## One Grain of Rice

• Lesson
6-8
1

In this lesson, students take on the role of a villager in a third-world country trying to feed her village. While listening to you read aloud the book One Grain of Rice by Demi, students work collaboratively to come up with a bargaining plan to trick the raja into feeding the village using algebra, exponential growth, and estimation.

The following excerpt is taken from the book One Grain of Rice by Demi. (If you do not have access to this book, consider telling students a similar story as a way of introducing the lesson. This will also provide the background needed for writing algebraic equations, as well as the other mathematical details of the lesson. When using this lesson plan, simply skip the parts that indicate which pages of the book to read aloud, but note that you can still ask the same questions.)

Long ago in India, there lived a raja who believed that he was wise and fair. But every year he kept nearly all of the people’s rice for himself. Then when famine came, the raja refused to share the rice, and the people went hungry. Then a village girl named Rani devises a clever plan. She does a good deed for the raja, and in return, the raja lets her choose her reward. Rani asks for just one grain of rice, doubled every day for thirty days. Through the surprising power of doubling, one grain of rice grows into more than one billion grains of rice — and Rani teaches the raja a lesson about what it truly means to be wise and fair.

Arrange the students into small groups (3 or 4 students per group usually works best) prior to beginning the lesson. Begin the lesson by introducing the book. Ask students to predict what the book might be about based on the title, front cover, and back cover. Explain to the class that this book is about a village in India that did not have enough food to support its population because of famine and because the raja kept all of the rice for himself.

Tell the students to listen carefully to the scenario presented in the book, as they will be creating their own plan to feed the village. Read One Grain of Rice aloud to the end of page 5, stopping immediately after, "The people had no rice to give to the raja, and they had no rice to eat." (This is where you could tell them your own story if you do not have access to the book. For now, stop before you reveal the main character's plan.)

Ask students what they think famine and hunger mean and what may cause famine in a country. Allow for class discussion of real-life issues about this worldwide problem. Continue reading pages 6‑11 aloud, finishing when the raja says, "Ask me for anything, and you shall have it." Upon finishing page 11, let students discuss in their small groups what their plan would be. Ask them, "If you were Rani, what would you ask the raja for as a reward?" Ask students to keep in mind that Rani is an unselfish girl who is trying to feed herself and the rest of the village. Continue asking questions and surveying the groups for their different ideas and opinions.

Continue reading pages 12‑15 aloud. Ask the students if Rani’s plan was similar or different to the plan that their group created. Continue to ask questions of the groups to get them to compare, contrast, and justify their explanations. After providing plenty of time for discussion, give the students the One Grain of Rice activity sheet and allow them approximately 5 minutes in their groups to complete Question 1 and estimate (without using calculators) how much rice Rani would receive in 30 days. Upon completion of the groups’ estimations, have students share their estimates with the entire class, as well as compare their plan with Rani’s plan.

Read through the end of the book. Ask students if they think Rani was clever for asking for the rice in the way that she did. Allow for discussion. In small groups, have students complete Questions 2 and 3 on the One Grain of Rice activity sheet. They will figure out exactly how many grains of rice Rani received in all. After students have finished these questions, the groups may continue to work on the activity sheet with their group members, where they will write Rani’s plan as a sentence using only numbers and symbols (i.e., as an algebraic equation).

After about 10 minutes of group work, allow students to share their equations with the entire class. Have students check each equation for accuracy, allowing them to point out problems and discrepancies as you go. If students did not generate an acceptable equation in Question 6, they should create a new equation in Question 7 based on the class discussion. Acceptable equations are:

• Grains of rice (g) that Rani receives on day n: g = 2n – 1
• Total grains of rice (t) that Rani receives through n days: t = 2n – 1

If you choose, have students record their initial plan in their journal and compare and contrast it with Rani’s plan. Students should answer questions such as:

• Which plan do you think is better?
• Which plan would feed more people?
• How many more grains of rice did Rani get than you would have received at the end of the 30 days?
• Can you think of another bargain that you could have made with the raja to get enough rice to feed the village?

