Episode Guide

1. Variables and Patterns of Change — In Part I, Janel Green introduces a swimming pool problem as a context to help her students understand and make connections between words and symbols as used in algebraic situations. In Part II, Jenny Novak’s students work with manipulatives and algebra to develop an understanding of the equivalence transformations used to solve linear equations.

2. Linear Functions and Inequalities — In Part I, Tom Reardon uses a phone bill to help his students deepen their understanding of linear functions and how to apply them. In Part II, Janel Green’s hot dog vending scheme is a vehicle to help her students learn how to solve linear equations and inequalities using three methods: tables, graphs, and algebra.

3. Systems of Equations and Inequalities — In Part I, Jenny Novak’s students compare the speed at which they write with their right hands with the speed at which they write with their left hands. In Part II, Patricia Valdez’s students model a real-world business situation using systems of linear inequalities.

4. Quadratic Functions — In Part I, Tremain Nelson and his students use a basketball toss as a launching point to learn how the constants in the equation y = a(x – h)2 + k transform the parent function y = x2. In Part II, Tremain and the students apply what they learned in the previous lesson to model several bounces of a ball dropped below a motion detector.

5. Properties — In Part I, Tom Reardon’s students come to understand the process of factoring quadratic expressions by using algebra tiles, graphing, and symbolic manipulation. In Part II, Sarah Wallick’s students conduct coin-tossing and die-rolling experiments and use the data to write basic recursive equations and compare them to explicit equations.

6. Exponential Functions — In Part I, Orlando Pajon uses a population growth simulation to introduce students to exponential growth and develop the conceptual understanding underlying the principles of exponential functions. In Part II, a scenario from Alice in Wonderland helps Mike Melville’s students develop a definition of a negative exponent and understand the reasoning behind the division property of exponents with like bases.

7. Direct and Inverse Variation — In Part I, Peggy Lynn’s students simulate oil spills on land and investigate the relationship between the volume and the area of the spill to develop an understanding of direct variation. In Part II, they develop the concept of inverse variation by examining the relationship of the depth and surface area of a constant volume of water that is transferred to cylinders of different sizes.

8. Mathematical Modeling — In Part I, Sarah Wallick’s students use a pulley system to explore the effects of one rotating object on another and develop the concept of transmission factor. In Part II, Orlando Pajon’s students conduct a series of experiments, determine the pattern by which each set of data changes over time, and model each set of data with a linear function or an exponential function.