This is a unit that formalizes the definition of functions. Students will connect the idea of mathematical relationships to the concept of functions. With a mix of direct instruction, guided notes with procedural practice, and individual practice, this unit will ground students in the concept and provide a deep understanding of its usefulness.

In this lesson, students relate constant speed and proportional relationships to linear functions using information from a table. Students know that distance traveled is a function of the time spent traveling and that the total cost of an item is a function of how many items are purchased.

In this lesson, students know that a function allows us to make predictions about the distance an object moves in any time interval. Students calculate average speed of a moving object over specific time intervals. Students know that constant rate cannot be assumed for every situation and use proportions to analyze the reasoning involved.

Using the LEGO MINDSTORMS(TM) NXT kit, students construct experiments to measure the time it takes a free falling body to travel a specified distance. Students use the touch sensor, rotational sensor, and the NXT brick to measure the time of flight for the falling object at different release heights. After the object is released from its holder and travels a specified distance, a touch sensor is triggered and time of object's descent from release to impact at touch sensor is recorded and displayed on the screen of the NXT. Students calculate the average velocity of the falling object from each point of release, and construct a graph of average velocity versus time. They also create a best fit line for the graph using spreadsheet software. Students use the slope of the best fit line to determine their experimental g value and compare this to the standard value of g.

Students come to see the exponential trend demonstrated through the changing temperatures measured while heating and cooling a beaker of water. This task is accomplished by first appealing to students' real-life heating and cooling experiences, and by showing an example exponential curve. After reviewing the basic principles of heat transfer, students make predictions about the heating and cooling curves of a beaker of tepid water in different environments. During a simple teacher demonstration/experiment, students gather temperature data while a beaker of tepid water cools in an ice water bath, and while it heats up in a hot water bath. They plot the data to create heating and cooling curves, which are recognized as having exponential trends, verifying Newton's result that the change in a sample's temperature is proportional to the difference between the sample's temperature and the temperature of the environment around it. Students apply and explore how their new knowledge may be applied to real-world engineering applications.

This mini-unit is part of a much larger content focus on Linear Functions in an 8th grade Resource Math class. Students will be learning about the basics in functions and their use in Pre-Algebra. This unit allows students to receive direct interaction with teachers to receive content in a managable format, while giving them opportunities to learn and discover some of the content on their own. The mini-unit focus solely on the different representations of functions in their basic form. By the end of the unit, students will be able to identifying and compare and contrast different representations of functions.

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 8th Grade Math. 

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 8th Grade Math. 

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 8th Grade Math. 

This task presents an opportunity to explore a more general and non-algebraic view of functions.