GEOMETRY

Presented by: Barbara Taijeron

Jamie Monaghan

Marvin Monaghan

Billy Neveready

- 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?

Basic Concepts of Lines, Rays, and Angles.

Lines!Different

Types:LineLine

SegmentRayPerpendicula

rParallelIntersecting

LineHas no beginning or end.

Continues indefinitely in both directions.

Can be illustrated by drawing arrows at each end.

Line SegmentHas a beginning point and an end

point.

Line segments on a shape are called sides.

Can be found in many shapes.

RayHas a beginning point but no end point.

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

Parallel

Two or more lines that meet at a point.

Intersecting

Perpendicular lines form a right or 90 degree angle.

Perpendicular

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

A Protractor.

Measure Angles with…

Zero Angles

Right Angles

Acute Angles

Obtuse Angles

Straight Angles

Supplementary Angles

Complimentary Angles

Different Angles

Are Parallel and equal 180 degrees.

Zero Angles

Two rays that create a 90 degree angle.

Right Angle

Two rays that have a smaller angle than a right angle.

<90 Degrees

Acute Angle

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

Obtuse Angle

Angles equal to two right angles.

Straight Angle

Two angles that sum to a straight angle

Supplementary Angles

Two angles that sum to one right angle

Complimentary Angles

PLANE FIGURES!

Teaching Shapes From: Kindergarten to 2nd

Grade2nd Grade to 4th Grade4th Grade to 8th Grade

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.

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 10Should start to examine the

number of sides and angles of some plane figures.

Concrete Have students sort out different shapes

that are familiar to them.

PictorialHave students count the sides on each

shape.Connect dots on paper that will form a

shape.

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.

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.

ConcreteHave students compare different

sizes and shapes of triangles, squares, rectangles, and circles.

PictorialHave students take the different shapes

to form another shape.Have students practice making shapes

on a Geoboard.

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

SymbolicSome shapes can be used to form

another shape.Two shapes that are different

sizes can be the same shape.

Size and ShapeChildren need to be well grounded in these concepts

before going on to high school.

Classifying ShapesShould 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.

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.

Pictorial (Size & Shape)Use dot paper or geoboard to illustrate

different size and shapes.

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Quadrilateral - a plane figure having four sides and four angles.

Parallelograms - a quadrilateral having both pairs of opposite sides parallel to each other.

                

      

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

SymbolicHave 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

EDGEFACE

VERTEX

Space Figures!

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

Activity

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

you see.

I have a Name!

Tesselation!

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

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

Symmetry

Line of Symmetry

Something that is not symmetrical.

Asymmetry

Symmetry in Planes

Symmetry in Space

Any Questions?