Let's share a lesson plan focused on teaching high school students (9th-10th grade) the rectangular coordinate system (e.g., the x,y plane), the distance formula, and the midpoint formula.

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### Overview of the Lesson

The purpose of this lesson is to introduce students to the rectangular coordinate system and how to calculate the distance and the midpoint between two points within this system. The teaching methods used in this lesson include lecturing and question-and-answer sessions.

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### Student Objectives

In this lesson, students will:

- Learn the components of the rectangular coordinate system
- Identify the x-axis and y-axis on the coordinate plane
- Learn new vocabulary words: perpendicular, point of intersection, origin, quadrant, distance formula, midpoint formula
- Learn how to implement the distance formula when given two points on a coordinate system
- Learn how to implement the midpoint formula when given two points on a coordinate system

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### Learning Activities

1) Introduce the students to the rectangular coordinate system by drawing an example on the chalkboard. Label the x-axis, y-axis, origin/point of intersection, and each quadrant, and explain to the students that the rectangular coordinate system is a system that allows for the labeling of points on the plane.

2) Show students several examples of coordinates, explaining that the ordered pair consists of a point on the x-axis and a point on the y-axis. Make sure students see examples within each quadrant so they understand ordered pairs consist of both positive and negative numbers.

3) Introduce students to the distance formula (d=[sqrt]((x1 - x2)[squared] + (y1 - y2)[squared])), explaining that this formula is derived from the Pythagorean Theorem. Demonstrate this derivation on the chalkboard.

4) Show students a few examples on how to calculate the distance formula, using ordered pairs (3,7) and (5,12), (-10, 6) and (8, 15), (-4, -11) and (9, 20), and (16, 4) and (-9, -13).

5) Introduce students to the midpoint formula (mp=(x1 + x2)/2, (y1 + y2)/2), and use several ordered pairs as examples to demonstrate how this formula can be applied.

6) Give students a few minutes to solve the following problem: Find the perimeter of a triangle with vertices at points (2, 2), (6, 5), and (0, 3). After a few minutes, call on a student to provide the answer.

7) Give students a few minutes to solve a second problem: Find the point that is one-quarter the distance from point (10, 14) to (-6, 12). After a few minutes, call on a student to provide the answer.

8) Conclude the class session by asking students if they have any questions. Assign them their homework for the next day.

### References

- Teaching experience.