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The Mathematical Foundations of Music 150 150 Deborah

The Mathematical Foundations of Music

Algebra and Geometry in Music? The mathematical foundations of music involve algebra and geometry, in a complex relationship that has been known for thousands of years.  Ancient mathematicians from China to Greece were interested in the relationship between music, nature, and numbers.  The acoustics of sound show the mathematical relationships that underlie pitch, loudness, and…

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Let’s Do a Pre-Algebra Review of Inequalities 150 150 Deborah

Let’s Do a Pre-Algebra Review of Inequalities

Overview:  What Are Inequalities? Most of the time, in order to solve problems in pre-algebra or algebra, students use equations, where number sentences are exactly equal.  However, some number sentences use expressions that are inequalities, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal…

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Sines, Cosines, and Tangents 150 150 Deborah

Sines, Cosines, and Tangents

Overview:  Introduction to Trigonometric Functions An angle is formed when a ray is rotated in a coordinate plane around the x axis (the horizontal axis).  The measurements of the length of the sides of a triangle have a special relationship to one another, called the sine, the cosine, and the tangent.  They are ratios, similar…

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How to: Factoring Square Trinomials 150 150 Deborah

How to: Factoring Square Trinomials

Overview:  What Are  Square Trinomials? Square trinomials are polynomials in the form ax2 + bx +c.  They have three terms, with the highest degree a squared exponent.  They are factored by multiplying binomials. Perfect Square Trinomials A perfect square trinomial is the exact square of a trinomial.  There are two conditions they follow.  The first…

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Biology in Action: Newly Discovered Fish Species 150 150 Deborah

Biology in Action: Newly Discovered Fish Species

Overview:  Newly Discovered Carp Found in Turkey In March 2013, a new type of freshwater fish was discovered in a stream inside Turkey.   It belongs to the largest family of fish that live in fresh water, the carp or Cyprinidae.  This family of fishes include goldfish, koi, and many different fish that are used for…

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Sentence Fragments and Run-On Sentences 150 150 Deborah

Sentence Fragments and Run-On Sentences

Overview:  Opposite Writing Errors Both sentence fragments and run-on sentences are writing errors that occur when writers aren’t careful about punctuation.  Although they may seem totally  different, they are really just opposites of the same type of error.  It is important to know when one sentence ends and a new one begins. What Is a…

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Prime Numbers and Factorization 150 150 Deborah

Prime Numbers and Factorization

Overview:  What Are Prime Numbers? The definition of a prime number is any number greater than one that can only be divided evenly by 1 and itself..  Therefore, 2 is a prime number because its only factors are 1 and 2, and  3 is a prime number because its only factors are 1 and 3. …

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Biology in Action: The Mystery of Eye Color 150 150 Deborah

Biology in Action: The Mystery of Eye Color

Overview:  Genetic Variation and Eye Color Eye color is determined by a number of genes that control the amount of pigmentation in the iris.  There are no blue or green pigments that determine eye color.  The amount of pigmentation controls the reflection of light from the iris, and the amount of light scatter governs the…

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Math Basics: Using Percents 150 150 Deborah

Math Basics: Using Percents

Overview:  What Are Percents? A percent is a special ratio that literally means “per 100.”  Therefore 5% is 5/100 or .05, 25% is 25/100, or .25, 200 % is 200/100 or twice as much, and so on.  In grade school students learn they can think of percent as how many cents of a dollar when…

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A Chemistry Lesson: Making Glass Flexible, Strong, and Tough 150 150 Deborah

A Chemistry Lesson: Making Glass Flexible, Strong, and Tough

Overview: What Is Glass? Glass is a peculiar state of matter with some of the properties of a solid and some of a liquid.  The scientific definition of “glass” refers to a solid structure in which the molecules do not form crystals but flow over one another.  In addition, when the substance is heated, rather than…

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