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Hannah Joyce Cartesian Coordinate System Unit Plan Introduction to Unit This unit was planned for a seventh grade class with 45-minute class periods. See the table below for a list of daily lessons incorporated into this unit. The check sheet at the bottom of this page is designed to allow for easy assessment during in-class activities. Teachers should mark checks or x’s if a student shows proficiency or a lack of proficiency, respectively. There is also a space for any additional comments or notes a teacher may need to make. Check sheets may be changed out daily. Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Introduction Coordinate Battleship with Coordinate World Maps Review and to the System in TI- the Cartesian Geometry and the Quiz Cartesian Navigator Coordinate with Online Cartesian Coordinate System Geoboards System System Applies grid concept to real life Given coordinate, graphs point Distracts from class discussion Given graph, identifies point Identifies axes and/or origin Cooperates in pairs/groups Identifies correct quadrant Adds to class discussion Student Name Comments i.e. Hannah X Understood similar triangles DAY 1: Intro to Cartesian Coordinate System Learning Objectives Given a Cartesian grid, students will be able to identify and label the axes of the coordinate plane. Given a Cartesian grid, students will be able to identify and label the quadrants of the coordinate plane. Given a point on the Cartesian plane, students will be able to identify the quadrant in which an ordered pair is positioned. Students will graph ordered pairs in the four quadrants of a coordinate plane. Students will identify ordered pairs represented by points in the four quadrants of the coordinate plane. Standards of Learning Geometry SOL 7.12: The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. Materials/Resources Classroom-size number lines, painters tape for axes, note cards for unit labels Assessment Teacher will use check sheet to assess understanding of concepts during whole-class activity. Assessment of homework should be based on the correct labeling of ordered pairs and quadrants. Time Required 40 minutes Schedule of Activities Create a classroom size number line so the point zero is at the center of the classroom. Have students stand on the line and determine at what point they are standing. After reviewing this concept, have a few students scatter around the room so that they are not standing on the number line. Ask the class how they would describe those students’ locations in the room. Responses may include something like, “He is at the point negative seven, but is off the line.” or, “She is above the point three.” Ask students how they know which side is above and which side is below the number line. Also, try placing a student in line with and on the same side of the number line as another student. Ask students how they would describe this person’s location without referring to another student’s location. This can bring up the idea that if all people in line with (say) negative seven [on the line x = -7] were described as being above (or below) the number line, then they could be standing within a relatively close proximity to one another or very far apart from one another. Once the inefficiency of this method is recognized, ask students to find a way to distinguish at what point “in-line” with negative seven a person is standing. Guide students to the answer of placing a number line in the other direction (perpendicular to the first to form a grid). This idea may come up earlier in discussion. If so, be sure all students understand why this method is more efficient. After another number line is put into place (so that the zeros of both number lines intersect), have students describe their classmates’ locations when they are not standing on the first number line. Responses may include, “Negative seven and up four.” Have students find similarities between points graphed in the same quadrant or on the same axis (signs or zeros of x and y-values). After having students describe other people’s locations, discuss confusion that may occur when a person hears the description this way, such as “Which number line is the description starting with?” This brings up a need to differentiate between the two (and a chance for lots of vocabulary). Discuss the convention of labeling axes and quadrants and writing points as ordered pairs or coordinates. Ask students if any of the quadrants look familiar. They should’ve seen the first quadrant before. Be sure to scale this life-size grid down (on the board or overhead) and to keep a running list of concepts and vocabulary. This will make things easier to visualize. Have students practice using fractions in their ordered pairs, as well. Make sure students also go from coordinate to plotting. In other words, give students an ordered pair and have them stand at the point. Don’t just have them determine at which points their classmates are standing. Review concepts and vocabulary and practice naming and plotting points for the remainder of class. Explain homework before the class period ends. Homework Have students draw a two-dimensional picture of the layout of their bedroom (or any other room) on a poster board or paper. Then, ask them to draw two axes intersecting at the center of the room. Have students report the location of the furniture, lamps, etc. in the room they choose using ordered pairs. Require students to label the four quadrants and to have at least three points in each quadrant. DAY 2: Cartesian Coordinate System in TI-Navigator Learning Objectives Given a Cartesian grid, students will be able to identify and label the axes of the coordinate plane. Given a Cartesian grid, students will be able to identify and label the quadrants of the coordinate plane. Given a point on the Cartesian plane, students will be able to identify the quadrant in which an ordered pair is positioned. Students will graph ordered pairs in the four