Geometry presentation

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

2. - 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. What is Geometry?

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

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

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

11. 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. Angles

12. A Protractor. Measure Angles with…

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

14. Are Parallel and equal 180 degrees. Zero Angles

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

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

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

18. Angles equal to two right angles. Straight Angle

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

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

21. PLANE FIGURES!

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

23. 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. Definition

24. 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. Kinder to 2nd Grade

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

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

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

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

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

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

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. 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. 2nd to 4th Grade

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

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

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

36. Making Flags

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

38. 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. 4th to 8th Grade

39. 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. 4th to 8th Grade

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

41. Using Dot Paper

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

43. Types of Triangles                         Equilateral Triangle Three equal sides Three equal angles, always 60°                         Isosceles Triangle Two equal sides Two equal angles                         Scalene Triangle No equal sides No equal angles                         Acute Triangle All angles are less than 90°                         Right Triangle Has a right angle (90°)                         Obtuse Triangle Has an angle more than 90°                         Right Isosceles Triangle Has a right angle (90°), and also two equal angles

44. Types of Quadrilaterals

45. 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. Make A Rule

46. Space Figures!

47. 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 EDGE FACE VERTEX Space Figures!

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

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

53. Symmetry

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

55. Something that is not symmetrical. As ymmetry

56. Symmetry in Planes

57. Symmetry in Space

58. Any Questions?