Counting by Weighing
The concept of counting by weighing may seem like a novel idea, but it is used extensively in business as well as chemistry.If you need a large number of small objects, it can be very difficult to count them.Frequently, businesses weigh the objects rather than counting them.For example, nails are sold in bulk by mass rather than by number.Let’s assume that a group needs to distribute flyers in a neighborhood and each person would needs 100 flyers.Counting the flyers would be very time consuming.But if you knew the weight of the 10 flyers, you could multiply that number by 10 to get the mass of the 100 flyers.Then all you would need to do is weigh that mass to get 100 flyers for each person.

Equipment:Matches and Pennies

Procedure:

A.Matches

  1. Obtain 10 matches. Weigh them and record their mass to 3 decimal places.
  2. Calculate the mass of 100 matches.
  3. Calculate the mass of 500 matches. If you needed 500 matches, would it be easier to count them or weigh them
B.Pennies
  1. Obtain 25 pennies. Separate the pennies into two stacks: pre-1982 and 1983 and later. Pennies made through 1981 are pure copper. In 1982, the US Government began to make pennies with a zinc core and copper on the outside. In 1982, both were made.  Do not use the 1982 pennies.
  2. Weigh each of the pre 1982 pennies and record their mass to three decimal places.
  3. Calculate the average mass of the pre 1982 pennies.
  4. Weigh each of the post 1982 pennies and record their mass to three decimal places.
  5. Calculate the average mass of the post 1982 pennies.
  6. Calculate the weighted average of the pennies.
  7. Using the weighted average of you pennies from part 6 calculate the total mass for the 25 pennies.
  8. Weigh the 25 pennies and see how close your calculation is to the measured value.
  9. Write the weighted average for your pennies on the board. Using the values for all the groups in the lab, calculate a class average for the weighted mass for pennies.
  10. Using the class average, how many grams of pennies would you need to weigh out to get 500 pennies.
Results:Name:__________________

A. Matches

1.Mass of 10 matches___________________________ grams
2.Calculated mass of 100 matches

_______________________ grams

3.Calculated mass of 500 matches

_______________________ grams

B. Pennies

Pre 1982 pennies
2.Mass of pre 1982 pennies
  1. ______________ grams
  2. ______________ grams
  3. ______________ grams
  4. ______________ grams
  5. ______________ grams
  6. ______________ grams
  7. ______________ grams
  8. ______________  grams
  9. ______________ grams
  10. ______________ grams
3.Average mass of pre 1982 pennies___________ grams

Post 1982 pennies

4.Mass of post 1982 pennies
  1. ______________ grams  13. ______________ grams
  2. ______________ grams  14. ______________ grams
  3. ______________ grams  15. ______________ grams
  4. ______________ grams  16. ______________ grams
  5. ______________ grams  17. ______________ grams
  6. ______________ grams  18. ______________ grams
  7. ______________ grams  19. ______________ grams
  8. ______________ grams  20. ______________ grams
  9. ______________ grams  21. ______________ grams
  10. ______________ grams  22. ______________ grams
  11. ______________ grams  23. ______________ grams
  12. ______________ grams  24. ______________ grams
5.Average mass of post 1982 pennies___________ grams
Name:_________________
6.Calculated weighted average of the pennies

A. Number of pre 1982 pennies:____________

B. Average mass of pre 1982 pennies: ____________grams

C.Number of post 1982 pennies: ____________
D.Average mass of post 1982 pennies: ____________ grams
Calculated weighted average of the pennies:

E.[(# of pre 1982)(average mass of pre 1982) + (# of post 1982)(average mass of post 1982)]¸25 = ____________ grams

7.Calculated mass of 25 pennies (E x 25)=____________ grams

8.Weigh your 25 pennies____________ grams

Compare the weighed value with the calculated value _______________________

_____________________________________________________________________

9.Class values:

Weighted averages

  1. ____________ grams
  2. ____________ grams
  3. ____________ grams
  4. ____________ grams
  5. ____________ grams
  6. ____________ grams
  7. ____________ grams
  8. ____________ grams
  9. ____________ grams
  10. ____________ grams 
Average of class data: ____________ grams
10.Using the class average, what mass of pennies would you need to weigh out to get 500 pennies?

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