Tuesday, August 12, 2014

Constructing a Four Star Mandala Tutorial

Beginning with a Mandala book, we selected a mandala which contained four six-pointed stars and figured out how to recreate it.

Mandalas are circular symmetric figures that are fun to create and color. When they are created with a compass and straight-edge math and art quickly combine. While drawing the figure below, we drew concentric circles, bisected angles, and drew circles with various specified radii. It served as a very natural way to introduce geometrical vocabulary and concepts.


The key to this project is a good quality compass that has a screw mechanism to hold it in place. Cheap compasses that can easily move while being used are frustrating for children.

Here is the step-by-step procedure we followed to recreate the mandala.

1. Draw a circle with a 4 inch radius near the center of the paper.

2. Create six evenly spaced tick marks around the circumference of the circle. With the radius of the compass still set at 4 inches. Place the point of the compass on the circumference of the circle. Draw a small tick mark with the led crossing the circumference. Rotate the compass and draw a tick mark on the other side. Move the compass point to the tick mark and create a new tick marks around the circumference until there are 6 tick marks total. - See photo below.


3. Create 6 sets of crossing tick marks on the inside and outside of the circle. Set compass to about 2 1/4", place the point on one of the six circumference tick marks and create marks inside and outside the circle. Rotate the compass and create marks on the other side. Continue, placing the compass on each circumference tick mark until six sets of inside/outside tick marks have been created.


This photo shows the figure after step 9 has been completed. The compass in the picture is doing step 3. The tick marks from step 2 become the points of the frontal star.

4. Draw a circle concentric with the initial circle with a radius of 1.75.
5. Draw six tick marks on internal circle which will become inner points of frontal star. Do this by aligning the ruler with the tick marks just inside and outside the circle.

6. Create the big frontal star by connecting the tick marks on the outer circle (points) and inner circle (inner points).
7. Create inner star tick marks on inner circle for the background star. Do this by aligning the ruler with the points of the foreground star and marking the inner circle where the ruler crosses.
8. Aligning the ruler with the inside/outside circle ticks created in step 3, add tick marks to the outer circle. They will become the points of the background star.
9. Connect the tick marks on the inner and outer circle with lines to create the background star.


10. Draw a 3/4" radius circle concentric with the others. (see photo below).


11. Draw a 1 1/8" radius circle concentric with the others. (see photo below).


12. Draw a 2 1/4" radius circle concentric with the others.
13. Draw a 2 3/4" radius circle concentric with the others.
14. Lining up the ruler with the points of the background star, place 6 tick marks around the circumference of the small 3/4" radius circle. (see photo below).


15. Connect ever second tick mark on the small circle with a straight line to create two overlapping triangles or a six-pointed star. (see photo below).


16. Draw straight lines from points of small center star to inner points of foreground star as shown in the photo below.


17. Lining up the ruler with the points of the foreground star as shown below, place 6 tick marks on the 2 3/4" radius circle.


18. Connect tick marks to create medium sized center star as shown below.
 

19. Erase all construction lines.



20. Outline with a black marker if desired.


21. Color.


Tips: Measure as accurately as possible. My son's first measurements were a little off, which greatly distorted his center star. He ended up replacing  it with straight lines.



For more math/art combo projects please visit our Math Page.
Check out these great blogs full of educational activity ideas. 

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