Helping Students Achieve Their Life Passions

 

 

  

 

 

 

 

 

  

Mrs. Wentzlaff Math      focus
 
Welcome to the Eighth Grade MathWeb Page.
This web page is brought to you by Mrs.Wentzlaff
and is meant to give you the latest and greatest news. 
 

 

Contact Information

Materials Needed for Class

Classroom Expectations

About Me

Mastery Statements

 

 
Please feel free to contact me if you have any questions. I can be reached at (708) 246-7360.   My e-mail address is mwentzlaff@d107.org
 
Bring two spiral bound notebooks to class each day. One of the notebooks is for class notes and the other notebook is for the homework assignments. Bring to class your homework in your math homework notebook. You should bring a red pen to class to do your math corrections. Textbook and your TI 30 scientific calculator should be brought to class daily. 
 
 
ASSESSMENTS:
• Combination of quizzes, tests and mastery outcome assessments
• Teacher and/or student can initiate one further attempt on tests, quizzes or assessments within one week. There may be circumstances under which further attempts may not be offered.
• A student is eligible for a further attempt only if he/she demonstrates that additional effort was put forth to improve learning. (e.g. study/learning)

 

TECHOLOGY:
Texas Instrument Scientific Calculator TI-30


HOMEWORK:
Students will have homework as needed to reinforce math concepts learned. This is usually 4 to 5 nights a week. Each homework assignment should take approximately 20-30 minutes per night.


RESOURCES:
University of Chicago School Mathematics Project: Algebra , Third Edition
Published by Wright Group/McGraw Hill

                       

  
 
All rules and expectations established in the building-wide Pleasantdale Middle School Code of Expectations are to be adhered to.
Come to class prepared and on time. Absence work must be completed in a timely manner.
 
I have been teaching math at Pleasantdale Middle School for twenty-one years.   I received a Bachelor of Science degree from the University of Illinois at Chicago and then continued my education and received a Masters of Science degree from Florida State University.
 
 On-level 8th grade Math
 

GOALS:  (What we learn)

 

Focus Statement:  Students will solve multi-step linear equations and inequalities using the algebraic properties of the real number system.  They will also graph linear equations using slope and intercept on the coordinate plane. 

 

M.8.1  Students will create a diagram of the real number system and apply the basic properties of the real number system to simplify algebraic expressions.

M.8.1.1  Define the real numbers which include the counting numbers, whole numbers, integers, rational numbers and irrational numbers.

M.8.1.2  Organize and create a model of the hierarchy of the real number system.

M.8.1.3  Apply the Opposite of Opposites property to simplify algebraic expressions.

M.8.1.4  Apply the Opposite of a Sum and a Difference property to simplify algebraic expressions.

M.8.1.5  Apply the Additive Identity and Additive Inverse Properties to simplify  algebraic expressions.

M.8.1.6  Apply the Multiplicative Identity and Multiplicative Inverse Properties to simplify  algebraic expressions.

M.8.1.7  Apply the Add-Opp Property to simplify algebraic expressions.

M.8.2  Students will solve multi-step linear equations and linear inequalities with the variable on one side of the equation only.

            M.8.2.1  Solve a linear equation of the form x + a = b; x – a = b; a – x = b

            M.8.2.2  Solve a linear equation of the form ax + b = c; c negative or positive

            M.8.2.3  Solve  a linear equation of the form d(x + b) = c

            M.8.2.4  Solve inequalities of the above formats.

            M.8.2.5  Graph on a real number line the solutions to the inequalities.

M.8.3  Students will solve multi-step linear equations and inequalities with the variable on both sides of the equation.

            M.8.3.1  Solve a linear equation of the form ax + b = cx + d

            M.8.3.2  Solve a linear equation of the form a(x + b) = c(x + d)

            M.8.3.3 Solve linear inequalities of the above formats.

            M.8.3.4  Solve literal equations and inequalities.

M.8.3.5  Interpret a percent problem-solving situation and write and solve an appropriate equation or inequality.

M.8.3.6  Interpret a geometric problem-solving situation and write and solve an appropriate equation or inequality.

M.8.4  Students will solve proportions generated by various problem solving situations.

            M.8.4.1  Identify and simplify complex algebraic fractions

M.8.4.2  Define rate, ratio and proportions and compare and contrast the      similarities and differences of each.

