VIEWS: 3 PAGES: 21 POSTED ON: 9/16/2011
Unit Overview Title: Getting in Shape Subject/Grade/Course: MATH/4 Total Days in Unit: 20 Days Degree of Difficulty: Moderate Summary: The emphasis of this 4th grade unit is to gain proficiency of basic geometric concepts and shapes. Students will be able to identify, define, describe, and draw geometric figures. Students will also gain competency in identifying polygons, angles, and lines. Finally, students will become familiar with identifying and locating ordered pairs on a coordinate plane. Stage 1: Desired Results State Standards | Understandings | Essential Questions | Knowledge & Skills | Misunderstandings Competencies Mississippi Competencies and Objectives addressed and assessed: 3. Geometry Analyze characteristics, properties, and relationships of two- and three- dimensional geometric shapes. Use coordinate geometry. -a. Analyze and describe the similarities and differences between and among two-and three-dimensional geometric shapes, figures, and models using mathematical language. (DOK 2) (major) -b. Identify and analyze the relationships between and among points, lines, line segments, angles, and rays. (DOK 2) (major) -c. Identify transformations (rotations [turns], reflections [flips], and translations [slides]) of two- dimensional figures. (DOK 1) (major) -d. Locate ordered pairs in the first quadrant of the coordinate plane. (DOK 1) (major) 4. Measurement Evaluate and justify measurable attributes of objects, units, systems, and processes. Perform measurements. -d. Use appropriate tools to determine, estimate, and compare units for measurement of weight/mass, area, size of angle, temperature, length, distance, and volume in English and metric systems and time in real-life situations. (DOK 1) (minor) Understandings By the end of this unit, what understandings will students have reached? Course and Program Level I Similar shapes can come in different sizes (congruence). II Shapes can be combined to make new shapes. III Lines, angles, and shapes are related through their properties. Unit Level IV When I transform a shape, I can predict the attributes that will be preserved. V Three-dimensional shapes are composed of two-dimensional shapes. Essential Questions What Essential Questions guide inquiry in this unit? Course and Program Level I How precise do I need to be? II Which is bigger/smaller? How do I know? III How can these be combined (broken down) to make new shapes? Unit Level IV What kind of shape is this? How can I explain or describe it clearly? V What shapes is this solid/shape made of? (What happens if I break this apart?) VI How are angles/lines/shapes related? Knowledge What Knowledge Questions will students be able to answer? I What does congruent mean? Similar? II What is this shape (angle, pair of lines) called? III What does the first number in an ordered pair represent? The second? Skills What Skills will students master or improve as a result of this unit? I Identify and classify two and three-dimensional figures. II Identify congruent and similar figures. III Identify, describe, and draw angles (acute, obtuse, right). IV Investigate and predict the results of motion (translation, reflection, rotation). V Identify, describe, and classify lines, segments, rays, parallel lines, and perpendicular lines. Misunderstandings Where are students likely to misunderstand important ideas? Where are they most likely to struggle in applying knowledge and skill? Students have difficulty identifying faces, edges, and vertices. (Have the students use cut out shapes and physically touch or label the attributes.) Students confuse pentagon, hexagon, and octagon. (Have the students draw an octopus and number its legs relating the prefix "oct" and eight. Then have the students create their own fictional animal for the prefixes "hex" and "pen." Have them use the prefixes as part of the animal's name and remind them that the animal must have the amount of arms or legs defined by the prefix, just like the octopus.) Students confuse points, lines, line segments, and rays. (Have students practice drawing and labeling each.) Students have difficulty identifying acute and obtuse angles. (Draw a right angle and then an acute angle and ask which is smaller. When they identify the acute angle, say, "Oh it's such a- cute little angle," just like when see a little baby. Now draw an obtuse angle and relate to the word large/thick. That is an obtuse cat.) Students have difficulty drawing similar or congruent figures. (Practice making/drawing figures using geoboards or graphing paper. Have the students count the pegs or squares.) Students have trouble seeing reflections, translations, and rotations. (Practice the three terms using two physical models. Have the students keep the one model in original form and move the other model as directed.) Interdisciplinary Competencies MS competencies and objectives addressed and assessed: arts 4. Develop perceptual skills and use visual arts vocabulary while creating and studying works of art. (CA)a. Utilize art vocabulary (e.g. color, shape, line, texture, balance, contrast, repetition, emphasis, proportion, unity) to describe or critique media, techniques, and processes in the environment and daily activity. 