Description

What our Polygons and Coordinate Planes lesson plan includes

Lesson Objectives and Overview: Polygons and Coordinate Planes introduces students to the coordinate plane and give them an opportunity to work with that plane by drawing polygons. At the end of the lesson, students will be able to draw polygons on the coordinate plane and find the length of various sides. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional addition to this lesson is to have your students imagine real world applications for when they would use these skills, such as putting a new pool or garden in their backyard. You could also have your students build a house on their grid paper using specific shapes. Finally, you could have your students create drawings and switch them with a partner to label and draw the shape.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.

POLYGONS AND COORDINATE PLANES LESSON PLAN CONTENT PAGES

Polygons in the Coordinate Plane

The Polygons and Coordinate Planes lesson plan includes two content pages. Coordinate planes have four quadrants, labeled using roman numerals starting with the top right and moving counter-clockwise. We can use these quadrants to name or label points using the x-axis and y-axis. Ordered pairs, written as (x, y), refer to specific points on a coordinate plane. The x-coordinate is always first. For quadrant I, we write the ordered pairs as (x, y); for quadrant II, (-x, y); for quadrant III, (-x, -y); and for quadrant IV, (x, -y).

Polygons are closed objects with straight sides. We can use ordered pairs to label and write all of their vertices (the angular points of polygons). Line segments connecting the vertices create the polygons.

Let’s look at an example. We can draw rectangles on a coordinate plane and assign each of the vertices a label (like a letter) and an ordered pair. In this example, the points are: A (-3, 5), B (-3, 2), C (4, 2), and D (4, 5). When we connect the points, they create a rectangle. Rectangles have four interior right angles and opposite sides which are parallel and equal in length. How do we know that the opposite sides are equal in length?

In this example, the points (-3, 5) and (-3, 2) have the same x-coordinate (-3). If we want to find the length, we subtract the y-coordinates: 5 – (2) = 3. This tells us that the side has a length of 3 units. We can then repeat this on the opposite side with the other coordinates, (4, 2) and (4, 5). The length of this side is also 3 units because 5 – 2 = 3.

The points for the other set of parallel lines, (-3, 5) and (4, 5), have the same y-coordinate (5). The points on the opposite side, (-3, 2) and (4,2), also have the same y-coordinate. Like with the first set, we can find the length using subtraction. This time, we subtract the x-coordinates for both sides: 4 – (-3) = 7 and (-3) – 4 = -7. Distance cannot be negative, so we always use the absolute value of the answer. Because the absolute value of -7 is 7, both sides equal 7 units.

Graphing Ordered Pairs on a Coordinate Plane with an Example

Next, we can look at an example of how to graph the ordered pairs on a coordinate plane and connect the points using straight lines to create a polygon. The points in the example are A (0, 6), B (0, 0), and C (4, 0). In this example, the polygon is a right triangle.

The points (0, 6) and (0, 0) have the same x-coordinate (0). Just like before, to find the length, we subtract the y-coordinates: 6 – (0) = 6. That side has a length of 6 units. When using a coordinate plane, we could also count the number of spaces in order to find the length.

Looking at another side, the points (0, 0) and (4, 0) have the same y-coordinate (0). To find the length, the x-coordinates are subtracted: 4 – (0) = 4, so that side has a length of 4 units.

For this lesson, don’t worry about diagonal lines such as the hypotenuse of the triangle. We use a different formula to find the distance between diagonals called the distance formula. Students will learn about that formula and how to use it in a future lesson. Right now, we are only focused on horizontal and vertical lines and finding their length.

POLYGONS AND COORDINATE PLANES LESSON PLAN WORKSHEETS

The Polygons and Coordinate Planes lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

SCRIBE AND SAGE ACTIVITY WORKSHEET

Students will work in pairs to complete the activity worksheet. One student is the scribe and the other is the sage. The sage chooses a shape and tells the scribe what to write for the ordered pairs. The sage also provides the distance between any two points. The scribe writes the information and cannot talk. The scribe can shake their head or make gestures if the sage makes an incorrect statement. The students reverse their roles after each shape!

PLOT THE POLYGONS PRACTICE WORKSHEET

For the practice worksheet, students will plot four polygons by first plotting the sets of ordered pairs, then labeling and connecting the points. They will then name the polygon and find the measure of the side given.

POLYGONS AND COORDINATE PLANES HOMEWORK ASSIGNMENT

The homework assignment asks students to draw a picture of at least five different polygons using the coordinate plane shown on the worksheet. They will include the ordered pairs for each polygon and calculate the length of one side of each polygon on another paper.

QUIZ

This lesson also includes a quiz that you can use to test students’ understanding of the lesson material. Like the practice worksheet, for the quiz, students will plot polygons by plotting the sets of ordered pairs, then labeling and connecting the points. They will then name the polygon and find the measure of the side given.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.