Understand Points on the Coordinate Plane (Day 1)
Lesson 5 of 8
Objective: Students will be able to understand the concept and representation of the coordinate plane.
Think-Pair-Share: In pairs, students use MP2 to pay attention to mathematical language used during a sample student's explanation of her answer to a problem. Emily graphed the point for the ordered pair (5, 2) on a coordinate plane. She said that the x-coordinate of the ordered pair,5, means that the point is a distance of 5 units from the y-axis and the y-coordinate of the ordered pair, 2, means that the point is a distance of 2 units from the x-axis. Is Emily correct? Explain your reasoning. Since this is a mouthful, I encouraged my students to take this step by step, and read it aloud. In pairs, one set of students listening and charted Emily's coordinates, and the other set explained their answers. Roles can then switch for a similar problem.
I know that students learn, in part, by being able to talk about the content. The Think-Pair-Share method is helpful because it structures the discussion. Students follow a process that limits off-task thinking and off-task behavior. Accountability is built in because each student reports to a partner, and then partners must report to the class.
It's important to know that fifth grade is the first time students work with coordinate planes (and only in the first quadrant). My students will create their own coordinate grids in a lesson later this week too; it's important for them to know how to construct this themselves. During this lesson, I encouraged students to articulate directions (MP3), and attend to precision (MP6) as they plotted points on the coordinate plane. Students can graph real-world problems by graphing points in the first quadrant of the coordinate plane. Gathering and graphing information helps students to develop an understanding of coordinates, and what the overall graph represents. Students also need to analyze the graph by interpreting the coordinate values in the context of the situation.This is the challenging part! We will build on the coordinate plane concept first, and then get to this in a few days.
I was happy to note that students found the above problem very easy to figure out. I had used a coordinate plane once, back in October, when reading the novel Holes with my class. Upon completing, the students hid Kissin' Kate Barlow's treasure on a grid. Their partner then attempted to find the hidden treasure. Another idea students could use it to play Battleship. I remember that they had a significant amount of trouble with remembering to start with the x-axis. Surprisingly, the students generally remembered to start at the x-axis now. To be sure of this we sky-wrote x's and y's. To do this we simply just took a pointer finger, and wrote in the air, in cursive writing. This incorporates some movement into the lesson, and my students need this to stay focused.
To introduce the lesson, I get students started with a sample problem. Using the table, students graph the coordinate points to determine the letter that Robert forms. Robert uses a coordinate plane to graph the points for the ordered pairs given in the table. He connected them in order. I facilitated students' conversations, and students connected their points to form a letter.
To further extend knowledge, I ask students to contemplate the following: Greg graphs the points for the ordered pairs (4.6) and (4,9) on a coordinate plane. Then he connects the points to form a line segment. Is the line segment parallel to the x-axis or parallel to the y-axis? In pairs, students pondered this.
Students are now challenged to use the coordinate grid to solve Hank’s problem. This is their first independent engagement with the coordinate grid, as the most appropriate mathematical tool, to solve this type of problem (MP5). Hank graphed a quadrilateral on a coordinate plane. The vertices of the quadrilateral are (1,1) (3,6), (6, 6), (8, 1). What quadrilateral does Hank draw when he connects the points? How do you know?
Students are now challenged to use a line segment to connect point to solve Gina's problem. Students routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense (MP4). Gina draws a line segment to connect the point at (2,1) and (7, 4). She draws a second line segment that is parallel to the first one by connecting the points at (2,3) and (7,6). If she wants to draw a third line segment parallel to the ones she has already drawn, what ordered pairs could she use? Students have to justify using words, drawings, or numbers.
Students are now challenged to connect line segments to determine ordered pairs. Students look for and make use of structure to solve Jaime's problem (MP7). Jaime draws a line segment to connect the points at (3,6) and (8,6). Then he graphs two more points that he connects to form a second line segment that is perpendicular to the first line segment. What could be the ordered pairs of the points he graphs? Students have to justify using words, drawings, or numbers.
To close this lesson, I read The Fly On The Ceiling. I'm reading this book so that students make a text-to-self connection that may result from the unique and funny story. This is a book about how the French philosopher, Renâe Descartes, invented a way to keep track of his belongings. The students got a kick out of how messy Renae was, and how using a coordinate system was practical in helping him to solve his problem. This book introduces the attributes of the coordinate plane and graphing ordered pairs. (Renae actually did create the Cartesian system of coordinates.) I ask: "When do you think this story may have taken place?" "How do you know?" A read aloud of the book can be found here: The Fly On The Ceiling.