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### More Trains

6-8, 9-12

In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns. ### Recursive and Exponential Rules

6-8, 9-12

In this lesson make connections between exponential functions and recursive rules. Students will use tables to create graphs, define recursive rules and find exponential formulas.### Road Trip!

9-12

Students will plan a road trip, starting in Cleveland, to visit friends in Cincinnati, Pittsburgh, Baltimore, and Boston. However, with the price of gas over $3.00 a gallon, they will figure out the shortest travel route to save on expenses. This lesson investigates three different methods to determine the shortest route: the Nearest Neighbor method, the Cheapest Link method, and the Brute Force method.### Predicting Your Financial Future

9-12

Students often ask, “When are we ever going to use this?” Compound interest is a topic that provides an inherent answer to this question. In this activity, students use their knowledge of exponents to compute an investment’s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt.### There Has to Be a System for This Sweet Problem

9-12

We are confronted with problems on a regular basis. Some of these are easy to solve, while others leave us puzzled. In this lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.### Security Cameras

9-12

In this lesson, students explore properties of polygons by trying to place the minimum number of security cameras in a room such that the full area can be monitored. From these polygons, students discover the formula for the maximum number of cameras needed. Students then use their discoveries to analyze the floor plan of a museum as a culminating activity.### How Should I Move?

6-8, 9-12

This investigation uses a motion detector to help students understand graphs and equations. Students experience constant and variable rates of change and are challenged to consider graphs where no movements are possible to create them. Multiple representations are used throughout the lesson to allow students to build their fluency with in how graphs, tables, equations, and physical modeling are connected. The lesson also allows students to investigate multiple function types, including linear, exponential, quadratic, and piecewise.### How Did I Move?

6-8, 9-12

A common problem when students learn about the slope-intercept equation *y*=

*mx*+

*b*is that they mechanically substitute for

*m*and

*b*without understanding their meaning. This lesson is intended to provide students with a method for understanding that

*m*is a rate of change and

*b*is the value when

*x*= 0. This kinesthetic activity allows students to form a physical interpretation of slope and

*y*-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship.

### Road Rage

9-12

In this lesson, students use remote-controlled cars to create a system of equations. The solution of the system corresponds to the cars crashing. Multiple representations are woven together throughout the lesson, using graphs, scatter plots, equations, tables, and technological tools. Students calculate the time and place of the crash mathematically, and then test the results by crashing the cars into each other.### Linear Alignment

6-8, 9-12

This lesson allows students to explore linear equations and the effects of changing the slope and *y*-intercept on a line. It gives students exposure to

*y*=

*mx*+

*b*, and can be used as an introduction to the topic. Using graphing calculators, students are challenged to overlap lines onto the sides of polygons. To achieve this goal, students change slopes and

*y*-intercepts of lines, noting observations about behavior as they work. As students change the

*y*-intercept of a line, they see it raise or lower the line. As students change the slope, they see it affect the steepness of the line.