8 REACCIONES QUÍMICAS Más Espectaculares

NORMAS DE SEGURIDAD EN EL LABORATORIO

Adding and Subtracting Fractions, Multiplying Fractions, and Dividing Fractions

GAME

MCM, MCD, reducción a común denominador y suma de fracciones

MCM

https://www.youtube.com/watch?v=-Vor5kKN4gI

MCD

https://www.youtube.com/watch?v=RGpZiQ17SH0

Suma de fracciones

https://www.youtube.com/watch?v=8C2sxLPLd48

Quadratic Equations

GAME

Resolución de Problemas: Método de los 8 pasos

MÉTODO DE LOS OCHO PASOS PARA LA RESOLUCIÓN DE PROBLEMAS

DATOS

1. Leer y comprender el problema.
2. Realizar un dibujo esquemático del problema incluyendo los datos conocidos con sus unidades de medida.
3. Escribir los datos conocidos con sus valores y unidades de medida.
4. Escribir las incógnitas, con sus símbolos y unidades de medida.
5. Escribir las fórmulas o ecuaciones que se necesiten.

OPERACIÓN
6. Indicar los pasos a seguir (aplicación de leyes, cambios de unidades, cálculo de variables intermedias, despejar incógnitas, etc...), justificándolos y numerándolos.
7. Realizar las sustituciones necesarias y procedimientos con sus unidades de medida.

SOLUCIÓN
8. Resultado. Interpretación de los resultados obtenidos con sus unidades de medida.

COMPROBACIÓN
+ Dos pasos de control

9. Revisión de todos los pasos en busca de errores.
10. Análisis del resultado o resultados.

Information

1. Read and understand the problem.

2. Make a schematic drawing of the problem, including the known data with its units of measurement.

3. Write down the known data with its values and units of measurement.

4. Write down the unknown data with its symbols and units of measurement.

5. Note down any formulas or equations that are needed.

Operation

6. Indicate the number of steps to follow, i.e. application of laws, changes of units, calculation of intermediate variables, obvious unknown information etc., and justify them.

7. Carry out the necessary method and substitutions with their units of measure.

Solution

8. Result. Interpret the obtained results with their units of measurement.

Checking

+ Two control steps

 9. Review all the previous steps to find any errors.

10. Analyse the result(s).

Solving Linear Equations GAME

GAME

FRACTIONS GAME

GAME

Christmas Reading - HLD

NASA Exercise: Survival on the Moon

ACTIVITY

Scenario: 

You are a member of a space crew originally scheduled to rendezvous with a 

mother ship on the lighted surface of the moon. However, due to mechanical 

difficulties, your ship was forced to land at a spot some 200 miles from the 

rendezvous point. During reentry and landing, much of the equipment aboard 

was damaged and, since survival depends on reaching the mother ship, the 

most critical items available must be chosen for the 200-mile trip. Below are 

listed the 15 items left intact and undamaged after landing. Your task is to 

rank order them in terms of their importance for your crew in allowing them 

to reach the rendezvous point. Place the number 1 by the most important item, 

the number 2 by the second most important, and so on through number 15 for 

the least important. 

Your Ranking NASA Ranking 
 _______ Box of matches _______ 
 _______ Food concentrate _______ 
 _______ 50 feet of nylon rope _______ 
 _______ Parachute silk _______ 
 _______ Portable heating unit _______ 
 _______ Two .45 caliber pistols _______ 
 _______ One case of dehydrated milk _______ 
 _______ Two 100 lb. tanks of oxygen _______ 
 _______ Stellar map _______ 
 _______ Self-inflating life raft _______ 
 _______ Magnetic compass _______ 
 _______ 20 liters of water _______ 
 _______ Signal flares _______ 
 _______ First aid kit, including injection needle _______ 
 _______ Solar-powered FM receiver-transmitter _______ 


Scoring: 
For each item, mark the number of points that your score differs from the 
NASA ranking, then add up all the points. Disregard plus or minus 
differences. The lower the total, the better your score. 

