MAE3270 Module 6 - Lecure 1: Geometry

Chapter 1: Introduction

Students develop understanding of size, shape, relative position, and movement of 2D and 3D objects
Students investigate properties, define, compare, and construct figures and objects
Students develop geometric arguments and make meaningful measurements
Plane Geometry is about flat shapes/figures (2D)
Solid Geometry is about solid objects (3D)

Students can recognize and identify shapes with 4 sides
They can name a rectangle and identify that b is not a rectangle
Shapes a and b have corners, but b looks lopsided
Students in middle to upper primary can identify that both shapes have 4 sides, edges, corners, and vertices
Shape a has perpendicular sides and right angles
Shape b consists of 2 pairs of parallel sides, but they are not perpendicular
Angles and opposite sides of shape a are equal, but they are not congruent
In upper primary to secondary, students identify that both shapes are parallelograms
Shapes have the same height, area, opposite angles, and rotational symmetry

Year 3:
- students make models of 3D objects and describe key features
In year 4:
- they compare area of regular and irregular shapes
In year 5:
- they connect 3D objects with their nets and other 2D representations
In year 6:
- they construct simple prisms and pyramids

Shapes have 0, 1, 2, or 3 dimensions
Vertices are corners, edges are line segments between faces, and faces are single flat surfaces
Shapes can be convex or concave based on the interior angles

Year 3:
- create and interpret simple grids
Year 4:
- use simple scales, legends, and directions to interpret information
- create symmetrical patterns, shapes, and pictures
Year 5:
- use a grid reference system
- describe routes using landmarks and directional language
- describe translations, reflections, and rotations
- identify line and rotational symmetry
- apply enlarging transformations to 2D shapes
Year 6:
- investigate combinations of different transformations
- learn about the Cartesian coordinate system