IM 6.7.1 Lesson: Positive and Negative Numbers
What do you notice? What do you wonder?
Here are three situations involving changes in temperature. Represent each change on the applet, and draw it on a number line. Then, answer the question.
At noon, the temperature was 5 degrees Celsius. By late afternoon, it has risen 6 degrees Celsius. What was the temperature late in the afternoon?
The temperature was 8 degrees Celsius at midnight. By dawn, it has dropped 12 degrees Celsius. What was the temperature at dawn?
Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered by adding salt to the water. A student discovered that adding half a cup of salt to a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is the freezing temperature of the gallon of salt water?
Discuss with a partner:
How did you name the resulting temperature in each situation? Did both of you refer to each resulting temperature by the same name or different names?
What does it mean when the resulting temperature is above 0 on the number line? What does it mean when a temperature is below 0?
Do numbers below 0 make sense outside of the context of temperature? If you think so, give some examples to show how they make sense. If you don’t think so, give some examples to show otherwise.
Here is a table that shows elevations of various cities.
On the list of cities, which city has the second highest elevation?
How would you describe the elevation of Coachella, CA, in relation to sea level?
How would you describe the elevation of Death Valley, CA, in relation to sea level?
If you are standing on a beach right next to the ocean, what is your elevation?
How would you describe the elevation of Miami, FL?
A city has a higher elevation than Coachella, CA. Select all numbers that could represent the city’s elevation.
Explain your reasoning.
Here are two tables that show the elevations of highest points on land and lowest points in the ocean. Distances are measured from sea level. Drag the points marking the mountains and trenches to the vertical number line and answer the questions.
Which point in the ocean is the lowest in the world? What is its elevation?
Which mountain is the highest in the world? What is its elevation?
If you plot the elevations of the mountains and trenches on a vertical number line, what would 0 represent? What would points above 0 represent? What about points below 0?
What would points above 0 represent?
What about points below 0?
Which is farther from sea level: the deepest point in the ocean, or the top of the highest mountain in the world? Explain.
A spider spins a web in the following way:
Assuming that the pattern continues, what will the spider’s elevation be after an hour has passed? Feel free to use the applet below to help you.