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[Music] did you know that we can find rules by observing patterns in tables in this video well be learning how to find a rule and any missing number in an input and an output table so what are input and output tables you can think of an input and an output table as a machine where one number is put in and a different number comes out that is your output think of an oven or a microwave we often place things in a microwave or an oven and once heat is added something different comes out for example kernels are placed in a microwave and after adding heat popcorn comes out input and output tables are very similar a number is placed in and after applying a rule a different number comes out we can think of a rule as a puzzle or riddle that we need to solve that will work with all of our number pairs in a table so lets find a rule by finding a pattern in our table our first number pair is 2 and 12. the number 2 was placed into our machine and the number 12 came out the first question we wan