About marutrevino

Guadalupe Trevino is a math teacher, holds a Bachelor´s Degree in Electric Engineering, and a Master Degree in Business Administration (TAMIU). She is a book author and an accomplished motivational speaker. Having worked as a college professor teaching engineering for over 20 years, she has an expertise in technology which has allowed her to develop customized interactive programs for her students.

Week 07 Review

Knowing your personal strengths and weaknesses in math is very important.

Verify your skill level to ensure success in Math.  

TS01 Diagnostic Test

TS02 Diagnostic Test

 

 

 

TIMES TABLES

  Please, give yourself time to thoroughly learn them.

>>>> TT53       Short_Times_Tables

Math Review

The following online activities are the perfect way to brush up your basic math skills.

 

⇨  Adding Whole Numbers

⇨  Subtracting Whole Numbers

⇨  Multiplying Whole Numbers

⇨  Dividing Whole Numbers

⇨  Multiplying by power of ten

⇨ Dividing by powers of ten

⇨ Adding Decimals

⇨ Subtracting Decimals

⇨ Multiplying Decimals

⇨ Dividing Decimals

⇨ ⇨ ⇨ ⇨ ⇨ ⇨ ⇨

monkey

⇨ Coloring Fractions

⇨ Identifying Fractions

⇨ Matching Equivalent Fractions

⇨ Fraction to Decimal

⇨ Ordering Fractions

⇨ Adding Fractions

⇨ Subtracting Fractions

⇨ Multiplying Fractions

⇨ Dividing Fractions

Algebraic Representations of Two-Variable Relationships

Multiplicative Relationship

Many real-life situations involve 2 variable quantities in which one quantity depends directly on the other. Suppose for example that today I went to the gas station, and I saw that a gallon of gas costs 3 USD. I can use the equation  Y=3X  to calculate what price I should pay.

The equation  Y=3X  handles 2 variables, X which is the number of gallons of gas and Y which is the price to pay. The value of Y depends on the value of X (the number of gallons). If I buy 1 gallon I must pay  $ 3 , if I buy 5 gallons I must pay  $ 15, if I buy 10 gallons, I must pay  $ 30.

A variable that depends on the value of another variable is called a dependent variable. In this case y is the dependent variable and x is the independent variable. The equation shows the relationship between the variables. It is a multiplicative relationship. To calculate the value of y we must multiply the value of x by 3. The 2 variables are related by a proportional relationship. The value of one variable is in direct proportion to the value of the other.

There are several ways to show how the variables are related. We can use an equation, a verbal description (rule), tables and graphs.

The equation is: “y = 3 x

The rule is “y is worth 3 times what x is worth“.

The table is:

X Y
0 0
5 15
10 30
15 45

If the amounts from the table above are graphed (number of gallons, price), the pairs (0,0), (5,15), (10,30) and (15,45) will form a straight line through the origin, indicating that these pairs are in a proportional relationship.

The chart is:

The price is the number of gallons multiplied by 3.  The equation is Y=3x. The two quantities are in a proportional relationship. The coefficient of X (the independent variable) is the unit rate, which is also the constant of proportionality. The constant of proportionality is 3.

Y is the dependent variable since its value depends on the value of the variable X.

The independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

The graph of a proportional relationship is always a straight line passing through the origin.

Additive Relationship

Example:

A removable dumbbell consists of several iron plates that are attached to a handle. The handle weighs 3 pounds. If we want to know the total weight of the dumbbell, we must add 3 to the weight of the plates.

The rule is:  “Y is equal to X plus 3”. Y is the dependent variable since its value depends on the value of the variable X.  (Y is the total weight of the dumbbell)

The equation is:  “Y=X+3

The table is:

X Y
0 3
5 8
10 13
15 18

This table shows an additive relationship between x and y, represented with y = x + 3

Additive relationships mean you add the SAME number to any x-value to get the corresponding y-value.

The chart is:

The independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

In an additive relationship, the origin  (0,0)  is not represented in the table and the graph.

Linear Relationship

linear relationship is any relationship between two variables that creates a line when graphed in the x y-plane.

In a linear relationship, the equation can have up to two variables. All the variables in the equation are to the first power (their coefficient need not necessarily be an integer; it may be a decimal or a fraction, and not zero in the denominator [because division by zero is undefined]). The equation must graph as a straight line.

Linear relationships can be expressed either in a table of values, a chart or as a mathematical equation of the form y = mx + b.

Types of Linear Relationship

1) Additive Relationship  (Simple Addition or Subtraction)

E.g.   y = x +3,  y = x -1, y = x ,  etc.

2) Multiplicative Relationship  (Simple Multiplication or Division)

E.g.  y = 3x, y = -2x, y = ½ x,  etc.

3) Multiplicative and Additive Relationship (y = mx + b, slope intercept form)

E.g. y = 2x + 2,  y = -x + 3, y = 3x -5,  etc.

Linear equationy = mx + b

X is the input variable, Y is the output variable, m is the slope (constant rate of change), b is the y-intercept.

Linear Equations Represent Lines

The equation  y = mx + b  describes a straight line on the graph.

Multiplicative and Additive Relationship  (y = mx + b)

Example:                                      

A plumber has a call out fee of $50 and then charges $10 per hour.  What will be the total cost for X hours of work?

Answer:

Slope (m): rate per hour = 10

Fixed amount (b): Initial charge = 50

Independent Variable: Number of hours = X

Dependent Variable: Cost of service = Y

Write an equation in slope-intercept form (y=mx + b) , to work out the total cost for any number of hours worked.

The equation is:           y=10x+50

The rule is:  “Y is equal to  ten times X plus 50”. Y is the dependent variable since its value depends on the value of the variable X.

The table is:                  The chart is:

Congratulations to all my students

Dear Students:

I am very proud to recognize the outstanding student academic achievement of my students in the last school year.

Awesome job students!

You shined like a star on the STAAR test!

Despite the fact that for reasons beyond my control I was unable to teach you the last four weeks of the school year, you received the highest grades not only from our school but from the school district.

The following graph compares the results obtained by my students, taking as a reference the average obtained by our school district.  The school that stood out the most was Memorial, and the grades of my students contributed greatly.

Be proud of your hard work and achievement.

May your future be as bright as the smiles you wear now and remember to be proud of yourself because we, your teachers, already are.

Mrs. Garcia

“Never stop dreaming, 
never stop believing, 
never give up, 
never stop trying, and 
never stop learning.” 

Roy T. Bennett

Results for STAAR grades 3–8 assessments will be made publicly available on June 24, 2022.

You can see more in the following link: TexasAssessment.gov.