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IM: 6.7.3: Comparing Positive and Negative Numbers (Lesson)

By Newsela Staff
Last updated 6 days ago
20 Questions
3.1: Which One Doesn’t Belong: Inequalities

Which inequality doesn’t belong?

3.2: Comparing Temperatures
Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.

Plot the temperatures on a number line.

Which day of the week had the lowest low temperature?

The lowest temperature ever recorded in the United States was -62 degrees Celsius, in Prospect Creek Camp, Alaska. The average temperature on Mars is about -55 degrees Celsius.

Which is warmer, the coldest temperature recorded in the USA, or the average temperature on Mars? Explain how you know, and write an inequality to show your answer.

On a winter day the low temperature in Anchorage, Alaska, was -21 degrees Celsius and the low temperature in Minneapolis, Minnesota, was -14 degrees Celsius.

Jada said, “I know that 14 is less than 21, so -14 is also less than -21. This means that it was colder in Minneapolis than in Anchorage.”

Do you agree? Explain your reasoning.

Another temperature scale frequently used in science is the Kelvin scale. In this scale, 0 is the lowest possible temperature of anything in the universe, and it is -273.15 degrees in the Celsius scale. Each 1 K is the same as 1^{o}C, so 10 K is the same as -263.15^{o}C.

Water boils at 100^{o}C. What is this temperature in K?

Ammonia boils at -35.5^{o}C. What is the boiling point of ammonia in K?

Explain why only positive numbers (and 0) are needed to record temperature in K.

3.3: Rational Numbers on a Number Line

Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.

Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.

-2 < 4

-2 < -7

4 > -7

-7 > 10

Label the follow point on the number line: \frac{-3}{2}, \frac{5}{8}, \frac{5}{4}, \frac{1}{4}, \frac{-3}{4}

Andre says that \frac{1}{4} is less than \frac{-3}{4} because, of the two numbers, \frac{1}{4} is closer to 0. Do you agree? Explain your reasoning.

Answer each question. Explain how you know.

Which number is greater: \frac{1}{4} or \frac{5}{4}?

Which number is farther from 0: \frac{1}{4} or \frac{5}{4}?

Which number is greater: \frac{-3}{4} or \frac{5}{8}?

Which number is farther from 0: \frac{-3}{4} or \frac{5}{8}?

Is the number that is farther from 0 always the greater number? Explain your reasoning.