quadrants of a coordinate plane. Students will identify ordered pairs represented by points in the four quadrants of the coordinate plane. Standards of Learning Geometry SOL 7.12: The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. Materials/Resources Classroom set for TI-Navigator system Class set of TI-83/84 graphing calculators CartesianExplorations.act file CaresianExplorations.pdf/attached sheet Assessment Teacher will use check sheet to assess understanding of concepts during whole-class activity. Student participation in discussion should be emphasized. Time Required 40 minutes Schedule of Activities From the Texas Instruments Activity CD or from http://education.ti.com/educationportal/activityexchange/Activity.do?cid=U S&aId=4186, download the CartesianExplorations.act Activity Settings file and the CartesianExplorations.pdf with teacher directions (also attached). Have students explore the concepts and patterns described in the activity. Before starting the exploration, however, review the labeling of the four quadrants and the horizontal and vertical axes. DAY 3: Battleship with Cartesian Coordinates Learning Objectives Given a Cartesian grid, students will be able to identify and label the axes of the coordinate plane. Given a Cartesian grid, students will be able to identify and label the quadrants of the coordinate plane. Given a point on the Cartesian plane, students will be able to identify the quadrant in which an ordered pair is positioned. Students will graph ordered pairs in the four quadrants of a coordinate plane. Students will identify ordered pairs represented by points in the four quadrants of the coordinate plane. Standards of Learning Geometry Strand, Grade 7 SOL 7.12: The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. Materials/Resources Two sheets of grid paper per student and a few extra for early finishers Copies of the list of coordinates for the homework drawing Assessment Teacher will use check sheet and observation methods to assess understanding of concepts during the paired learning activity. The action of calling out coordinates and marking them down [the act of going from coordinate to grid], particularly, will be assessed in this way. Returned Battleship grids will be graded on the accuracy of corresponding hits on the grids to coordinate pairs [going from grid to coordinates]. Homework will be assessed on the ability of the student to correctly draw the picture [go from coordinates to grid]. Time Required 40 minutes Schedule of Activities Have students volunteer to show their homework assignments from the previous night’s homework. Students love to share their art work and what their room looks like! Review concepts from Day 1. Then, have students play Battleship with grid paper (or Geoboards) in pairs. Make sure ships are aligned on coordinates (horizontally and vertically only). “Ships” can just be circled coordinates or could be cut out ships glued to the game grid. If using Geoboards, students can simply wrap a rubber band around the coordinates for their ships. All students must use the same grid paper with the same scaling. The game rules should remain the same. Students should receive two grids each: one to put their “ships” on and one to record “hits” and “misses”. Unlike the traditional game, however, each grid should be divided into four quadrants. At least one ship must be placed in all of four quadrants. When guessing the location of their competitor’s ships, students must state the quadrant and the ordered pair. “Hit” coordinates should be colored red on one student’s guess grid and the other student’s ship grid, while “miss” coordinates should be colored blue (for water). After one student wins, all hit coordinates (along with their quadrants) should be recorded by both players and turned in to the teacher. Each student should turn in two grid sheets – one hit and miss sheet with labeled coordinates and one grid with the ship locations represented. This way, an assessment can be made. Assessment should be based on teacher observations of student interaction and student’s abilities to report the correct coordinates and quadrants. An example of how to play the game would be beneficial to students who had never played before. If students complete the game before the allotted time is up, they can begin playing another round of Battleship. Time should be called after twenty minutes of play. Materials should be returned to teacher, and homework should be explained. Giving a brief example (like a star- shaped figure) may help. Homework Before class, the teacher should create a picture on a coordinate grid, marking any points that intersect integer coordinates. List the intersected coordinates in the order that students should draw and connect points. Disjoint shapes require a different list. Distribute the list(s) of coordinates and have students recreate the picture, only using the coordinates provided. Pictures can be related to a holiday, school mascot or emblem, patriotic symbol, etc. DAY 4: Coordinate Geometry Learning Objectives Given a Cartesian grid, students will be able to identify and label the axes of the coordinate plane. Given a Cartesian grid, students will be able to identify and label the quadrants of the coordinate plane. Given a point on the Cartesian plane, students will be able to identify the quadrant in which an ordered pair is positioned. Students will graph ordered pairs in the four quadrants of a coordinate plane. Students will identify ordered pairs represented by points in the four quadrants of the coordinate plane. Students will create right triangles and parallelograms in the coordinate plane. Given triangles and/or parallelograms in the coordinate plane, students will compute the area and/or perimeter of a shape. Given triangles in the coordinate plane, students will determine if the triangles are similar (by definition). Standards of Learning Measurement SOL 7.7: The student, given appropriate dimensions, will estimate and find area of polygons