Telephone Numbers
Task
A telephone number has 3 parts: an area code, an exchange and a suffix.
How many different telephone numbers are possible? Are all of these probable?
Alternate Versions of Task
| More Accessible Version:
The area code of a telephone number has 3 digits.
How many different telephone area codes are possible? Are all of these probable?
More Challenging Version:
A telephone number has 3 parts: an area code, an exchange and a suffix.
How many different telephone numbers are possible? Are all of these probable? What is the probability that the area code and exchange are identical? What is the probability that the digits in the suffix are consecutive?
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Context
We had worked with exponents and combination problems. I wanted a problem that would combine the two concepts.
What This Task Accomplishes
This is a real-world application. I was looking to see who could come up with the idea of combinations, but also to see who would take this task realistically. Some research would be necessary for a deep understanding of the problem.
What the Student Will Do
Many students began with 10 possibilities for each slot in the number and used exponents successfully. There were different levels of understanding of what numbers were probable.
Time Required for Task
50 minutes
Interdisciplinary Links
This problem could be nicely integrated with a social studies discussion of communication systems. The dialing system will be changed because the country is running out of numbers for telephone exchanges.
Teaching Tips
You may want to have telephone books available (I may not hand them out, but if asked for one I would be ready) to give an opportunity for more students to reach a higher level of understanding.
Suggested Materials- Telephone books
- Graph paper
Possible Solutions
See the Expert solution.
| More Accessible Version Solution:
10 x 10 x 10 = 1,000
No, they are not all probable. For instance 000 would probably not be used.
More Challenging Version Solution:
The probability that the area code and exchange are identical is 1/1000. The probability that the digits of the suffix are consecutive is 7/10,000.
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Task Specific Assessment Notes
Novice:
There is no accurate solution, little evidence of a strategy or reasoning and little explanation.
Apprentice:
The student uses a strategy that is partially useful. There is some evidence of reasoning, but an incomplete explanation for finding how many numbers were not probable.
Practitioner:
This student has a broad understanding of the problem and uses a strategy that finds all numbers if 10 digits are allowed for each slot. S/he uses effective reasoning in subtracting out the improbable numbers. His/her explanation is clear.
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Expert:
This student shows a deep understanding of the problem and is solving a realistic interpretation of the problem efficiently. S/he is explaining and subtracting out the impossible combinations as s/he sets up the problem.
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