Tag Archives: Algebra Works

Parabolas all have the same basic “U” shape.

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1 There are only three colors, ten digits, and seven notes, it’s what we do with them that’s .

The Babylonians

It all started around 3000 BC with the Babylonians. They were one of the world’s first civilisations, and came up with some great ideas like agriculture, irrigation and writing. They plotted the paths of the Sun, the Moon and the planets, and recorded them on clay tablets (which you can still see in the British Museum). To the Babylonians we owe the modern ideas of angle, including the way that the circle is divided up into 360 degrees (owing to a small miscalculation, one per day). We also owe the Babylonians for the rather less pleasant invention of the (dreaded) taxman. And this was one of the reasons that the Babylonians needed to solve quadratic equations.

if $x$ is the length of the side of the field, $m$ is the amount of crop you can grow on a square field of sidelength 1, and $c$ is the amount of crop that you can grow, then

\[ c = m x^2. \]

 Quadratic equations and areas are linked together like brothers and sisters in the same family. However, at the moment we don’t have to solve anything – until the tax man arrives, that is! Cheerily he says to the farmer “I want you to give me $c$ crops to pay for the taxes on your farm.” The farmer now has a dilemma: how big a field does he need to grow that amount of crop? We can answer this question easily, in fact

\[ x = \sqrt { \frac{c}{m} }. \]

01 uses of a quadratic equation

 

William Glasser’s Choice Theory We all make choices according to basic needs that come from within ourselves. The needs drive our choices and influence how we behave in those choices.
Survival O Physiological O The need for food, shelter, safety O Safe from bullying Schools should be a safe environment from bodily harm, mental or physical intimidation, abuse.

5 Basic Needs (according to Glasser) o Fun o Freedom o Power o Belonging o Survival

 

Recognizing Factoring Patterns

Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth’s orbit.

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The numbers -15, -5, -3, -1, 1, 3, 5, and 15 are all factors of 15 because they divide 15 without a remainder.
Factoring is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations.

A composite expression is similar in that it can be written as the product of two or more expressions. For example: x2 + 3x + 2 is composite because it can be written as (x + 1)(x + 2). (Recall that the FOIL Method shows that (x + 1)(x + 2) is equivalent to x2 + 3x + 2.) Here, (x + 1) and (x + 2) are factors of x2 + 3x + 2.

In general, a number is a factor of another number if the first number can divide the second without a remainder. Similarly, an expression is a factor of another expression if the first can divide the second without a remainder.

Definition

A prime number is a number greater than 1 which has only two positive factors: 1 and itself. For example, 11 is a prime number because its only positive factors are 1 and 11.

Factoring is a process by which a the factors of a composite number or a composite expression are determined, and the number or expression is written as a product of these factors. For example, the number 15 can be factored into: 1 * 15, 3 * 5, -1 * -15, or -3 * -5. The numbers -15, -5, -3, -1, 1, 3, 5, and 15 are all factors of 15 because they divide 15 without a remainder.

Factoring is an important process in algebra which is used to simplify expressions, simplify fractions, and solve equations. The next few lessons explain how to factor numbers, expressions, and equations.

  1. Factoring Numbers — Start Here
  2. Finding a Greatest Common Factor
  3. Factoring a GCF from an expression
  4. Factoring a Difference Between Two Squares
  5. Factoring Trinomials
  6. Factoring Completely
  7. Solving Equations by Factoring

Introduction To Factoring

A composite number is a number that can be written as the product of two positive integers other than 1 and the number itself. For example: 14 is a composite number because it can be written as 7 times 2. In this case, 7 and 2 are called factors of 14.

refresh on Solving Equations by Factoring

bany algebra factoring baby algebra

Solving Equations by Factoring babt algebra

refresh on Solving Equations by Factoring

The Golden Arches ® Exposed!

On the blog dy/dan, there was a recent discussion about the shape of a bridge.  One commenter joked about the Golden Arches of McDonald’s as being the most famous parabolas in America.  As I am teaching quadratic modeling in College Algebra right now, I though I would find an equation for these parabolas.  The problem is that the Golden Arches are not parabolas.

