Place Value: Hands-on role play activity
Counting the Rice

Grade Levels:

2^nd to 8^th

Summary:

Through this hand-on and role play activity the students will discover the concept of place value. Using different bases, this activity can be used through middle school.

Objectives:

The students should end up with a real good understanding of the place value concept because they learn it by doing it.

Materials:

1. About 200 small objects such as pebbles, marbles, or candy (m&m's might work well)
2. Blackboard and chalk
3. All the students in the class

Procedure:

The activity is designed so that the students discover the concept of place value by themselves. You should allow them to try to develop the concept on their own. I recommend that you do not tell them the story but go directly into the Activity section. When they complete that you can tell them the story. This activity also allows, by going into the Extra Activity section, to learn other bases and really synch in the concept of place value! You can conclude the lesson or activity by sharing with them some of the very interesting historical facts.

Feedback:

I'd love to hear from you if you end up using it in class!

Background Information

I read this some time ago but I don't recall where. I also don't know if it is historically accurate, but I think that this activity can really help kids grasp the notion of place value and specifically our common base ten numeric system. The activity has been fictionalized a little to help in its presentation.

The Story

Long time ago, probably more that that six thousand years before there was a written numerical system, somewhere in Mesopotamia or Egypt, there was a king who ruled a land that was rich and fertile and produced plentiful rice. The people of the land had to pay taxes to the king in the form of sacks filled with rice. Once a month, exactly on the day of full moon, people from all over the kingdom would arrive very early to the King's castle with lots of rice sacks. They would stand in line and each of them delivered their sacks onto a big pile. The king, being so egotistic and self-centered, wanted to have an accurate count of the number of rice sacks that he collected, so he pushed his priests to come up with a method to count and record the number of sacks collected on those special days.

They had three (or more) people standing next to the king. Each of them represented one of the place value digits or columns and had ten finger to count. As the farmers started bringing the sacks of rice, the first person next to the king started adding the sacks with his fingers until he ran out of fingers. At that point, once he reached ten, the next person over started counting how many times the first person ran out of fingers (so to speak). On a good day (lots of rice being brought to the king) the second person would also run out of fingers and that is when the third person would start counting (with his fingers), how many times the second person ran out of fingers. And on and on for the whole day. It must have been very boring and tiring for the third and fourth persons doing the counting; standing there all day with one or two fingers raised. At the end of the day, when all the rice sacks had been collected, they would capture the finger count into special symbols, one for each counting person and a different symbol depending on how many fingers the person had raised. This became the written base ten numerical system.

The Activity

I would follow these steps to re-enact the Counting the Rice story with the students in the class:

1. Ask the class to think why it is that we have a decimal system, i.e. one consisting of ten symbols, 0 (zero) to 9 (nine). Allow 5 minutes or so to hear as many of their theories as possible. Don't mention the story to allow them to come up and express any ideas that might be in their minds. Remember that the fact that our standard numerical system is decimal might be because we have indeed ten fingers, but it might not. I don't know that we know this for a fact.
2. Tell them the story. Better yet, you might decide not to tell them the story. Get them going (as described in the next step), have them "run out of fingers" and let them figure out a solution or mechanism. Make sure that they can all participate in coming up with a solution.
3. Use pebbles or marbles or candy to represent the rice sacks. Select a king and three counters, distribute the "sacks" to the rest (the farmers), and start the play. The first time I would only give one sack to each farmer to make it easy.
4. The first time they reach ten and they need to get the second counter to capture this information (i.e. raise one finger) is a great opportunity to reflect on the concept of zero that we take for granted. That is right, the first person counting the rice sacks has no fingers up! Let them continue counting until they reach a little past twenty. You may want to write down the results on the board.
5. Select a new king (you can even hold elections, just make sure that the ballots are fair), three new counters, re-distribute the riches (rice sacks), and have them count them again. This time I would give random numbers of sacks (two to five) to each farmer and have them count to at least past one hundred.
6. Repeat as many times as necessary until they all feel comfortable counting sacks with the base ten numerical system.

Once you have them going, and before they start eating the rice, it is very straight forward to introduce them to the concept of other base systems. Make sure that you change the players and here are the activities that I would recommend:

1. You can first introduce them to the base five system but without even telling them that they'll be using a different base. Simply tell them that they can each use only one hand or five fingers to do the counting.
2. Have them count sacks a few times and write the answers down.
3. Ask them if they notice that they are only using five different symbols. Open up the discussion with the whole class and help them realize that they are counting with a system that only needs five symbols, 0 (zero) to 4 (four). You can now mention that this represents a different base, the base five numerical system.
4. If you had them count the same number of rice sacks using base ten and base five, you can show them how the two numbers equate to each other, for example, 25 (in base ten) equates to 100 (in base five).
5. You can then introduce base eight by allowing them to use all fingers in both hands except for the thumbs. You'll be repeating steps 1 through 4 above but this time using base eight.
6. To introduce base two, have them use both whole hands and not the individual fingers. Again, make sure that you change the players and that you have at least five counter people. Repeat steps 1 through 4 above now using base two.
7. Finally, you may want to consider bases larger than ten. Say base sixteen. At this point you don't have to re-enact the counting. You can just describe the counting process on the board. The interesting point in using base systems above base ten is the fact that one needs symbols other than the ten digits. You can have them invent their own symbols or use the letters a, b, c, d, etc.
8. To conclude, spend five minutes to have them reflect and express their final thoughts on the fact that one can count in any base system and the significance of the place value.

In this last section I present a few interesting facts about different counting systems around the world all the way from antiquity to the modern day.

• The Tasmanian tribes counted up to two "Parmery, calabawa, cardia", meaning, "one, two, plenty."¹
• The Guaranis of Brazil adventured further and said: "One, two, three, four, innumerable."¹
• The New Hollanders had no words for three or four; three they called "two-one"; four was "two-two."¹
• At some point the idea of using a system based on base twelve (duodecimal) became a favorite because it was so pleasantly divisible by five of the first six digits and that system still survives in English measurements today: twelve months in a year, twelve inches in a foot, twelve units in a dozen, etc.¹
• The Egyptians' hieroglyphic system consisted of different symbols, mainly strokes, to represent the numbers from one to ten, one hundred, and one thousand. Numbers in between consisted of additions on these thirteen symbols. For example, 310 was represented as the addition of three one hundreds plus one ten. They had no zero and therefore fell short of the decimal system.¹
• The sign for one million in the Egyptian system was a picture of a man striking his hands above his head, as if to express amazement that such a number could exist.¹
• The Babylonians used the sexagesimal system, based on the number 60, and the Romans used (for some purposes) the duodecimal system, based on the number 12. The Mayans used the vigesimal system, based on the number 20.²
• The decimal system was known to Aryabhata, the greatest of Hindu Astronomers and Mathematicians, long before its appearance in the writings of the Arabs and the Syrians.¹
• The oldest known use of the zero in Asia or Europe is in an Arabic document dated 873 c.e., Three years sooner than its first known appearance in India, but by general consent, the Arabs borrowed this too from India, and the most modest and most valuable of all numerals is one of the subtle gifts of India to mankind. The Mayans also used the zero as early as the first century c.e. It should be noted that the concept of zero was developed thousands of years after the first numeric systems were developed.¹

[Note 1] -- Quotes from: Will Durant, The Story of Civilization, Volume I, Simon and Schuster, New York, 1954.

[Note 2] -- From: Microsoft Encarta 98 Encyclopedia, Microsoft Corporation, 1998.

Last Updated: Saturday, 17-Mar-2001 07:00:04 GMT

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