Lesson 3Comparing Positive and Negative Numbers
Learning Goal
Let’s compare numbers on the number line.
Learning Targets
I can explain how to use the positions of numbers on a number line to compare them.
I can explain what a rational number is.
I can use inequalities to compare positive and negative numbers.
Lesson Terms
- opposite
- positive number
- rational number
Warm Up: Which One Doesn’t Belong: Inequalities
Problem 1
Which inequality doesn’t belong?
Activity 1: Comparing Temperatures
Problem 1
Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.
day | Mon | Tues | Weds | Thurs | Fri | Sat | Sun |
---|---|---|---|---|---|---|---|
temperature |
Plot the temperatures on a number line. Which day of the week had the lowest low temperature?
Problem 2
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.
Write an inequality to show your answer.
Problem 3
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.
Are you ready for more?
Problem 1
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
Water boils at
. What is this temperature in ? Ammonia boils at
. What is the boiling point of ammonia in ? Explain why only positive numbers (and 0) are needed to record temperature in
.
Activity 2: Rational Numbers on a Number Line
Problem 1
Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.
Print Version
Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.
Problem 2
Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.
Problem 3
Drag each point to its proper place on the number line. Use your observations to help answer the questions that follow.
Andre says that
Print Version
Andre says that
Problem 4
Answer each question. Be prepared to explain how you know.
Which number is greater:
or ? Which is farther from 0:
or ? Which number is greater:
or ? Which is farther from 0:
or ? Is the number that is farther from 0 always the greater number? Explain your reasoning.
Lesson Summary
We use the words greater than and less than to compare numbers on the number line. For example, the numbers -2.7, 0.8, and -1.3, are shown on the number line.
Because -2.7 is to the left of -1.3, we say that -2.7 is less than -1.3. We write:
We can see that -1.3 is greater than -2.7 because -1.3 is to the right of -2.7. We write
We can also see that