12. Recognize ways that major concepts, technologies, media, and processes of the visual arts are employed in arts and other disciplines. (C)b. Describe ways that math, language arts, social studies, history, science, and technology are related to the visual arts (e.g. the process of creating in the arts as well as through inventions, discoveries, and the development of ideas). Stage 2: Evidence Tasks | Other Evidence Performance Tasks Through which complex tasks will students reveal their ability to transfer their learning to a new situation? Task #1 Title: Drawing Contest Summary: The art club has organized an abstract drawing contest. It is awarding prizes for first, second & third place drawings based on contest rules. All drawings are to be completed on an 8 X 10 sheet and must include all of the following: -At least two of each different angle -The side of an octagon touching the side of a triangle -Two congruent trapezoids combined to form a hexagon -Two similar polygons that are touching -One set of each line (perpendicular, intersecting and parallel) After completing your drawing, you will need to give it a title and write a brief description for the panel of judges to read. Look For: -Identification of polygons, parallel lines, perpendicular lines -Interpretation of congruence and similarity -Descriptions using math vocabulary -Level of independence in completion of task Differentiation: minor This performance task is addressed in the following events: Performance Tasks Alignment Competencies: 3a 3b Essential Questions: IV VI Knowledge: I II Skills: I II III V Rubrics Rubric Drawing Contest Attachments Student Checklist Drawing Contest Student Sheet Task #2 Title: Design School Summary: Your design school final examination involves the application of geometry to design. You must select existing fabric or wallpaper, or design your own, to show that you understand how the incorporation of geometric ideas is creatively used. In order to show this, you must illustrate similarity, congruence, parallel lines, and angles in a manner that explains how the ideas of geometry are in agreement with the elements and principles of design: line, shape and form, direction, texture, color, value, space and balance, rhythm, repetition, unity, contrast, proportion, emphasis, movement. You need to explain which elements and/or principles of design can be shown through use of geometry in these ways: -Create or reproduce the design. -Select at least two elements that are shown in the wallpaper and link them to the geometry you have studied. -Select at least two principles of design that are shown in the wallpaper and link them with the geometry you have studied. Look For: -Use of transformations that reflects elements or principles of design. -Explicit statement of choice that reveals awareness of the connection between the math and the art. -Correct identification of math elements. Differentiation: major This performance task is addressed in the following events: Performance Tasks Alignment Competencies: 3a 3b 3c Understandings: IV Essential Questions: IV V Knowledge: I II Skills: I II III IV V Rubrics Rubric for Design School Attachments Design School Task Other Evidence Which other evidence can be used to reveal students ability to transfer their learning to a new situation? Evidence #1 Title:Other Evidence 1: Formative Assessments Summary: Throughout the unit, students are assessed formatively to document progress and growth. Text resources and attachments in this unit can be used for that purpose, as can journal entries. In addition, students self-reflect though the use of journals and Exit Tickets. A sample is attached that gives a variety of possible exit tickets. This evidence is assessed in the following events: I Spy Transformation Draw Centers Angles and Shapes Parallel and Perpendicular Another Scavenger Hunt Alignment Competencies: 3a 3b 3c 3d Understandings: IV V Essential Questions: IV V VI Knowledge: I II Skills: I II III IV V Evidence #2 Title:Other Evidence 2: Unit Test Summary: Students take a written test on the discrete knowledge and skills of the unit. This evidence is assessed in the following events: Unit Test Alignment Competencies: 3a 3b 3c 3d Understandings: IV V Essential Questions: IV V VI Knowledge: I II Skills: I II III IV V Stage 3: Learning Plan Calendar | Lessons & Events Day 1 Day 2 Day 3 Day 4 Day 5 Ship Shape Ship Shape Ship Shape Ship Shape Transformations Discovery Discovery Discovery Discovery Day 6 Day 7 Day 8 Day 9 Day 10 Transformations Transformations What's My Line? What's My Line? What's My Line? Day 11 Day 12 Day 13 Day 14 Day 15 What's My Line? What's My Line? What's My Line? What's My Line? Ordered Pairs Ordered Pairs Day 16 Day 17 Day 18 Day 19 Day 20 Ordered Pairs Ordered Pairs Show What You Show What You Show What You Know Know Know Lesson 1 Ship Shape Discovery Days in lesson: 4 Begins