# Sorting out the Change

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## Objective

SWBAT analyze the rate of change to determine whether a relationship is linear or exponential and write the corresponding equation.

#### Big Idea

Students identify the type of function (linear or exponential) which represents a situation & writes equations to model these situations.

## Warm-up

10 minutes

Depending on where class left off and how students responded to the Thumbs Assessment yesterday, I will have students complete the Isotope Problem and/or review the various solution methods. I may have students present their approaches. Hopefully I can find an example of the three approaches that I am seeing (and maybe even ones that I’m not thinking about) and have those students just slip their work under the document camera with a quick explanation.

The three main approaches I will be looking for to be demonstrate (or I will demonstrate) are:

1) Finding from two points (like page 19 of flipchart)

2) Writing the exponential function in terms of number of half-lives and then substituting in the half lives as a function of time.

3) Identifying the rate of change in the table and using the initial value to write the equation.

## Sorting Out the Change

35 minutes

The next task I want students to work through is the Student Handout Sorting out the Change.docx. Check out this video, Sorting the Change, video narrative, middle.MP4, for more details on how I like to run this activity.

This activity was adapted from a task written by The mathematics Vision Project.  The original lesson can be found at www.mathematicsvisionproject.org.

## Closure: 3-2-1 Assessment

5 minutes

Technically, students have been exposed to everything of extreme importance in this unit at this point. Over the next week students will be practicing a bit more with finding equations of exponential functions and real world applications and will also take a more in-depth look at stretching exponentials. So at this point I would like to know how students feel that they are progressing. I want students to complete a 3-2-1 Assessment for this unit. I will ask students for 3 things they’ve learned, 2 questions they still have, and 1 thing they want to tell me.