard is 75% less than the old dartboard).
  • Explains how the comparison was acquired.

1 point - Response makes a partially accurate connection by stating that there was a better chance with the old dartboard. The explanation is unclear, incorrect, or missing.

0 points - Response shows no connection within or between conceptual areas.

Now that you know what is required for the answer to this problem, it is time to score some student responses.

Response #1:

The area of the picture on the dartboard = 1/2 x 8 x 8 = 32 square units, and the area of the picture on the new dartboard = 1/2 x 4 x 4 = 8 square units. 32 square units is 4 times greater than 8 square units, therefore a person's chance of winning with the old dartboard was 4 times greater than with the new dartboard.

Score this response:

Write your explanation to support the score you have given this student.

Click the button below to see how this student was actually scored and see if your score was the same.

Response #2

Small one is 8 units squared and the big one is 32 units squared. The smaller one has a 1% chance and the big one has a 6% chance. 8 divided by 576 is .013 and 32 divided by 576 is .055.

Score this response:

Write your explanation to support the score you have given this student.

Click the button below to see how this student was actually scored and see if your score was the same.

Response #3:

The total number of squares on the dartboard is 576. The old triangle took up 32 squares equaling 32/576 = 1/18. The new triangle is 8 squares equaling 8/576 = 1/72. Now the chances of winning a free ticket on the slide have gone down.

Score this response:

Write your explanation to support the score you have given this student.

Click the button below to see how this student was actually scored and see if your score was the same.

©Internet Academy