Module on Geometric and Spatial Sense for Kindergarten By Cindy Clark, Kelly Brown, and Shawna Hudson Table Of Contents Math Module Outline Pretest Form A Lesson 1: Three Dimensional Figures Lesson 2: Constructing Figures Using Three-dimensional Shapes Lesson 3: Two-dimensional Figures Lesson 4: Constructing Figures Using Two-dimensional Shapes Posttest Form B Module development was partially funded by the Missouri Coordinating Board for Higher Education through the Eisenhower Professional Development Program. Translations were partially funded by NSF ESIE SGER Project 0086580.
Math Module Outline Strand: Geometric and Spatial Sense Grade Level Span: Kindergarten Concept(s) Included in Module: All students should recognize: Two-dimensional figures (shapes) as having length and width with no depth. Examples: Triangles, Circles, Rectangles including squares. Three-dimensional figures (shapes) as having length, width, and height. Examples: Cubes, Spheres, Cones, and Cylinders. Author(s): Cindy Clark, Kelly Brown, and Shawna Hudson District: Canton R-V School District Brief Statement of Basis for Selection on Strand/Concepts: This module was selected based upon assessment data and the lack of fully developed and consistent geometry units in K-4. Module Resources: Geometric shapes (overhead, 3-D models, real-world examples) and student geometry packet Adapted from: Korean Mathematics, Grades 1-6. (2001). Edited by Janice Grow-Maienza, translated by Sue Chung Nugent. Kirksville, MO: Truman State University. From Ministry of Education. Arithmetic, Grades 1-6. Seoul, Korea: National Textbooks Inc, l993.
Pretest Form A Directions should be read to the students. Color the triangle shape blue. Color the sphere shape pink. Color the cube shape yellow. Color the rectangle shape black. Color the circle shape orange. Color the cone shape purple. Color the cylinder shape red. Color the square shape green. Teacher should record student answer. What is the difference between a circle shape and a sphere shape? Scoring Guide Student verbal answer to the following question: What is the difference between a circle shape and a sphere shape? 3pt Student uses any of the words height, width, depth, or length correctly. Student states a circle is flat while a sphere has space inside. (Or a similar statement) Student correctly uses words such as flat, round, filled, space inside, takes up more space, or inside/no inside when describing both objects. 2pt Student uses some hand gestures or shapes in classroom in addition to words such as flat, round, filled, space inside, takes up more space, or inside/no inside. Student describes one shape and uses only the statement, the other one is not in their description. 1pt Student uses hand gestures or shapes in the classroom with limited words. Student correctly describes one shape, but fails to mention the other shape or to differentiate between the two shapes. 0pt Student does not attempt answer. Student says shapes are the same.
Lesson 1 Objective: The student will be able to recognize three-dimensional figures (cubes, spheres, cones, and cylinders) 100% of the time when presented with numerous threedimensional figures. Lesson Resources: Megaphone, orange safety cones, birthday party hat, various balls, geometric shape manipulatives, 20 24 paper bags labeled with shape and name from real-life problem, and student packet. Standards Addressed: Show-Me Goal#: 1 Geometric Spatial Sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes Missouri Frameworks Written Benchmark: C Visualize, draw and compare NCTM Content Standard: Analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Real Life Problem: Mrs. Smith collects sphere shaped objects. Mr. Brown collects cube shaped objects. Mrs. Day collects cone shaped objects. Mrs. Pike collects cylinder shaped objects. They would like to add to their collections. We have been asked to help. Your job will be to find objects for these teachers here in our classroom. Demonstration of Process(es)/Exploration: Divide students into groups of 2 or 3. Give each group a set of geometric shape manipulatives. Allow students time to play with shapes. Redirect students to real-life problem stated above. Give each group of students four bags. Each bag is labeled with teacher s name (Mrs. Smith, Mr. Brown, Mrs. Day, and Mrs. Pike) and shape (drawn). The groups are instructed to collect items in the classroom. After collection, students empty bags into designated area in classroom. The teacher places geometric manipulatives in each designated area. Students lead discussion of checking each collected item for features that make each shape. Teacher should use guiding questions dealing with length, width, depth, and height during discussion. Guided Practice: Student packet page 44. Start with cube shape. Discuss each cube shape. Students circle each cube shape in selected color. Each shape is completed in same manner using different color. Independent Practice: Student packet page 45. Teacher guides students to color each shape at the top of the page a different color. Students are instructed to color remaining shapes accordingly.
Note(s) for Teachers: Lesson length should be 30 45 minutes. Emphasize the following vocabulary: length, width, depth, and height. At the kindergarten level, students are expected to recognize the shape when given both two- and three-dimensional shapes and to explain the difference between any one twodimensional shape and any one three-dimensional shape. Explaining the difference using length, width, height, and depth or the words two- and three-dimensional will be assessed at a higher-grade level.