by subdividing them into rectangles and right triangles; and apply perimeter and area formula in practical situations. Geometry SOL 7.9: The student will compare and contrast the following quadrilaterals: a parallelogram, rectangle, square, rhombus, and trapezoid. Deductive reasoning and inference will be used to classify quadrilaterals. SOL 7.11: The student will determine if geometric figures – quadrilaterals and triangles – are similar and write proportions to express the relationships between corresponding parts of similar triangles. SOL 7.12: The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. Materials/Resources One computer with Internet access per student One activity sheet per student Assessment Throughout class, the teacher will assess students through observation and questioning, using the unit check sheet provided. The manipulative task will be assessed on the student’s ability to correctly plot and label vertices, to correctly draw specified shapes in specified quadrants; to communicate and explain procedures used in finding area and perimeter; and the to create similar triangles. The writing prompt will be assessed for completion and communication of a clear, realistic idea. Time Required 40 minutes Schedule of Activities Before starting the day’s activity, quickly review the characteristics of a right triangle, rectangle, square, rhombus, and trapezoid; how to find the area and perimeter of such shapes; and what it means for shapes to be similar. Providing examples on the board or overhead may help. Also, be sure that students understand that x- and y-values represent the horizontal and vertical distance a point is from the origin (respectively). After reviewing, have students access the Web site below and complete the attached activity entitled “Coordinate Geometry with Geoboards”. http://nlvm.usu.edu/en/nav/category_g_2_t_3.html Be sure that you (the teacher) are available for student questions throughout the whole activity. The teacher should assess through observation and questioning and keep marks on the unit check sheet provided. When students are finished, have them turn in the worksheet for assessment. If a student needs more time on the activity, allow he/she to take it home, as the last task does not require use of the online manipulative. Finally, introduce the writing prompt for homework and allow students to work on it for the remainder of class. Homework Writing Prompt: Today, we used the coordinate plane to assist us with certain geometry topics. Brainstorm another way a coordinate grid system is or could be used in the real-world to make something easier or more efficient. DAY 5: World Maps and the Cartesian System Learning Objectives Given a Cartesian grid, students will be able to identify and label the axes of the coordinate plane. Given a Cartesian grid, students will be able to identify and label the quadrants of the coordinate plane. Given a point on the Cartesian plane, students will be able to identify the quadrant in which an ordered pair is positioned. Students will graph ordered pairs in the four quadrants of a coordinate plane. Students will identify ordered pairs represented by points in the four quadrants of the coordinate plane. Students will understand the meaning of certain geography terms (including prime meridian, equator, hemisphere, longitude, and latitude) and will compare them to Cartesian coordinate system features. Standards of Learning Geometry Strand, Grade 7 SOL 7.12: The student will identify and graph ordered pairs in the four quadrants of a coordinate plane. World Geography WG.1: The student will use maps, globs, photographs, and picture to obtain graphical information and apply the concepts of location, scale, and orientation. Materials/Resources Globes or small copies of a world map A large world map Rebecca Aberg. (2003). Rookie Read-About Geography: Latitude and Longitude. Children’s Press: San Francisco, CA. Assessment The check sheet should be used to assess students through observation and questioning. The writing prompt should be graded on clarity and the number of correct comparisons made. Time Required 40 minutes Schedule of Activities Read Latitude and Longitude by Rebecca Aberg, aloud in class. Be sure to pull out vocabulary and to discuss the topics below. Map Math by Orli Zuravicky may also be used for this lesson. With a large world map or sketch of a world map and a large copy of a Cartesian grid (could be on the board), have pairs of students identify corresponding parts of the world map and the Cartesian grid. As students point out these features, have them describe the relationships between the equator and the x-axis, the prime meridian and the y-axis, the point of origin and the origin on a Cartesian grid, longitudinal lines and vertical lines (x = constant lines), latitude lines and horizontal lines (y = constant lines), and the quadrants of the Cartesian system to hemispheres on a globe or map. Also, be sure to explore the similarities between points on the equator (all have zero degrees latitude) and points on the x-axis and points on the prime meridian (all have zero degrees longitude) and points on the y- axis. Also, have students discuss the similarities and differences in the units of measure used on maps and globes and the units of measure in the Cartesian coordinate system. Next, provide students with world maps and/or globes and have them find the location of a particular city/country/island using longitude and latitude notation. Conversely, have students find a city/country/island given a particular location. Note: It may be a good idea to coordinate this activity with a history or geography teacher. Homework Write a note to a family member or friend describing the similarities and differences between a world map or globe and a Cartesian grid. Include words like prime meridian, quadrant, point of origin, north/south/east/west, etc. Suggestion: A diagram may be helpful in explaining.

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