Thursday, August 28, 2014

Triangle Area on the Coordinate Plane

The last section in chapter 1 of my Geometry book is about finding area and perimeter.  This is introductory level area and perimeter, as an entire chapter is devoted to area and perimeter later in the year.  Students do well on this material, with the exception of finding area and perimeter on a coordinate plane.

The Geogebra presentation below was my attempt at helping students practice finding area given the coordinates of the vertices of the triangle.  For now our textbook ensures that the base is either horizontal or vertical.  I made another presentation to use to help students find the area given the vertices if the base is not horizontal or vertical.  It is intended to help students see the rectangles that encloses the triangle.

For the diagram above, deselect "Show Triangle Area" to give students a chance to think through the problem.  Reveal the area when students are ready to check answers.

A few other teachers on my team took a look at this, and we came up with a list of basic and higher level questions that students could practice with.  We liked that the practice reinforced reasoning using the coordinate plane, because this is a skill that is useful later in the course, as well as in future math classes.  We also liked that students would have a visual to use to justify their reasoning.  The open ended problem types are also helpful because they encourage students to listen to each other explain the thinking process when different solutions to arise.

Questions to ask: (Sorry we didn't make a worksheet!  You can substitute in other coordinates and areas as needed for extra practice)

1.  What is the area of the triangle with the given vertices?  

2.  Find the third vertex of a triangle with area 8 that has vertices at (-1,1) and (3,1).
Note:  you can change the vertices by dragging each point or by typing into the input box.  I am tempted to hide the points so that students have to go through the thinking process to find the third vertex.  Otherwise if they are practicing on their own, they can simply reveal the triangle area, and then drag the third vertex until the answer appears.  No thinking required.  If I am using this solely for demonstration, then it makes more sense to be able to drag points to save time.

3.  Given one vertex at (1,-1) and an area of 6, find the other vertices of the triangle.

What other questions can we ask?  

Ideally I would have students practicing on their own device or in pairs with a device.  That usually isn't possible at my school, so I would set the problem up on the Geogebra presentation and project to the class.  Then lots of individual and pair think time given before we finish a problem up whole class.

The Geogebratube version of this presentation is more friendly when it comes to zooming in/out or recentering the screen.  I also wrote a blogpost on how to zoom in/out, along with some other tips to get started with Geogebra.

1 comment:

  1. >What other questions can we ask?

    Here's one: