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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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• ### Transcript

• 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.
• 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
• Students manipulate objects to match poem.
• 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)
• 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
• 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