The Correct Answer and Explanation is:
Correct Answer:
Aisha compares the absolute values of her four scores in her statement. A score of -16 represents the greatest loss of points for these four turns. The number for Aisha’s highest score will be furthest to the right on the number line. That number is 10.
Explanation:
The problem requires correcting Aisha’s misunderstanding about her game scores. Her scores for the four turns were -3, 10, -16, and 9. Aisha’s mistake is a common one involving negative numbers where she confuses the magnitude of a number with its actual value.
Aisha incorrectly concludes that her score on Turn 3 is the highest because she is only looking at the number 16. She is comparing the absolute values of her scores, which are |-3| = 3, |10| = 10, |-16| = 16, and |9| = 9. The absolute value of a number is its distance from zero on a number line, ignoring its sign. While 16 is the largest of these absolute values, it does not represent the highest score.
In the context of the game, a negative score signifies a loss of points. Therefore, a score of -16 represents a loss of 16 points. When comparing this to her other scores, which include a loss of 3 points and gains of 10 and 9 points, the score of -16 is clearly the greatest loss she experienced.
To find the highest score, we must compare the actual values, not their absolute values. The correct way to visualize this is by placing the scores on a number line. On a number line, values increase from left to right. The score of -16 would be the furthest to the left, making it the lowest score. The score of 10 would be positioned furthest to the right, making it the highest score. Therefore, Aisha’s actual highest score was 10, which she achieved on Turn 2. Her score of -16 on Turn 3 was, in fact, her lowest score.