You may want to write these questions on the board for students to use to guide their responses.

It is important that students record the algebraic equation that their group devised and write in words why the equation does or does not work. If their equation does not work, they should create a new equation and explain why the new equation is correct. Be sure to encourage thorough answers to Question 7 on the activity sheet.

### Reference

Demi. 1997. One Grain of Rice. New York: Scholastic Press.

Assessment Options

1. While students are involved in small-group work, circulate among the groups, listening to their conversations and judging participation and accuracy among the members. Give students a minimal amount of help on their algebraic equation. Allow them to struggle and generate an equation on their own. Assess the students on their participation in class, their completed activity sheet, and their journal entries.
2. Ask students to write an entry in their journal explaining why Rani's plan was so effective. Emphasize that they should use a mathematical explanation to justify their response. Additionally, ask them to create a plan that would be as effective as Rani's.

Extensions

1. Challenge students to calculate the volume of their classroom. Ask them to determine the volume of the total number of grains of rice that Rani receives, and then figure out how many classrooms would be required to store all of Rani's rice.
2. Have students weigh rice and figure out how many animals it would take to carry all of Rani’s rice, much like the book did.
3. Have students estimate the number of grains in a box of rice purchased at a store. Then, based on the cost of the box, have them figure out how much one grain of rice would cost (and how much it would cost to feed Rani’s entire village).

Questions for Students

1. If you were Rani, what would you ask the raja for as a reward? How would you phrase your request to trick the greedy raja into thinking that he is not giving you very much rice?

[Some students may just ask for a large enough number of rice grains that they feel will feed the village people. If that happens, ask the students whether the greedy raja would be willing to give up such a large amount. Some other students might also come up with plans of their own similar to Rani’s. They may or may not be in algebraic form. Challenge students who come up with ideas to write a corresponding algebraic equation.]

2. Estimate how many grains of rice Rani will have at the end of 30 days using her plan.

[Answers will vary; she will have 1,073,741,823 grains of rice at the end of 30 days — more than one billion grains of rice!]

3. How many more grains of rice did Rani get than you would have received at the end of the 30 days using your plan?

[This will vary greatly depending on the different plans the groups or individuals devise.]

4. Devise another plan that you could have made with the raja to get 2 billion grains of rice in 30 days.

[Answers will vary, although students should be able to describe their plan mathematically.]

5. How did you translate your plan into an algebraic equation?

[Explanations will vary depending on the plan. An acceptable answer would be something like, "We tried to write down step by step what we would do if we were Rani. Then, we looked for patterns. Once we figured out what the pattern was, we put in a variable for the number of days. Finally, we plugged in different numbers of days to see if we got the same answer as we had when we wrote it out."]

6. Did your equation work when you put Rani’s numbers into it? Why or why not?

[Answers will vary depending on the plan. Make sure students have an explanation for why they believe their equation did or did not work.]

Teacher Reflection

• Was your lesson developmentally appropriate? If not, what was inappropriate? What would you do to change it?
• How did students demonstrate understanding of the material presented?
• Were concepts presented too abstractly? Too concretely? How would you change them?
• What were some of the ways that students demonstrated that they were actively engaged in the learning process?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments, and were they effective?

### Learning Objectives

By the end of this lesson, students will:

• Create a general algebraic formula using variables.
• Understand how to express mathematical thinking in a concise written or verbal manner.
• Use estimation skills to make predictions.

### NCTM Standards and Expectations

• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
• Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

### Common Core State Standards – Mathematics

• CCSS.Math.Content.6.EE.A.3
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

• CCSS.Math.Content.7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that ''increase by 5%'' is the same as ''multiply by 1.05.''

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.
• CCSS.Math.Practice.MP8
Look for and express regularity in repeated reasoning.