Use a compass to scribe a circle. Keeping the compass at the exact same width, choose a point on the circumference and scribe an arc from one side of the circle to the other. Make sure that the top of the arc goes through the needle-point of the original circle's center. Take the compass needle to one of the intersection points of the arc and the original circle; scribe another arc, again making sure that the top of the arc passes through the center of the original circle. Repeat this until you have gone around the whole circle and each arc has intersected to create the design of a six-petal flower.
Help children color this design, find out the diameter of the circle by measuring the leaves, and make hexagons and triangles by ruling lines between every second petal tip. Make a 12-petal flower by finding the center point between two petal tips and scribing arcs around the circle starting from that midpoint.
Drawing a Nautilus shell can help illustrate the geometry of the Fibonacci series and the resulting Fibonacci rectangles. To get the proper curve of the Nautilus shell, start with a 1-cm square. Draw another 1-cm square that shares one of the sides of the original square. Now draw a 2-cm square on top that uses the sides of both 1-cm squares. Draw a 3-cm square that uses both the 2-cm and 1-cm squares.
The pattern continues in the Fibonacci series, so the next square will be 5 cm, followed by 8 cm and 13 cm. For art projects it is best to stop at 13 cm, as this will just fit on an A4 page (which is incidentally itself a Fibonacci rectangle with sides 13 and 21 cm long). Starting from the first square, sketch a spiral that goes diagonally across each square in a rotation. This creates the base spiral of the Nautilus shell. Students can then free-form sketch the rest of the shell onto the page. Encourage children to find Fibonacci rectangles in other every day objects, like bank cards.
Make paintings or pictures of the Pyramids at Giza to help illustrate different geometric aspects of the triangle, like angles and area. Finding out the area of a pyramid is much more fun for children than just finding out the area of an ordinary triangle, as it engages their imagination. This is also a good opportunity for teachers to tell students about how geometry helped the Pharaoh's and their architects construct the pyramids and how it helps modern architects today.