0 - 25 excellent 
26 - 32 good 
33 - 45 average 
46 - 55 fair 
56 - 70 poor -- suggests use of Earth-bound logic 
71 - 112 very poor – you’re one of the casualties of the space program! 
... published in the July 1999 issue of the NightTimes 

Movimiento Rectilineo Uniforme

Polynomials

A polynomial looks like this:

example of a polynomial this one has 3 terms

Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

A polynomial can have:

constants (like 3, -20, or ½)

variables (like x and y)

exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed

that can be combined using addition, subtraction, multiplication and division ...

... except ...

... not division by a variable (so something like 2/x is right out)

So:

A polynomial can have constants, variables and exponents,
but never division by a variable.

Polynomial or Not?

These are polynomials:

3x
x - 2
-6y² - (⁷/₉)x
3xyz + 3xy²z - 0,1xz - 200y + 0,5
512v⁵+ 99w⁵
5

(Yes, even "5" is a polynomial, one term is allowed, and it can even be just a constant!)
And these are not polynomials

• 3xy^-2 is not, because the exponent is "-2" (exponents can only be 0,1,2,...)
• 2/(x+2) is not, because dividing by a variable is not allowed
• 1/x is not either
• √x is not, because the exponent is "½"

But these are allowed:

• x/2 is allowed, because you can divide by a constant
• also 3x/8 for the same reason
• √2 is allowed, because it is a constant (= 1,4142...etc)

Monomial, Binomial, Trinomial

There are special names for polynomials with 1, 2 or 3 terms:

How do you remember the names? Think cycles!

There is also quadrinomial (4 terms) and quintinomial (5 terms),
but those names are not often used.

Can Have Lots and Lots of Terms

Polynomials can have as many terms as needed, but not an infinite number of terms.

Variables

Polynomials can have no variable at all

Example: 21 is a polynomial. It has just one term, which is a constant.

Or one variable

Example: x⁴-2x²+x has three terms, but only one variable (x)

Or two or more variables

Example: xy⁴-5x²z has two terms, and three variables (x, y and z)

What is Special About Polynomials?

Because of the strict definition, polynomials are easy to work with.
For example we know that:

• If you add polynomials you get a polynomial
• If you multiply polynomials you get a polynomial

So you can do lots of additions and multiplications, and still have a polynomial as the result.

You can also divide polynomials (but the result may not be a polynomial).

Degree

The degree of a polynomial with only one variable is the largest exponent of that variable.

Example:

The Degree is 3 (the largest exponent of x)

For more complicated cases, read Degree (of an Expression).

Standard Form

The Standard Form for writing a polynomial is to put the terms with the highest degree first.

Example: Put this in Standard Form: 3x² - 7 + 4x³ + x⁶

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x⁶ + 4x³ + 3x² - 7

POLYNOMIALS OPERATIONS

https://courses.lumenlearning.com/waymakercollegealgebra/chapter/characteristics-of-polynomials/

https://jeopardylabs.com/play/polynomial-operations-8

LEYENDA DEL TABLERO DE AJEDREZ

Reading Fractions

Slice a pizza, and we get fractions:

1/2	1/4	3/8
(One-Half)	(One-Quarter)	(Three-Eighths)

The top number says how many slices we have. 
The bottom number says how many equal slices the whole pizza was cut into.

Some fractions may look different, but are really the same, for example: 

4/8	=	2/4	=	1/2
(Four-Eighths)		(Two-Quarters)		(One-Half)
	=		=

It is usually best to show an answer using the simplest fraction ( ¹/₂ in this case ). That is calledSimplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

NumeratorDenominator

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

1/4	+	1/4	=	2/4	=	1/2
(One-Quarter)		(One-Quarter)		(Two-Quarters)		(One-Half)
	+		=		=

One-quarter plus one-quarter equals two-quarters, equals one-half

Another example:

5/8	+	1/8	=	6/8	=	3/4
	+		=		=

Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

But what about when the denominators (the bottom numbers) are not the same? 