on day 1 of the unit Purpose: Students will review 2 dimensional shapes and become more familiar with 3- dimensional shapes. In addition, students will describe and compare the shapes using attributes and geometrical vocabulary including congruent and similar. Alignment Competencies: 3a Understandings: V Essential Questions: IV V VI Knowledge: I II Skills: I II Events in this Lesson: Mummy Math A 90 minute activity I Spy A 90 minute activity Scavenger Hunt Walk A 90 minute activity Practice A 90 minute activity Event Mummy Math Event Aim: Make Meaning Summary: Ask: What is Geometry? Why do you think it is important to learn about figures, lines, circles, etc.? Ask students to answer this question in their math journal. Ask students to share their answers. Read and discuss "Mummy Math" by Cindy Neuschwander. Review names and descriptions of: polygons, 2- dimensional figures, and 3-dimensional figures. Discovery: Arrange students in groups of 4 or 5. Give each group a set of 3-D figures. Pose this question: How can these shapes be classified into 2 different groups? After students have had time to classify the figures, have each group explain how the figures were classified. For example, students might say, "The cube and the rectangular prism figures all have flat sides." Or, "These (the sphere and cone figures) have no corners." If students do not use vocabulary to identify the shapes/attributes, incidentally remind them of the correct vocabulary. What attributes were used? etc. Repeat this process by asking students to classify the shapes into 3 groups; 4 groups; 1 group. (Make sure students recognize that the 3-D shapes contain 2-D shapes, i.e. the rectangular prism has rectangles as faces, the cube has square faces, etc.) (This activity can be done again after the vocabulary for face, edge, and vertex is introduced.) Minutes Devoted to this Activity: 90 Alignment Competencies: 3a Understandings: V Essential Questions: IV V VI Knowledge: I II Skills: I II Event I Spy Event Aim: Acquire This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: While students are in groups, review the concept of congruent and similar figures. Ask students to look around the room and make a group list of congruent and similar figures in the classroom. For example: Congruent - sections of the board (same size and same shape); Similar - the top of the teacher's desk and a section of board (same shape, different size). This can be continued using cutout shapes of congruent and similar shapes. When students are comfortable with identifying the figures and congruency, introduce the vocabulary for face, edge and vertex (vertices). Using the 3-D shapes, demonstrate and explain a face, edge, and vertex. Use dry erase boards to allow students to practice using the vocabulary: the teacher points to the edge, vertex, or face and students write it down. I Spy: Give each student 6 sticky dots (2 red, 2 blue, 2 yellow). Explain that they will play I Spy. Objective: The object is to identify faces, edges, and vertices in the classroom by placing the sticky dots according to color (Red = face; Blue = Edge; Yellow = Vertex). Play: 1. Give students 5 minutes to place sticky dots on appropriate places in the classroom. 2. After students have had time to place dots, ask students to look around room at the dots. If anyone sees a dot in the wrong place they are to say: "I Spy a vertex that is not a vertex." That student may change the dot to the correct place and explain why it is now correct. If all dots are placed correctly, student says: "I Spy a vertex that is a vertex." That student points out a vertex, face, or edge and explains why it is a vertex (or an edge, face). 3. Repeat this activity if students need more practice. Conclusion: Ask students to come up with a definition of each attribute. Discuss how precise math language must be in order to communicate exactly what we want. After the class agrees on the definition of each, have students write the definitions in their math journals. Teacher Notes: Students complete an Exit Ticket. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a Understandings: V Essential Questions: IV V VI Knowledge: I II Skills: I II Event Scavenger Hunt Walk Event Aim: Transfer Summary: Give each student a Scavenger Hunt sheet. Take students on a walk around the school and school grounds. As students walk, they are to write the names of items they see that will fit in each category. Remind students that some objects are combinations of shapes. Think of a milk carton: What shapes make a milk carton? After returning to class, allow students to share their findings. Discuss how each is used in real life. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a Essential Questions: IV V VI Knowledge: I II Skills: I II Event Practice Event Aim: Acquire Summary: Proceed from recognizing edges, vertices, and points to counting the number of each in a figure. This can be done in a number of ways: * Grouping students: Giving each group a set of 3-D shapes and allowing them to make a table to list the number of each attribute per figure. * Take another "walk": Use the original Scavenger Hunt list and number the attributes of each object mentioned on the list (for example, door has 6 faces, 12 edges, 8 points). Complete Shape Definition worksheet as practice or assessment. Use text materials for additional practice. