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1 Ohio Standards Connection Geometry and Spatial Sense Benchmark C Specify locations and plot ordered pairs on a coordinate plane. Indicator 6 Extend understanding of coordinate system to include points whose x or y values may be negative numbers. Mathematical Processes Benchmark H Use representations to organize and communicate mathematical thinking and problem solutions. Lesson Summary: In this lesson, students label and represent ordered pairs on a four-quadrant grid. Students demonstrate prior knowledge of plotting ordered pairs in the first quadrant. Introduction to the four-quadrant grid begins with students creating and discussing number lines that include negative numbers. Practice in creating the axes on a coordinate grid is a component of the lesson. Students discuss the importance of direction in plotting ordered pairs and explain how to plot ordered pairs. Estimated Duration: One-and-a-half hours Commentary: As students ideas about the number system expand to include negative numbers, they can work in all four quadrants of the Cartesian plane. Provide opportunities for students to describe each quadrant to build understanding. Common errors occur when students switch the order when plotting the pair. Strategies, such as, thinking x comes before y in the alphabet will help students remember the order. Have students compare points such as (3, -4) and (-3, 4). Also, mistakes occur when the coordinate pair includes a zero. Pre-Assessment: Informally assess students abilities to plot ordered pairs in Quadrant I. Distribute Plotting Ordered Pairs on a Grid Pre- Assessment, Attachment A, to individual students. Circulate around the room to observe students plotting the ordered pairs in the first quadrant. Make note of students who reverse the order when plotting the ordered pairs. Select different students to plot the ordered pairs on an overhead transparency and explain how they arrive at the location. Scoring Guidelines: Informally assess as students plot the ordered pairs. Write anecdotal notes of misconceptions students have. Discuss any misconceptions as students explain plotting the ordered pairs. 1

4 For the teacher: grid paper, overhead projector, overhead transparency coordinate grids For the students: pencils, grid paper, journals Vocabulary: coordinates ordered pairs origin quadrant x-axis y-axis Research Connections: Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement, Alexandria, Va.: Association for Supervision and Curriculum Development, Pask, Gordon. Conversation, Cognition and Learning. New York: Elsevier, Reimer, Wilbert and Luetta Reimer. Historical Connections in Mathematics, Volume III. Fresno, Calif. AIMS Education Foundation, Wickett, Marilyn, Katherine Kharas and Marilyn Burns. Lessons for Algebraic Thinking. Math Solutions Publications Attachments: Attachment A, Plotting Ordered Pairs on a Grid, Pre-Assessment Attachment B, Plotting Ordered Pairs on a Grid, Pre-Assessment Answer Key Attachment C, Numerology Island, Post-Assessment Attachment D, Numerology Island, Post-Assessment Answer Key Attachment E, The Rene Descartes Story Attachment F, Paths on a Grid 4

5 Attachment A Plotting Ordered Pairs on a Grid, Pre-Assessment Name Date Directions: Plot each ordered pair on the grid. Label the points as give. 1. Point A (1, 1) 2. Point B (5, 1) 3. Point C (7, 3) 4. Point D (4, 0) 5. Point E (0, 6) 6. Explain how to plot the ordered pair (4, 2). 5

6 Attachment B Plotting Ordered Pairs on a Grid, Pre-Assessment Answer Key Name Date Directions: Plot each ordered pair on the grid. Label the points as give. 1. Point A (1, 1) 2. Point B (5, 1) 3. Point C (7, 3) 4. Point D (4, 0) 5. Point E (0, 6) 6. Explain how to plot the ordered pair (4, 2). Begin at (0, 0) and go to the right 4 spaces or go to 4 on the x-axis. Then go up 2 places and place a point. 6

7 Attachment C Numerology Island, Post-Assessment Directions: Plot the following ordered pairs on the Island of Numerology and label with the given letter. A. City Hall (0, 0) B. Tourist Center (-5, -5) C. Sanders Elementary School (3, -7) D. Library (-4, 2) E. Police Department (6, 6) Directions: Give the ordered pair for each location. 1. Post Office 2. Hospital 3. Fire Department 4. Community Swimming Pool 5. Movie Theater 7

8 Attachment D Numerology Island, Post-Assessment Answer Key 1. Post Office (-1, 9) 2. Hospital (2, -3) 3. Fire Department (-8, -4) 4. Community Swimming Pool (0, -10) 5. Movie Theater (5, 7) 8

9 Attachment E The Rene Descartes Story Rene Descartes (day-kart) was a French mathematician, philosopher and scientist who is often called the father of modern mathematics. His studies of mathematics opened up many doors in the areas of geometry and algebra. His studies of geometry lead to the development of analytic geometry, a way of connecting algebra and geometry that enables mathematicians to display an equation as a set of points on a graph. One late morning Descartes was lying in bed. He noticed a fly crawling on the ceiling. As the fly was crawling to a corner, Descartes thought of how he could mathematically describe the fly s position. He realized he could express the fly s position in terms of its distance from the adjacent wall. The story goes that this was the birth of coordinate geometry, also known as the Cartesian coordinate system (the position of a point in a plane may be determined relative to intersecting lines known as axes). 9

10 Attachment F Paths on a Grid The school is located at (-1, 0) on the grid. Plot the following points on the grid. Amy s house (-1, 6) Kim s house (2, -3) Chris s house (-5, -5) Kevin s house (4, 3) The four students walk to school. Answer the questions by identifying the shortest paths on grid lines for each student and comparing the distance of the paths. Who walks the farthest distance to school? Which two students walk the same distance to school? Who walks 8 units to the school? You walk 12 units to school. Plot a point to show where your house could be. 10

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