Lesson 12Constructing the Coordinate Plane
Learning Goal
Let’s investigate different ways of creating a coordinate plane.
Learning Targets
When given points to plot, I can construct a coordinate plane with an appropriate scale and pair of axes.
Lesson Terms
- quadrant
Warm Up: English Winter
Problem 1
The following data were collected over one December afternoon in England.
time after | |||||||||
---|---|---|---|---|---|---|---|---|---|
temperature |
Activity 1: Axes Drawing Decisions
Problem 1
Here are three sets of coordinates. For each set, draw and label an appropriate pair of axes and plot the points.
Problem 2
Discuss with a partner:
How are the axes and labels of your three drawings different?
How did the coordinates affect the way you drew the axes and label the numbers?
Activity 2: Positively A-maze-ing
Problem 1
Here is a maze on a coordinate plane. The black point in the center is (0, 0). The side of each grid square is 2 units long.
Enter the above maze at the location marked with a green segment. Draw line segments to show your way through and out of the maze. Label each turning point with a letter. Then, list all the letters and write their coordinates.
Choose any 2 turning points that share the same line segment. What is the same about their coordinates? Explain why they share that feature.
Print Version
Here is a maze on a coordinate plane. The black point in the center is (0, 0). The side of each grid square is 2 units long.
Enter the above maze at the location marked with a green segment. Draw line segments to show your way through and out of the maze. Label each turning point with a letter. Then, list all the letters and write their coordinates.
Choose any 2 turning points that share the same line segment. What is the same about their coordinates? Explain why they share that feature.
Are you ready for more?
Problem 1
To get from the point
Find as many points as you can that have a taxicab distance of eight units away from
Lesson Summary
The coordinate plane can be used to show information involving pairs of numbers.
When using the coordinate plane, we should pay close attention to what each axis represents and what scale each uses.
Suppose we want to plot the following data about the temperatures in Minneapolis one evening.
time | temperature |
---|---|
We can decide that the
In this case,
-values less than 0 represent hours before midnight, and and -values greater than 0 represent hours after midnight. On the
-axis, the values represents temperatures above and below the freezing point of 0 degrees Celsius.
The data involve whole numbers, so it is appropriate that the each square on the grid represents a whole number.
On the left of the origin, the
-axis needs to go as far as -4 or less (farther to the left). On the right, it needs to go to 3 or greater. Below the origin, the
-axis has to go as far as -8 or lower. Above the origin, it needs to go to 3 or higher.
Here is a graph of the data with the axes labeled appropriately.
On this coordinate plane, the point at