### MA 105: Linear Lima Beans

Name:
Partner's name (if any):

This is a graded activity. Work with 1 or 2 other students. Each student should hand in her or his own work.

The object of this activity is to measure volume and to discover the linear relationship between the volume of a collection of lima beans and the number of lima beans in the collection.

1. Fill your group's measuring container up to (but not over) the top with dried lima beans. Count the number of lima beans and record it in the table below. Then trade containers with another group. Share data with other groups in the class to fill in the table below.

 Volume # Beans (trial 1) # Beans (trial 2) # Beans (trial 3) Sample Mean 1/8 c. 1/4 c. 1/3 c. 1/2 c. 1 c.

2. How many beans fit in an 1/8 c. measure, on average?

3. How many beans fit in a 1/4 c. measure, on average?

4. How are your answers to the previous two questions related? Is this what you expected? Why or why not?

5. How many beans do you think would fit in a 3/8 c. measure?

6. How many beans do you think would fit in a 4/8 c. measure?

7. Compare your answer to the previous question to the average number of beans that fit in a 1/2 c. measure. Do they match? Why or why not?

8. Fill in the table below with your estimates:
 Volume 1/8 c. 1/4 c. 3/8 c. 1/2 c. 5/8 c. 3/4 c. 7/8 c. 1 c. # Beans
9. Write an equation estimating the number of beans in a volume of n/8 c., where n is some unknown number.

Your equation for the number of beans in a given volume is a simple mathematical model you can use to predict the number of beans in a container.
1. According to your model, how many beans would it take to fill a 1 pint (2 c.) measure? To answer this, first figure out how many eighths of a cup go into one pint, then use your model.
• Number of eighths of a cup in 1 pint: n =

• Number of beans that would fit in 1 pint:

2. There are 16 cups in a gallon. How many eighths of a cup are there in a gallon?

3. One liter is 0.264 gallons. How many eighths of a cup are there in one liter?

4. How many beans would fit in an empty 2 liter soda bottle?

5. Suppose you needed to know how many packing peanuts were needed to fill a box with volume 1 m3 (perhaps to estimate the postage needed to ship the box). Describe a method you could use to estimate this number.