Introduction

Have you ever looked through old family pictures and constructed yourself, or looked at, a family tree? In this activity you will explore some mathematics related to family trees, and also the question of how to properly apply mathematics to real-world situations.

1. For the purpose of the following questions, we will ignore divorces, second marriages, adoptions, etc. By ``how many great-grandparents did you have?'' we mean, ``while they were alive''
   1. With the above understanding, how many parents do you (does anyone) have? __________

   2. And how many grandparents (two generations before yours) do you (does anyone) have? __________
   3. How about your direct ancestors three generations before yours (your great-grandparents) how many do/did you have? __________
   4. How many direct ancestors four generations before yours? __________
   5. Do you see a pattern? How many direct ancestors did you have 7 generations ago? __________ How many direct ancestors did each of them have, 3 generations before them?__________ This number must equal the number of direct ancestors you have from 10 generations ago. What mathematical rule about powers does this suggest? _______________

      
      Can you give an expression for the number of ancestors i generations ago? __________

      
      

2. Assume that the average number of years per generation is 20. Estimate the number of direct ancestors you had:
   1. In the year 1750? __________

   2. In the year 1500? __________

   3. In the year 1450? __________

      
      

   Before you go on, what do you notice so far? [write in your comments below]
   
   
   
   
   

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   Only after you've thought about your answer, discussed it within your group, and written down your thoughts, should you look on the next page, and then continue with this Activity.