Fermi Questions
A Fermi question requires the estimation of physical quantities to arrive at an answer. One example of a Fermi question is "How many jelly beans fill a 1 litre bottle?" Additional Fermi questions can be found in this general collection.
A Fermi question requires the estimation of physical quantities to arrive at an answer. One example of a Fermi question is "How many jelly beans fill a 1 litre bottle?" Additional Fermi questions can be found in this general collection.
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Class assignment 1 - Solving Fermi questions
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Estimating large numbers
Estimating the number of people in a large crowd is very challenging and often leads to controversies. One method sometimes used is to focus on a small section of the crowd, such as a rectangular area. Photographs are good tools to use to estimate a static crowd. Think of a method that would be effective to estimate the size of a moving crowd.
Class assignment
Class reflection: What other methods could be used to estimate the size of a large crowd? What if the crowd is moving around? Describe how and why the crowd size estimate supplied by event organizers might differ from estimates made by your group.
Select the link below to complete the student survey. This counts as 20% of your grade.
Student Survey
Class assignment
- Make a square measuring 5 feet by 5 feet, and have your classmates stand inside it as if they are watching a band performing in a small club. Count the number of your friends that fit in the rectangle and find the ratio of this number to the rectangle's surface area. Explain what this ratio means. How many people fit in each square unit?
- Draw a diagram of a parade route that is one mile long and is 10 feet deep on both sides of the street. If you choose, include and label trash cans, light poles, benches, barricades and any other obstacle you would expect to see on the side of the street during a parade. Calculate the amount of square footage that is available for people to stand in order to watch a parade. Click on this link if you need to print graph paper.
- Take the diagram, square footage, and the ratio then estimate the size of the crowd.
Class reflection: What other methods could be used to estimate the size of a large crowd? What if the crowd is moving around? Describe how and why the crowd size estimate supplied by event organizers might differ from estimates made by your group.
Select the link below to complete the student survey. This counts as 20% of your grade.
Student Survey
Fundamental counting principal
Take a quick survey and ask students how many phone numbers they have in their family.
Framing question - Do you think we will ever run out of telephone numbers?
How many telephone numbers are available for use in the US? The North American Numbering Plan (NANP) numbers are ten-digit numbers consisting of a three-digit Numbering Plan Area (NPA) code, commonly called an area code, followed by a seven-digit local number. The format is usually represented as:
NXX-NXX-XXXX
where N is any digit from 2 through 9 and X is any digit from 0 through 9. Using this format, approximately how many telephone numbers are available in Georgia?
Review the Fundamental Counting Principle
What happens when numbers can't repeat?
If there are A ways for one activity to occur, and B ways for a second activity to occur, then there are A x B ways for both activities to occur.
Example: If ice cream comes in 5 flavors and there are 4 toppings, then how many combinations of one flavor of ice cream with one topping can be made? Rather than list the entire sample space with all possible combinations of ice cream and toppings, we can simply multiply 5 x 4 and get 20 combinations.
Test your knowledge in this activity.
Extension Activities
The worksheet below is a great remediation tool for students to practice combinations. It also contains extension problems and other deliverables that can be used in conjunction with the main project for this unit.
Take a quick survey and ask students how many phone numbers they have in their family.
Framing question - Do you think we will ever run out of telephone numbers?
How many telephone numbers are available for use in the US? The North American Numbering Plan (NANP) numbers are ten-digit numbers consisting of a three-digit Numbering Plan Area (NPA) code, commonly called an area code, followed by a seven-digit local number. The format is usually represented as:
NXX-NXX-XXXX
where N is any digit from 2 through 9 and X is any digit from 0 through 9. Using this format, approximately how many telephone numbers are available in Georgia?
Review the Fundamental Counting Principle
What happens when numbers can't repeat?
If there are A ways for one activity to occur, and B ways for a second activity to occur, then there are A x B ways for both activities to occur.
Example: If ice cream comes in 5 flavors and there are 4 toppings, then how many combinations of one flavor of ice cream with one topping can be made? Rather than list the entire sample space with all possible combinations of ice cream and toppings, we can simply multiply 5 x 4 and get 20 combinations.
Test your knowledge in this activity.
Extension Activities
The worksheet below is a great remediation tool for students to practice combinations. It also contains extension problems and other deliverables that can be used in conjunction with the main project for this unit.
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Additional resources for this unit
Area code map Class assignment - Fundamental counting principal
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UPC codes & check digits
A check digit is typically a decimal digit added to a number for the purpose of detecting human error. When we use numbers, whether keying them into computers, dialing them on telephones, or reading them and telling them to others we tend to make certain mistakes more often than others. According to Richard Hamming (Coding and Information Theory), the two most common human errors are:
How to calculate UPC check digits
Codabar check digit algorithm
Every credit card is uniquely identified by a 16-digit number. The first 15 digits are assigned by the bank issuing the card. The last digit (called the check digit) is determined by a formula which enables a computer to check that the number has been correctly entered when the card is used in a transaction.
What is a check digit, and how is it used?
UPC check digit
5 steps to check UPC
Credit Card Numbers
What do all of the numbers represent?
Check that digit
A check digit is typically a decimal digit added to a number for the purpose of detecting human error. When we use numbers, whether keying them into computers, dialing them on telephones, or reading them and telling them to others we tend to make certain mistakes more often than others. According to Richard Hamming (Coding and Information Theory), the two most common human errors are:
- Interchanging (transposing) adjacent digits of numbers (67 becomes 76)
- Doubling the wrong one of a triple of digits, two adjacent ones of which are the same (667 becomes 677)
- Single errors (a becomes b) - 60% to 95% of all errors
- Omitting or adding a digit - 10% to 20% of all errors
How to calculate UPC check digits
Codabar check digit algorithm
Every credit card is uniquely identified by a 16-digit number. The first 15 digits are assigned by the bank issuing the card. The last digit (called the check digit) is determined by a formula which enables a computer to check that the number has been correctly entered when the card is used in a transaction.
What is a check digit, and how is it used?
UPC check digit
5 steps to check UPC
Credit Card Numbers
What do all of the numbers represent?
Check that digit
upc_and_codabar_ws.docx | |
File Size: | 33 kb |
File Type: | docx |