**Counting and Measuring Name**

*Today we are going to create a unit to group numbers. A “dozen” is a useful grouping for things like donuts and eggs. A “pair” is a useful grouping for things like shoes and socks. A “bushel” is a useful grouping for things like apples and corn. I would like to propose a new unit called the “Seneca”. For the rest of the day, we will use the word “Seneca” just like you use the word “dozen”. One Seneca is equal to the number of students in this class.*

1 Seneca = items

Practice questions:

a. How many apples are in 2.0 dozen apples?

b. How many copper atoms are in 3.5 dozen copper atoms?

c. How many dozens are in 50. apples?

d. How many dozens are in 100. copper atoms?

e. How many apples are in 2.0 Senecas of apples?

f. How many copper atoms are in 3.5 Senecas of copper?

g. How many Senecas are in 50. apples?

h. How many Senecas are in 100. copper atoms?

Get the idea?

Now we will explore how the masses of one Seneca of various items compare. Using the items supplied by your teacher, fill in the following chart to show the mass of one Seneca of each item. **Make sure to record your mass to the farthest decimal place possible (how many is that for the triple beam balance?)!**

**Count out 1 Seneca of each item and record the mass. **

in 1 Seneca / Mass (g) of

**1 Seneca of items**

1.

2.

One more question: Explain how you could use the balance to count out 235 of one of the items.

Seeing the relationships (mass and counting):

1. Grab a small handful of item 1 (grab less than one whole Seneca).

2. Weigh and record the mass of the sample you chose.

3. WITHOUT counting, calculate the number of items in the sample (show the calculation).

4. Now count and record the # of items in the sample.

5. How do the answers to #3 and 4 compare?

6. Grab a small handful of item 2 (grab more than one whole Seneca).

7. Weigh and record the mass of the sample you chose.

8. WITHOUT counting, calculate the number of items in the sample (show the calculation).

9. Now count and record the # of items in the sample.

10. How do the answers to #8 and 9 compare?

11. Make a statement about the relationship between mass and # of items.

Seeing the relationships (mass and Senecas):

12. Look at your answer to #2 above. Calculate the # of Senecas that would be in this mass of item 1 (show the calculation).

______g X = ______Senecas

13. Look at your answer to #4 above. Calculate the # of Senecas that would be in this number of item 1 (show the calculation).

______items X =______Senecas

14. How do your answers to #12 and #13 compare? Does this make sense? Explain.

15. Look at your answer to #7 above. Calculate the # of Senecas that would be in this mass of item 2 (show the calculation).

______g X = ______Senecas

16. Look at your answer to #9 above. Calculate the # of Senecas that would be in this number of item 2 (show the calculations).

______items X =______Senecas

17. How do your answers to #15 and #16 compare? Does this make sense?

18. Make a statement about the relationship between Senecas and mass and # of items.

Practice the concepts:

19. Take one dozen of each item and answer the following questions:

- Which sample, if any, has the most pieces? Explain.

- Which sample, if any, has the most Senecas? Explain.

- Which sample, if any, has the most mass? Explain.

20. Pretend you had enough to measure 100.00 grams of each item. Answer the following questions about the samples:

- Which 100-g sample, if any, has the most pieces? Explain.

- Which 100-g sample, if any, has the most Senecas? Explain.

- Which 100-g sample, if any, has the most mass? Explain.

21. When counting the number of pieces in each of these samples, is it possible to have a count that is not a whole number? Explain.

22. When counting the number of Senecas in a sample, is it possible to have a Seneca amount that is not a whole number? Explain.

23. We will use a unit that is similar to Senecas when counting atoms in our lab. Is it possible to have a number of atoms that is not a whole number? Explain.

24. If we count atoms in the unit, Senecas, is it possible to have a number of Senecas of atoms that is not a whole number? Explain.