Exponential Functions – One Grain of Rice

Read the book, One Grain of Rice, to your students. You will be amazed at how older students will pay attention when you read the book to them. It is a nice way to introduce the concept of Exponential Functions and start the class differently than the norm.

One Grain of Rice Activity

Give them a calendar page and have them fill in the first eight days with the number of grains of rice they would receive if they had made the deal described in the story.

Next, have the students make a T-chart that has the domain as the day and the range as the number of grains of rice for that day. Have the students express the range in prime factorization in exponential form.

Ask them if they see a pattern. Working and discussing with other students is always a good idea. The instructor acts as a facilitator and asks questions such as:

• What do all range elements in the set have in common?
• Do you see a pattern in the exponents?
• Is there a way to express the number 1 so that it fits the pattern?

Results

What you want students to see is that each element in the range is the number 2 with an exponent that is one less than the corresponding domain element, including 2⁰.

Ask them to write an equation for the table. Guide discussion to come up with f(n) = 2ⁿ⁻¹. Then ask students to find and compare the number of grains of rice for any other day on the calendar you choose.

Have students establish equations if the number of grains of rice were tripled or quadrupled. The equations will be f(n) = 3ⁿ⁻¹.and f(n) = 4ⁿ⁻¹ respectively.

Freebie Pre-Requisite Resources for this Lesson:

• Properties of Real Numbers – The Importance of Differentiating Directions in Algebra
• The Nightmare of Exploring Conic Sections
• Area Under a Curve – Is your Umbrella Big Enough?
• The Distributive Property – Cupcakes and Algebra
• How to Teach Patterns and Linear Functions
• Rate of Change and Slope – Ski Through Algebra!
• Factoring to Solve Quadratic Equations – Know Your Roots
• Hybrid Flipped Classroom Model
• Irrational Numbers – K.I.S.S.
• Adding and Subtracting Fractions – Cut the Cheese
• Solving Two-Step Equations – Push the Undo Button