            M.8.4.3  Apply the Means-Extremes Property to solve a given proportion.

M.8.4.4   Interpret a percent problem-solving situation and  write and solve an appropriate proportion.

 

 

 

 

M.8.5  Students will graph a linear equation of the form y = mx + b using the slope and y-intercept.

M.8.5.1  Define the slope of a line as the rate in change of the dependent variable to the independent variable.

M.8.5.2  Calculate the slope of a line from a given graph of the line using the definition of slope.

M.8.5.3  Define the y-intercept of a line and identify the y-intercepts of the graphs of given lines.

M.8.5.4  Predict the effect that changing the value of slope in a given equation  will have on the graph of the  line.

M.8.5.5  Graph a linear function of the form y = mx + b by using the slope and y-intercept of the line without a graphing calculator.

M.8.5.6   Graph a linear function of the form y = mx + b using a graphing calculator.

            M.8.6  Students will graph a linear equation of the form y = c and x = c.

M.8.6.1  Apply the definition of a “Well-defined operation” to explain why division by zero is undefined.

M.8.6.2   Compute the slope of a line of the form y = c and x = c.

M.8.6.3   Graph a line of the form y = c and x = c.

M.8.6.4   Graph a line which does not have a y-intercept through a given point and write the equation of the line.

            M.8.7  Students will identify and graph an exponential equation of the form y = x2

                        M.8.7.1  Calculate x to a given power with and without a calculator.

                        M.8.7.2  Identify an exponential equation.

            M.8.7.3  Identify the exponential growth and exponential decay curve.

M.8.7.4  Sketch an appropriate exponential growth or exponential decay curve from a problem solving situation.

M.8.7.5  Graph an exponential equation of the form y = x2 without and with a graphing calculator.

M.8.8  Students will apply the power properties to simplify algebraic expressions.

M.8.8.1 Apply the Product of Powers Property to simplify an algebraic expression with positive exponents

M.8.8.2  Apply the Power of Powers Property to simplify an algebraic expression with positive exponents.

M.8.8.3  Apply the Quotient of Powers Property to simplify an algebraic expression with positive exponents.

M.8.8.4  Apply the power properties to simplify an algebraic expression with negative exponents.

M.8.8.5   Add, subtract, multiply and divide algebraic fractions.

M.8.9  Students will apply the properties of radicals to simplify algebraic expressions.

M.8.9.1  Calculate square roots and cubic roots of positive rational numbers with a calculator.

M.8.9.2  Apply the Pythagorean Theorem to find the leg of a right triangle and the diagonal of a rectangle.

M.8.9.3  Apply the rules of standard radical form to simplify an algebraic radical expression.

M.8.9.4  Apply the Properties of Radicals to add, subtract, multiply and divide radical expressions without a calculator.

 

 

           

M.8.10  Students will graph and solve quadratic equations.

M.8.10.1  Identify  the characteristics of vertex, maximum or minimum, and axis of symmetry of a parabolic shaped graph.

M.8.10.2  Graph a quadratic equation of the form y = ax2 without a calculator.

M.8.10.3  Graph a quadratic equation of the form y = ax2 + bx + c with a graphing calculator.

M.8.10.4  Apply the Quadratic Formula to solve a quadratic equation.

M.8.11  Students will solve a system of linear equations.

M.8.11.1  Apply the Graphing Method with/without a graphing calculator to solve a system of linear equations.

M.8.11.2  Apply the Substitution Method without a calculator to solve a system of linear equations.

M.8.11.3  Identify consistent independent, consistent dependent and inconsistent linear systems.

            M.8.12  Students will classify and perform operations on polynomials.

                        M.8.12.1  Define a polynomial in standard form.

                        M.8.12.2  Classify  polynomials by number of terms and degree of terms.

                        M.8.12.3  Add and subtract polynomials.

                        M.8.12.4  Multiply a polynomial by a monomial using the Distributive Property.

                        M.8.12.5  Multiply a binomial by a binomial using FOIL.

                        M.8.12.6  Factor  polynomials with a greatest common monomial factor only.

                        M.8.12.7  Factor trinomials using reverse FOIL.

