Geometry is the branch of mathematics concerned with properties of points, lines, angles, curves, surfaces and solids. It involves visualizing shapes, sizes, patterns and positions. The presentation introduced basic concepts like different types of lines, rays and angles. It also discussed plane figures from kindergarten to 8th grade, including classifying shapes by number of sides. Space figures like cubes and pyramids were demonstrated by having students construct 3D models. The concepts of tessellation, symmetry, and line of symmetry were explained.

1. GEOMETRY Presented by: Barbara Taijeron Jamie Monaghan Marvin Monaghan Billy Neveready

2. What is Geometry? - the branch of mathematics that is concerned with the properties and relationships of: - points, lines, angles, curves, surfaces, and solids. - The visual study of shapes, sizes, patterns, and positions.

3. Basic Concepts of Lines, Rays, and Angles.

4. Lines! Different Types: Line Line Segment Ray Perpendicular Parallel Intersecting

5. Line Has no beginning or end. Continues indefinitely in both directions. Can be illustrated by drawing arrows at each end.

6. Line Segment Has a beginning point and an end point. Line segments on a shape are called sides. Can be found in many shapes.

7. Ray Has a beginning point but no end point.

8. Parallel Lines in the same plane that do not intersect or cross each other.

9. Intersecting Two or more lines that meet at a point.

10. Perpendicular Perpendicular lines form a right or 90 degree angle.

11. Angles Made up of two rays with the same start point. The start point is called the vertex. The two rays are called the sides of the angle.

12. Measure Angles with… A Protractor.

13. Different Angles Zero Angles Right Angles Acute Angles Obtuse Angles Straight Angles Supplementary Angles Complimentary Angles

14. Are Parallel and equal 180 degrees. Zero Angles

15. Two rays that create a 90 degree angle. Right Angle

16. Acute Angle Two rays that have a smaller angle than a right angle. <90 Degrees

17. Angles larger than a right angle and smaller than two right angles. >90 Degrees Obtuse Angle

18. Straight Angle Angles equal to two right angles.

19. Two angles that sum to a straight angle Supplementary Angles

20. Complimentary Angles Two angles that sum to one right angle

21. PLANE FIGURES!

22. Plane Figures Teaching Shapes From: Kindergarten to 2nd Grade 2nd Grade to 4th Grade 4th Grade to 8th Grade

23. Definition Plane Figure: A two-dimensional shape (2D). A shape on a plane. Includes points, lines, polygons, circles, triangles, hexagon, pentagons, etc. A plane figure is any set of points on a plane.

24. Kinder to 2nd Grade Familiarize children with different shapes. Classify and categorize shapes. Observe and listen to gain insight on the children’s level of reasoning. Refer to square as a square, and a rectangle is a rectangle. Counting to 10 Should start to examine the number of sides and angles of some plane figures.

25. Kinder to 2nd Grade Concrete Have students sort out different shapes that are familiar to them.

26. Kinder to 2nd Grade Pictorial Have students count the sides on each shape. Connect dots on paper that will form a shape.

27. Count The Sides 1 2 4 3 This Shape Is A Square

28. Count The Sides 1 2 3 This Shape Is A Triangle

29. Count The Sides 1 2 4 3 This Shape Is A Rectangle

30. Count The Sides No Sides 0 This Shape Is A Circle

31. Symbolic A square has 4 sides that are the same. A triangle has 3 sides. A rectangle has 4 sides. A circle has no sides. Make A Rule

32. 2nd to 4th Grade Child’s perception matures and can handle mathematical reasoning. Explore relationship between size and shape. Most children will claim that all triangles have the same shape. Have them explore to see that this concept is not true.

33. 2nd to 4th Grade Concrete Have students compare different sizes and shapes of triangles, squares, rectangles, and circles.

34. 2nd to 4th Grade Pictorial Have students take the different shapes to form another shape. Have students practice making shapes on a Geoboard.

35. Using Geoboard http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities

36. Making Flags

37. Make A Rule Symbolic Some shapes can be used to form another shape. Two shapes that are different sizes can be the same shape.

38. 4th to 8th Grade Size and Shape Children need to be well grounded in these concepts before going on to high school. Classifying Shapes Should engage in many classifying tasks. build criteria that accurately defines sets of shapes. A square is a rectangle, a parallelogram, and quadrilateral. Introduce different terms of shapes.

39. 4th to 8th Grade Concrete (Size & Shape) Have cut outs of different sized shapes. Ask students to show you: Same shape and size. Same shape, not same size. Same size, not same shape. Different shape, different size.

40. 4th to 8th Grade Pictorial (Size & Shape) Use dot paper or geoboard to illustrate different size and shapes. . . . . . . . . . . . . . . . . . .

41. Using Dot Paper

42. Introduce Terms Quadrilateral- a plane figure having four sides and four angles. Parallelograms - a quadrilateral having both pairs of opposite sides parallel to each other.

43. Types of Triangles

44. Types of Quadrilaterals

45. Make A Rule Symbolic Have all the name of the shapes and have them come up with a rule for each. Example: Triangle – has 3 sides. Equilateral Triangle– has 3 equal sides.

46. Space Figures!

47. Space Figures! Space figures are three dimensional figures. Faces: Side of the space figure Edges: Where two faces meet Vertex or Vertices: the corners of the space figures VERTEX EDGE FACE

48. Activity Take out the papers in front of you and construct each container you see.

49. Activity! Take out the papers in front of you and make each item you see.

50. I have a Name!

51. Tesselation!

52. Repeating a shape over and over and over and over and over and over again, leaving no gaps between each shape to form a BIGGER shape. Another word for “tesselation” is TILING! Tesselation

54. Symmetry

55. Symmetry is having two sides of a whole look like they reflect each other. Symmetry Line of Symmetry

56. Something that is not symmetrical. Asymmetry

57. Symmetry in Planes

58. Symmetry in Space

60. Any Questions?