This lesson gives students an opportunity to apply their work with distances and slopes in the plane to a real-world context. In this lesson, students examine figures in the Nazca lines. First, students orient themselves to the context by researching the Nazca lines, sharing their findings, then coming up with mathematical questions. 

Students then engage in quantitative and abstract reasoning as they consider a representation of one of the figures as a triangle in the coordinate plane. They find the area and perimeter of the figure in the plane, then connect it to the quantities involved in the very large real-life figure (MP2). 

Next, students build on these skills with an activity in which students engage in aspects of mathematical modeling as they consider additional figures, create their own mathematical questions, and answer them (MP4). 

Finally, students create an equation for a circle, using the same coordinate measurement system, in an optional activity that is designed to give extra practice with equations of circles as students apply their work in a context. 

Each of these activities gives students the opportunity to apply their knowledge of the Pythagorean Theorem, equations of lines, slopes of lines, or equations of circles in the coordinate plane as they answer a variety of questions about the Nazca lines.