To find the equation, I scanned the Golden Arches from a placemat that I found at McDonald’s tonight.  I took the scanned picture and imported it into GeoGebra.  I picked five points on the outside of one arch, and five points inside of the arch.  The picture is below.

giphy

Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape Baby algebra400px-Fountain583b729941d13958d8635aed92e9e7d88742731_f520
 What’s Your Angle
Doors to Math class

Angle- The amount of turn between two straight lines that have a common end point (the vertex).

Baby Algebra for Baby and You: Now Algebra Is for Everyone Paperback – June 19, 2012

Free Down Load College Lesson Plan Prep Hot Sheets

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FREE Download Pre-College Prep Sheets Careful Driving while Black

No greater criminal offender not doing life in Prison Industry

No greater criminal offender not doing life in Prison Industry

Administration: Darrell Issa can’t be trusted On ObamaCare Implementation. In an letter sent Thursday, the administration argues that because of Issa’s history of selective leaks to the media, he can’t be trusted with the materials.Nancy Pelosi has had enough of Darrell Collateral Damage Issa.

House Minority Leader Nancy Pelosi (D-CA) is calling for a high level security briefing on the operations of Darrell Issa (R-CA), the chairman of the House Oversight and Government Reform Committee, in which he would have to be forthcoming about what information he has released and to whom after he got his hands on sensitive documents surrounding HealthCare.Gov. It would then be up to the Department of Justice to make a determination.

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Free Down Load College Lesson Plan Prep Hot Sheets

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research-style-and-usage            calculus 1

sociology

Driving While Black

“Stop and frisk” isn’t just a reality in New York City. New data shows how police target African Americans on highways across America.

 In investigatory stops, a black man age twenty-five or younger has a 28 percent chance of being stopped for an investigatory reason over the course of a year; a similar young white man has a 12.5 percent chance, and a similar young white woman has only a 7 percent chance. And this is after taking into account other possible influences on being stopped, like how you drive. Police focus investigatory stops on younger people, and so as people grow older they are less likely to be stopped in this way. But a black man must reach fifty—well into the graying years—before his risk of an investigatory stop drops below that of a white man under age twenty-five.

Americans Don’t Care What Race Santa Is. Except For Republicans — They Think He’s White

http://www.huffingtonpost.com/2013/12/20/white-santa-poll_n_4475627.html?ir=Black+Voices&ref=topbar

http://www.huffingtonpost.com/2013/12/20/driving-while-black_n_4480611.html?utm_hp_ref=tw

Now Where do drugs come from ?

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Stamp Out Classroom Bullying Meeting Basic Needs Reality Therapy: Power; Love and Belonging; freedom and Fun; Safety

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CLASSROOM STRUCTURE: REALITY THERAPY  As educators become increasingly aware of the prevalence and harm of bullying, there have been major conferences, school-wide programs, and legislation in 47 states intended to curtail it. But a recent study suggests how simple exercises in the classroom, involving just small groups of students at a time, may also have a positive impact.ImageAnchor Charts      Cooperative Learning Resources

Accountable Talk

Cooperative Learning in the Classroom

A Simple Bully Buster: Cooperative Learning

The Best Sites For Cooperative Learning Ideas

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Conflict arises from a discord of needs, drives, wishes, and/or demands. – Wm Glasser ATTENDING TO THE SOCIETAL EMOTIONAL INDIVIDUAL NEEDS FOR ONES OWN SENSE OF HAVING (1) POWER: (2) LOVE AND BELONGING; (3.) FREEDOM; (4) FUN; (5) SAFETY.

 When a Government seizes drug money, where does it go? Where does it end up. The Gov might as well sell the drugs directly–helping to ease the violence associated with dope sells. What’s the difference between the Gov seizing drug money and apportioning drug related property (BACK TO TAXPAYERS) and drug dealers making a living on the drug monies industry? WHICH NEEDS ARE/ARE NOT BEING MET AS CONFLICT EMMERGES?

 (1) POWER: (2)LOVE AND BELONGING; (3.) FREEDOM; (4) FUN; (5) SAFETY.

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