# Roving the Distance

 Author: Jennifer Harvey Unit Title: Roving the Distance Grade Level: 8th grade Subject Area: Mathematics Total Estimated Duration: 9 days Poster: Roving the Distance Background Knowledge: Students from 7th grade are familiar with the Pythagorean Theorem, but not the distance formula. Students need to know how to: solve equations, find the square root of a number & graph data Additional Resources: Roving on The Moon Rover Activity Date: December 2012
##### The Big Idea (global relevance)

This unit is designed to re-teach the Pythagorean Theorem and to introduce the distance formula to students.  The students will complete various activities that will help them understand and use the Pythagorean Theorem and the distance formula appropriately.

The Pythagorean Theorem and the distance formula are used in the areas of science and technology: all types of construction projects(including bridge building, buildings, homes, road construction).  This unit will introduce students to the variety of areas in which the Pythagorean Theorem can be applied.

##### Essential Questions
1. How do you calculate the distance of a diagonal line?
2. What if you had no ruler or tape measure, how would you be able to find the distance between two locations?
##### The Challenge

How can you use the Pythagorean Theorem to plot the best route between locations on the moon’s surface?

##### The Hook

Pythagorean Theorem Video

##### Guiding Questions
1. How do you find the length of a diagonal line?
2. If you were in space and you had no measurement tools, how would you be able to calculate distance?
3. What variables would affect distance traveled by the constructed rover?
##### Engineering Design

Students will design and build a rover to calculate the distance the rover traveled.  Students will then re-design their rover and try to make it go a further distance.

1. Explain a proof of the Pythagorean Theorem and its converse.
2. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
3. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
##### ACS (Real world applications; career connections; societal impact)
• Computer and information systems managers
• Construction managers
• Engineering and natural sciences managers
• Professional and Related
• Computer software engineers
• Mathematicians
• Architects, except landscape and naval
• Landscape architects
• Surveyors, cartographers, photogrammetrists, and surveying technicians
• Aerospace engineers
• Chemical engineers
• Civil engineers
• Computer hardware engineers
• Electrical and electronics engineers, except computer
• Environmental engineers
• Industrial engineers, including health and safety
• Materials engineers
• Mechanical engineers
• Nuclear engineers
• Drafters
• Biological scientists
• Conservation scientists and foresters
• Atmospheric scientists
• Chemists and materials scientists
• Environmental scientists and geoscientists
• Physicists and astronomers
• Lawyers
• Archivists, curators, and museum technicians
• Writers and editors
• Optometrists
• Physicians and surgeons
• Veterinarians
• Opticians, dispensing
• Farming and Related
• Agricultural workers
##### Assessments

Summative Assessment
Final Unit Assessment