• # Algebra Conic Parabola Equation Derivation

Parabola

Definition:  all points whose perpendicular distances from them to the directrix equals the distances from them to the focus.

We'll use these properties from the … more

• # Algebra Conic Section Applications

CONIC SECTIONS APPLICATIONS

The parabola has an electromagnetic signal reflection property. Four signals are shown in green and blue. These signals are shown with arrows on both ends to indicate … more

• # Algebra Conics Circle Explanation

Circle

In the following figure we are passing a plane (red cross hatch) from the front to the back of the cone. And we are doing this parallel to the base … more

• # Algebra Conics Hyperbola Introduction

Hyperbola

The hyperbola is created when the intersecting plane is not parallel to an edge of the cone. The following diagram illustrates this intersection, the hyperbola. Although the diagram … more

• # Algebra Conics Introduction

Introduction to Conic Sections

Conic Sections

A conic section or more simply, conic, is the intersection of a plane and a right circular conical surface. This intersection is a curve (or curves) … more

• # Algebra Conics Parabola Introduction

Parabolas

The intersection of a plane parallel to the edge of a nappe of a cone is called a parabola.

The red dashed lines are parallel, one is along the edge of the cone and the other is in the … more

• # Algebra Distance Rate Time

Distance, Rate and Time

Distance is a measurement that answers “how far?”

Time measures the length of time to travel that distance and answers “how long?”

Rate is a … more

• # Angle Definition and Construction

Angles

Definition: An angle is the shape created in a plane when two rays share the same endpoint.  Below we see the plane P that contains two rays, a and b, that share the same endpoint V.& … more

• # Calendaring

Learn to use a calendar.

Calendaring lesson plans, printables, and additional resources coming soon!

• # Cartesian Coordinate System

Cartesian Coordinate System in Geometry

Coordinate Systems

Suppose we have these points in the plane:

We can see that they are spatially related. First of all they are all in the same … more

• # Algebra Conic Ellipse Equation Derivation

Derivation of the Ellipse Equation

Study the following diagram for an ellipse:

Recall the definition of an ellipse requires that d₁ + d₂ = 2a.

Let (x,y) be the coordinates for the point P. In … more

• # Conic Intersections - Advanced Examples

Solving Conic Intersections

1) Plot:

x2 -6x + y2 +4y + 4 = 0

Complete the square to get standard form. … more

• # Conics Ellipse Introduction

This figure shows a plane slicing a right circular cone at an angle, β, greater than 900 measured from the the axis of the cone.

When β starts at 900 the plane slices the cone parallel … more

• # Counting

Definition: The ability for a student in 1st grade to recognize the proper sequence of base 10 numbers.

Basics:

What is base 10 math?

What are the order … more

Common Core: Grade 1, Number and Operations in Base Ten

• # Decimals

Tags: decimal, number, math concept

Decimals

Decimals are numbers written using 10 as the base.  Each position of the decimal number represents a power of 10 and the decimal point, the period '.',  is used to … more

Common Core: Grade 2, Number and Operations in Base Ten

• # Derivatives

Question:

Can anyone take the first and second derivatives of y=3x2/3 –  x2 ?

1st and 2nd derivatives by repeated application of the exponent rule

& … more

• # Algebra Lines

Tags: lines, equation, algebra, math concept

Equations of the Line

For pre-algebra students, focus on the slope intercept form; the others will be addressed in Algebra 1 and  Algebra 2.

… more

• # Geometry Circles Definition

Exploring Circles

This circle explanation is the basis for teaching advanced 6th grade Geometry concepts including Radius, Diameter, pi (π), Perimeter, and Circumference.  … more

• # Geometry Circles Pi Estimation

Exploring Circles - Hexagon and Triangle estimation  of   π

The following shows the hexagon and triangle estimation technique for the value of π.  Right click on … more

• # Geometry Circles Pi Estimation and Radians

Exploring Circles - Explanation of radians and π

Right click on the image below and save it to your desktop, then print off the circle teaching resource for your students.

& … more

• # Geometry Deductive Reasoning

A mathematical theorem is a statement that can be proved using deductive reasoning.

