Question bank: Absolute Value and Number Order

During a shot put competition, four athletes achieved the following marks: Joana threw her weight 10 meters, Pedro -8 meters, Carlos 6 meters, and Alice -12 meters. A negative distance indicates that the weight was thrown backwards.

In a math competition, students Ana and Bruno are solving problems involving integers. They are given the task of calculating the distance between two points on a number line, represented by the numbers -15 and 20. For this, they must understand the concept of absolute value and know how to order integers. 1. Define what the absolute value of an integer is and explain how it is calculated. 2. Calculate the distance between the points -15 and 20 on the number line. 3. List the integers between -15 and 20 in ascending order and then in descending order.

During an educational expedition in a mountainous region, a group of 7th-grade students decided to investigate local temperatures at different altitudes. They collected data during a day, noting that the temperature at n meters above sea level recorded the value of -n degrees Celsius. Considering that the students recorded temperatures every 100 meters of ascent, they noticed a gradual increase in the absolute value of temperatures as they climbed, followed by a decrease in the same proportion as they descended. Based on this observation and the mathematical concepts involved, how can the students describe the relationship between the recorded temperatures and altitudes, using the concept of absolute value and understanding of the order of rational numbers?

João and Maria are participating in a game that involves darts and a number line. In this scale, they have to hit rational numbers and then calculate their absolute values. João threw the dart three times and hit the numbers -3, 4, and -9, while Maria threw the dart and hit 7, -2, and -6. (a) Calculate the absolute value of each number hit by João and Maria. (b) Sort the absolute values in ascending order. (c) Identify which of the two players had the highest sum of absolute values hit and indicate the difference between the sums.

In a math competition, students were challenged to sort a list of integers in ascending order, but they made a mistake with one of the numbers. The original list was: -5, 7, 3, 0, -2. However, one of the students recorded the absolute value of a negative number instead of the number itself. After correcting this error, the corrected list became: -5, 7, 3, 0, 2. Which number was incorrectly recorded by the students, and what is the absolute value of that number? Explain how the absolute value was used to correct the error in the list. Then, reorder the corrected list in ascending and descending order.