Checking the Numbers

Checking the Numbers

CRA Description : 
A Universal Product Code (UPC) is found on most items you buy. The code is given as a bar code for instantaneous machine reading. But if the machine reader fails, then the code may be entered by a human being as a string of 11 digits followed by one more digit, called the “check digit” number. These 11 digits along with the check digit are found just below the bar code itself. Since it is so easy to make a mistake when entering a string of numbers, the “check digit” numberʼs purpose is to immediately reveal if an entering error has been made; the bar code can then be entered a second time for correction. A similar system is used for identifying books, called the International Standard Book Number (ISBN). This assignment gives students experience with these codes and teaches them how to recognize when entering errors occur.
Independent Study
Algebra I
Algebra II
Key Concepts and Terms: 
Check Digit
Identification Number
Single-digit Error
Transposition Error
Prior Knowledge: 
Students should be able to combine algebraic expressions into altered forms and read meaning into the resulting expression. Calculations for the check-digit method can be performed easily on a calculator.


I really like "Checking the Numbers."  There is a lesson regarding UPC codes in Advanced Quantitative Reasoning that I have used.  I had no idea that there was a mathematical connection, that UPC numbers weren't random numbers, until I trained for that course.  I imagine students frequently take those things for granted too.  That the assignment can be done independently is a bonus!   I had to chuckle that the instructions suggest bringing in 10 key machines.  I'm sure my students have not seen these.  For modification, ISBNs could be left out (time depending) or the assignment could be extended for examining credit card 'card verification values.'

Submitted by elukasik (not verified) on

I have taught this same basic lesson in AQR, as the person before commented. I see the gradevlevel is algebra 1 or 2, and I am curious as to where to fut it in those packed courses.
One new thing I see in this lesson that I had not thought about is the use of matrices in these problems. We are doing that unit during second semester,  so I can incorporate that as well as the ISBN number.

Submitted by psather (not verified) on