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

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