Integrated Math B. Syllabus. Course Overview. Course Goals. Math Skills

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1 Syllabus Integrated Math B Course Overview Integrated Math is a comprehensive collection of mathematical concepts designed to give you a deeper understanding of the world around you. It includes ideas from algebra, geometry, probability and statistics, and trigonometry, and teaches them as interrelated disciplines. It s likely that you ve been studying some form of integrated math since elementary school. In Integrated Math B, you will study the connections between algebra and geometry. You will learn about geometric theorems, or rules, and write proofs to support them. A proof is a logical sequence of statements that begins with an educated guess and leads to an established conclusion. You will learn about some special properties of polygons and compute the perimeter and area for a variety of shapes. You will also explore congruency and similarity of triangles and be introduced to a branch of mathematics called trigonometry the study of the relationships between the sides and angles of triangles. Finally, you will study probability and statistics by calculating simple probability and the central tendencies and variability for sets of data. Course Goals By the end of this course, you will be able to do the following: Understand, recognize, and label the basic terms of geometry. Write two-column geometric proofs, including indirect proofs. Apply theorems concerning parallel and perpendicular lines. Use congruence postulates to prove whether two triangles are congruent. Solve triangle problems using inequality relationships. Solve problems using the special properties of quadrilaterals. Use similarity theorems to prove whether two triangles are similar. Understand the relationships between the sides and angles of a right triangle. Calculate the area and perimeter of a variety of polygons. Prove theorems using coordinate geometry. Calculate simple probability. Find the mean, median, mode, and range for a set of data. Math Skills Integrated Math A is a prerequisite for Integrated Math B. Before beginning this course, you should be able to do the following: Describe linear relationships using graphs and equations EDMENTUM, INC.

2 Apply the rules of exponents. Add, subtract, multiply, divide, and factor polynomials. Describe quadratic relationships using graphs and equations. Define, identify, and graph a variety of functions. Simplify rational expressions and solve rational equations. General Skills To participate in this course, you should be able to complete basic operations with word processing software, such as Microsoft Word or Google Docs. For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course. Credit Value Integrated Math B is a 0.5-credit course. Course Materials Notebook A scientific calculator is required. A graphing calculator (TI-83 or equivalent) is optional. You can use a graphing calculator to explore the course math topics in greater depth. Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class. Day Activity/Objective Type 1 Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at the beginning of this course. Course Orientation 2

3 2 7 4 days: days: days: Mathematical Thinking and Logic Decide whether information drawn from a passage is true, false, or cannot be determined. Recognize the hypothesis and conclusion of a conditional statement. State conditionals in if then form. Recognize and state the converse, inverse, and contrapositive of a statement. Draw correct conclusions from given statements. Points, Lines, and Planes Understand, recognize, and label the basic terms of geometry. Apply the concepts of segment addition, bisection, and congruence. Know and apply postulates dealing with points, lines, and planes. Rays and Angles Define rays and angles. Understand and use angle addition and subtraction. Define and use complementary, supplementary, and adjacent angles. Define and use linear pairs and vertical angles. Two-Column Proofs List the reasons that can be used in proofs. Write proofs in the standard two-column form. Recall and apply theorems dealing with vertical, complementary, and supplementary angles. Parallel Lines and Planes State the difference between intersecting, parallel, and skew lines. State and apply the theorem concerning the intersection of a plane with two parallel planes. Classify the angles formed when parallel lines are cut by a transversal. Apply parallel line postulates and theorems. Apply theorems concerning lines parallel and perpendicular to a given line. Recognize the statement in an indirect proof that needs to be contradicted. Write an indirect proof. 3

4 5 days: days: Congruent Triangles Classify triangles according to their sides or angles. Identify the corresponding sides and angles of congruent triangles. Use the congruence postulates to prove that two triangles are congruent. Identify corresponding parts that are also congruent once triangles are proven congruent. Inequality Relationships Recall the properties of algebraic inequalities. Solve problems using inequality relationships in one triangle. Solve problems using inequality relationships between two triangles. Solve problems using the inequality relationship involving the shortest distance. Quadrilaterals Define concave and convex polygons. State the number of sides of a polygon, given its name. Solve problems using the definitions of trapezoid, parallelogram, rhombus, rectangle, and square. State and solve problems using the special properties of parallelograms, rhombuses, rectangles, and squares. Determine if a quadrilateral is a parallelogram. Apply theorems concerning the medians of a trapezoid. Midterm Exam Similarity Set up a ratio and express it in simplest form. Solve a proportion for an unknown term. Find the geometric mean of two numbers. State and apply the properties of similar polygons. State and apply the AAA/AA, SAS, and SSS theorems for proving triangles similar. State and apply the theorems concerning a line parallel to one side of a triangle. State and apply the theorem concerning a bisector of an angle of a triangle. Assessment 4

5 days: Right Triangle Relationships State and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle. State and apply the Pythagorean Theorem. Recognize some common Pythagorean triples. State and apply the relationships of the sides of an isosceles right triangle ( ). State and apply the relationships of the sides in a triangle. State and apply the sum of the angles of a triangle theorem. State and apply the theorem about the exterior angles of a triangle. State and apply the theorems that prove right triangles are congruent. Areas and Perimeters of Polygons Describe the concepts of area and perimeter of plane geometric figures. Recognize which formulas for area are used with each figure. Compute the area of quadrilaterals (trapezoids, parallelograms, rhombuses, rectangles, and squares) and triangles. Use Heron s Theorem to find the area of a triangle. Explain the concept of scale factor in similar polygons and how it can be used to compute area and perimeter. Coordinate Geometry Locate points in the coordinate plane using their coordinates. Know and use the distance and midpoint formulas. Prove theorems using coordinate geometry. Statistical Graphs Create line plots, line graphs, bar graphs, and scatter plots. Determine best fit lines. Describe real-world situations using direct, joint, and inverse variations. Use statistics appropriately, and recognize inappropriate uses of statistics. Counting and Probability Count objects in different ways. Calculate simple probability. Find the expected value. 5

6 Data Analysis Determine the mean, median, mode, and range of data. Construct a stem-and-leaf plot. Construct a box-and-whisker plot. Evaluate a data set for outliers. Find the mean absolute deviation of a data set. Semester Review Final Exam Assessment 6