SWBAT demonstrate a method for counting large numbers of things using estimating.

Students will use a pound of rice to discovery how scientist can estimate large numbers of cells.

Students often hear large numbers. In this lesson we will be talking about the human body which has as many as 100 trillion cells. Just how do scientists know this information? A quick internet search finds this information when asked how long it would take to count to a trillion.

There are **24 hours** in a day so you would count 24 X 60 x 60 = 8,6400 in **one day**. There are **365 days** in a year so you would count 24 X 60 x 60 x 365 = 31,536,000 in **one year**. To find how long it would take to count to a trillion dollars divide 1 trillion by **31,536,000**. That is 1,000,000,000,000/**31,536,000** = **31,709.79 years**.

Source: Math Central

With this knowledge we can infer that it would be impossible to count all the cells in a body because people simply do not live that long. Students will devise a way to find the answer using estimation.

10 minutes

*Investigation Summary & Preparation*

Our bodies are made up of trillions of cells. Estimates are as high as 100 trillion. Students will construct a model to estimate the number of cells using a pound of rice. (**MS-LS1-3** *Use argument supported by evidence for how the body is a system of **interacting subsystems composed of groups of cells*.) (**SP5** *Using Mathematics and Computational Thinking*)

Additionally, this lesson supports the NGSS cross-cutting concept of Scale, Proportion and Quantity. Students apply logic to count the grains of rice in a very concrete task, they can then apply this concrete experience to how scientist estimate the number of cells in a human body.

This lesson uses a pound of rice for every two students. Students will need a variety of materials they may use to estimate the total number of grains of rice in a pound. For each group of 6 students, I supply various size measuring spoons, small cups and a collection container.

A complete materials list is located in the resources section.

45 minutes

*Students in Action*

Our bodies our made up of cells. Here is a brief history of Cell Theory and how we came to know and understand that we are made of cells.

Not only are we made of cells, but scientists have estimated that there are as many as 100 trillion cells in our body. You might be surprised to know that not all of the cells in our body are human. We have bacteria cells in our gut for instance that help digest our food.

100 trillion is a large number. *How do you think scientist know that there are 100 trillion cells? *Students suggest that they have some way of counting them.

*How long do you think it would take to count to 100 trillion?* Students answers vary but no one suspects that it might take in excess of 3 million years to count the cells.

I share this little tidbit from a recent internet search.

There are **24 hours** in a day so you would count 24 X 60 x 60 = 8,6400 in **one day**. There are **365 days** in a year so you would count 24 X 60 x 60 x 365 = 31,536,000 in **one year**. To find how long it would take to count to a trillion dollars divide 1 trillion by **31,536,000**. That is 1,000,000,000,000/**31,536,000** = **31,709.79 years**.

Source: Math Central

I tell students that today, they are going to develop a way to count the grains in a pound of rice. They will have about 20 minutes as they also have to write-up a summary of the process in their journal. I deliberately tell students they have only 20 minutes to count the grains of rice because I do not want them to really count ALL the grains of rice.

Students quickly understand that the various measuring devices at their work station are to be used to count the rice.

Most groups busily begin to count the number of grains in a spoon, then how many spoons in a cup and how many cups in a pound of rice.

I ask groups to share their answers with me in writing to avoid other groups over hearing their totals. I am looking for a total close to 20,000. Since we are estimating I accept a range 18,000 - 25,000. The range allows for some grains to have been lost throughout the day as students from each class have counted the pound of rice. If they are not close, I advise them to check their work.

Once the group has a reasonable number, they can write-up the procedure. Their procedure should include the counts of each measuring device they used.

In the following video, I share a student sample journal entry and discuss the many layers of instructional strategies in this lesson.

5 minutes

*Connecting the Learning*

I ask a couple of groups to share out their procedure for determining the number of grains of rice in a pound. Each student group has a slightly different procedure they followed for counting the rice. Some groups used spoons and cups to count the grains of rice, others used only spoons to count the grains of rice.

Next we consider how what we learned about counting rice can be used to understand how scientists know that we have as many as 100 trillion cells in our body.

With some encouragement, students conclude that scientisst would take a tissue sample and count the cells the same way we took a small sample of rice and counted the individual grains. Then they find the total area and calculate the number of cells.

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