#### Unit 5: Rational Numbers

Introduction:

This Project Based Pre-Algebra unit is meant to provide supplemental support to a standard Pre-Algebra course.  The topics covered are typical to a standard Pre-Algebra course and the sequence follows:  Glencoe - Pre-Algebra (2003 ed.).  The projects are meant to connect the world of math to that of art. They allow students to make connections that would not normally occur while completing problem sets. These projects follow the typical sequence of a 7th/8th grade Pre-Algebra course. The major concepts covered will be integers, equations, factors and fractions, rational numbers, ratios, proportions, percents, inequalities, functions, graphing, right triangles, and two-dimensional figures. These projects are to be used in conjunction with a standard Pre-Algebra curriculum.

Prerequisites:

The Project Based Pre-Algebra unit should be used concurrently with a standard Pre-Algebra course and should be preceded by Math 6.

Scope:

1.  Topics covered during Pre-Algebra:

Tools of Algebra:

• Problem Solving Plans
• Numbers and Expressions
• Variables and Expressions
• Properties
• Simplifying Algebraic expressions using the Associative and Commutative Properties
• Ordered Pairs and Relations
• Scatter Plots

Integers:

• Integers and Absolute Value
• Subtracting Integers
• Multiplying and Dividing Integers
• The Coordinate System

Equations:

• The Distributive Property
• Simplifying Algebraic Expressions
• Solving One Step Equations
• Solving Two Step Equations
• Writing Two Step Equations
• Using Formulas

Factors and Fractions:

• Factors and Monomials
• Powers and Exponents
• Prime Factorization
• Greatest Common Factor
• Simplifying Algebraic Fractions
• Multiplying and Dividing Monomials
• Negative Exponents
• Scientific Notation

Rational Numbers:

• Writing Fractions as Decimals
• Rational Numbers
• Multiplying Rational Numbers
• Dividing Rational Numbers
• Adding and Subtracting Like Fractions
• Least Common Multiple
• Adding and Subtracting Unlike Fractions
• Measures of Central Tendency
• Solving Equations with Rational Numbers

Ratios, Proportions, and Percents:

• Ratios and Rates
• Using Proportions
• Scale Drawings and Model
• Fractions, Decimals, and Percents
• Using the Percent Proportion
• Using Percent Equations
• Percent of Change
• Probability and Predictions

Equations and Inequalities:

• Solving Equations with Variables on Each Side
• Solving Equations with Grouping Symbols
• Inequalities
• Solving Inequalities

Functions and Graphing:

• Functions
• Linear Equations in Two Variables
• Graphing Linear Equations Using Intercepts
• Slope
• Rate of Change
• Slope-Intercept Form
• Writing Linear Equations
• Best-Fit Lines
• Solving Systems of Equations
• Graphing Inequalities

Real Numbers and Right Triangles:

• Squares and Square Roots
• The Real Number System, Angles
• Triangles
• The Pythagorean Theorem
• The Distance and Midpoint Formulas
• Similar Triangles and Indirect Measurement
• Sine, Cosine, and Tangent Ratios

Two Dimensional Figures

• Line and Angle Relationships
• Congruent Triangles
• Transformations of the Coordinate Plane
• Area of Parallelograms, Triangles, and Trapezoids
• Polygons
• Circumference and Area of Circles
• Area of Irregular Figures

2.  Skills to be taught:

• Fluency with Rational Numbers
• Graphing and graphical analysis
• Collaborative and group learning
• Communication: oral and written
• Computation
• Critical thinking
• Problem Solving
• Observation

Sequence:

The entire unit corresponds with a yearlong Pre-Algebra course.   The projects range from 90-120 minutes.  Each unit has one project and they usually align with the one or two topics, so assign them accordingly.  The projects will typically require at least two 45 minute periods to complete.

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