6th Grade - Math

LESSON PROBLEM: Computation: What happens if the amount of rice is doubled each day for 64 days?


STUDY GUIDE

There is a story about a king who insists on giving a gift to his wise man. The man wants no gift but finally points to a game board and suggests that the king give him one grain of rice for the first square of the game board and on subsequent days double the amount of the previous day's unit until all 64 squares of the game board are covered. Not understanding how much rice would be needed, the king agrees. After 31 days, he realizes that he can't fulfill his agreement.

The wise man asks to receive 1 grain of rice on the first day, then 2 grains on the second day, then 4, 8, 16, and so on:

1,2,4,8,16

There were 64 squares on the king's game board. What is happening to the number of grains each day?

"Yes, they are doubling!"

You multiply the number by 2 to get the next number on the game board: 1 time 2 equals 2, then 2 times 2 equals 4, and 4 times 2 equals 8, and so on. Each number in the list is a power of 2 since each number in the list is the result of a multiplication by 2.

How many grains of rice will be delivered on the 64th day? Write it down on a piece of paper so you can explain it.

Did you find that with doubling, the number of grains grew very fast?

Let's try to solve another mathematical question. You will need a small bag of rice, a teaspoon and a measuring cup for this question.

On which square would enough rice arrive to feed everyone in a group of 33 people. One half cup is a standard serving size of rice.

33 people

1/2 cup per person

Using your rice, spoon and measuring cup, count how many teaspoons their are in 1/2 cup of rice. You should have come to about 24 teaspoons of rice.

Now figure out how many grains of rice are in a teaspoon. Did you count about 228 grains of rice?

How can we figure out how many grains of rice are in 1/2 cup?

There are 24 teaspoons of rice in 1/2 cup and 228 grains of rice in a teaspoon, so multiply 228 time 24. In 1/2 cup there will be approximately 5,472 grains
of rice.

Because our measurements aren't really exact, our answer is an approximation. But a number like 5,472 seems to imply that we know exactly how many grains of rice. Do you know a number we can use that is a reasonable approximation for 5,472?

Can you round it up? Perhaps to 5,500 or to 6,000?

Is 1/2 cup of cooked rice the same as 1/2 cup of uncooked rice? Rice generally expands to three times its original uncooked size. Does this change how we should approach our problem? Now what should we do? If you said divide 6,000 by 3, then you are correct. Your calculations should tell you that 6,000 divided by 3 is about 2,000 grains per 1/2 cup of rice.

The problem is to figure out how many grains of rice it would take to feed a group of 33. Find out on what square there would be enough rice to feed the entire group.

If you multiplied the number of people in the group (33) by how many grains or rice each person eats (2,000) you are correct. 33 time 2,000 equals 66,000. To feed everyone in the group we will need approximately 66,000 grains of rice. Go back to the game board again. Look at the figures you arrived at in determining how many grains of rice would be given each day. Sometime between the 17th and 18th day there will be enough rice to feed the group of 33 people.

If you continue filling your game board you will find huge amounts of rice accumulating at each square. For instance, on the 32nd square, enough rice would arrive to fill 256 wheelbarrows. The King did not understand how much rice he was talking about!




ACTIVITIES

Using the information in the lesson, on what day would you have enough rice to feed five people? 12 people? 21 people? Show your work on paper.




EXTENDED LEARNING

Create a story that is similar to this one that will illustrate the everyday use of exponents.


VOCABULARY
  • power
  • exponent
  • approximation
  • calculations
  • subsequent
  • gameboard



Click here to play Rice Rampage!
The Milling Process for Rice:
Getting rice from the field to you takes
a few more steps. Click here to see a video & learn more about the rice milling process.
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