Problem Solving in Pre-algebra
Problem Solving in Pre-algebra is a CTY Online course which requires a qualifying math score on the SCAT or SAT and completion of Pre-algebra or equivalent in school. It's course code is PS3 and the course lasts about 3 months. And it is for people in grades 6-8.
Contents
Course Description
From the CTY Online Catalog:
CTY's Problem Solving and Enrichment Math courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on software provided by Riverdeep, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and module tests. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.
Problem Solving in Pre-algebra prepares students for a more formal study of mathematics in middle school. It is appropriate for students who have a good understanding of concepts in pre-algebra, but who wish to enrich their skills through interesting word problems. Students continue the study of numbers and their operations by exploring:
ratios proportions algebraic concepts radicals and exponents geometry statistics probability Students apply what they have learned to solve sets of questions at varying levels of difficulty. Students are also invited to participate and ask questions in an open Help Room guided by instructors.
This course provides an excellent foundation for students who will be advancing into Honors Algebra I.
Topics
Module 1: Essentials of Algebra
- Algebra Fundamentals
- Introducing Variables
- Identifying Components of Algebraic Expressions
- Replacing Variables in a Formula
- Evaluating an Algebraic Expression
- Representing the Dimensions and Area of a Rectangle
- Combining Like Terms
- Evaluating Expressions Using Substitution
- Simple Equations
- Using Variables to Express Relationships
- Simplifying Algebraic Expressions
- Solving Simple Equations
- Variables on Both Sides of the Equation
- Writing Equations
- Simplifying Both Sides of an Equation
- Checking the Solution to an Equation
- Solving Literal Equations
- Identifying the Variables in a Given Formula
- Rewriting a Formula in Terms of a Different Variable
- Substituting Values and Solving an Equation
Module 2: Fundamentals of Geometry
- Geometry Fundamentals
- Naming and Measuring Angles
- Defining Complementary and Supplementary Angles
- Recognizing Congruent Angles
- Triangles
- Classifying Triangles by Sides
- Exploring the Area of a Triangle
- Classifying Triangles by Angles
- Volume and Surface Area
- Calculating Volume of a Right Triangular Prism
- Calculating Surface Area of a Right Triangular Prism
- Calculating Volume and Surface Area of a Right Cylinder
Module 3: Radicals and Exponents
- Introduction to Radicals & Pythagorean Theorem
- Exploring the Pythagorean Theorem
- Investigating Squares and Square Roots
- Defining Irrational Numbers
- Introduction to Scientific Notation
- Writing Numbers Using Scientific Notation
- Comparing Numbers in Scientific Notation
- Writing Numbers Between 0 and 1 in Scientific Notation
Module 4: Ratio and Proportion
- Ratio
- Defining Ratio
- Expressing Ratios as Equivalent Fractions and Decimals
- Forming Ratios Between Unlike Quantities
- Proportion
- Defining a Proportion
- Solving for a Variable in a Proportion
- Applying the Means/Extremes Property
- Direct and Inverse Variation
- Exploring and Solving Direct Variation Problems
- Exploring Inverse Variation
- Solving Inverse Variation Problems
- Similar Polygons
- Defining Similarity
- Identifying Equivalent Ratios
- Setting Up and Solving Proportions in Similar Polygons
Module 5: Statistics
- Interpreting and Constructing Graphs
- Exploring Line Graphs
- Exploring Bar Graphs
- Interpreting Pie Charts
- The Mean, Median, and Mode
- Defining the Mean and Median
- Defining the Mode
- Calculating the Mean, Median, and Mode
- Frequency Distribution and Histograms
- Creating and Interpreting a Frequency Table
- Defining a Histogram
- Exploring Cumulative Frequency Graphs
Module 6: Probability
- Simple Probability
- Defining and Expressing Probability
- Calculating Probabilities on a Color Wheel
- Determining Probability of Complementary Events
- Probability of Combined Events
- Calculating the Probability of Independent Events
- Determining the Sample Space of an Experiment
- Calculating the Probability of Dependent Events