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Lesson 2 Objective: The student will be able to construct figures using three-dimensional shapes (cubes, spheres, cones, and cylinders) 100% of the time when given pictures of figures to construct. Lesson Resources: 5 sets of the following: 1 large ball, 2 small balls, 1 large rectangular box, 4 cubes, 2 small, tall cylinders, 4 small, short cylinders, 2 medium rectangular boxes, and 2 small rectangular boxes 5 sets of the following: 2 long rectangular boxes, 2 tall rectangular boxes, 4 cubes, 2 tall cylinders, 2 small spheres, and 6 small rectangular boxes Standards Addressed: Show-Me Goal#: 1 Geometric Spatial Sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes Missouri Frameworks Written Benchmark: C Visualize, draw and compare NCTM Content Standard : Analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Real Life Problem: You are a construction crew. You have been hired to build three figures. After you build each figure, the crew leader (teacher) will inspect your work. Follow your plans carefully. Demonstration of Process(es)/Exploration: Student packet 46 Guided Practice: Independent Practice: Student packet 47 Note(s) for Teachers: Lesson length should be 30 45 minutes. Emphasize the following vocabulary: length, width, depth, and height.
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Lesson 3 Objective: The student will recognize two-dimensional figures (triangles, circles, and rectangles including squares) 100% of the time when presented with numerous twodimensional figures. Lesson Resources: Student geometry packet & chart paper Standards Addressed: Show-Me Goal#: 1 Geometric Spatial Sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes Missouri Frameworks Written Benchmark: E Explore Geometry in their world NCTM Content Standard: Analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Real Life Problem: Miss Weir needs our help with an art project. She needs a list of objects for a still life drawing project. She would like for the objects to have circle shapes, triangle shapes, rectangle shapes, and triangle shapes in them. Demonstration of Process(es)/Exploration: Students will work in pairs. The class will take a math walk through the school and outside the building. Students will look for objects that have geometric shapes (circle, square, rectangle, circle) in them or shapes that are made of geometric figures. Teacher will record what the students find by drawing the shape and labeling. After the class returns to the classroom, students will share things they saw and discuss how they knew what shape it was. Students should discover attributes of each shape through this discussion. Teacher should guide with questions on length, width, height, and depth. A class table or chart could be constructed showing at least one contribution from each pair of students. Guided Practice: Student packet 48 Start with triangle shape. Discuss each triangle shape. Students circle each triangle shape in selected color. Each shape is completed in same manner using different color. Independent Practice: Student packet 49 Teacher guides students to color each shape at the top of the page a different color. Students are instructed to color remaining shapes accordingly. Note(s) for Teachers: Lesson length should be 45 minutes. Emphasize the following vocabulary: length, width, depth, and height.
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Lesson 4 Objective: The student will construct figures using two-dimensional shapes (triangles, circles, and rectangles including squares) 100% of the time when given pictures of the figures. Lesson Resources: 5 sets of the following: 2 circles, 12 assorted coins, 5 squares, 2 triangles, 2 rulers, and 1 rectangle 5 sets of the following: 1 square, 3 triangles, 1 large circle, 2 small circles, and 1 rectangle Standards Addressed: Show-Me Goal#: 1 Geometric Spatial Sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes Missouri Frameworks Written Benchmark: E Explore Geometry in their world NCTM Content Standard: Analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships Real Life Problem: You own a sign company. Your sign company only has one machine. This machine can only make the shapes you see in front of you. Mr. Jones placed an order for the following signs: a sailboat, a truck, a house, a flower, a fish, and an angel. You have been asked to make the signs for Mr. Jones using only the shapes your sign company can make. Demonstration of Process(es)/Exploration: Student practice page 50 Guided Practice: Independent Practice: Student practice page 51 Note(s) for Teachers: Lesson length should be 30-45 minutes. Emphasize the following vocabulary: length, width, depth, and height.
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Posttest Form B Directions should be read to the students. Color the triangle shape blue. Color the sphere shape pink. Color the cube shape yellow. Color the rectangle shape black. Color the circle shape orange. Color the cone shape purple. Color the cylinder shape red. Color the square shape green. Teacher should record student answer. What is the difference between a circle shape and a sphere shape? Scoring Guide Student verbal answer to the following question: What is the difference between a circle shape and a sphere shape? 3pt Student uses any of the words height, width, depth, or length correctly. Student states a circle is flat while a sphere has space inside. (Or a similar statement) Student correctly uses words such as flat, round, filled, space inside, takes up more space, or inside/no inside when describing both objects. 2pt Student uses some hand gestures or shapes in classroom in addition to words such as flat, round, filled, space inside, takes up more space, or inside/no inside. Student describes one shape and uses only the statement, the other one is not in their description. 1pt Student uses hand gestures or shapes in the classroom with limited words. Student correctly describes one shape, but fails to mention the other shape or to differentiate between the two shapes. 0pt Student does not attempt answer. Student says shapes are the same.