## Understanding by Design: Complete Collection

#### Document Type

Instructional Material

6-2016

#### Abstract

The purpose of this unit is to make mathematical concepts more concrete and real for students using maps. Students will be asked to think about mathematical objects through cartography or map-making. When teaching the formulas for midpoint and distance, I have found that more concrete understanding of the topic helps students to understand and apply the process for midpoints and distances. A distance between two arbitrary coordinate points is more difficult for students to grasp conceptually than the distance between San Antonio and Dallas or the distance from school to their favorite restaurants.

Students will begin the unit with a pre-assessment, in which they attempt to find distances and midpoints on a map without formulas or a grid and explain their process. On the pre-assessment day, students will also learn about map distortion and think about how a spherical surface turns into a flat map by projecting through a sphere with a flashlight. Teachers will also use a map to introduce the terms point, line, and plane. Students will continue learning these basic terms of geometry with a kinesthetic activity and discover the midpoint and distance formulas through investigation activities. After practicing with the formulas, students will return to maps of ancient civilizations and use their learning of the formulas to calculate distances and find midpoints on maps. After calculating simple straight distances, students will look at more complicated paths or multi-leg journeys. Students will mathematically develop their own “Google Maps” with multi-leg and straight path journeys.

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