1. Filling Your Classroom w/ Tennis Balls Not Enough Numbers

2. WARM UP
Consider the situation of determining the number of tennis balls needed to fill your classroom. With a partner or small group, take 5 minutes and make an estimate of the number of tennis balls required to fill the room.
Do you think your estimate is too small or too large? Why?

3. Diameter of tennis ball = 2.70 inches
How It’s Done!
Determine the volume of a sphere (tennis ball) and the container (the classroom).
Number of tennis balls =
Diameter of tennis ball = 2.70 inches

4. Filling the Classroom
Using the materials provided, make another estimate. This time, find a lower bound and upper bound for the number of tennis balls you think it would take to fill your classroom. Draw sketches as needed.
3)REFLECTION: In determining your group’s estimate, what mathematical model of a tennis ball did you use? What model of the classroom did you use? Did you make other simplifications or assumptions (for example, assuming there are no desks in the room)?

5. Volume of the room:
Length:
400 inches
Width:
304 inches
Height:
112 inches
Volume of Room 1204:
V1204=13,619,200 cubic inches
Volume of a Tennis Ball:​ ​
Diameter:​
2.70 inches​
Radius:​ ​​
Volume of a tennis ball:
1.35 inches
V = cubic inches
13,619,200 / = 1,320,970 Tennis Balls

6. area code - exchange code - station code
Not Enough Numbers
1) How many area codes were possible before 1995?
NYZ - ABC - XXXX
area code - exchange code - station code
Before 1995, all area codes had the form NYZ, where N was any digit from 2 to 9 (2–9), Y was 0 or 1, and Z was 1–9 if Y was 0 or Z was 2–9 if Y was 1. The restrictions on N saved 0 for call operator and 1 for long-distance calls. In addition, codes such as 800 and 911 were (and still are) used for special purposes.
8 x 1 x 9
8 x 1 x 8
CASE 1 = 72
CASE 2 = 64
Total = 136

7. Not Enough Numbers 1 x 1 x 10 = 10 1 x 1 x 10 = 10 8 x 9 x 9
2) According to post-1995 rules, how many area codes are possible?
The restriction that Y = 0 or 1 was removed in 1995 because all possible area codes had been assigned. Today N is 2–9, Y is 0–8, and Z is 0–9; the exception to these rules are codes of the form 37Z and 96Z, which are being reserved for future use.
1 x 1 x 10 = 10
1 x 1 x 10 = 10
8 x 9 x 9
= 20
Area Codes = 720
Exceptions = 20
Total = 700

8. Not Enough Numbers
3) The 7-digit numbers in a given area code have the form ABC-XXXX, where X, B, and C can be any digit 0–9 and A is restricted to 2–9. There are two other restrictions:
•B and C cannot both equal 1 since these values are designated for other purposes such as 911 (emergency) and 411 (information), and
• through are reserved for fictional uses such as in television shows or movies. According to these conditions, how many 7-digit numbers are possible in a single area code?
8 x 10 x 10 x 10 x 10 x 10 x 10 = 8,000,000
<8 x 1 x 1 x 10 x 10 x 10 x 10 = 80,000>
through
<100>
𝟕,𝟗𝟏𝟗,𝟗𝟎𝟎

9. Not Enough Numbers
4) Using your answers to the previous questions, determine how many 10-digit numbers are possible in North America.
5) New Jersey license plates are determined by a system of one letter, two numerical digits, and three letters. How many plates can the state of New Jersey provide to its drivers?
700(7,919,900) = 5,543,930,000
26 x 10 x 10 x 26 x 26 x 26 = 45,697,600

10. Cool Down 2,310 people 27,473 people
How many people can fit on a H.S. basketball court?
HS Court length = 84 feet
HS Court width = 60 feet
Circle w/ 30 inch radius = 9 people
How many people can fit on a football field?
Football field length = 120yds
Football field width = yds
1 foot = .33 yards
12 square feet = 17 people
2,310 people
27,473 people