3/8	+	1/4	=	?
	+		=

Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

In this case it is easy, because we know that ¹/₄ is the same as ²/₈ :

3/8	+	2/8	=	5/8
	+		=

Three-eighths plus two-eighths equals five-eighths

Arithmetic and Geometric Sequences

GAME

Addition add(ed) to all together both combined in all increase by more than perimeter plus sum total	Subtraction decreased by difference fewer than how many more left less less than minus remaining take away
Multiplication a area multiplied by of per product of rate times triple twice	Division divided  half how many each out of percent quarter quotient of percent

Solving math word problems

There are two steps to solving math word problems:

1. Translate the wording into a numeric equation
   that combines smaller "expressions"
2. Solve the equation!

Suggestions:

• Read the problem entirely
  Get a feel for the whole problem
• List information and the variables you identify
  Attach units of measure to the variables (gallons, miles, inches, etc.)
• Define what answer you need,
  as well as its units of measure
• Work in an organized manner
  Working clearly will help you think clearly
  • Draw and label all graphs and pictures clearly
  • Note or explain each step of your process;
    this will help you track variables and remember their meanings
• Look for the "key" words (above)
  Certain words indicate certain mathematical operations:

Math expressions (examples):
after you review the keywords, test yourself

addition: 5+x	subtraction: 5-x
multiplication: 5*x; 5x	division: 5 ÷ x; 5/x
Exercise: ("mouse over" the block for answer)
Key words for addition + increased by; more than; combined together; total of; sum; added to
What is the sum of 8 and y?	8 + y
Express the number (x) of apples increased by two	x + 2
Express the total weight of Alphie the dog (x) and Cyrus the cat (y)	x + y
Key words for Subtraction -  less than, fewer than, reduced by, decreased by, difference of
What is four less than y	y - 4
What is nine less than a number (y)	y - 9
What if the number (x) of pizzas was reduced by 6?	x - 6
What is the difference of my weight (x) and your weight (y)	x - y
Key words for multiplication * x or integers next to each other (5y, xy):of, times, multiplied by
What is y multiplied by 13	13y or 13 * y
Three runners averaged "y" minutes. Express their total running time:	3y
I drive my car at 55 miles per hour. How far will I go in "x" hours?	55x
Key words for division ÷ / per, a; out of; ratio of, quotient of; percent (divide by 100)
What is the quotient of y and 3	y/3 or y ÷ 3
Three students rent an apartment for $ "x" /month. What will each have to pay?	x/3 or x ÷ 3
"y" items cost a total of $25.00. Express their average cost:	25/y or 25 ÷ y

More vocabulary and key words:

• "Per" means "divided by"
  as "I drove 90 miles on three gallons of gas, so I got 30 miles per gallon."
  (Also 30 miles/gallon)
• "a" sometimes means "divided by"
  as in "When I filled up, I paid $10.50 for three gallons of gasoline,
  so the gas was 3.50 a gallon, or $3.50/gallon
• "less than"
  If you need to translate "1.5 less than x", the temptation is to write "1.5 - x". DON'T! Put a "real world" situation in, and you'll see how this is wrong: "He makes $1.50 an hour less than me." You do NOT figure his wage by subtracting your wage from $1.50.
  Instead, you subtract $1.50 from your wage
• "quotient/ratio of" constructions
  If a problems says "the ratio of x and y",
  it means "x divided by y" or x/y or x ÷ y
• "difference between/of" constructions
  If the problem says "the difference of x and y",
  it means "x - y"

What if the number (x) of children was reduced by six, and then they had to share twenty dollars? How much would each get?	20/(x - 6)
What is 9 more than y?	y + 9
What is the ratio of 9 more than y to y?	(y + 9)/y
What is nine less than the total of a number (y) and two	(y + 2) - 9 or  y - 7
The length of a football field is 30 yards more than its width "y". Express the length of the field in terms of its width y	y + 30

GAME