Coordinate Plane Unit Plan

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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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