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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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Foundation of Geometry | Introduces basic geometric terms commonly used throughout the course. Postulates, theorems, hypotheses, and other definitions. Review of geometric problems. |
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Geometric Concepts | A review of geometric concepts including all types of angles, intersecting, perpendicular and parallel lines, rays and transversals. |
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Geometric Measurement | The use of a protractor in the measurement of angles and circles is discussed. A review of the measurement of line segments utilizing a pop up ruler that can be displayed in inches or centimeters. |
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Points, Lines and Planes | Definition of points, lines, and plans, collinear points, points and lines as intersections. |
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Segments, Rays and Angles | Number lines and corresponding points, identification of segments, congruency and segments, averaging endpoints, definition and examples of rays, bisectors. |
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Angles | Identification of sides and vertices of angles, interior and exterior angle points, adjacent angles, acute, obtuse, and right angles, complementary and supplementary angles, linear pairs, vertical angles. |
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Transversals | Parallel and skew lines, parallel segments and planes, identification and examples of transversals, corresponding angles and transversals, alternate interior and exterior angles. |
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Parallelism | Rules for congruency in corresponding angles, alternate exterior and interior angles, transversals and parallelism. |
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Triangles | Identification and examples of acute, obtuse, and right triangles, scalene, isosceles, equilateral and equiangular triangles, determining angles in triangles. |
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Congruent Triangles | Definition and examples of congruent triangles, comparing lines and angles in triangles, order in labeling angles and triangles, congruence statements, side-side-side, side-angle-side, angle-side-angle, angle-angle-side congruent triangles. |
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Triangles Inside and Out | Identification and examples of vertices, base angles, and congruent sides in isosceles triangles, comparing isosceles and equilateral triangles, exterior angles and remote interior angles in triangles, comparing angles and drawing conclusions about measurement. |
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Review 1 | Review of previous lessons. |
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Right Triangles 1 | Parts of right triangles, legs, hypotenuse. Focus on 45-45-90 degree right triangles. Using the Pythagorean Theorem to solve geometric problems. |
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Right Triangles 2 | Common right triangles, 30-60-90 degree right triangles, patterns in calculating the hypotenuse of a right triangle. |
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Quadrilaterals | An examination of the properties of quadrilaterals including the concept of opposite, consecutive and adjacent sides, angles and vertices. |
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Parallelograms | Definition and examples of quadrilaterals and parallelograms. |
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Special Parallelograms | Rectangles, rhombuses, squares, rectangle diagonals, rhombus diagonals, trapezoids, isosceles trapezoids, base angles and diagonals in trapezoids, finding parallels in triangles, finding medians in trapezoids. |
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Trapezoids | Examples of various trapezoids and rhombuses; angles and sides; calculating perimeters, examples of parallelism in trapezoids. |
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Areas of Polygons | Formulas for measuring the perimeter and volume and area of trapezoids, measuring surface area. |
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Conditional Statements | An examination of statements that can be derived from the manipulation of conditional statements. Topics include converse, inverse, contrapositive and biconditional statements. |
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Review 2 | Review of previous lessons. |
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Similar Polygons | Testing for congruency of quadrilaterals, similarity in polygons, proportional ratios, determining scale factors, proportionality, perimeters of polygons. |
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More About Polygons | Definition and examples of regular and irregular polygons. Identification of vertices and sides. Students identify polygons. |
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Area Revisited | Area of squares and rectangles, parallelograms and triangles, trapezoids, and regular polygons. |
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Solids 1 | Prisms, pyramids and determining the areas and volumes |
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Solids 2 | Cylinders, cones, spheres; areas and volumes of similar solids |
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Circles | Arcs, chords, and central angles; circumference and area |
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Circles & Angles | Inscribed and interior angles, tangents, and angle measurement |
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Circles, Arcs, & Sectors | Arc lengths and sector area |
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Trigonometric Functions | The focus of this lesson is the basic principles of trigonometry and its relation to geometry, definition and examples of sine, cosine, tangent, and other trigonometric terms. |
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Review 3 | Review of previous lessons |
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Comprehensive Exam | Test covering entire unit. |
