MathRealm Algebra Part 2

Grade Level 8 & Up

Students learn detailed concepts, visualizations and multiple techniques for working with equations, systems of equations and higher order equations. Includes:

• Writing Linear Equation
• Systems of Linear Equations    
• Exponents & Powers
• Quadratic Equations
• Polynomials & Factoring

The following table is an outline of the interactive multimedia assignments in our algebra part 2 programs -- Reporting and Web programs. The outline is organized by units. Each unit may also include a Pre- and Post-Test, depending on the program and has multiple assignments that include lessons, practice, learning tools and enrichment activities (Extras). Try an Activity: Each unit only has one sample assignment that is active – this is the assignment in red. Trial requirements.
Note: Trial Assignments are opened in a pop-up window. You need to be sure pop-up windows are enabled for www.mathrealm.com. Sometimes just holding down the 'Ctrl' key when clicking a link will work.

Writing Linear Equations
	Line Slope Tool	Slope Calculation: Interactively move two-points on a plane and see the slope and line change.
	Slope as a Rate	Review rate and explore the concept of slope as a rate. Uses speed and changes in altitude as examples. Uses verbal models to generate slope (rate) calculation problems.
	Slope-Point Graph Tool	Graph a line from a slope and point and generate slope-intercept form of a linear equation. Interactively change the slope and move a point and see the line change.
	Writing Linear Equations	Writing linear equations in slope-intercept form from verbal models and from graphs. Uses cell phone billing rates and sky diving as example problems to model.
	Writing Equations Practice	Writing linear equations in slope-intercept form from verbal models and from graphs. Uses cell phone billing rates and sky diving as example problems to model.
	Linear Equations from Points	Writing a linear equation in slope-intercept form given verbal models with a rate and a point or a slope and a point. Writing a slope-intercept equation given two points. Uses factory production rates as a verbal model.
	Practice Line Eqn from Points	Practice writing a linear equation in slope-intercept form given a slope and point or two points. Drag and drop the line slope and intercept into the equation.

System of Linear Equations
	Solve System by Graphing	A verbal problem with rates is presented. A model of the problem is developed and a system of linear equations is generated. The problem is modeled graphically and mathematically and a solution is developed as the linear graph's intercept. Interactive tools are used to explore the graphing and intercept of a linear system. Several examples are developed to show getting an approximate solution to a linear system by graphing.
	Linear Equation System (2 x 2)	A two variable, 2x2 linear system in slope intercept form. Manipulate the slope and intercept coefficients with sliders.
	Practice System by Graphing	Practice solving a linear system by interactively graphing the system and entering in the approximate solution. Lines are graphed by moving two points for each line to define each line.
	Solve System by Substitution	With a verbal investment problem a linear system of equations is developed. A solution is developed using a substitution method. A four step procedure for solving linear systems by substitution is developed. Several examples are developed using the procedure.
	Practice System Substitution	Practice solving a linear system by substitution. Graphing and detailed substitution answers are shown for each problem answered.
	Linear Combination for Systems	Linear combination is adding or subtracting one equation from another to eliminate a variable. The concept of solving a linear system is developed with balance beams using weights and objects, modeling a linear system. The substitution method is used to solve the linear system. A more efficient and easier method is developed by subtracting the equations. A procedure and examples are developed.
	Practice Linear Combination	Practice solving a linear system by linear combination. Graphing and a detailed linear combination answers are shown for each problem answered.
	Linear System Review	A linear system of equations can have one solution (lines intercept), many solutions (lines are the same), or no solution (lines are parallel). Guidelines for when to use graphing, substitution or linear combination to solve a linear system.
	Linear Inequality System	A two variable, 2x2 linear inequality system in slope intercept form. Manipulate the slope and intercept coefficients with sliders.

Exponents and Powers
	Exponents	Introduces exponents as repeated multiplication. Introduces squared and its relationship to area. Introduces the relationship between volume and cubes.
	Exponent Properties	Learn the multiplication and division properties of exponential terms. Develops the meaning of zero and negative exponents.
	Exponent Practice	Practice manipulating exponential terms using exponent properties.
	Exponential Growth and Decay	Investigate compound interest as an application of exponential growth. Explore exponential growth and decay interactively with tables and bar graphs.
	Scientific Notation	Learn about scientific notation using powers of ten to represent and manipulate very small and large numbers.
	Scientific Notation Practice	Practice representing large and small numbers in scientific notation.

Quadratic Equations
	Square Roots	Learn about square roots and evaluation of expressions with square roots. Introduces the Pythagorean Theorem and solving for one of its variables.
	Practice Pythagorean Theorem	Practice solving square roots and solving the Pythagorean equation.
	Orbital Velocity	Use the Pythagorean Theorem to calculate the orbital velocity of a spacecraft.
	Quadratic Equations	Learn about quadratic equations. Learn about applications of the quadratic equation and solving using square roots.
	Quadratic Equation Practice	Practice solving quadratic equations using square roots.
	Parabolas	Graphing the quadratic equation (a parabola). Learn about the direction the parabola opens, the vertex and the axis of symmetry.
	Graphing Parabolas	Graphing quadratic equation in standard polynomial form. Manipulate the standard form coefficients with sliders.
	Practice Graphing Parabolas	Practice graphing quadratic equations by identifying the vertex and setting up a table of values.
	Quadratic Inequality Graphing	Graphing quadratic inequality in standard form. Manipulate the standard form coefficients with sliders.
	The Quadratic Formula	Solve a quadratic equation by using the quadratic formula.
	Practice Quadratic Formula	Practice applying the quadratic formula.
	Quadratic Absolute Values	Quadratic absolute value functions y=f(x), y=|f(x)|, and y =f(|x|) of parabolas are explored. Manipulate the coefficients with sliders.

Polynomials and Factoring
	Adding & Sub. Polynomials	Polynomials in standard form of any degree are introduced. Examples of what polynomials can represent. Adding and subtracting polynomials by combining the coefficients of like terms.
	Practice Polynomial Addition	Practice adding and subtracting polynomials by combining the coefficients of like terms.
	Multiplying Polynomials	Learn to multiply polynomials using the distribution properties of multiplication. Modeling polynomial multiplication using area and expression blocks. Multiply binomials using the FOIL method. Multiply a binomial and a trinomial using the vertical format.
	Practice Multiply Polynomials	Practice multiplying polynomials. Multiply binomials using the FOIL method and multiply a binomial and a trinomial with the vertical format method.
	Special Products and Factors	Multiply polynomials of the form (ax + b)(ax + b) and (ax + b)(ax - b). Learn to recognize polynomials with factors (ax + b)(ax + b) or (ax + b)(ax - b). The patterns are developed and formulas derived.
	Practice Special Products	Practice multiplying binomial polynomials with special forms. Practice the sum and difference pattern, (ax + b)(ax - b), and the square of binomial pattern, (ax + b)(ax + b). A FOIL method solution can also be viewed.
	Practice Special Factoring	Practice factoring trinomial polynomials with special forms. Practice factoring polynomials with the sum and difference pattern, (ax + b)(ax - b), and the square of binomial pattern, (ax + b)(ax + b).
	Factoring Quadratic Equations	Visually and mathematically learn to factor quadratic trinomial equations. Builds pattern recognition and rules of thumb skills to factor quadratic equations. Learn when a quadratic trinomial can not be factored.
	Practice Factoring Quadratics	Practice factoring quadratic trinomial equations, including identifying non factorable quadratic trinomial equations.