# Making Sense of Fractional Exponents Unit (Teachers)

Students explore the growth of magical beanstalks. The height of one beanstalk quadruples each day and the height of another triples each day. They model the growth of the beanstalks by creating timelines and equations. They then use these models to investigate the meaning of fractional exponents in this context

##### Lesson 1: Investigating the Growth of Magical Beanstalks

Arobindo and Josh explore the growth of magical beanstalks. These beanstalks’ heights increase by the same factor each day. In this lesson, the students draw pictures that show these factors. They also explore how the beanstalks are growing over several days.

##### Lesson 2: Creating a Timeline

Arobindo and Josh create a timeline that shows the growth of the beanstalk over several days. They find several mathematical relationships among the heights and among the days on their timeline.

##### Lesson 3: Creating an Equation

The students use their timeline to find expressions for the height of the beanstalk on several days. They use similar reasoning to create an equation that gives the height of the beanstalk on any day.

##### Lesson 4: Exploring the Equations for Other Magical Beanstalks

The students explore the growth of new magical beanstalks. While all the beanstalks are similar in that they grow by a consistent factor each day, the factors they grow by are different and their heights on Day 0 are not always 1 cm. Josh and Arobindo explore how these changes affect the equations that model their growth.

##### Lesson 5: Introduction to Fractional Exponents

The students begin to explore the height of a magic beanstalk at times between Day 0 and Day 1. Specifically, the investigate the height of a beanstalk on Day ½, day ¼, and Day ⅓.

##### Lesson 6: Finding the Height at Any Time between Day 0 and Day 1

The students continue to explore the height of their beanstalk at fractional times of day. In this lesson, they discover how to find the height of the beanstalk at any time between Day 0 and Day 1.

##### Lesson 7: Finding the Height at Any Time

The students build on what they have learned to discover how to find the height of the beanstalk at any time.