Hands on Geometry for K-2 Learners
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The document discusses key geometric concepts that should be taught in early elementary grades, including two and three dimensional shapes, coordinate geometry, transformations, symmetry, and spatial reasoning. It provides rationale for why geometry is important even at a young age. Several hands-on activities are described to help students explore and develop an understanding of these foundational geometric ideas in a developmentally appropriate manner through exploration and play.
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Hands on Geometry for K-2 Learners
- 1. Developing and Assessing Geometric and Measurement Concepts By Michelle Flaming
- 2. Agenda Geometry: Defining and Rationale Two and Three Dimensional Shapes Coordinate Geometry and Other Representational Systems Transformational Geometry Visualization and Spatial Reasoning Assessing Geometric Concepts through Student Interviews Student Interviews
- 3. Geometry Brainstorm If a parent asked you, “What is geometry at your grade level, what types of activities do you do?” How would you respond? Sort your list into categories.
- 4. Why Teach Geometry So Early? If a parent approached you and asked, “Why do you teach geometry at such an early age? I didn’t learn it until high school.” How would you respond?
- 5. The Why Geometry enables us to describe, analyze, and understand the physical world in which we live. Clements and Battista in 1992 states “positive correlations have been found between spatial ability and mathematics achievement at all grade levels”. Numerous mathematical concepts have an obvious visual dimension. For example:
- 6. The Why Different, yet connected to the concept of number. Connected to other topics such as: art, science and social studies. Often students who are not strong with numbers, excel in geometric and spatial concepts.
- 7. What Is Geometry? National Council of Teachers of Mathematics (NCTM) Two and Three Dimensional Shapes Coordinate Geometry and Other Representational Systems Transformational Geometry Visualization and Spatial Reasoning
- 8. Two and Three Dimensional Shapes Relate shapes to their real-world. May call rectangles “doors”. May call spheres “balls”. May call cubes “boxes”.
- 9. Two and Three Dimensional Shapes - Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. recognize, name, build, draw, compare, and sort two and three dimensional shapes.
- 10. Research on Two and Three Dimensional Shapes Circles are the easiest for students to recognize from a variety of shapes. Rectangles are the next easiest. Although students don’t recognize that squares are a “special” rectangle. Triangles are the hardest for students to recognize from a variety of shapes. Clements Research indicates only 60% accuracy.
- 11. Research on Two and Three Dimensional Shapes Triangles are the hardest for students to recognize from a variety of shapes. Clements Research indicates only 60% accuracy.
- 12. Activity: Different Shape Greens Pigs On The Ball - by Amy Axelrod 1. Sort the “greens” into categories of their choice. 2. Describe categories, introduce vocabulary. 3. Find appropriate “green.”
- 13. Two and Three Dimensional Shapes - Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. - describe attributes and parts of two and three dimensional shapes:
- 14. Activity: Shape Blackout Partner Game Choose 6 shapes, place on card Shuffle name/property cards. Take turns, if card matches the shape on board, cover with a marker. Game is over when all shapes are covered.
- 15. Three Dimensional Shapes - Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. recognize, name, build, draw, compare, and sort two and three dimensional shapes . Cube: Sphere: Cone: Cylinder: Rectangular Prism: -- Number and Shape of faces -- Number of edges and corners (angles, vertices)
- 16. Terminology Students should begin by using their own vocabulary, such as “pointedness” to represent the corners and/or vertices. Look for similarities and differences between shapes. -- McRel #1 Instructional Strategy. Terminology should not be the focus in the early grades.
- 17. Two and Three Dimensional Shapes - Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships. - investigate and predict the results of putting together and taking apart two and three-dimensional shapes.
- 18. Activity: Combining Shapes Each person needs 30 triangles on card stock. Work with partner, find all the possible composite shapes from 4 triangles. Describe the new shape Share and discuss all the shapes.
- 19. Teachers’ Role Provide materials for Hands On explorations. Toothpicks, marshmallows String Manipulatives Real-world Objects Structures the classroom which encourages students to explore and communicate. Look at examples and nonexamples - Frayer Model
- 20. Coordinate Geometry and Other Representational Systems Specify locations and describe relationships using coordinate geometry and other representational systems. Describe, name, and interpret relative position and direction and distance in navigating space and applying ideas about direction and distance; Find and name locations with simple relationships such as “near to” and in coordinate systems such as maps.
- 21. Coordinate Geometry and Other Representational Systems Specify locations and describe relationships using coordinate geometry and other representational systems. Navigational questions: 1. Which way?(direction) 2. How far? (distance) 3. Where? (location) 4. What objects? (representation)
- 22. Coordinate Geometry and Other Representational Systems Specify locations and describe relationships using coordinate geometry and other representational systems. Conversations Demonstrations Stories (Acting out/Making Models) Poems Songs
- 23. Coordinate Geometry and Other Representational Systems Terminology: Over/Under Far/Near Next to Inside/Outside - Closed Shapes Only Above/Below - For 2D (Label paper “top”) Right/Left - Direction Up/Down Forward/Backward
- 24. Activity: Poetry Geometry Read Five Little Chickens Students manipulate objects to match poem. Read Monkey March Students act out the poem.
