Interactive Algebra I: Learn By Doing

Place values; Naming number; Rounding.

Learning to identify prime versus composite numbers.  Building factor trees.  Creating prime factorizations for composite numbers.

A quick refresher on exponents and inequalities.  An introduction to translating from English into Math language.

Reviewing the Order of Operations (PEMDAS); Evaluating expressions by substituting in a value.

Identifying terms and coefficients and learning to combine like terms.

Working with negative numbers.  Understanding absolute values.

Adding and subtracting postive and negative numbers.

Multiplying positive and negative numbers.

Translating multiplication and division from English into Math Language.

Working with basic algebraic fractions.  Reducing, multiplying and dividing these fractions.

Division of Fractions; Order of Operations (PEMDAS) involving Fractions.

Adding and subtracting basic algebraic fractions.

Working with complex fractions.  Evaluating expressions with two variables.

Naming Decimals.  Rounding Decimals.  Adding and Subtracting Decimals.

Multiplying and Dividing Decimals.

Converting decimals to fractions and converting fractions to decimals.

Classifying numbers as counting numbers, whole numbers, integers, rational, irrational, and real.

Locating decimals and fractions on a number line.

Understanding the basic properties of mathematics, including the associative and commutative properties.

Using the distributive property.

Converting within the standard system or the metric system.

Converting between the standard system and the metric system.

Solving one-step equations involving addition and subtraction.

Learning to translate basic word problems from English to Math langauge.  These problems involve one-step equations requiring addition or subtraction.

Learning to solve one-step equations which require Multiplication or Division.  These are what I will refer to as Factor Puzzles.

Learning to translate basic word problems from English into Math Language.  These problems involve one step with multiplication or division.

Solving two-step equations with variables on both sides.

Solving equations which involve moving both variables and constants on both sides of the equal sign.

Solving complex, multi-step equations.

Solving equations with solutions of "all real numbers" or "no solution."

Learning to clear fractions from equations by multiplying by the least common denominator.

Learning to clear decimals from equations.

Using the formula distance equals rate times time.

Solving an equation for a variable when the equation has multiple variables.

Learning to solve basic equations involving inequalities.

Learning to solve more complex equations involving linear inequalities.

An introduction to word problems.  Learning to translate from English to Math Language and making a dictionary.

Solving a group of word problems called "number problems."

Introduction to porportion problesm.  "Is" over "Of" equals "%" over "100."

Working problems involving percent change and simple interest.

Solving problems involving percent mark up and percent discount.

Solving word problems which require adjusting for values.  For instance, coin problems.

Solving word problems involving mixtures.

Solving word problems involving the properties of triangles.

Solving word problems which require the Pythagorean Theorem.

Learning to solve word problems which involve the perimeter or area of a rectangle.

Solving word problems which involve distance, rate and time.

Solving distance, rate and time word problems which include decimals.

Solving word problems which involve inequalities.

Learning to plot points on the coordinate plane.

Graphing lines by plotting points.

Using the properties of fractions to make the plotting of lines with fractional slopes easier.

Graphing vertical and horizontal lines.

Learning to graph lines using the x and y intercepts.

Introduction to the slope of a line.

Graphing a line using the slope of the line and a point on the line.

Graphing lines using the slope-intercept form.

Reviewing the methods for graphing lines.

Determining if two lines are parallel or perpendicular.

Using the point-slope equation.

Finding a line which is parallel (or perpendicular) to a given line.

Graphing linear inequalities.

Solving systems of linear equations by graphing.

Using the substitution method to solve systems of linear equations.

Using the elimination method to solve systems of linear equations.

Using a systems of linear equations approach to solving word problems.

Using a system of linear equations to solve distance, rate and time problems.

Using a systems of linear equations approach to solve word problems which involve accounting for value.

Using a system of linear equations to solve investment problems.

Systems of linear inequalities.

Solving word problems using a system of linear inequalities.

Introduction to polynomials.  Learning to add and subtract polynomials.

Evaluating polynomials.

Learning exponents rules when working with monomials.

Multiplying a polynomial by a monomial.

Multiplying binomials.

Multiplying two of the same binomials.

Multiplying together binomials which are conjugates of each other.

Learning exponent rules for fractions.

Exponent rules for algebraic fractions.

Dividing monomials.

Dividing a monomial by a polynomial.

Dividing polynomials.

Working with negative exponents.

Multiplying and dividing monmials involving negative exponents.

Learning the basics of scientific notation.

Finding the greatest common factor of a polynomial.

Learning the approach of factoring by grouping.

Factoring basic trinomials where the leading term has a coefficient of 1.

Factoring basic trinomials which have a leading coefficient of 1 and have two variables.

Using the trial and error method to factor trinomials with a leading term having a coefficient other than 1.

Using the A/C method to factor trinomials with a leading coefficient other than 1.

Learning to factor perfect square trinomials.

Learning to factor the difference of squares.

Learning to factor the difference of cubes.

Presenting a strategy for factoring polynomials when each type is mixed.

Solving equations using the zero-product property.

Solving word problems using the zero-product property.

Introduction to rational expressions.  Learning to evaluate rational expressions.

Simplifying rational expressions by factoring and reducing.

Learning to simplify rational expressions by pulling out a -1 to reverse a factor.

Multiplying rational expressions.

Dividing rational expressions using Keep, Change, Flip.

Learning to add or subtract rational expressions which have a common denominator.

Using the -1 trick to add or subtract rational expressions with a common denominator.

Adding rational expressions without a common denominator.

Subtracting rational expressions which do not have a common denominator.

Simplifying complex rational expressions.

Using the least common denominator approach to simplify complex rational expressions.

Solving equations involving rational expressions.

Solving for a variable by factoring out a greatest common factor.

Solving rational expressions set up as a proportion.

Solving word problems with rational expressions set up as proportions.

Solving proportion word problems involving similar figures.

Solving distance, rate, time problems involving rational expressions.

Solving rate of work problems.

Solving direct variation problems by finding the constant of variation.

Solving indrect variation problems by finding the constant of variation.

Introduction to roots.

Roots involving variables.

How to work with roots which don't completely simplify.

Working with fractions beneath roots.

Adding and subtracting roots.

Simplifying roots and then adding and subtracting.

Multiplying roots.

Multiplying roots as binomials.

Simplifying two square roots involving a fraction bar.

Rationalizing denominators.

Rationalizing denominators using conjugates.

Solving equations which involve roots.

Using formulas which involve roots.

Simplifying higher order roots.

Working with higher order roots which don't completely simplify.

Simplifying higher order roots which involve fractions.

Adding and subtracting higher order roots.

The connection between fractional exponents and roots.

Exponent rules for fractional (rational) exponents.