With this dynamic worksheet we can construct squares with sides equal to the first several Fibonacci numbers and a Fibonacci spiral which is made up of quarter-circular arcs whose radii are consecutive Fibonacci numbers.
The order of the steps is important. There are detailed instructions under the applet and short instructions at the left side of the applet .

Click on the Quarter Circle button.

Click on the green square to create a square underneath it (the color will change).

Drag the green square to align the blue point with the free end of the quarter circle.

Rotate the green square by dragging the red point. We want to align the red side of the green square with the radius of the quarter circle.

Click the Increase button until the side of the square equals the sum of the sides of the previous two squares.