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For each problem, use at least one negative number to represent the situation. Then, answer the question, and explain or show your reasoning.
A hiker is climbing Mount Kilimanjaro. On day 2, the hiker starts at an elevation of 2,785 meters. He hikes up 278 meters, down 87 meters, up 548 meters, and back down 20 meters. What elevation does he end the day at?
On day 4, he hikes up 732 meters to Lava Tower and then back down 641 meters. He ends the day at an elevation of 3,986 meters. What elevation did he start the day at?
On day 6, he starts at an elevation of 4,662 meters. He hikes 1,233 meters up to Uhuru Peak and then 2,789 meters back down. What is the difference between his final and beginning elevations that day?
Plot and label these points in the coordinate plane:
Connect the dots in order. What shape is made?
What are the side lengths of figure
What is the difference between the
What is the difference between the
How do the differences of the coordinates relate to the distances between the points?
Sometimes we use positive and negative numbers to represent quantities in context. Here are some contexts we have studied that can be represented with positive and negative numbers:
Using positive and negative numbers (and operations on positive and negative numbers) helps us understand and analyze the situations in context. To solve problems in these situations, we just have to understand what it means when a quantity is positive, what it means when a quantity is negative, and what it means to add and subtract quantities.
When two points in the coordinate plane lie on a horizontal line, we can find the distance between them by subtracting their
When two points in the coordinate plane lie on a vertical line, we can find the distance between them by subtracting their
Five line segments on a coordinate plane with the origin labeled “O”. The numbers negative 5 through 5, are indicated on the horizontal axis and the numbers negative 4 through 5 are indicated on the vertical axis. Each line segment is either vertical or horizontal. The first line segment is vertical that begins at the point negative 5 comma 3 and ends at the point negative 5 comma negative 4; the line segment is labeled with the expression 3 minus negative 4. The second line segment is horizontal and begins at the point negative 5 comma negative 4 and ends at the point negative 2 comma negative 4; the line segment is labeled with the expression negative 2 minus negative 5. The third line segment is vertical and begins at the point negative 2 comma negative 4 and ends at the point negative 2 comma 2; the line segment is labeled with the expression 2 minus negative 4. The fourth line segment is horizontal and begins at the point negative 2 comma 2 and ends at the point three comma 2; the line segment is labeled with the expression 3 minus negative 2. The fifth line segment is vertical and begins at the point 3 comma 2 and ends at the point 3 comma five; the line segment is labeled with the expression 5 minus 2.
Remember: The distance between two numbers is independent of the order, whereas the difference depends on the order.
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