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 Title Determine a rule that relates arithmetic operations on four consecutive odd and even numbers.   Problem Statement Determine a rule that relates arithmetic operations on four consecutive odd and even numbers. Choose four consecutive odd counting numbers. Take the product of the middle two numbers and subtract the product of the first number and the last number. Try a few samples and formulate a rule. Explain why the rule works. Problem setup The problem is to determine the pattern that 4 consecutive odd numbers follows, then subtract the product of the outer two numbers with the product of the inner two numbers.   Plans to Solve/Investigate the Problem My initial plan was to try a few sequences on paper and see what the difference of the products would be to determine if there was a pattern. After that try to determine a procedure to follow to use with excel.   Investigation/Exploration of the Problem I first tried the obvious, 3, 5, 7 and 9.  (5x7) – (3x9) = 8 then, 23, 25, 27, 29 (25x29)  - (23x29) = 8   A pattern for odd consecutive numbers is: (2n +1), (2n +3), (2n +5), (2n+7) Using this for my four consecutive odd numbers and subtracting the products: (2n +3) (2n +5)   -   (2n +1) (2n+7) 4n2  + 10n + 6n + 15 - 4n2 - 14n - 2n - 7 = 8,  the magic number! Click here to see an excel worksheet for the above problem   Extensions of the Problem If I used 4 consecutive even numbers, the outcome was an eight. A pattern for 4 even consecutive numbers is: (2n +2),  (2n +4), (2n +6) (2n+8)  (2n +4) (2n+6) – (2n +2) (2n +8) 4n2  + 12n + 8n + 24 - 4n2 - 16n - 4n - 16 =  8 Click here to see an excel worksheet for the above problem. Author & Contact Insert name and contact information. Insert Email Link(s) to resources, references, lesson plans, and/or other materials Link 1 Link 2