Family Tree : A Lesson by Mathalicious

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You've got two parents. They each had two parents: your four grandparents. Each of them had two parents: your great-grandparents. So as you go back in time, how many direct ancestors do you have?

In this lesson, students are introduced to the principle of exponential growth, and use it model the mathematics of ancestry. By doubling the number of direct ancestors with each generation, they'll find that eventually the number of direct ancestors would've equaled the human population. They'll then discuss the implications: does this mean everyone is related? Or is there something wrong with the model?

Students will

Use a doubling rule to calculate the number of direct ancestors a person has in each previous generation
Determine how far back you'd have to go to have a given number of direct ancestors
Using estimates for the length of a generation, determine how many direct ancestors you would have had at different points in history
Discuss the reasonableness of an exponential growth model for studying ancestry

Before you begin

Students should be able to fluently multiply multi-digit whole numbers, and should be able to graph points in a coordinate plane. Though we're using an exponential model for counting ancestors, the mathematics only involves repeated doubling, so should be accessible to middle-school students.