Territorial Shapes on the Coordinate Plane

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SWBAT use the coordinate plane to find the area of plane figures that have been graphed on the coordinate plane.

Big Idea

This is my territory! Determining how much area a plane figure takes up on a coordinate plane.

Curriculum Reinforcer

10 minutes

Students will complete 3 problems to review units 1 through 6. The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.


10 minutes

In today’s opening exercise, I will give my students three shapes on a grid. I will ask them to estimate the area of each of the shapes using the grid as their units.

Instruction & Teacher Modeling

10 minutes

Using the opening exercise, I will demonstrate how to use the coordinate plane to calculate area of a plane figure.


To do this, I will take the same plane figures that I used for the opening exercise and place them on the coordinate plane to illustrate to my students that there really is not much difference between finding area using a regular grid and using a coordinate plane.


I will show my students how they can estimate area by counting the squares within the presented polygon and I will also show them that they can use the squares to find the lengths of the sides of the polygons so that they can use the area formulas to find the area as well.

Try It Out

5 minutes

To practice this skill, I will have my students find the area of two polygons that are presented on the coordinate plane. The first of the two, I will ask them to simply count the squares within the figure. The second of the two, I will ask my students to calculate the area using the coordinate plane to find the side lengths and then using those side lengths to calculate the area using formulae.

Independent Exploration

20 minutes

To ensure that my students fully understand today’s lesson, I will have them complete a worksheet. That worksheet is attached to this section of this lesson. To complete this worksheet, my students will have to find the area of several shapes that are presented on a coordinate plane. To do this, students will have to be able to figure out the lengths of the necessary sides of the polygons presented by using the units on the coordinate plane. This worksheet will also require students to manipulate the shapes to double the area by changing an aspect of the shape. For example, they may have to change the height of the shape to double the area.

Closing Summary

15 minutes

To close out the lesson, we will go over the worksheet that they completed during the "Independent Exploration" portion of this lesson.

The students will be placed in pairs to discuss, compare, and contrast their solutions. This will be done using the "Think, Pair, Share" strategy.

During this time, I will answer any lingering questions and clear up any misconceptions, while the students are huddled together, as well as while they are sharing out what they discussed with each other.


Ticket Out the Door:

Then, I will ask my students how well did they understand today’s lesson. To inform me of their understanding of today's concept, they will write either the word "green," "yellow," or "red."

  • Green means that they feel that they completely understand what was taught during today's lesson.
  • Yellow means that they understand, but still have a few lingering questions.
  • Red means that they do not understand the concept and need further support.