Comparing Temperatures

Task

1. Here are the low temperatures (in Celsius) for one week in Juneau, Alaska:

   Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
   5	-1	-6	-2	3	7	0

   Arrange them in order from coldest to warmest temperature.

2. On a winter day, the low temperature in Anchorage was $23$ degrees below zero (in $^\circ C$ ) and the low temperature in Minneapolis was $14$ degrees below zero (in $^\circ C$ ). Sophia wrote,

   Minneapolis was colder because $-14 \lt -23$.

   Is Sophia correct? Explain your answer.

    

3. The lowest temperature ever recorded on earth was $-89^\circ C $ in Antarctica. The average temperature on Mars is about $-55^\circ C $. Which is warmer, the coldest temperature on earth or the average temperature on Mars? Write an inequality to support your answer.

IM Commentary

The purpose of the task is for students to compare signed numbers in a real-world context. It could be used for either assessment or instruction if the teacher were to use it to generate classroom discussion.

Solution

1. Let’s begin by plotting them all on the same number line.

   

   The number line has positive numbers to the right of zero and negative numbers to the left of zero. This means that numbers farther to the right are always greater than those to the left. In terms of temperature, the coldest temperature (the least number) is all the way to the left, and the warmest temperature (the greatest number) is all the way to the right.

   We can now list the temperatures from coldest to warmest:

   $$ -7, -6, -2, -1, 0, 3, 5 $$

2. Sophia is incorrect. It is common for students to compare negative numbers as if they were positive and to assume that the one with the greatest magnitude is the greatest number. However, $-23$ is to the left of $-14$ on the number line, and so it is less than $-14$. Thus $$-23 \lt -14$$ and Anchorage was colder.

3. Again, the coldest temperature corresponds to the least number. So the warmest temperature corresponds to the greatest number. Since $$-55 \gt -89$$ the average temperature on Mars is warmer than the coldest temperature on Earth.