Geometric Design - Shapes in Five Circle Grids

We created five circle grids and then found shapes in the circles.

This activity was very similar to the seven-circle grid shape finding activity we recently did and also based on Islamic Art and Geometric Design from the Metropolitan Museum of Art. All that was needed for this activity was a sheet of paper, straight edge and a compass. Colored pencils made it more fun to color when complete.

A vertical line and horizontal line running through the middle of the paper were the main elements required to construct the circles.

To construct a horizontal line through the center of the paper, the compass point was placed on the corner of the paper, set at a radius greater than 1/2 the width of the paper (around 6 inches), and used to sketch an arc near the mid-line of the paper. Repeating the procedure using the other three corners of the paper resulted in two arced x's which were connected with a straight line as shown in the image above.

A perpendicular line through the center of the first line was constructed by placing the point of the compass at the center of each X and drawing additional arc lines above and below the line and connecting them as shown in the image above.

At this stage the paper had one vertical and one horizontal line. The horizontal and vertical center could have been found much easier by folding the paper in half, but learning to use the compass to bisect lines and create horizontal and vertical lines is a valuable skill used in the art of mechanical drawing. After the lines were created, the rest was easy.

The compass was set to a radius near one inch and a circle was constructed with the center at the intersection of the two lines. Four additional circles were constructed where the center circle crossed each line.

Looking at the center circle it was possible to create many different shapes by connecting points created where circles intersected with each other and straight lines. After finding a shape in the center circle, additional circles and two additional vertical lines were created.

The vertical lines were created by widening the radius of the compass to around 3 inches, placing the point at the point where the additional center circle and horizontal line met, and creating tick marks above and below the line to be connected with a straight-edge.

Some shapes found:
six-pointed star
eight pointed star
twelve pointed star

Before proceeding to the next phase, creating patterns with five-circle grids, this activity was repeated several times over the course of a few weeks. It was exciting for both the kids and for me to discover the shapes in the circles.

Creating the grid was a valuable learning activity, but when repeating the project grid creation becomes a chore. Below is a grid I created. Please feel free to use it for personal or classroom use.

5 Circle Grid for Finding Shapes

Many more hands-on math activities are on our Math Page.

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  1. Love this idea! Thanks for sharing such a great idea!

    PAWSitively Teaching.

  2. This is way cool! Thanks so much for sharing your math ideas with After School!

  3. What a neat activity! Thanks for sharing your grid!


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