PRE-ALGEBRA PREP. Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002.

Transcription

1 PRE-ALGEBRA PREP Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., Course Description: The students entering prep year have differing ranges of exposure to and skill with mathematics. By covering a wide range of topics, this course ensures that all students in the prep year have the skills necessary to succeed in Algebra I. The course begins with a review of the fundamentals of working with numbers. Students learn about decimals, negatives, powers, fractions, percentages, units of measurements, conversions of measurements, and analyzing graphs. Geometry is also introduced. Students will go over angles, how to compute area, volume, and surface area of several shapes, polygons, perimeter, dimensions, reflections, translations, size changes, and similar figures. As algebraic techniques are introduced, students learn to apply those techniques to solve problems including distance/rate/time problems, probability, uses of variables, algebraic equations, graphing equations, and proportional thinking. Calculators are allowed in this course. However, students should not expect to be able to use their calculator on every quiz, test, and homework assignment. Course Goals: 1. Provide students with a solid foundation in working with numbers (powers, roots, percents, ratios, fractions, decimals, signed numbers, etc.) 2. Students will learn to solve basic algebraic equations. 3. Students will be able to create a formula for and compute: the area of geometric shapes, the volume of three-dimensional solids, and the surface area of three-dimensional solids. 4. Students will learn to translate word problems into algebraic equations and solve the algebraic equation. 5. Ensure that all students are prepared for Algebra I.

2 Course Outline/Sequence: A. Chapter 1: Decimal Notation 1.1 Decimals for Whole Numbers 1.2 Decimals for Numbers in Between Whole Numbers 1.3 Estimating by Rounding Up or Rounding Down 1.4 Estimating by Rounding to the Nearest 1.6 Decimals for Simple Fractions 1.7 Decimals for Mixed Numbers 1.8 Negative Numbers 1.9 Comparing Numbers 1.10 Equal Fractions B. Chapter 2: Large and Small Numbers 2.1 Multiplying by 10, 100, 2.2 Powers 2.3 Scientific Notation for Large Numbers 2.4 Multiplying by 1 / 10, 1 / Percent of a Quantity 2.6 From Decimals to Fractions and Percents 2.7 Circle Graphs 2.8 More Powers of Ten 2.9 Scientific Notation for Small Numbers C. Chapter 3: Measurement 3.1 Measuring Length 3.2 Converting Lengths 3.3 Weight and Capacity in the Customary System of Measurement 3.4 The Metric System of Measurement 3.5 Converting Between Systems 3.6 Measuring Angles 3.7 Kinds of Angles 3.8 Measuring Area

3 3.9 Measuring Volume D. Chapter 4: Uses of Variables 4.1 Order of Operations 4.2 Describing Patterns with Variables 4.3 Translating Words to Algebraic Expressions 4.4 Evaluating Algebraic Expressions 4.5 Parentheses 4.6 Grouping Symbols 4.7 Formulas 4.8 Probability 4.9 Open Sentences 4.10 Inequalities E. Chapter 5: Patterns Leading to Addition 5.1 Models for Addition 5.2 Zero and Opposites 5.3 Rules for Adding Positive and Negative Numbers 5.4 Combining Turns 5.5 Adding Positive and Negative Fractions 5.6 Adding Probabilities 5.7 The Commutative and Associative Properties 5.8 Solving x + a = b 5.9 Polygons 5.10 Adding Lengths F. Chapter 7: Patterns Leading to Subtraction 7.1 Two Models for Subtraction 7.2 The Slide Model for Subtraction 7.3 Solving x a = b 7.4 Solving a x = b 7.5 Counting and Probability with Overlap 7.6 Angles and Lines 7.7 Angles and Parallel Lines

4 7.8 Special Quadrilaterals 7.9 The Triangle-Sum Property G. Chapter 8: Displays 8.1 Graphs and Other Displays 8.2 Bar Graphs 8.3 Coordinate Graphs 8.4 Graphing Lines 8.5 Translations (Slides) 8.6 Reflections 8.7 Reflection Symmetry H. Chapter 9: Patterns Leading to Multiplication 9.1 The Area Model for Multiplication 9.2 Volumes of Rectangular Solids 9.3 Multiplication of Fractions 9.4 Multiplying Probabilities 9.5 The Rate Factor Model for Multiplication 9.6 Multiplication with Negative Numbers and Zero 9.7 Size Changes Expansions 9.8 Size Changes Contractions I. Chapter 10: Multiplication and Other Operations 10.1 Multiplication as Shortcut Addition 10.2 Solving ax = b 10.3 Using ax = b 10.4 Solving ax + b = c 10.5 Solving ax + b = c when a Is Negative 10.6 The Distributive Property 10.7 The Surface Area of a Box 10.8 Dimensions and Units 10.9 Areas of Triangles Area of Trapezoids

5 J. Chapter 11: Patterns Leading to Division 11.1 Integer Division 11.2 The Rate Model for Division 11.3 Division of Fractions 11.4 Division with Negative Numbers 11.5 The Ration Comparison Model for Division 11.6 Proportions 11.7 The Means-Extremes Property 11.8 Proportions in Similar Figures 11.9 Proportional Thinking K. Chapter 12: Real Numbers, Area, and Volume 12.1 Converting Decimals to Fractions 12.2 Square Roots 12.3 The Pythagorean Theorem 12.4 The Circumference of a Circle 12.5 The Area of a Circle 12.6 Surface Areas of Cylinders and Prisms 12.7 Volumes of Cylinders and Prisms 12.8 Spheres L. Coordinate Graphs and Equations 13.1 Graphing y = ax + b 13.2 Situations Leading to ax + b = cx + d 13.3 Solving ax + b = cx + d 13.5 Graphs of Formulas Course Method: The method varies by teacher, but typically includes review of previous homework assignments, introduction of new material, working through example problems, and assignment of new homework. Frequency of quizzes and tests varies by teacher. Evaluation: The evaluation procedures vary by teachers, but typically include a combination of homework, quizzes, and tests. Some teachers also collect and review student notes.

6 Supplemental Material: Varies by teacher.