These lessons are designed to give teachers a script to follow when using the activities and discussions developed for Project Interactivate. They are arranged according to the NCTM Principles and Standards for School Mathematics and the NCEE Performance Standards for Middle School:

Number and Operation Concepts: Includes working with fractions and decimals, clock arithmetic, and finding number patterns. (NCTM Content Standard and NCEE Standard M1)

Geometry and Measurement Concepts: Includes basic notions of lines, rays and planes, working with tessellations, fractals. (NCTM Content Standards and NCEE Standard M2)

Function and Algebra Concepts: Includes an introduction to functions, special properties of linear functions, graphs and the coordinate plane, and reading graphs. (NCTM Content Standard and NCEE Standard M3)

Probability and Data Analysis Concepts: Includes an introduction to probability, conditional probability, sampling, expected value, statistics, histograms, boxplots, and the normal curve. Also includes statistical simulations. (NCTM Content Standard and NCEE Standard M4)

Each lesson gives prerequisites, preparation instructions, a suggested outline, and alternate outlines. Teachers who have designed alternative versions of lessons are encouraged to submit them to the Interactivate Archives. Contact the Project Interactivate Team for details.


Number and Operation Concepts

Fraction Facts Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.
Multiplying Decimals and Mixed Numbers Reinforces skills associated with multiplying decimals and mixed numbers.
Patterns In Fractals Introduces students to the idea of finding number patterns in the generation of several different types of fractals.
Patterns In Pascal's Triangle Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.
Sets and Venn Diagrams Introduces students to the notions of sets, elements, and Venn diagrams.
An Introduction to Sequences Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
Clock Arithmetic and Cryptography Introduces students to modular (clock) arithmetic and how it can be used to encode messages using simple shift, multiple and affine ciphers.

Geometry and Measurement Concepts

Perimeter Introduces students to the concept of perimeter.
Area Introduces students to the concept of area.
Length, Perimeter and Area Introduces students to length, perimeter and area.
Lines, Rays, Line Segments, and Planes Introduces students to lines, rays, line segments, and planes.
Angles Introduces students to acute, obtuse, and right angles as well as alternate interior angles, alternate exterior angles, vertical angles, and adjacent angles.
Quadrilaterals Introduces students to quadrilaterals, with an emphasis on parallelograms, rectangles, and trapezoids as well as the characteristics that define each type of quadrilateral.
Surface Area and Volume Introduces students to the concepts of surface area and volume.
Pythagorean Theorem Demonstrates the Pythagorean Theorem and its applications.
Translations, Reflections, and Rotations Introduces students to the concepts of transformations.
Geometry in Tessellations Explores lines, planes, angles and polygons in tessellations
Symmetry in Tessellations Examines plane symmetry
Visual Patterns in Tessellations Explores the mathematical nature of art and tilings and looks at the role of math in nature and our culture
Introduction to Fractals: Infinity, Self-Similarity and Recursion Introduces the ideas and motivates the activities
Geometric Fractals Outlines the approach to building fractals by cutting out portions of plane figures
Fractals and the Chaos Game Outlines the approach to playing the chaos game and how it relates to geometric fractals
Properties of Fractals A capstone lesson that allows students to build a working definition of a fractal
Chaos Discusses the concept and application of chaos
Pascal's Triangle Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results
Irregular Fractals Looks at how irregular fractals can be generated and how they fit into computer graphics
The Mandelbrot Set Introduces all of the Two Variable function and prisoner/escapee notions necessary to understand the Mandelbrot set

Function and Algebra Concepts

Introduction to Functions Introduces the basic concept of an algebraic function
Introduction to Linear Functions Introduces the basic concepts and definitions of linear functions
Graphing and the Coordinate Plane Introduces the basic concepts of graphing
Cartesian Coordinate System Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."
Graphs and Functions Demonstrates the connections between formulas and graphs
Functions and the Vertical Line Test Introduces students to the vertical line test for graphs of functions
Reading Graphs Demonstrates the connections between formulas, graphs and stories
Impossible Graphs Provides information on the distinguishing features of both possible and impossible graphs of functions, as well as the causes of graphical impossibility

Statistics and Probability Concepts

Probability and Sports Considers probability concepts from the practical questions that arise in professional sports
Ideas that Lead to Probability Introduces concepts concerning probability
Introduction to the Concept of Probability Continues the introduction of concepts about probability
Probability and Geometry Considers the connections between geometry and probability
Conditional Probability and Probability of Simultaneous Events Introduces conditional probability and the probability of simultaneous events
Replacement and Probability Extends the notion of conditional probability by discussing the effects of replacement on drawing multiple objects
From Probability to Combinatorics and Number Theory Looks at data structures and their applications to probability theory
Expected Value Introduces payoffs and expected value
Unexpected Answers Considers probability problems with unexpected and surprising answers
Statistics and Shopping Looks at statistics and data analysis concepts from the practical questions that arise in everyday life
Mean, Median and Mode Introduces statistical measures of center
Stem-and-Leaf Plots Introduces students to stem-and-leaf plots and calculating the mean, median, and mode from the plots.
Histograms and Bar Graphs Introduced the fine points of using bar graphs and histograms
Box Plots Introduces students to quartiles and box plots
The Bell Curve Introduces the normal distribution and looks at the bell curve controversy

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