Exploring Distance Between Two Points

Objective:

Students will be able to calculate the distance between two points on the x-y plane using the distance formula and identify whether lines are horizontal or vertical.

Assessment:

Students will demonstrate their mastery of the objective by accurately calculating the distance between two points provided on the x-y plane and correctly identifying whether the lines connecting these points are horizontal or vertical.

Key Points:

• Distance is the measure of length between two points on the x-y plane.

• The distance formula involves calculating the absolute value of the difference between the x-coordinates and the y-coordinates of two points.

• Lines are horizontal if they have the same y-coordinate and vertical if they have the same x-coordinate.

Opening:

• Start the lesson by posing a scenario where students need to determine the shortest distance to reach a particular destination, sparking their curiosity about calculating distances between points on a map.

Introduction to New Material:

• Explain the concept of distance between two points on the x-y plane.

• Introduce the distance formula and guide students through examples of applying it to calculate distances.

• Anticipate the misconception that distance is the same as displacement and clarify the distinction.

Guided Practice:

• Provide practice problems for students to calculate distances between points on the x-y plane.

• Scaffold questioning from simple to complex to deepen understanding.

• Monitor student performance by circulating the classroom, offering guidance as needed.

Independent Practice:

• Assign a set of practice problems for students to work on independently to demonstrate mastery of calculating distances between points.

• Behavioral expectations: Students should show their work and justify their calculations.

Closing:

• Summarize the key concept of calculating distances between points using the distance formula.

• Review examples from the lesson to reinforce understanding.

Extension Activity:

• For early finishers, provide a challenge where students have to calculate the distance on a 3D coordinate plane.

Homework:

• Homework suggestion: Students are tasked with finding the distance between two points in a real-world scenario (e.g., distance between two landmarks on a map).

Standards Addressed:

• CCSS Standard: G-GPE.B.7 - Use coordinates to prove simple geometric theorems algebraically.

• CCSS Standard: G-GPE.B.7 - Apply the Pythagorean Theorem to determine distances between points in the x-y plane.