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Question about Absolute Value and Number Order

Subject Mathematics

Mathematics

Source Originais Teachy

Originais Teachy

Topic Absolute Value and Number Order

Absolute Value and Number Order

Difficulty Hard

Hard

(Originais Teachy 2024) - Question Hard of Mathematics

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?

The relationship between altitude and temperature is directly proportional, therefore, the higher the altitude, the higher the recorded temperature; when descending, the temperature increases even more rapidly.

As altitude increases, the recorded temperatures increase in absolute value, indicating a more intense cold; when descending, temperatures decrease in absolute value, but continue to be colder as altitude increases (in negative terms).

As altitude increases, the recorded temperatures decrease in absolute value, indicating a more intense heat; when descending, temperatures decrease in absolute value and are lower as altitude decreases (in negative terms).

The absolute value of temperatures is constant regardless of altitude, showing that the cold is the same at all altitudes; the variation is only in the sign of the temperatures.

As students climb the mountain, the absolute value of temperatures remains the same, indicating that the cold is constant; when descending, the cold increases proportionally to altitude.

Answer sheet:

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