GEOMETRY Presented by: Barbara Taijeron Jamie Monaghan Marvin Monaghan Billy Neveready
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.
Basic Concepts of Lines, Rays, and Angles.
Lines! Different Types: Line Line Segment Ray Perpendicular Parallel Intersecting
Line Has no beginning or end. Continues indefinitely in both directions. Can be illustrated by drawing arrows at each end.
Line Segment Has a beginning point and an end point. Line segments on a shape are called sides. Can be found in many shapes.
Ray Has a beginning point but no end point.
Parallel Lines in the same plane that do not intersect or cross each other.
Intersecting Two or more lines that meet at a point.
Perpendicular Perpendicular lines form a right or 90 degree angle.
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.
Measure Angles with… A Protractor.
Different Angles Zero Angles Right Angles Acute Angles Obtuse Angles Straight Angles Supplementary Angles Complimentary Angles
Are Parallel and equal 180 degrees. Zero Angles
Two rays that create a 90 degree angle. Right Angle
Acute Angle Two rays that have a smaller angle than a right angle. <90 Degrees
Angles larger than a right angle and smaller than two right angles. >90 Degrees Obtuse Angle
Straight Angle Angles equal to two right angles.
Two angles that sum to a straight angle Supplementary Angles
Complimentary Angles Two angles that sum to one right angle
Plane Figures Teaching Shapes From: Kindergarten to 2nd Grade 2nd Grade to 4th Grade 4th Grade to 8th Grade
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.
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.
Kinder to 2nd Grade Concrete Have students sort out different shapes that are familiar to them.
Kinder to 2nd Grade Pictorial Have students count the sides on each shape. Connect dots on paper that will form a shape.
Count The Sides 1 2 4 3 This Shape Is A Square
Count The Sides 1 2 3 This Shape Is A Triangle
Count The Sides 1 2 4 3 This Shape Is A Rectangle
Count The Sides No Sides 0 This Shape Is A Circle
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
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.
2nd to 4th Grade Concrete Have students compare different sizes and shapes of triangles, squares, rectangles, and circles.
2nd to 4th Grade Pictorial Have students take the different shapes to form another shape. Have students practice making shapes on a Geoboard.
Using Geoboard http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities
Make A Rule Symbolic Some shapes can be used to form another shape. Two shapes that are different sizes can be the same shape.
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.
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.
4th to 8th Grade Pictorial (Size & Shape) Use dot paper or geoboard to illustrate different size and shapes. . . . . . . . . . . . . . . . . . .
Using Dot Paper
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.
Types of Triangles
Types of Quadrilaterals
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.
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
Activity Take out the papers in front of you and construct each container you see.
Activity! Take out the papers in front of you and make each item you see.
I have a Name!
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
Symmetry is having two sides of a whole look like they reflect each other. Symmetry Line of Symmetry