Geometry and Spatial Reasoning

Transcription

1 Geometry and Spatial Reasoning Activity: TEKS: Treasure Hunting (5.8) Geometry and spatial reasoning. The student models transformations. The student is expected to: (A) sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid; (5.9) Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane. The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers. Note: Portions of this lesson address TEKS at other grade levels as well; however, the intent of the lesson fits most appropriately at the grade level indicated. Overview: Materials: In this two-part investigation, students will first plot coordinate points on a Quadrant I grid and then extend their plotting skills in order to uncover and fill a hidden treasure chest. Part One Deck of cards with face cards removed (one per group) What Are Your Coordinates? Handouts/Transparencies 1a and 1b (one per group; should be color-copied) Pencil (one per student) Part Two (x, y) Marks the Spot! Handout/Transparency 2 (one per student) What s in the Treasure Chest? Handout/Transparency 3 (one per student) Pencil (one per student) Grouping: Time: Partners Two 50-minute class periods Lesson: Procedures 1. Part One In Part One of Treasure Hunting, students will locate and name points on a coordinate grid using ordered pairs of whole numbers. Notes Treasure Hunting Page 1

2 Procedures 2. Have each pair of students separate cards into two piles red cards in one pile and black cards in one pile. Shuffle each pile of cards well. Notes 3. Introduce the coordinate grid to the students by discussing the x-axis (horizontal runs from left to right) and y- axis (vertical runs from bottom to top). Tell students that these axes are just two number lines that intersect at the origin (0,0) and are never-ending. Use the grid from What Are Your Coordinates? (see Handout/Transparency 1b) as you introduce the coordinate grid. 4. Model the next part of the lesson by asking for two student volunteers. The volunteers should demonstrate the following: Partner #1 draws a card from the red pile and records the quantity indicated on the recording sheet provided on What Are Your Coordinates? (Handouts/Transparencies 1a and 1b). Partner #1 should keep this card in front of him/her. Partner #2 draws a card from the black pile and records the quantity indicated on the card on the recording sheet. Using both of the cards that were drawn, the students should follow the directional instructions on the recording sheet to plot the point on the coordinate grid. The cards should then be placed in a discard pile. 5. Have each pair of students draw cards to generate ordered pairs. Each group should repeat the steps that have been modeled At first, it may help students if words (across or up) along with the corresponding numbers are used. For example, if a 4 of hearts and 2 of clubs is drawn during your demonstration, say, 4 across and 2 up. Have students work together to plot points on their handout. Treasure Hunting Page 2

3 Procedures by the student volunteers until they have plotted a total of 10 ordered pairs on the coordinate grid. 6. After each group has generated and plotted 10 ordered pairs, lead the students in discussion to debrief on the first part of the lesson. The following questions may help to open up the discussion: Which of your points was closest to the top of Quadrant I? Which of your points was closest to the x-axis? Which of your points was farthest away from the x-axis? Which of your points was closest to the y-axis? Which of your points was farthest away from the y-axis? Did anyone plot a point on the origin (0,0)? If not, why? Optional: If we played again, do you think we would plot the same points? Why or why not? Notes Color-coding of the coordinate grid should assist students in which direction to move first. This part of the lesson should be repeated (or other basic coordinate graphing activities done) until students have mastered plotting points on a Quadrant I coordinate grid. 7. Part Two In Part Two of Treasure Hunting, students will uncover a hidden treasure chest given a description and one vertex of the rectangular chest. 8. Before starting, instruct students that rectangular chests can only be horizontal or vertical. No diagonal chests are hidden. 9. Give students the following information to record/plot: The treasure chest is 4 units wide and 3 units tall. The upper-left corner has been located at (2,6). How many corners of the chest are still hidden? Where are they located? Treasure Hunting Page 3

4 Procedures Notes Each student should record the description of the chest and the initial corner that has been found on (x, y) Marks the Spot! (see Handout/Transparency 2). Have students plot the initial corner of the chest on the grid provided, then identify the coordinates of the remaining corners. 10. Now that the treasure chest has been found, it should be filled with treasure with What s in the Treasure Chest? (see Handout/Transparency 3). Before beginning, guide students to determine the area of the pieces that are to be moved. Also, guide students to determine the corresponding area of the chest to be filled. Model the translation of Piece A, explaining that it may make things easier if students focus on placement of just one vertex of the piece and describe the corresponding movements of that vertex. Piece A covers an area of 4 square units. Piece B covers an area of 7 square units. Piece C covers an area of 1 square unit. The total area covered by pieces A, B, and C is 12 square units. The area of the chest is b h (or l w), which gives 4 x 3, or 12 square units. Have students record descriptions of translations of the given treasure pieces (left, right, up or down) to fill the treasure chest, one piece at a time. Lead the class in a discussion to debrief over this portion of the lesson. Assessment: Extensions: Handouts and teacher observations The Part One activity can be made into a game where points are plotted and connected to form lines. The objective of the game would be to predict the grid location of the intersection of the lines constructed. Have students create their own hidden chest, descriptions, and pieces to fill the chest in order to have the class uncover and fill their chest. Treasure Hunting Page 4

5 Resources: Van de Walle, J. A. (2004). Elementary and middle school mathematics teaching developmentally. Boston: Pearson Education, Inc. Modifications: For Part Two, it may aid some students to have an extra set of fill pieces cut out so that they can physically slide the pieces into place in the treasure chest. Treasure Hunting Page 5

6 What Are Your Coordinates? Separate your cards into two piles red cards in one pile and black cards in another. Shuffle each pile of cards well. Partner #1 draws a card from the red pile and records the quantity indicated on the card on the table below. Partner #1 should keep this card in front of him/her. Then, Partner #2 draws a card from the black pile and records the quantity indicated on the table below. Using both of the cards that were drawn, follow the directional instructions on the third column of the table in order to plot the point on the coordinate grid on the next page (see Handout/Transparency 1b). The two cards should then be placed in a discard pile. Repeat until you and your partner have plotted a total of 10 points. Red Card x-coordinate move across Black Card y-coordinate move up Coordinate Pair ( x, y ) ( across, up) ( across, up) ( across, up) Handout/Transparency 1a Treasure Hunting Page 6

7 What Are Your Coordinates? Handout/Transparency 1b Treasure Hunting Page 7

8 (x, y) Marks the Spot! I know that the hidden treasure chest is units wide and units high. I also know that the corner, or vertex, of the treasure chest can be found at (, ). I FOUND THE TREASURE CHEST!!! The upper-right corner is located at. The lower-right corner is located at. The lower-left corner is located at. The upper-left corner is located at. Describe the steps you followed to show how you found the other vertices of the treasure chest. Handout/Transparency 2 Treasure Hunting Page 8

9 What s in the Treasure Chest? I FILLED THE TREASURE CHEST!!! Remember, Pieces A, B, and C can only be translated, or slid, horizontally (left or right) and vertically (up or down). No diagonal movement is allowed. Describe how you translated, or slid each piece into its proper place. Piece A has to be moved across 1 unit and _3_ units up. Piece B must be moved. Piece C must be moved. Handout/Transparency 3 Treasure Hunting Page 9