### Lesson Plan

# Measuring Polygons on the Coordinate Plane

In this Designing With Geometry lesson, students will calculate length, perimeter, and area, as well as find missing coordinates and more.

Grades

6–8

Duration

40 MINUTES

### Objectives

**Students will:**

- Draw polygons on the coordinate plane when given the coordinates
- Find the length of a polygon's sides drawn on the coordinate plane
- Find the area and perimeter of polygons drawn on the coordinate plane
- Find the "missing" coordinate when given three of the coordinates for a rectangle
- Use these concepts to calculate distance on a map

### Materials

- Get Moving: Polygons on the Coordinate Plane printable
- Answer Key: Designing With Geometry printable
- Standards Chart: Geometry printable
- Graph paper
- Whiteboard or large graph paper and markers

### Set Up

- Make a class set of the Get Moving: Polygons on the Coordinate Plane printable.
- Print a copy of the Answer Key: Designing With Geometry printable for your use.

### Lesson Directions

### Introduction to Polygons on the Coordinate Plane

**Step 1:** If necessary, review key concepts pertaining to the coordinate plane including how the (x, y) structure works (students sometimes have difficulty remembering that the x-coordinate comes first), and the quadrant system. Make sure that students know how to locate points with one or two negative numbers as coordinates.

**Step 2:** On the board, write the points (-2, -3), (4, -3), (4, 4), and (-2, 4). Plot these points on a coordinate grid. Ask what shape the points would make if connected (rectangle). Ask the class to provide a definition of a rectangle (four interior right angles and opposite sides are parallel and equal in length). Connect the points to make the rectangle.

**Step 3:** Ask the class how we know the opposite sides are equal in length. Demonstrate this to the class. In this case, the points (-2, 4) and (-2, -3) have the same x-coordinate (-2). To find the length, Subtract the two y coordinates: 4 - (-3) = 7, so the side has a length of 7 units. If the class needs a refresher in how to subtract negative numbers, do so at this point in the lesson. Repeat with the opposite side (4, 4) and (4, -3) and show how the side length is also 7 units. Wrap up by showing that the other pair of opposite sides is 6 units per side.

**Step 4:** Ask the class to determine the perimeter of the rectangle (26 units = 7 + 7 + 6 + 6). If necessary, review the formula for perimeter and ensure that students know that a square is also a rectangle.

**Step 5:** Ask the class to determine the area of the rectangle (42 square units = 7 x 6). If necessary, review the formula for area.

**Step 6:** Draw the following three coordinates on the board: (-2, 0), (3, 0), and (3, 4). Ask, "If we wanted to draw a rectangle, what would the coordinates be for the fourth corner?" Show how the length of the bottom side is 5 (3 — -2), and the right side is 4 (4 — 0). That means that the x-coordinate of the missing corner is -2 (3 — 5) and the y coordinate is 4 (0 + 4).

### Guided Practice

**Step 7:** Draw the following coordinates on the board: (-2, -1), (1, -1), and (1, 4). Assign the following problems for students to complete in pairs while discussing their thinking:

**Find the coordinates of the point that would make a rectangle.**Answer: (-2, 4)**Find the perimeter of the rectangle.**Answer: 16 units = 2 x (3 + 5)**Find the area of the rectangle.**Answer: 15 square units = 3 x 5

**Step 8:** **Checking for Understanding:** Review answers as a class and respond to any questions.

### Independent Practice

**Step 9:** Assign the Get Moving: Polygons on the Coordinate Plane printable for classwork or homework.

**Step 10: Checking for Understanding:** Review the answers to the Get Moving: Polygons on the Coordinate Plane printable, which are provided on page 1 of the Answer Key: Designing With Geometry printable. Make sure students explain their mathematical thinking. Address any misconceptions that may arise.

### Standards

**Grade 6:**Polygons on the Coordinate Plane (**CCSS**6.G.3)**Grades 6–8:**Making Sense of Problems, Reasoning, Constructing an Argument, and Attending to Precision (**CCSS**MP1-3, and 6);**NCTM**Geometry

For more information, download the comprehensive Standards Chart: Geometry printable.