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The A+LS Mathematics curriculum is a comprehensive, completely integrated curriculum for grade levels 1-12. A sequence of 18 titles provides an extensive, integrated solution that is fully correlated to major mastery standards and leading, adopted textbooks.
In addition to a complete mathematical curriculum that is appropriate at each grade level, each title contains exercises that require the student to choose operations and develop strategies to solve problems. Students learn to use common sense, mental math, estimation, and other methods to solve problems and check answers for reasonableness.
The Mathematics titles develop knowledge of mathematics skills and their use in practical situations by utilizing a four-step approach: Study, Practice, Test, and Essay modules are used to define the instructional environment. The Study module provides a text- and graphics-based delivery of material that is reinforced by pictures and diagrams supported by a wealth of content. All graphics magnify to full screen size to concisely present and reinforce these concepts. The Practice module provides the students, in a non-scored and non-graded environment, to practice skills acquired through studying. Engaging, interactive feedback prompts the student to right answers when wrong answers to questions are entered. The student has instant access to the study material for reference. In the Test module, the student takes a scored examination, the results of which are recorded in the A+LS Management System. Upon completion of the Test, the student electronically "turns in" the test and may instantly see test results and correct answers to questions missed. The Essay module allows the student to compose individual, free-form answers to a wide variety of questions and problems.
| LESSON # | LESSON TITLE | LESSON CONTENT |
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Rules of Algebra | Review of the real number system including rational numbers, integers, whole numbers, counting numbers, and irrational numbers; rules for combining and multiplying real numbers, and order of operations. |
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Real Number Properties | Review of properties of real numbers; associative property of multiplication and division, distributive property, substitution property; terms associated with real number properties and operations, and review of inequalities. |
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Algebraic Expressions | Connecting words and numbers through expressions, students practice writing and simplifying expressions. |
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Algebraic Equations | Difference between expressions and equations, symbols used in writing equations, identifying unknowns. |
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Solving Equations | Rules for solving equations, combining like terms, step-by-step examples of simplifying and solving equations. |
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Problem Solving 1 | Developing equations to solve for unknowns, developing a plan to solve problems, and working related problems that develop from one original problem and checking answers for reasonability. |
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Rewriting Formulas | Solving for variables with more than one unknown, converting Celsius to Fahrenheit and vice versa, isolating variables, multiplying by reciprocals. |
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Solving & Graphing | Definition and examples of ordered pairs, x and y axes, and the coordinate plane, students write equations from information on grids, positive and negative slope. |
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Properties of Inequality | Rules and properties of inequalities, review of divisibility and multiplication properties. |
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Inequalities | Relating inequalities to variables, intersection and union, examples of solving and graphing inequalities. |
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Absolute Value Equations | Review of absolute values, determining absolute values as related to equations, comparing absolute values as solutions to equations, checking answers for reasonableness. |
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Absolute Value Inequality | Examples of positive and negative numbers in inequalities, inequalities having no solution. |
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Problem Solving 2 | Converting words in problems into symbols, converting answers to similar terms, various problem solving examples and strategies. |
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Relations & Functions | Review of coordinate plane, quadrants, identifying origin, abscissa, ordinate, domain, range, and function, representing relations on graphs. |
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Graph Linear Functions | Defining linear equations, rise, run, slope, writing linear equations in standard form, graphs as linear functions, constant functions, x and y intercepts. |
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Slope of a Line | Identification of positive, negative, zero, and undefined slopes, rise, run, relating slope to graphs. |
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Graph Linear Inequalities | Half planes and boundaries, writing equations and graphing in slope-intercept form, double-checking linear equality graphs. |
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Parallel & Perpendicular | Defining and graphing parallel and perpendicular lines on the coordinate plane, solving for parallel lines from points and slope, negative reciprocals as slopes. |
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Identify Linear Equations | Difference of slope-intercept form and standard form for linear equations, determining when to use point-slope, slope-intercept, x-intercept or y-intercept to graph linear equations, review of relations and functions, |
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Problem Solving 3 | Identifying relationships between variables, checking answers for reasonableness, using equations to solve problems, using charts or other visual tools as aids in solving problems. |
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Direct Variation | Definition of direct variations and examples of graphs of direct variations, proportionality constants, means as a product of extremes, using proportions to solve problems. |
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Graphing Equation Systems | Characteristics of intersecting, coinciding, and parallel planes and systems of equations for each, comparing equations that have same slope, different slope, and different intercepts, |
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Graphing Systems | Solving equations by graphing intersecting, coinciding, and parallel lines in planes, equations with infinite solutions, equations that have no solution. |
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Addition & Substitution | Solving linear systems by addition and substitution, comparing solutions to problems worked using both methods, practicing using linear equations to solve everyday problems, hints for evaluating problems to find the best way to solve. |
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Solving Inequalities | Illustrating inequalities with graphs and using them to find solutions, the effect of absolute value on graphs, adding and subtracting numbers inside and outside absolute value symbols. |
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Linear Programming | Identifying variables, various constraints, and feasible regions in graphs, determining maximum and minimum values within feasible regions, the importance of linear programming as it relates to various careers, |
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Three-Variable Equations | Using matrices, Cramer’s rule, and/or addition to solve equations with three variables, graphing ordered triples, three-dimensional thinking in solving problems. |
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Data in Matrices | Identifying and labeling data in matrices, performing operations using matrices, dimensions of matrices. |
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Matrix Multiplication | Checking the dimensions of matrices before multiplication, products of matrices, step-by-step examples of multiplying matrices. |
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Size & Reflections | Changes in size or magnitude and scale factor, examples using matrices in everyday life situations, coordinates of reflected images, graphing reflections. |
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Transformation | Definition of transformation, formula, point, and matrix transformations, commutative, associative, and identity properties with matrix multiplication, closed sets. |
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Rotation | Definition and examples of rotation, relating rotation to angles, negative and positive magnitude, algebraic formulas for rotation, finding the images of rotations. |
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Matrix Addition | Discussion of rules of matrix addition and subtraction of elements, addition properties in matrices, adding three matrices, multiplying elements in matrices, subtracting matrices, using matrices to solve problems in everyday life. |
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Exponents | How to utilize exponents as a shortcut method when multiplying variables and simplifying fractions. |
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Polynomial Types | Definition and examples of monomials, binomials and polynomials, examples of like and unlike terms, determining the degree of polynomials. |
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Polynomial Operations | Graphing and factoring quadratic trinomials, linear terms, ascending and decreasing order of polynomials. |
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Factoring Quadratics | Graphing and factoring quadratic trinomials, linear terms, ascending and decreasing order of polynomials. |
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Polynomial Equations | Solving problems using polynomials equations. 5-step approach to solving problems. Formulas and computations for solving problems. |
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Negative Exponents | Review of exponents and their uses, zero as an exponent, negative exponents, simplifying problem using positive and negative exponents. |
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Scientific Notation | Definition and examples of scientific notation, using negative and positive exponents. Converting expressions from decimal form to scientific notation, significant digits. |
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Rational Operations 1 | Common denominators, finding higher variables, step by step factoring and solving, adding subtracting, rationals by simplifying. |
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Rational Operations 2 | Products of rational expressions, factoring numerators, and denominators of polynomials solving problems using rational expressions to solve practical problems. |
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Simplifying Rationals | Formula for quotient of 2 polynomial, factoring polynomials review of ACF, quadratic trinomials, perfect squares and difference of squares. |
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Complex Rationals | Definition and examples of complex rationals using shortcuts to simplify and solve complex rationals. |