- 25. Coordinate Geometry and Other Representational Systems Research shows that students as early as 3 years old can build simple 3D maps (Blaut and Stea in 1974) Technology can also support this concept: Can You Get the Turtle to the Pond? Illuminations.nctm.org Click I-Math investigation Click turtle and pond icon. E-example 4.2 Navigating Paths and Mazes (Part 1) Students can learn orientation, directions, and measurement concept.
- 26. Transformational Geometry Apply transformations and use symmetry to analyze mathematical situations. Recognize and apply slides, flips, and turns. Recognize and create shapes that have symmetry.
- 27. Transformational Geometry Apply transformations and use symmetry to analyze mathematical situations. Recognize and apply slides, flips, and turns. 4 and 5 year old students can move objects to determine whether they are the same or identical to other shapes (Congruent)
- 28. Activity: Transformational B-I-N-G-O Geometry Each student plays on one transformational bingo card. As the teacher places one shape on the overhead, if the student has that shape on their board, they cover it with a marker.
- 29. Terminology Sl ide/Tran sl ation “ An image is formed by moving every point on a figure the same distance the same direction.” Geometry To Go
- 30. Terminology Fl ip/Re fl ection: “ a figure is flipped over a line called the line of reflection. All corresponding points in the image and preimage are equidistance from the line of reflection.” Geometry To Go
- 31. Terminology Ro t ation/ T urn : “ The image is formed by turning it’s preimage about a point.” Geometry To Go
- 32. Terminology Congruent - Changing the shape’s position or orientation but not it’s shape or size. Any of the basic transformations creates a congruent shape.
- 33. Transformational Geometry Solving puzzles Technology - Illuminations Website Kid Pix Deluxe 3 (The Learning Company 2000) Geometer’s Sketch Pad
- 34. Activity: 5 Squares Use 5 square tiles. Place the squares side by side to find all the possible composite shapes. How will you know if it is a different shape?
- 35. Transformational Geometry Recognize and create shapes that have symmetry Research by Clements (2000) shows that vertical symmetry develops earlier and continues to be easier for young students to see than horizontal.
- 36. Activity:Easter Eggs Use watercolors, color 1/2 of the “Easter egg”. Fold over the line of symmetry to create the other side.
- 37. Visualization and Spatial Reasoning Create mental images of geometric shapes using spatial memory and spatial visualizations; Recognize and represent shapes from different perspectives Relate ideas in geometry to ideas in number and measurement Recognize geometric shapes and structures in the environment and specify their location.
- 38. Visualization and Spatial Reasoning Visualization - the ability to construct one or more images and/or directions within the mind. First - Static Eventually be able to manipulate in the mind.
- 39. Visualization and Spatial Reasoning Ties to other areas of mathematics: Quickly recognize a set Commutative Property
- 40. Research Clements and Battista in 2000 states: “Positive correlation’s have been found between spatial ability and mathematics achievement at ALL grade levels.”
- 41. Ideas for Building Visualization Skills 1st - Building and Manipulating Concrete Objects: Use of tangrams, pattern blocks, and other concrete materials. 2nd - Mental Representations Quick Images
- 42. Ideas for Building Visualization Skills Mentally think about a square, what would you get if you cut the square in half from diagonal to diagonal? Think about a circle, what would the shape look like if you cut it in half? Draw what you see. “Quick images”
- 43. Activity: Enhancing Visualization Place objects/pictures on overhead. Turn overhead on and off quickly. Ask students to draw what they saw. Images can be modified after another quick glance. Teacher Questions: “ What did you see?” “ How did you decide what to draw?”
- 44. Recognize geometric shapes and structures in the environment and specify their location. Look for geometric shapes in nature and in the world in which we live.
- 45. Activity: Face Cards Students copy the face of each 3-D shape onto a tag board. Pairs share their tag board and shapes with other students to guess which shape goes with each tag board.
- 47. Review of Geometric Concepts Two and Three Dimensional Shapes Sort shapes into: Circles, Rectangles (excluding the square), and Triangles Describe the properties (# of sides, angles, congruent length) of the basic shapes using their own vocabulary. Take apart a shape and describe the shapes that made up the whole. Coordinate Geometry and Other Representational Systems Specify locations and describe relationships using terminology such as: under/below, right/left, etc. Transformational Geometry Recognize and apply slides, flips and turns. Recognize and create shapes that have symmetry. Visualization and Spatial Reasoning Recognize and represent shapes mentally. Recognize geometric shapes from a variety of perspectives.
- 49. For more information … www.lulu.com (search Michelle Flaming) Contact me at [email_address] Thank you for joining me in PreK-2 Math Foundations