Problem Solving in Pre-algebra

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Course Description

Description

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. It provides an excellent foundation for students who will be advancing into Honors Algebra I.

Materials Needed

There are no required materials for this course.

List of 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

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System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, bluejay.cty.jhu.edu, and any other course web sites.

This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment. (Note: iOS & Android devices cannot run Java applets.)