Using a number line and a coordinate graph, students develop their own formulas or
techniques for determining the distance between two points and the midpoint of two
What is in the lesson?
• The lesson begins with a Do Now where the students find the horizontal and vertical change made between two points.
• Then the students use a copy of a number line to graph two points and determine the midpoint and the distance between the two points. Students complete a chart as they complete each pair of points.
• After students have studied the chart of points, midpoints and distances, they make some observations and then try to fill in a similar chart where different information has been left out. Students summarize how they found the missing information.
• Then students graph two points on a coordinate grid. After they are given directions on finding the midpoint of a line segment on a coordinate grid, students use their coordinate grid to find other midpoints.
• After making observations of how they filled in the chart, students are given a similar chart where different information has been left blank. Students use the coordinate grid to help them fill in the missing information.
• In the final part of the lesson, the students find the distance between two points on a coordinate grid by drawing a right triangle and applying the Pythagorean Theorem.