Volumetric Displacement Counting Lab - (Draft)

7500Mini Erasers, various shapes$108.80

121000ml Polypropylene Graduated bottles (AqEco 501100)$55.04

12250 ml Graduated cylinders(AqEco LGC250) @ $6.21$93.15

12100 ml Graduated cylinders (AqEco LGC100) @ 4.99$59.88

1Plastic 1 gallon clear jar (plastic preferred)

2 4Plastic 1 gallon ziplock bags

3SB2 Top loading portable scales, 2000 g x 1.0 g @ $95.40$286.20

3SB200 Top loading scales, 200g x 0.1g @ $95.40$286.20

24AA batteries

1Lockable storage trunk for transportation

12 Plastic trays to dry out erasures

Lab procedures

Weigh the empty one gallon jar. Fill the jar with erasers, KEEPING TRACK of how many of each shape go in and the total number. We will only have to do this one time. Record the total number and percentages of each of the shapes. Weigh the full jar. Keep the total number a secret. You will provide the information to the students in two separate ways. You will be providing one half of the students with items 1 and 2 and the others with items 3, 4, and 5.

  1. Volume of the 1 gallon jar =
  2. Percentage of the volume that each shape occupies =
  3. Percentages of the weight of the shapes in the jar =
  4. the weight of the empty jar =
  5. the weight of the full jar =
  • Allow students to guess how many erasers there are in the jar.
  • Ask them to write their guess on a piece of paper and hand it in. Offer a prize to the person that comes closest.
  • Now ask them to think about scientific ways that they could estimate how many are in the carboy.
  • Give each group a mixed bag of erasers, a graduated cylinder, 1 liter graduated bottle, and access to a scale. Give them a few minutes to think and then ask for suggestions.

There are two methods to solve this problem and formulate a good guess.

  • Think about how they count baby catfish fry. They use what is called volumetric displacement. They count several batches of 100 fry and place them into a graduated cylinder with a known volume of water. They record the change in the volume to get how many mls are displaced per 100 fry. How can you apply this to the erasure problem? Is there a way to take into account the different shapes?
  • Think about how they determine how to stock 5,000 fingerlings per acre in a 20 acre pond. Would the volumetric method work? It would but it would not be practical. Instead they take and weigh several samples of 100 fish and use the average fish weight to determine how many pounds to stock total. For our project you can weigh a sample of each eraser shape and calculate the total number based on the total weight of the jar.

Method 1. Volumetric Displacement

  1. Count out 10 of each shape
  2. Fill the graduated cylinder with water to the 50 ml mark
  3. Drop 10 of one of the shapes into the cylinder (without splashing)
  4. Record the new volume of water in the cylinder
  5. Determine how many mls of water are displaced for each of the different shapes.
  6. Since you know the volume of the1-gallon jar and the percentage of the volume that each shape occupies in the jar you should be able to come up with a good guess for the total number of erasers in the jar.

Eample: each star = .75 ml displacement

23% of the volume of the jar is taken up by stars

(0.23 x 1gallon x 3785.4ml/gallon) = 870.6 ml of stars

870.6 ml of stars x 1 star/.75ml = 1160.8 stars

Method 2: Sampling a portion of the population to determine the weight of the whole population

  1. Count out ten of each shape.
  2. weigh a sample of ten of each shape
  3. determine the weight of each piece individually
  4. determine the total wt. of the erasers in the jar
  5. determine the portion of the total weight for each shape
  6. determine the how many individual erasers it takes to make up the portion of the total weight for that shape. (this will tell you how many of that shape there are in the large jar)
  7. repeat these steps for each of the shapes
  8. add the total number of each shape to get a total number

Example:

-10 stars weighs 14 miligrams

-14grams/10 stars = 1.4 grams per star

-The total weight of eraser in the jar is the full jar minus the wt. of the empty jar (3.5 kg – 0.52 kg) = 2.98 kg

-16.5% of the total weight of the jar is stars (2980 g x 0.165) = 491.7 g of stars

-491.7 grams of stars x 1 star/1.4g = 351.2 stars in the jar

-

Information for My Specific Lab Project

Use this information to help you determine the total number of erasers in the jar

Wt. Jar Empty = 166.7 g

Wt. Jar Full of erasures = 3.11 Kg

Volume of jar = 3.91 liters

Conversion factors

1 gallon = 3785.4 milliliters (ml)

1 kilogram (kg) = 1000 grams (g)

1 ml water = 1 gram

1 pound = 454 grams

Shape / % total weight / Number of each shape / % total volume / Number of each shape
Heart
Star
Fish
Circle

2010 Volumetric Displacement Lab - Volume

Use this chart to help you organize your data.Your Name ______

Shape / Beginning volume of water (ml) / End volume of water (w/ 10 shapes) / Change in volume / Volume of individual erasure / % total volume / Total volume of each shape / Number of that shape
Heart
Star
Tall Fish
Circle
Total Volume of Jar / liters
Total

Total number of erasures in the jar = ______

2010 Volumetric Displacement Lab - Weight

Use this chart to help you organize your data.Your Name ___________

Shape / Weight of 10 (g) / Weight of one (g) / % of total weight / Total wt of each shape
(grams) / Number of that shape / Actual Numbers of shapes in Jar
Heart
Star
Tall Fish
Circle
Jar / g Empty
kg Full
Total

Total number of erasures in the jar = ______

Differences between the measured Numbers and the actual numbers are likely the result of rounding the numbers