Background:

When working with atoms, scientists sometimes have to invent new ways of doing simple things. For instance, scientists can't use a ruler to measure the size of an atom's nucleus. This activity shows how ratios can be used to calculate the area covered by an object.

Objectives:

In this activity students will:

- use creative problem-solving to determine the area of a dime

- multiply fractions

- compare two sets of data

- record data

Minimum Materials Needed for Each Student Group:

- Student data sheet

- Dime sheet

Notes:

- A real dime has an area of ~2.54 cm²

Detailed Directions:

1. Have each student place a number of dots (50 is a good number) within the large square on their data sheet. The dots should be as small as possible and should be randomly scattered over the area of the square.

2. Record the number of dots used.

3. Place the dime sheet under the data sheet and align the squares.

4. Circle every dot that landed on a dime and circle half of the dots that partially landed on a dime.

5. Record the number of dots circled.

6. Find the fraction of dots that are circled. This is related to the area covered by the dimes. For example, if 20% of your dots are circled, you can assume that 20% of the square is covered by dimes.

7. Use the fraction of dots that are circled to calculate the fraction of the square covered by dimes.

8. Since there are 10 dimes on the dime sheet, you must divide the area covered by dimes by 10 to find the area of one dime.