IM Alg2.1.9 Lesson: What’s the Equation?

Author:GeoGebra Classroom Activities, IM Algebra 1, Geometry, Algebra 2

For the function , evaluate mentally:

A large cake is in a room.

The first person who comes in takes

of the cake. Then a second person takes

of what is left. Then a third person takes

of what is left. And so on.

Complete the table for C(n), the fraction of the original cake left after n people take some.

Write two definitions for : one recursive and one non-recursive.

What is a reasonable domain for this function? Be prepared to explain your reasoning.

On graph paper, draw a square of side length 1.

Draw another square of side length 1 that shares a side with the first square. Next, add a 2-by-2 square, with one side along the sides of both of the first two squares. Next, add a square with one side that goes along the sides of the previous two squares you created. Next, do it again. Pause here for your teacher to check your work.

Write a sequence that lists the side lengths of the squares you drew.

Predict the next two terms in the sequence and draw the corresponding squares to check your predictions.

Describe how each square’s side length depends on previous side lengths.

Let be the side length of the square. So and . Write a recursive definition for .

Is the Fibonacci sequence arithmetic, geometric, or neither? Explain how you know.

Look at quotients . What do you notice about this sequence of numbers?

The 15th through 19th Fibonacci numbers are 610, 987, 1597, 2584, 4181. What do you notice about the quotients?

IM Alg2.1.9 Lesson: What’s the Equation?

A large cake is in a room.

Complete the table for C(n), the fraction of the original cake left after n people take some.

On graph paper, draw a square of side length 1.

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