TeXes EC-6 Mathematics - Competency 004 (Geometry and Measurement):

Area of a circle

A = (pi)r2

Complementary angles

Angles that add up to 90 degrees

Similar

If figures have the exact same shapes, even if they do not have the same sizes.

Area of a prism

Multiply the area of the prism's base by its height.

Comparing a variety of objects for measuring -

using body parts, blocks, cubes, etc. to compare to other things.

Comparing objects using standard units -

using standard and metric systems.

Reflection

(also called a flip) - This is known as a transformation that means to reflect an object or to make the figure/object appear to be backwards or flipped. It produces a mirror image of a geometric figure.

Translation

(also called a slide) - simply means moving. Has a direction and a distance.

Rotation

(also called a turn) - This is known as transformation that means a rotation or to turn the shape around. Each one has a center and an angle for movement around a given number of degrees.

Area of a trapezoid

A = 1/2(b1 + b2)h

Scalene Triangle

A polygon with three unequal sides.

Isosceles Triangle

A polygon with two equal sides and two equal angles.

Prism or polyhedron

A three dimensional solid consisting of a collection of polygons - with two congruent, parallel faces and whose lateral (side) faces are parallelograms.

Cube

A three dimensional solid figure.

Parallel lines

Lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point

Perpendicular Lines

Lines that are at right angles (90°) to each other.

Points

Most often considered within the framework of Euclidean geometry, where they are one of the fundamental objects. "that which has no part", an ordered pair of numbers, where the first number conventionally represent the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y.

Radius of a circle

One half of a circles diameter (from the center to the edge).

Metric Unit: Volume Measurement

Units of capacity include milliliters and liters.

Metric Unit: Linear Measurement

Units of length include millimeters, centimeters, meters, and kilometers.

Metric Unit: Measurement of Mass

Units of weight include grams and kilograms.

Volume of a rectangle

V = L x W x H

Angles

When two rays (or lines) share an endpoint, this is formed. Measured in degrees.

Circle

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Comparing using suitable units for specific measurements -

choosing standard units.

Temperature

measured using a thermometer.

Comparing objects by matching -

ordering items based on size

Area of a triangle

A = 1/2bh or A = bh/2

Area of a rectangle

A = L x W

Area of a square

A = s^2

Parallelogram

A four sided polygon with two pairs of parallel sides.

Edge

A line segment where two faces of a three-dimensional figure meet.

Axiomatic structure

A mathematical rule, with a basic assumption about a system allows theorems to be developed. For example, this system could be the points and lines in the plane. Then the axiom would be that given any two distinct points in the plane, there is a unique line through them.

Diameter of a circle

A straight line segment that goes from one edge of a circle to the other side, passing through the center.

Right Angle

An angle that is 90 degrees.

Acute Angle

An angle that measures less than 90 degrees.

Obtuse Angle

An angle that measures more than 90 degrees, but less than 180 degrees.

Types of clocks

Analog and Digital

Supplementary angles

Angles that add up to 180 degrees

Chord

Any segment that goes from one spot on a circle to any other spot (all diameters are these, but these are not all diameters).

Grids

Are usually based on regular polygons: squares, equilateral triangles, and hexagons. Or they can be based on rectangles, parallelograms, and rhomboids.

Volume of a Cylinder

Area of the cylinder's base is multiplied by the height.

van Hiele Level 4 - Rigor

Associated with college level geometry.

Customary Unit: Volume Measurement

Customary units of capacity include teaspoons, tablespoons, cups, pints, quarts, and gallons.

Customary Unit: Linear measurement

Customary units of length include inches, feet, yards, and miles.

Customary Unit: Measurement of Mass

Customary units of weight include ounces, pounds, and tons.

Faces

Each of the plain regions of a geometric body.

Octagon

Eight sided polygon

Perimeter

Finding the distance around the object (think fence).

Pentagon

Five sided polygon

van Hiele Level 3 - Formal Deduction

Focus on higher levels of geometry; using various theorems to teach how two triangles are congruent (e.g. side-angle-side theorem).

In the elementary classroom, geometry should provide:

For the development of the concepts of direction, shape, size, symmetry, congruence, and similarity in using two-dimensional and three-dimensional shapes.

Quadrilateral

Four sided polygon

Equilateral Triangle

If the measurements of all sides of a triangle are equal, it is this kind of triangle.

SSS (side-side-side)

If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

AAS (angle-angle-side)

If two pairs of angles of two triangles are equal in measurement and a pair of corresponding sides equal in length, then the triangles are congruent.

ASA (angle-side-angle)

If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

SAS (Side-angle-side)

If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.

Inductive Reasoning

Involves examining particular instances to come to some general assumptions, is informal and intuitive. Make hypotheses, extend thought patterns, use analogies, and make reasonable conclusions from examining what appears to be in a large enough body of evidence.

Pythagorean Theorom

It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. a^2 x b^2 = c^2

van Hiele Level 1 - Alalysis

Learners begin to talk and notice the properties of the shapes. Teachers can focus on the various components of the geometric shape.

van Hiele Level 0 - Visualization

Learners develop a mental picture of each shape; therefore, teachers need to provide a multitude of good physical examples and non-examples for exploration.

van Hiele Theory

Recognized for its role in describing the levels of thinking associated with the learning of geometry, it has also been developed as a general theory of mathematics education. (Visualization, Analysis, Informal Deduction, Formal Deduction, Rigor)

Volume

Refers to how much space is inside of a three-dimensional, closed container.

Deductive Reasoning

Requires moving from the assumption to conclusion, general to specific. This type of reasoning is used in daily life, for example: "It is raining so I need to take my umbrella to school." Note that the conclusion reached via this method of reasoning are only sound if the original assumptions are actually true.

Hexagon

Six sided polygon

Reasoning Skills

Skills include drawing conclusions using the principles of similarity, congruence, parallelism, and perpendicularity; and using inductive and deductive reasoning.

van Hiele Level 2 - Informal Deduction

Students stop relying on visualization, they now use relationships to make a conclusion. Focus on the firs to levels for students K-8.

Tessellations

The arrangement of polygons that forms a grid, however other shapes may also do this. It is a pattern formed by the repetition of a single unit or shape that, when repeated, fills the plane with no gaps and no overlaps.

Symmetry

The correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point.

Circumference of a circle

The distance around the edge of a circle. C = 2(pi)r or C = (pi)D. Pi is the ratio of a circles circumference to its diameter.

Pi

The ratio of a circles circumference to its diameter. 3.14159...

Triangles

The sum of the angles of this shape equal 180 degrees and has three sided polygons.

Competency 004 (Geometry and Measurement):

The teacher understands concepts and principles of geometry and measurement.

Vertex

The union of two segments or point of intersection of two sides of a polygon.

Congruent Angle

Two angles that are the same size (regardless of how long their rays might be drawn)