Coordinating Shapes

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Objective

SWBAT find the distance between two points on the coordinate plane as well as plot points on the coordinate plane to create plane figures and find the areas of those shapes.

Big Idea

Shape Up! Problem solving with regular plane figures on the 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.

Engagement

10 minutes

During today’s opening I will discuss the meaning of the word “plane” as it pertains to mathematics with my students. I will be sure to make a connection between plane figures and the coordinate plane. During this discussion, I will ensure that my students know the following:

  • A plane is flat
  • A plane is infinite
  • There are a infinite number of planes
  • A plane figure is a shape that has been "cut out" from a plane.

 

This concept can be very difficult for students to grasp so be sure to help them to visualize what a plane is. For example, I like to talk about laser grids that you see in the movies and imagining that laser grid going on forever. Or, a flying carpet hovering above us and imagining it growing longer and wider and it just keeps growing longer and wider forever, it never stops.

Instruction & Teacher Modeling

10 minutes

For today’s instruction, I will demonstrate to my students how to graph points to create regular plane figures on the coordinate plane. The figures that I will focus on are as follows:

  • Rectangles
  • Triangles
  • Trapezoids
  • Squares
  • Simple irregular figures

 

The reason for focusing on these figures is because regular plane figures have characteristics that can be seen using a coordinate plane. For this reason, I will use the coordinate plane to highlight these characteristics. For instance, we will talk about how a square is the same number of units tall as it is wide, or how a trapezoid is the same height all the way across but, its bases are different lengths. I will then go into area of these plane figures based upon the number of units wide or tall these figures are. We will also talk about and explore area by looking at the number of units inside the figures.

While this lesson will not focus on area necessarily, this will be a great way to review and reinforce the concept of area while teaching about regular plane figures on the coordinate plane.

Try It Out

5 minutes

In the guided practice portion of this lesson my students will be given an opportunity to graph coordinates given to them on the giant coordinate plane on the floor. They will be asked to connect the points using string, in the order that they were given to them. The students will graph the points and reveal what type of polygon was created by the given coordinates.

Independent Exploration

20 minutes

For their independent practice, my students will be given 10 problems where they are graphing coordinates to create polygons on the coordinate plane or figuring out which coordinate point is needed to complete a particular type of polygon. For instance, my students may be given three points and asked to provide the fourth point that would create a rectangle.

Closing Summary

15 minutes

To close out today’s lesson, I will choose 5 students to present their work under the document camera. Each of the chosen students will present 2 of the 10 problems that they completed during the independent practice. 

TOTD: Before my students leave my classroom, I will have them write down the types of problem they think they would be able to solve using polygons on the coordinate plane.

This writing piece will give me an idea as to how well my students are able to apply what they have been taught to real world situations.