Symmetry and Kolam

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In the previous exercise where the students drew freehand kolams, they seemed to follow their instincts to create symmetrical patterns. When I commented on the symmetry in their kolams, the kids looked surprised. That motivated us to expand on the theme symmetry in kolam. We decided to do an introductory lesson on symmetry before moving on to the kolams.

We introduced the concept of symmetry by looking at a bunch of leaves that showed reflection symmetry. The students traced the stalk of the compound leaf and identified it as the line of symmetry. The leaves are slightly turned in my pictures and show some variation but take a peek at them here:

symmetry-in-leaves

symmetry-in-leaves

symmetry-in-leaves

symmetry-in-leaves

In simple leaves they traced the primary vein and checked to see if the secondary veins were exact mirror images.

symmetry-with-sea-shells

Next the students looked through a tray of bivalve shells. The shells were all jumbled up and the students had to match the identical halves. After matching they checked to see if the shells were indeed symmetrical.

This led us to question if other objects in our environment showed symmetry. One student pointed out that the neem leaves and coconut fronds were symmetrical. Another said butterflies and dragonflies were symmetrical too. This led to a recital of a list animals that show bilateral symmetry.

Next the kids looked into a mirror to see if they could identify how their face was symmetrical. During their discussions, they commented on how there were one side of the face looked like it as turned around and placed on the other side.Then one student remarked, “Miss if I keep my mouth closed it is symmetrical but if I smile it is not symmetrical.” (She had lost a tooth on one side and the permanent tooth was still too small to be counted.) Immediately there was a flurry of activity as the others checked their smiles.

Here’s another demonstration of how the human body shows symmetry (bilateral symmetry) using a spool of white rope or ‘nadaa’ for the line of symmetry.

bilateral-symmetry-in-human-body

In the final activity, students chose three pairs of geometric shapes. They created their own symmetrical patterns (reflection symmetry) using these shapes.

symmetry-in-shapes

symmetry-in-shapes

symmetry-in-shapes

Here is an interesting site where students can create their own symmetrical patterns. They can see the reflected half form as they draw the pattern.

Symmetry Artist

On the third day of the kolam theme, the kids were eager to let me know that they had been drawing many kolams with their mothers. While drawing kolams is a Hindu tradition, the two non-Hindu students said that they watched their neighbours draw big Marghazhi kolams and practiced a few so they could share their work with their friends in school. One of the boys said he helped his mother by bringing the kolam maavu while another boy said, “I told my mother I liked her kolam, Miss. She was very happy.”

Having completed the introductory lesson on symmetry, we decided to tackle symmetry in kolams. We focused only on reflection symmetry in this activity.

symmetry-in-kolam

I had a collection of simple kolams from which each student selected a familiar pattern. I drew dots on the board for one pattern at a time and completed one-half of the kolam. The students guided each other as they took turns to complete the other half of the kolam.

A couple of students directed themselves by narrating ‘ulle-velliye’ (in-out) as they tried to copy the second half of the kolam. (The children thought aloud and shared comments in their native tongue. I translated/modeled their comments and questions in English afterward). After a few trials, the students learned to complete the kolam in one continuous line (without lifting the chalk off the board).

Next, they drew the line of symmetry. Most of them drew a line through a vertical axis while two identified that their kolam was symmetrical on a vertical and horizontal axis.

symmetry-in-kolam

symmetry-in-kolam

The final activity was similar but on paper. I folded the paper into two halves and drew the dots for a kolam on each paper. The dots were positioned on either side of the fold, creating a line of symmetry. The students selected a kolam design each and traced the completed half with their finger. Here they counted the dots and compared the weaving patterns of the lines to complete the identical second half.

symmetry-in-kolam

symmetry-in-kolam

symmetry-in-kolam

symmetry-in-kolam

symmetry-in-kolam

symmetry-in-kolam

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