 

 

 

Above-level 8th grade Math

 

Focus Statement:  Students will solve multi-step linear, quadratic and absolute value equations and inequalities using the algebraic properties of the real number system.  They will also graph linear, quadratic and absolute value equations and inequalities      

 

MA.8.1 Students will create a diagram of the real number system and apply the basic properties of the real number system to simplify algebraic expressions.

MA.8.1.1  Define the real numbers which include the counting numbers, whole numbers, integers, rational numbers and irrational numbers.

MA.8.1.2  Organize and create a model of the hierarchy of the real number system.

MA.8.1.3  Apply the Opposite of Opposites property to simplify algebraic expressions.

MA.8.1.4  Apply the Opposite of a Sum and a Difference property to simplify algebraic expressions.

MA.8.1.5  Apply the Additive Identity and Additive Inverse Properties to simplify  algebraic expressions.

MA.8.1.6  Apply the Multiplicative Identity and Multiplicative Inverse Properties to simplify  algebraic expressions.

MA.8.1.7  Apply the Add-Opp Property to simplify algebraic expressions.

MA.8.2  Students will solve multi-step linear equations and linear inequalities with the variable on one side of the equation only.

            MA.8.2.1  Solve a linear equation of the form x + a = b; x – a = b; a – x = b

            MA.8.2.2  Solve a linear equation of the form ax + b = c; c negative or positive

            MA.8.2.3  Solve  a linear equation of the form d(x + b) = c

            MA.8.2.4  Solve inequalities of the above formats.

            MA.8.2.5  Graph on a real number line the solutions to the inequalities.

MA.8.3  Students will solve multi-step linear equations and inequalities with the variable on both sides of the equation.

            MA.8.3.1  Solve a linear equation of the form ax + b = cx + d

            MA.8.3.2  Solve a linear equation of the form a(x + b) = c(x + d)

            MA.8.3.3 Solve linear inequalities of the above formats.

            MA.8.3.4  Solve literal equations and inequalities.

MA.8.3.5  Interpret a percent problem-solving situation and write and solve an appropriate equation or inequality.

MA.8.3.6  Interpret a geometric problem-solving situation and write and solve an appropriate equation or inequality.

MA.8.4  Students will solve proportions generated by various problem solving situations.

            MA.8.4.1  Identify and simplify complex algebraic fractions

MA.8.4.2  Define rate, ratio and proportions and compare and contrast the      similarities and differences of each.

            MA.8.4.3  Apply the Means-Extremes Property to solve a given proportion.

MA.8.4.4   Interpret a percent problem-solving situation and  write and solve an appropriate proportion. 

MA.8.5  Students will graph a linear equation of the form y = mx + b using the slope and y-intercept.

MA.8.5.1  Define the slope of a line as the rate in change of the dependent variable to the independent variable.

MA.8.5.2  Calculate the slope of a line from a given graph of the line using the definition of slope.

MA.8.5.3  Define the y-intercept of a line and identify the y-intercepts of the graphs of given lines.

MA.8.5.4  Predict the effect that changing the value of slope in a given equation  will have on the graph of the  line.

MA.8.5.5  Graph a linear function of the form y = mx + b by using the slope and y-intercept of the line without a graphing calculator.

MA.8.5.6   Graph a linear function of the form y = mx + b using a graphing calculator including lines of regression.

MA.8.5.7   Write linear equations in slope-intercept, point-slope and standard form.

            MA.8.6  Students will graph a linear equation of the form y = c and x = c.

MA.8.6.1  Apply the definition of a “Well-defined operation” to explain why division by zero is undefined.

MA.8.6.2   Compute the slope of a line of the form y = c and x = c.

MA.8.6.3   Graph a line of the form y = c and x = c.

MA.8.6.4   Graph a line which does not have a y-intercept through a given point and write the equation of the line.

         MA.8.7 Students will identify and graph an exponential equation of the form y = a

                        MA.8.7.1  Calculate x to a given integer power with and without a calculator.

                        MA.8.7.2 Compute with numbers in scientific notation.

                        MA.8.7.3  Identify an exponential equation.

            MA.8.7.4  Identify the exponential growth and exponential decay curve.

MA.8.7.5  Sketch an appropriate exponential growth or exponential decay curve from a problem solving situation.

MA.8.7.6  Graph an exponential equation of the form y = a  without and with a graphing calculator.

MA.8.8  Students will apply the power properties to simplify algebraic expressions.