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a Understandings: V Essential Questions: IV V VI Knowledge: I II Skills: I II Lesson 2 Transformations Days in lesson: 3 Begins on day 5 of the unit Purpose: Students will work with various manipulatives to identify types of transformations, as well as identify real-life examples of transformations using specific vocabulary. Finally students will be able to construct models/drawings of translations, rotations and reflections (singular and multi-step). Their ability to transfer these skills to an authentic situation will be realized in the authentic performance task, in which they connect transformational geometry to the elements and principles of visual art in the critique of wallpaper designs. Alignment Competencies: 3c Understandings: IV Essential Questions: IV Skills: IV Events in this Lesson: Simon Says A 90 minute activity Transformation Draw A 90 minute activity Centers A 90 minute activity Event Simon Says Event Aim: Make Meaning Summary: Pose this question: Does the movement of an object always affect its appearance? In groups of 3 or 4, ask students to discuss and respond to this question. List responses and discuss for clarity. After discussion of answers ask students to stand. Tell class they will play "Simon Says." Ask all students to face the front of the room. Give the following directions: 1. Simon Says: Slide to the left 2. Simon says: Turn to the right 3. Simon says: Turn to the left 4. Simon says: Flip to the back 5. Simon says: Slide to the to the right 6. Etc. Continue directions until most students are able to make transformations easily. After Simon Says, discuss the opening question again. Did responses change? Tell students: These movements are also called transformations. Transformation is another word for "change." What changed here? What stayed the same? Demonstrate the same movements with a trapezoid (or manipulative of your choice), interchanging the words, saying, "Sometimes we call a slide a translation: both words contain the /sl/; sometimes we call a turn a rotation: both words contain the /t/; sometimes we call a flip a reflection: both words contain the /fl/." Minutes Devoted to this Activity: 90 Alignment Competencies: 3c Understandings: IV Essential Questions: IV Skills: IV Event Transformation Draw Event Aim: Acquire This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: Play Simon Says again using teacher-selected manipulatives and new transformation vocabulary. When students show proficiency with new vocabulary, introduce the following game: Transformation Draw: 1. Put students in groups of 2. Pass out Draw cards and manipulative of choice. Ask students to cut cards apart and shuffle. 2. When cards are cut apart, place pile face down in center of playing area. 3. Student 1 draws a card and follows direction on card by performing that transformation with manipulative. 4. Points are scored by correctly performing task. When the game is over, ask students to draw an example of the three transformations discussed. Teacher Notes: Students complete an Exit Ticket. Minutes Devoted to this Activity: 90 Alignment Competencies: 3c Understandings: IV Skills: IV Event Centers Event Aim: Acquire This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: Centers are set up for students to practice skills and revisit activities. Some options are listed. 1) Using Geoboards to form a shape and then a transformation of that shape. Draw shape and result on grid paper. 2) Using dot paper to form shapes and asking students to draw a specific transformation of that shape. 3) Create another center to practice the transformation concepts or revisit activities. 4) The "Meet the Teacher" center allows the teacher to meet with students for extensions and for re- teaching. After students have demonstrated an understanding of singular transformations, allow them to explore multiple transformations. Students can be paired again to write the multiple transformations that their partners have performed. For example, Student 1 displays several like manipulatives in multi transformations: slide, flip, slide, turn. Student 2 writes the transformations that have occurred using the specific vocabulary. Teacher Notes: Students complete an Exit Ticket. Minutes Devoted to this Activity: 90 Alignment Competencies: 3c Understandings: IV Skills: IV Lesson 3 What's My Line? Days in lesson: 7 Begins on day 8 of the unit Purpose: Students will work with figures to identify angles, lines, line segments, rays, and points. In addition, students will become familiar with the various kinds of angles and lines. Finally, students will be able to create figures containing designated angles, lines, and points. Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Events in this Lesson: Angles and Shapes A 90 minute activity Protractors A 60 minute activity Protractors A 90 minute activity Lines, Segments, Rays A 90 minute activity Parallel and Perpendicular A 90 minute activity Another Scavenger Hunt A 90 minute activity Flex Day A 90 minute activity Event Angles and Shapes Event Aim: Acquire This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: Materials needed: Drinking straws/coffee stirrers Clay Index cards Flashlight Pose the question: What are angles and how are angles and shapes related? Give students time to work in groups to discuss this idea. Generate a discussion about angles. After the discussion about the relationship of shapes and angles, distribute 12 coffee stirrers and 1 small ball of clay to each group. Ask groups to cut the stirrers in half (now the groups will have 24 stirrer pieces). 1. Ask groups to assemble an angle using 2 of the stirrers and a small piece of clay for the vertex. 2. Give each group an index card and tell them that this will be their "angle tester." They will test their angles to determine if the angle is the same, larger, or smaller than the corner of the index card. Demonstrate how to use the angle tester. (Place the assembled angle on the corner of the card. Ask students to describe how the angle fits on the corner of the card.) Now ask them to "test" their angle by placing the angle at the corner of the card. Does the angle fit the corner? Is it smaller than the corner? Is it bigger than the corner? 3. Introduce the names of the angles. Right: fits the corner of the card; Acute: smaller than a right angle; Obtuse: larger than a right angle. Give students time to practice this, asking them to make the smallest acute angle they can; make the smallest obtuse angle; make the largest obtuse angle; etc. 4. After some practice with this concept, challenge students to make shapes using angles. "Can you make a square? What kinds of angles make the square? Rhombus? What kinds of angles did you use?" 5. After students are able to distinguish between the different types of angles, have class work in groups (or alone) to make a categorized list of the angles they see in the classroom. Use attached sheet. Set timer for 5 minutes. After timer goes off, generate a discussion about angles in real life through the students' lists. Ask: "What conclusions were you able to draw? What kinds of angles did you find the most? The least? Why do you think that is the case?" 6. Use exit slip to determine progress. Ask students to quickly draw a picture that contains each of the angles. Label the angles. Students should take "Angles I See" home and record various angles. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Protractors Event Aim: Acquire Summary: Direct instruction in measuring angles using a protractor. Practice with text materials. Students verify the measures of the acute, right, and obtuse angles they have been drawing. Students draw angles for others to measure. Students draw an angle of a certain size (90 degrees, 30 degrees, 120 degrees) without a protractor, then compare the actual measurement of what they drew to the angle asked for. Repeat this activity until they show some proficiency. Be sure the angles point to the right as well as to the left. Have students turn their paper and see that the angle measure is the same whether they use one ray or the other as the base for their protractor. Minutes Devoted to this Activity: 60 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Protractors Event Aim: Make Meaning Summary: Extension activity: Give students a piece of paper and a piece of card stock. By only using the piece of paper, and folding, how many different-sized angles can you make? (For example, the corner of the paper is a 90-degree angle. Folding that corner in half is a 45-degree angle. Placing those adjacent to one another forms a 135-degree angle.) On the piece of card stock, they will trace every angle they make without measuring, label the degrees size, and then check the measurement with a protractor. Continue with the previous day's activity if necessary. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Lines, Segments, Rays Event Aim: Acquire Summary: Begin class by asking students to write a definition of the following: Line Ray Line segment Set the timer for 5 minutes. After the timer goes off, ask students for definitions. List their thoughts and save for later use. Ask students to make a number line in their journal or notebook. Set timer for 30 seconds. When timer goes off, ask: Are you finished? Students will say no. Ask students if they are including negative numbers. Set timer for another 30 seconds. Repeat question. After this, ask: When will you be finished? Why aren't you finished? Students will see that the number "line" is never finished. It can keep going in both directions infinitely. Next ask students to draw a sun. Set timer for one minute. As students draw, observe for those who are drawing rays on the sun. After one minute, ask students to show their sun. Question students about the