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Question: ruby is at the end of a line of 50...

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Ruby is at the end of a line of 50 students waiting for their lunch. She is a bit sneaky, and well liked by her school mates, so she is able to sneak up the line two places every time the the next student at the front of the line is served. So, for example, while the first student gets their lunch, Ruby moves ahead so there are two students behind her. If at some point it is possible for Ruby to move only one place, she does that instead of moving ahead two places. How many students get served before Ruby? a. Predict a solution in your head and discuss your prediction with others to get started. It doesnt have to be right, or even close, just a prediction. b. Use any manipulatives or drawings to solve these two problems where the line is much shorter: Number in front of Ruby Number served before Ruby c. What pattern did you notice that could help you solve the original problem in which Ruby is at the end of a line of 50 students? d. Explore other numbers and put the results into a table. Number in front of Ruby Number served before Ruby e. Describe how you could work out the answer for any number of students in the line.

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