MA.8.8.1 Apply the Product of Powers Property to simplify an algebraic expression with positive exponents

MA.8.8.2  Apply the Power of Powers Property to simplify an algebraic expression with positive exponents.

MA.8.8.3  Apply the Quotient of Powers Property to simplify an algebraic expression with positive exponents.

MA.8.8.4  Apply the power properties to simplify an algebraic expression with negative exponents.

MA.8.8.5   Add, subtract, multiply and divide algebraic fractions.

MA.8.9  Students will apply the properties of radicals to simplify algebraic expressions.

MA.8.9.1  Calculate square roots and cubic roots of positive rational numbers with a calculator.

MA.8.9.2  Apply the Pythagorean Theorem and Converse of Pythagorean Theorem to find the leg of a right triangle and the diagonal of a rectangle.

MA.8.9.3  Apply the rules of standard radical form to simplify an algebraic radical expression.

MA.8.9.4  Apply the Properties of Radicals to add, subtract, multiply and divide radical expressions without a calculator.

MA.8.9.5  Apply the Distance and Midpoint Formulas on a coordinate plane.

            MA.8.10  Students will graph and solve quadratic equations.

MA.8.10.1  Identify  the characteristics of vertex, maximum or minimum, and axis of symmetry of a parabolic shaped graph.

MA.8.10.2  Graph a quadratic equation of the form y = ax2  + bx + c without a calculator.

MA.8.10.3  Graph a quadratic equation of the form y = ax2 + bx + c with a graphing calculator.

MA.8.10.4  Apply the Quadratic Formula to solve a quadratic equation.

MA.8.10.5  Apply the Zero-Product Property to solve a quadratic equation.

MA.8.10.6  Solve a quadratic equation by Completing the Square Method.

MA.8.10.7  Use the Discriminant to determine the number of solutions for a quadratic equation.

MA.8.11  Students will solve a system of linear equations.

MA.8.11.1  Apply the Graphing Method with/without a graphing calculator to solve a system of linear equations.

MA.8.11.2  Apply the Substitution Method without a calculator to solve a system of linear equations.

MA.8.11.3  Apply the Adding or Subtracting Method without a calculator to solve a system of linear equations.

MA.8.11.4  Identify consistent independent, consistent dependent and inconsistent linear systems.

MA.8.11.5 Solve systems of linear inequalities

            MA.8.12  Students will classify, perform operations on and factor polynomials.

                        MA.8.12.1  Define a polynomial in standard form.

                        MA.8.12.2  Classify  polynomials by number of terms and degree of terms.

                        MA.8.12.3  Add and subtract polynomials.

                        MA.8.12.4  Multiply a polynomial by a monomial using the Distributive Property.

                        MA.8.12.5  Multiply a binomial by a binomial using FOIL.

                        MA.8.12.6  Factor  polynomials with a greatest common monomial factor only.

                        MA.8.12.7  Factor trinomials using reverse FOIL.

                        MA.8.12.8  Factor using special product patterns.

MA.8.13  Students will solve and graph multi-step compound equations and inequalities.

            MA.8.13.1  Identify the the difference between an “and” and “or” statement.

            MA.8.13.2  Solve compound equations using “and” and “or”.

            MA.8.13.3  Solve compound inequalities.

            MA.8.13.4  Graph compound inequalities.

MA.8.14  Students will solve and graph multi-step absolute value equations and inequalities.

            MA.8.14.1  Graph  on number line and f(x) =  on coordinate plane.

             MA.8.14.2  Solve absolute value equations.

             MA.8.14.3  Solve absolute value inequalities.

MA.8.15  Students will simplify rational expressions and solve rational equations.

             MA.8.15.1  Simplify rational expressions.

            MA.8.15.2   Multiply and divide rational expressions.

            MA.8.15.3   Add and subtract rational expressions.

            MA.8.15.4  Solve rational equations.

MA.8.16  Students will calculate probabilities and measures of central tendency.

            MA.8.16.1  Calculate probability and odds of an event.

            MA.8.16.2  Calculate mean, median, mode, range and mean absolute deviation                    for a given data set.

            MA.8.16.3  Create and interpret Stem-and-Leaf plots.

            MA.8.16.4  Create and interpret histograms and Box-and-Whisker plots using a graphing calculator.