parts coming off of the sun. What are they? Some students will say they are rays. Turn lights off and shine a flashlight. Ask students about the light coming from the flashlight. What do we call these? Rays. Now question students about the difference between a "line" and a "ray." Instruct students about the meaning of lines, rays, and line segments. Demonstrate how the three are identified. A line continues on in both directions (as the number line does). The ray has a beginning point and continues on in one direction (as sun rays and light rays). A line segment has a beginning and an end - two endpoints (as the leg of a table, board on a fence). A point is the place of origin or ending. A point actually has no dimension at all! Because line segments have 2 endpoints, we see line segments all around us. Use text materials for students to practice identification and use of terms. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Parallel and Perpendicular Event Aim: Acquire This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: Ask students to identify points, line segments, lines, and rays in the classroom. Use letters to show students that points, lines, rays, and line segments can be named for identification. 1. Draw a line and label the line as AB. Tell students this would be line AB (use notation). 2. Draw a ray and label the ray as CD. Tell students this would be ray CD (use notation). 3. Draw a line segment and repeat. Use dry erase boards to practice this with students. First ask them to identify the lines, points, line segments, and rays that you draw. Next ask them to draw specified lines (e.g. line segment xy). Make sure students show the line segment with 2 endpoints. When asking them to draw rays and lines, make sure they use arrows where appropriate to designate infinity. When students are comfortable with identifying and naming lines, line segments, and rays, show them that sometimes lines can go on and never touch. These are called parallel lines. Demonstrate. Compare parallel lines to highways. Ask students to find parallel lines in the classroom. Say, "Sometimes lines cross each other. These are called intersecting lines." (Compare this to a stoplight where streets cross.) Tell students that sometimes lines cross to make right angles. These are called perpendicular lines (compare this to most 4 way stops). Practice with dry erase boards. Students take "Check Up for Lines" home to create a drawing. Teacher Notes: Students complete an Exit Ticket. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Another Scavenger Hunt Event Aim: Transfer This event contains the Stage 2 other evidence: Other Evidence 1: Formative Assessments Summary: Go on another scavenger hunt, this time looking for lines in real life situations. Use the attached activity sheet to identify objects for each category. As exit slip or homework, ask students to write a "Who am I?" question. For example: "I am the angle you see at the bottom left corner of every door. Who am I?" Students can share these with the class, or teacher can collect and use to play a jeopardy game as a review. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Event Flex Day Event Aim: Acquire Summary: Students practice the skills of the unit, using text materials, revisiting games and activities from before, and meeting with the teacher for focused instruction. At one of the centers, students begin thinking about the final performance tasks of the unit, and checking that they understand the criteria for scoring. Minutes Devoted to this Activity: 90 Alignment Competencies: 3b 4d Essential Questions: VI Knowledge: II Skills: III V Lesson 4 Ordered Pairs Days in lesson: 4 Begins on day 14 of the unit Purpose: Students will become familiar with the use of ordered pairs. In addition, students will practice locating ordered pairs in the first quadrant of the coordinate plane. Alignment Competencies: 3d Knowledge: III Events in this Lesson: Where Am I? A 90 minute activity Treasure Hunt A 60 minute activity Battleship A 90 minute activity Plotting Points A 90 minute activity Event Where Am I? Event Aim: Make Meaning Summary: Pose this question: Suppose a ship, while on a cruise, has engine trouble. If the captain radios to shore, how can he tell someone where he is so help can be sent? Allow students to brainstorm ways to determine location. Using colored masking tape, create a large grid on the floor in the classroom. (If this is not possible, use chalk to create a large grid on a blacktop area.) Label each line of the grid as 1,2,3, to 8 or a,b,c to h. Have students stand around the grid. Tell students that you are going to play "Treasure Hunt," but they can only find the treasure by first walking along the x axis before moving up on the y axis. Demonstrate. Start with the following clues: * The treasure is located at point 3,7. Demonstrate how to find it. Ask students to stay there. * The treasure is located at point 7,3. Ask: "Will this be the same point?" Allow students to find that point. Compare the students' points on the grid. Why aren't they