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Hands on Geometry for K-2 Learners
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Hands on Geometry for K-2 Learners

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Activities and strategies to help teachers engage K-2 learners with geometric concepts

Activities and strategies to help teachers engage K-2 learners with geometric concepts

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  • 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.
  • 46.  
  • 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.
  • 48. Student Interviews
  • 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