The purpose of this activity is to introduce a context where exponent notation is naturally useful. The task lends itself to connecting repeated calculations with an expression involving exponents (MP8). The situation described in the task is based on a legend that has a rich mathematical history. If time permits, consider inviting students to research the different versions of the legend and their connections to mathematical communities in Asia over time.

In the digital version of the activity, students use an applet to see how the number of grains of rice increases each day through day 16. The applet allows students to stop at any time and see an expression that represents the amount of rice on any given day. Use the digital version to help students visualize how quickly the amount of rice increases or to simply provide an additional tool for all students to better understand the nature of exponential growth.

If students don't have individual access, displaying the applet for all to see would be helpful after students answer the second question.

The goal of the discussion is for students to connect the idea of multiplying factors of 2 to get the expression and to define exponent more generally. Display the expression , and explain that this notation is convenient for communicating and computing repeated multiplication. Remind students that the 3 in is called an “exponent.” Explain that it is used to indicate how many factors of 2 to multiply, so means: . 

Invite students to share their responses. Ask questions, such as: 

• “How did you know what represents? How did you find its value?”
• “How many times as much as is ? Could you answer this without finding the value of both expressions?”
• “How did you organize your work to answer questions 3 and 4?”
• “How many grains of rice would the inventor receive at the end of 32 days (half the chessboard)? After 64 days? Does this surprise you?”

In this activity, students practice finding the value of exponential expressions and writing equivalent expressions. To determine equivalence, students need to apply the meaning of exponents and to look for structure (MP7).

When evaluating exponential expressions, students might apply the order of operations incorrectly. For example, they might interpret as instead of 2 multiplied by itself 4 times. Students might also multiply the base and exponent, for instance, writing  instead of . If so, ask students to rewrite the expressions without exponents, for example, .    

The purpose of the discussion is to highlight that we can use exponents to express numbers in multiple ways. 

Review students’ responses to the first question and address any misconceptions. Then invite students to share some of their expressions for the second question. Look for expressions that go beyond the more obvious choices and that involve other operations. If students only share expressions that include or , challenge them to come up with one more expression that involves an exponent and another operation. For any expression presented, ask other students confirm that it has the value of 81.