on the same point? * Continue with this activity. * At some point change the activity so the student is asked to stand on a point and identify the location of the point on which they are standing. * Continue to alternate between these two activities. Ask students how this is useful in real life. Show students a map. Point out the grid lines on the map. Ask: "How would these lines be useful?" Generate a discussion about boat travel, air travel, and how coordinates are used to determine location. Read "The Fly on the Ceiling: a Math Reader," by Julie Glass. This is a story about how Rene DesCartes thought of the coordinate system while watching a fly crawl across his ceiling. Minutes Devoted to this Activity: 90 Alignment Competencies: 3d Knowledge: III Event Treasure Hunt Event Aim: Acquire Summary: Give students grid paper and ask them to label the x and y axis on their grids (attached). Next, ask them to plot a point where a "treasure" is located. They are not to show anyone their location. Pair students and have them play a game similar to Battleship. Player 1 names a point on the grid as an ordered pair. If that is not the correct point on the partner's map, then player 1 puts an x on his own map. Player 2 does the same thing, guessing a point and putting an x on his own map to designate a miss. Minutes Devoted to this Activity: 60 Alignment Competencies: 3d Knowledge: III Event Battleship Event Aim: Transfer Summary: Students practice plotting, reading, and identifying points by playing a game of Battleship in pairs. Each student has two blank grids which show Quadrant I from 0 to 10, horizontally and vertically. A ship occupies 4 consecutive points that are intersections of grid lines (no fractional coordinates). Place students in pairs, with a divider between them. Each student plots the four points for his ship on one grid, and saves the other to use while guessing the position of his opponent's ship. In turn, each player makes a guess by stating an ordered pair. The other player responds "Hit" or "Miss." Upon a "Hit," the player gets another turn. Upon a "Miss," the turns change. The first player to sink the other ship by hitting all four points is the winner. Teacher Notes: There are many books that contain lists of points for students to plot and ultimately create a picture. In addition, this website contains an activity in which students guide Billy Bug to his food through a coordinate system: http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html Minutes Devoted to this Activity: 90 Alignment Competencies: 3d Knowledge: III Event Plotting Points Event Aim: Transfer Summary: Students are given 6 grids, and attempt to create some of the figures discussed on a coordinate grid. 1) Students plot three points to make a small triangle. They then plot three more points to make a congruent triangle. What transformations might they be looking at? (translation) 2) Students plot two points and carefully join them to make a line. They then try to plot points and join to create a parallel line. What have they found out about parallel lines? 3) How could students create a 45-degree angle in the coordinate plane? How do they know? 4) Students create a square and a similar square. Students create a right triangle and a similar right triangle. For each, justify that they are truly similar and not just "sort of" alike. 5) Students plot and draw the letter "L" and its reflection over a given line. They do the same thing for "A." What is significant about the two reflections? Minutes Devoted to this Activity: 90 Alignment Competencies: 3d Knowledge: III Lesson 5 Show What You Know Days in lesson: 3 Begins on day 18 of the unit Purpose: Students complete the performance tasks for the unit, and take a written exam. Alignment Competencies: 3a 3b 3c 3d 4d Understandings: IV V Essential Questions: IV V VI Knowledge: I II III Skills: I II III IV V Events in this Lesson: Unit Test A 90 minute activity Performance Tasks A 90 minute activity Performance Tasks A 90 minute activity Event Unit Test Event Aim: Transfer This event contains the Stage 2 other evidence: Other Evidence 2: Unit Test Summary: Students take a written test on the discrete knowledge and skills of the unit. They use the remaining time to work on the performance tasks. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a 3b 3c 3d 4d Understandings: IV V Essential Questions: IV V VI Knowledge: I II III Skills: I II III IV V Event Performance Tasks Event Aim: Transfer This event contains the Stage 2 performance task: Design School Summary: Students work on performance tasks. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a 3b 3c 3d 4d Understandings: IV V Essential Questions: IV V VI Knowledge: I II III Skills: I II III IV V Event Performance Tasks Event Aim: Transfer This event contains the Stage 2 performance task: Drawing Contest Summary: Students work on performance tasks. Minutes Devoted to this Activity: 90 Alignment Competencies: 3a 3b 3c 3d 4d Understandings: IV V Essential Questions: IV V VI Knowledge: I II III Skills: I II III IV V