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 Write-up

Title
Number Machine

Problem Statement
I have a "number machine" that always affects in the same way whatever number I put in it. For example, when I put in 1, the machine gives me 6; when I put in 3, it gives me10; when I put in 6, it gives me 16; and when I put in 9, it gives me 22. What will the machine give me if I put in 100?

Plans to Solve/Investigate the Problem

The problem can be set-up initially in a table to identify a pattern. Then an equation can be determined.

Investigation/Exploration of the Problem

The following is a table reflecting number input and output and the rule/linear equation.

 Input Output Rule 1 6 2(input#) + 4, or y = 2x +4 3 10 6 16 9 22

Extensions of the Problem

My "number machine" gave me 42. What number did I put in my machine?   Based on the above equation, the problem could be solved by subtracting 4 from 42, then dividing 38 by 2 or 42-4=38/2=19

I purchased a new "number machine." This one gives me 1 when I put in 1;3 when I put in 2; 6 when I put in 3; 10 when I put in 4; and 15 when I put in 5. What number will I get when I put in 10? 20? 1000?  A table will help identify the pattern.  See the following:

 Input Output Observations/Assumptions/Rules 1 1 There is a unique relationship between input and output. 2 3 The pattern between input and output when both are known appears to be new input plus old output. 3 6 Rule:  n(n+1)  or n2+n                2            2 4 10 5 15 6 21 7 28 8 36 9 45 10 55 11 66 12 78 13 91 14 105 15 120 16 136 17 153 18 171 19 190 20 210

The equation should be used to calculate the answer to “What number will I get when I put in 1000?”

Author & Contact
Susan Kelly
mailto:skelly@rockdale.k12.ga.us