Geometry and Spatial Reasoning

Transcription

1 Activity: TEKS Baggy Shapes (K.8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different. The student is expected to: (A) describe and identify an object by its attributes using informal language; (B) compare two objects based on their attributes; and (C) sort a variety of objects including two-and three-dimensional geometric figures according to their attributes and describe how the objects are sorted. (K.9) Geometry and spatial reasoning. The student recognizes attributes of two- and three-dimensional geometric figures. The student is expected to: (A) describe and compare the attributes of real-life objects such as balls, boxes, cans, and cones or models of three-dimensional geometric figures; Overview: Materials: Grouping: Time: During this lesson, students will locate objects in their surroundings that match a particular shape and will describe objects based on various attributes. Students will also sort and compare the found objects by their attributes. This lesson should follow the initial lesson of introducing the various shapes and discussion about the attributes of each shape. Paper sack (1 per student) Three-dimensional shape cut-outs: spheres, rectangular prisms (including cubes), cylinders, and cones Models of two-dimensional shapes: circle, triangle, rectangle, square (special rectangle) Models of three-dimensional shapes: spheres, rectangular prisms (including cubes), cylinders, and cones 4 hula-hoops or 4 large sheets of butcher paper for sorting Whole group 45 minutes Lesson: 1. Day before lesson: Glue/staple one of the 3-D shape cut-outs onto each bag. There should be one bag with a shape on it for each student. Teacher may ask for more than one object. The class can sort the various objects throughout the week, and then return items at the Baggy Shapes Page 1

2 Send bag home for homework. Ask students/parents to find an object around the house that matches the shape located on the bag and send the object back to school. 2. Introduce lesson by placing the objects from home side by side where they are visible to ALL students. end of the week. Teacher may need to have extra objects for those students who were not able to bring one from home. 3. Ask the following questions: 1. Look at all of our objects. Do you see any that are alike? (Students will name some.) 2. How do you know they are alike? Well, let s try to count the objects that are the same shape. 3. Which shape shall we count first? 4. Begin by touching the first object and asking, Is this a? If it is, then count it. If not, proceed to the next object and repeat the question. After doing this 3 or 4 time, begin to act tired and start loosing count. 4. In exasperation, state: This is going to take forever. Is there another way we can count these objects faster? Possible responses for Question #2: they are same shape, or they are the same size moving hands up and down to indicate height Question #4: You want the students to see how long and hard this will be if we continue in this manner Possible responses: all the shape objects can be put together, all the same colors can be put together, and all the same shapes can be put together. Teacher response: So by putting the same type of object together we will be able to count them faster. Right? Then proceed to explain sorting: when you separate items by a certain or particular way and put them into groups. Baggy Shapes Page 2

3 5. I heard someone say by the same shape. Let s see if we can sort our objects by the same shape. If students did not state the idea of sorting by shape, then you need to make that suggestion. Lay out 4 hula-hoops or 4 large pieces of butcher paper for sorting. Return objects to students, and place objects where they are visible to ALL students. 6. Quickly go around the room/circle asking students to share their object (by stating the name of the object and what you do with it) and placing it into one of the hula-hoops. NOTE: Having students state the name of the object and its purpose is a great vocabulary development strategy. This strategy is not only good for ELL and inclusion students but for students who have not had a lot of experiences with language. At this time, if students are not understanding how to sort or do not understand how to begin the sorting process, the teacher may need to place a three-dimensional model inside each of the hulahoops. This way the students are able to look at the 3-D models and their object from home to determine which shape matches their object the best. Hula-hoop #1: sphere Hula-hoop #2: rectangular prisms (including cube) Hula-hoop #3: cylinder Hula-hoop #4: cone It is important to note that in, mastery of naming two-dimensional figures is required. Mastery of naming three-dimensional figures is a first grade requirement. Baggy Shapes Page 3

4 7. Once all students have placed their object into a hula-hoop, examine relationships of objects in each hula-hoop and justify placements. 8. Begin with the cone. Ask students the following questions: 1. Are all the objects inside this circle the same shape? Do we need to move any objects out of this group? 2. While holding up one of the objects ask, What can you tell me about this object. What shapes do you see on this object? Lead students to discover how many sides, edges, faces there are with this shape. 3. State: If we were to stand this (ex: party hat) up and trace around it, what shape would we be tracing? (solution: circle) 9. Proceed examining the contents of each of the hula-hoops using the same procedures as earlier. Possible attributes to examine with each shape: Number of sides Number of edges Number of faces Number of corners/vertices What shape (2-D) best describes the object? What shape (2-D) is drawn when you trace around the object? Can the object roll? Can the objects be stacked on top of each other? When examining the rectangular prisms, students may point out that all of the objects are not the same shape. Hold up a cube and another type of rectangular prism from the hulahoop. Examine and compare the attributes of each. They will have the same attributes except the square has all four sides that are the same length. This is why a square is called a special rectangle. 10. Closure of the lesson: Ask students who brought an example of a cone to get their objects from the hula-hoop. Then ask students who brought an object shaped like a rectangular prism/box, sphere/ball, and cylinder/can to get their objects from the hula-hoops. This closure allows for continuing assessment by having children identify their objects by its mathematical name. Baggy Shapes Page 4

5 Homework: Assessment: Extensions: Resources: Have students draw their favorite shape and explain why it is their favorite shape. Ask parents to record what their child states. Observation throughout the lesson for participation. During the closing of the lesson, teacher may observe which students had success in collecting their object from the hula-hoop when a shape was described. Class-generated Venn-diagrams comparing 2 shapes National Council of Teachers of Mathematics. (2004). Navigating through Geometry in Prekindergarten-Grade 2. Reston, VA: NCTM Van de Walle, J.A. (2004) Elementary and middle school mathematics: Teaching developmentally (5 th ed.) Boston, MA: Allyn and Bacon Van de Walle, J.A. (2006). Teaching Student-Centered MATHEMATICS Grades K-3. Boston, MA: Pearson Education, Inc. Modifications: ELL and Inclusion students: Giving more time for students responses and using the 3-D models will help with the sorting process. The time allotment may be adjusted to where you have students sort and process one day and then compare and explain the following days. Baggy Shapes Page 5