Setting Up the Lesson
Start by asking students how much a million grains of rice really is
and what they think it would look like. Inform students that they are
going to see for themselves, by visualizing whaht a million grains of
rice looks like through an investigation. For younger students, reading
How Much Is a Million?
by David M. Schwartz is a great introduction. Ask students how long it
would take to count to a million themselves. It would take a very long
time to count to a million if each number takes 1 second. Ask the
students how long they think it would take. [A million seconds is a
little over 11 days!] As a class, they will figure out how much rice
constitutes 1,000,000 grains, and determine how much a million grains
of rice would weigh.
Ask the class for ideas about techniques for counting a million
grains of rice. Hold up a package or cup of rice. Ask students, Do you
think that the package contains a million grains? Ask how knowing the
number of grains in the package or the cup would help a person know how
much a million is.
For the class to count a significant sample:
- Put students into groups of 2 or 3.
- Give each group a cup that contains some rice (100–200 grains).
- Have each group count the grains of rice in their cup. Ask
students to write the number of grains on the cup. For the first few
groups that finish, you may want them to count a second cup. Ask if any
groups are finding efficient ways to count the numbe of grains of rice
in their cups.
- After each group has counted theier grains, have students
record their data in some way for the class to see (e.g., draw a chart
on the board or poster paper, or enter the data into a spreadsheet).
- Review the results as a class. Encourage students to
estimate the total number of grains of rice that have been counted so
far. Add the estimates to the data. Ask students how they obtained
- Add up the total number of grains and compare the actual number to the estimates. Which estimates are close?
Here is an example:
Ask students to discuss and answer the following questions in their groups:
- How many more cups about this size do we need to count in order to reach 1 million grains?
[Answers will vary.]
- If each student in our school had a cup of rice about the size of ours to count, would the total reach a million?
[Answers will vary.]
- What does a million grains of rice look like? Where could it be stored?
[Students may not yet have an idea of the volume of rice, so answers will vary greatly]
- Hold up a 907‑gram (2‑;pound) package of rice. Ask students to estimate how many grains of rice are in the bag.
Show the class that a package of rice is measured by weight, and in
order to determine the weight of a million grains of rice, we'll have
to weigh some rice and do some calculations.
Weight of a Million Grains of Rice
Use a balance or a scale to determine the weight of the total
number of counted grains of rice using a balance. Be sure to exclude
the weight of the cups that you are using to hold the rice. You can
weigh each cup seperately, or pour the rice into a larger cup or jar
and weigh the whole thing at once.
Once students have the weight of the rice they counted, they can
calculate the weight of 1 million grains. This problem can be solved by
using a proportion, since the relationship between the number of grains
and their weight is a direct proportion. Be aware that some rate
problems cannot be solved using a proportion because the relationship
is not directly proportional.
To find the weight of a million grains of rice, use the known ratio of
517 grains of rice to 14.5 grams. Set this ratio equal to 1,000,000
grains of rice to the unknown weight.
number of grains (517 in this case) is obtained by students counting
the rice in their cups. The weight of the grains that you counted is
found using a balance. An electronic postal scale is another
inexpensive way of finding the weight. To solve for the weight of
1,000,000 grains of rice, first cross multiply:|
|to obtain the equation: |
|And now, divide both sides by 517: |
This means that 1,000,000 grains of rice weighs about 28,046 grams.
Your calculations will be different, but the process is the same to
obtain an estimate in the neighborhood of 28,000 gm for a million
grains of rice.
Use the Weight to Determine What a Million Grains Looks Like
Conclude the class by discussing how much space students think
would be needed to store a million grains of rice. The 2 lb bag is
about 907 grams, so 28,046/907 ≈ 31.
This means that 31 packages of rice would make a million grains. A discussion of what that looks like can follow.