Stage Three: Angles (Straight, Obtuse, Acute, and Right)

Angles Introduction

Angles are two rays with the same endpoint. They measure the rotation of these rays which are considered the sides of the angle. These rays have a common endpoint which is called the vertex. 

Angles can be a hard concept to understand when measuring, so it is important to know those fundamental building blocks of geometry: points, lines, and planes. When I was younger, I struggled a lot to understand angles and geometry in general for that matter. Without understanding the building blocks, you cannot understand geometry. 

Straight, Obtuse, Acute, and Right Angles

There are a few different types of angles to remember: straight, obtuse, acute, and right. A straight angle is exactly 180 degrees and an obtuse angle is greater than 90 degrees but less than 180 degrees. An acute angle is less than 90 degrees and a right angle is exactly 90 degrees.

A trick you can use to help your students remember the differences between these angles is to associate the pronunciation of the words with its meaning. OBtuse angles are big while acute angles are cute and small. Straight angles can only be 180 degrees while right angles can only be 90 degrees so they should be easier to comprehend.

WEBSITE: http://www.mathsisfun.com/angles.html

Stage Two: Polygons and Polyhedrons

Polygons

After teaching the building blocks of geometry, I like to focus on polygons and polyhedrons. A polygon is a simple, closed curve with sides that are line segments. What are simple and closed curves?

Simple curve = a curve that does not cross itself

Closed curve = a curve that starts and stops at the same point

Here are examples of polygons and the number of sides they have:

With polygons, we also look at convex and concave curves:

Convex curves are simple, closed curves such that the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve. Concave curves are simple, closed curves that are not convex meaning that it is possible for a line segment connecting two interior points to cross outside the interior of the curve.

Polyhedra

A polyhedron is a simple closed surface made up of polygonal regions, or faces. Faces are flat surfaces that forms part of the boundary of an object. Vertices are the points an object has and edges are particular line segments that join the vertices.

To find the relationship between these parts of a polyhedron, we use the formula:

VERTICES + FACES - EDGES = 2 or V + F - E = 2

WEBSITE: http://world.mathigon.org/Polygons_and_Polyhedra