This theorem is stated within a mathematical model that has

& … more

• # Geometry Line Ray and Segment Definitions

Tags: line segment, ray, line, math concept

Line Segment, Ray, and Line Definitions

Line Segment: the shortest path between two points Q and R. We visualize this segment as a trace without bends, that is drawn straight between Q and R. … more

• # Geometry Similar Triangles

Two triangles are similar if:

1) the corresponding angles of the first in the second are the same, or

2) the ratios of corresponding sides of the two triangles are equal

… more

• # Algebra Integers Part 4 Properties

Properties of Integers

The set of Integers obey certain properties that are used heavily in algebraic manipulations. We'll investigate each now.

A.   Well Ordered Set

Each … more

• # Integer Addition Mixed Numbers

Operations with Integers:

Remembering the debit/credit analogy for negative and positive numbers, it would make sense that debits should add to a larger debit, and credits should add to a larger … more

• # Introduction to Integers

Tags: algebra, integers, math concept

Introduction to IntegersThe Natural numbers are those numbers with which we first became aware, "I have 1 marble, 2 jacks, 9 pennies..." We then had to add the place holding number "0& … more

• # Irrational Numbers

Irrational Numbers

...are numbers that cannot be expressed as the ratio of two integers.   See rationals.

One of the first irrational numbers discovered was √2.  The Greeks … more

Common Core: Grade 8, The Number System

• # Irrational Numbers

Irrational Numbers

...are numbers that cannot be expressed as the ratio of two integers.   See rationals.

One of the first irrational numbers discovered was √2.  The Greeks … more

Common Core: Grade 8, The Number System

• # Least Common Multiple

Least Common Multiple

The least common multiple (lcm) of two or more integers, is the number all these integers divide.

Procedure:   to find the lcm

1.& … more

• # Line Properties

Line Properties

Line property 1: two distinct lines in a plane either intersect in exactly one point in the plane or do not intersect and are parallel.

Line property 2: through any given point … more

• # Line Properties Orthogonal

Line Property Orthogonal Lines

Line property 4: if two lines are parallel (notation: L1 || L2), then from a given point on one line there exists a shortest line segment whose other endpoint lies … more

• # Linear Systems

Linear systems of equations are equations whose variables have exponen

Linear systems of equations are equations whose variables have exponents equal to one, and the system contains one equation … more

• # Money

Money

Teaching your child about money reinforces the basic number facts of the base 10 number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.   At first, for younger … more

• # Multiplication

Multiplication

The signs used for multiplication are x and ·

2 x 3 means to add 2 to itself 3 times: 2 + 2 + 2 = 6

-3 · 2 means to add -3 to itself 2 times: -3 + -3 = -6

4 x -2 … more

• # Multiplication

Multiplication of Integers

'•'  means multiply  2 • 3  = 2 x 3 = 6

2 • 3  means  to add 2 to itself 3 times: 2 + 2 + 2 = 6

-3 • … more

• # Point Definition

Tags: point, line, pythagoras, math concept

Point Definition

Point: Pythagoras defined a point as "unity with position." For the purposes of planar geometry, a point is location in the plane. More practically, a point is a dot on … more

• # Positive and Negative Operations

Operations with Integers:

Remembering the debit/credit analogy for negative and positive numbers, it would make sense that debits should add to a larger debit, and credits should add to a larger … more

• # Pythagorean Theorem Proofs

Pythagorean Theorem

In a right-angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a² + b²  = c²

Various … more

• # Rational Numbers

Rational Numbers

A rational number is any number that can be represented by the ratio of two integers.

Examples:

, , ,

The horizontal bar is … more

• # Rotating Circles Solution

Exploring Circle Rotation

Question: Two circles(r1, r2) of radius 10, and 25 are touching each other and spins without slippage. when r1 is spinning at 50 rpm, at what rpm is r2 … more

• # Algebra Areas Circles Triangles Rectangles

Areas of Circles, Triangles and Rectangles

(Review Measurement before proceeding.)

The area of a rectangle, shown below, is  its length multiplied by its width.  For example if its … more