Have students view attached dividing video clip and follow with a discussion. Sample questions:
What is the machine doing to the dough?
What do you notice about all the pieces of dough?
Make sure students notice that all pieces of dough are of equal size. Conclude the discussion with telling the students they are going to investigate how to divide a line segment into two equal parts by finding the midpoint.
Have students in groups of 4. Give each student an Investigation of Midpoint of a Line activity sheet (attached), and each group a piece of chart paper, markers and meter stick. Students will work together to complete the activity sheet and then come to a consensus on a formula for midpoint. They should then complete the chart paper for their presentation. Teacher should monitor groups and ask leading questions such as:
What could you use to represent the numbers so you can write a formula?
How did you find that midpoint?
Are you sure that is really the midpoint?
Can you prove your point is the midpoint?
Groups make presentations and teacher asks probing questions and leads the class to a consensus of the formula for midpoint. Teacher should monitor groups and ask leading questions such as:
- How did you find the midpoint given two endpoints?
- How is the challenge problem different from the original problems where you were finding the midpoint?
- Can you write the formula for midpoint including the equals sign, and then substitute the information that you have and then solve for the missing parts?
- What is the equation of a line in slope intercept form?
- Can you find the slope of the line between the original two points?
- What is the slope of the perpendicular line?
With students still in their groups, have them complete the Midpoint Formula Extra Practice and Extension activity sheet. Encourage groups to work together on the challenge questions.