Finding the Distance or the Midpoint of a Line Segment on the Coordinate Plane

This Warm Up is intended to take about 10 minutes for the students to complete and for me to review with the class.  

My students have previously been introduced to the Distance and Midpoint Formulas in eighth grade. This year, we have already used the Distance formula to find the distance between two points on a coordinate plane.  This is the first lesson in which students will use the Midpoint Formula.  I want to focus not only on using the Midpoint Formula, but on the reasoning behind it.  Therefore, I will be implementing as many Math Practices as possible to make the lesson more in depth.  I model reviewing the Warm Up in the video below.

The WILD WONDERS AMUSEMENT PARK  activity requires students to apply the Distance Formula and the Midpoint Formula.  The Distance Formula is used to find the distance between two endpoints of a line segment on a coordinate plane.  The Midpoint Formula is used to find the halfway point, or the coordinates of the midpoint of a line segment on the coordinate plane. Modeling these formulas with a carnival map helps students relate the formulas to navigation and maps as models of geographic position (MP4). 

I allow students about 30 minutes to work on the  AMUSEMENT PARK tasks. As I walk around to monitor and assist with questioning, I have students compare work if they are done, and see if they have questions or need to make corrections.  I encourage students to critique each other's work and provide peer tutoring if needed (MP3).  I also assist if they cannot move forward, or cannot agree on an answer.

Student progress on the Independent Practice is listed below.

• Students understand the beginning of the practice well, as long as they have identified that each unit of the graph represents two units.  
• Students have to verify that (2,0) is the midpoint in number four, which requires reasoning supported by the math(MP2). 
• I expect some of the students will struggle with finding the Midpoint in number five.  This is due partly to not understanding the question of when to apply Midpoint, and partly of applying it incorrectly.
• Number six often gives students difficulty.  It is a multi-step problem that takes some Perseverance (MP1).  To find the location of the Spider Ride on the coordinate plane, students have to find the missing endpoint of the line segment instead of the midpoint.  I model problem six in the video below. 

I allow students about 15 minutes at the end of class to work on this Exit Slip.  This Exit Slip is a multi-step problem, and I want to provide adequate time to complete it.  It requires the student to demonstrate the following skills:

1. Find the length of 4 line segments given their coordinates on the graph. 
2. Find the midpoint of a line segment.
3. Find the perimeter of the closed polygon formed by the line segments.

I have students hand in the Exit Slip when it is completed, and I use it as a quick formative assessment on each student's progress with this lesson.  Students that drew out a picture of the situation did better than students that just tried to solve it.  Without the picture, students would leave out some of the line segments, or important information.