An activity for grades 7 and up that applies the Pythagorean Theorem and investigates the special square root ratios that appeared in Maya architecture

- Place students in groups of 4 or 5. Allow each group to choose the ratio they want to use or assign ratios. Using lightweight rope or cord and sidewalk chalk in a parking lot (or playground or other flat area), have each group lay out a square and then a rectangle of the chosen ratio.
- For a shorter amount of time or younger students, students can “eyeball” in the right angles. To make the activity more authentic, rope can be used to check that diagonals are equal while constructing the initial square. If more time is available, the equilateral triangle method of using a knotted cord to construct right angles can be used.
- To complete the activity, the rope and chalk can be used to draw rounded ends on each “house”.
- The activity can also be expanded to fit in with Common Core Standard 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale) by first having students do a scale drawing of their Maya house on paper and then having them reproduce the scale drawing with a larger scale with sidewalk chalk in a parking lot or playground.

This activity can be carried out on a large scale as in the video above or on a smaller scale. For the larger scale activity, using ten to twelve students and about 75 feet of rope, follow the instructions below. For the smaller version, have students work in pairs or groups of three with about 12 inches of string for the knotted cord. If desired, the equilateral triangles can be formed over a sheet of paper with tape used to hold down the knots. Having students use knotted cords to make right angles in the Maya way ties in with Common Core Standard G.CO.12, which recommends making formal geometric constructions with a variety of tools and methods.

The rope or string needs to be “knotted” with eight equally-spaced “knots” which divide the rope or string into seven congruent segments. The “knots” can be actual knots or just “virtual knots” marked on the rope or string. For the video, we used 75 feet of yellow nylon rope with pieces of red tape marking “knots” at ten-foot intervals and with one person assigned to each of the seven knots and others available to help.

- Starting with “knot 1” held stationary, pull the second “knot” out horizontally to form a leg of the first equilateral triangle. Once the first two knots are firmly in position, place “knot 3” above the first two knots, forming an angle of approximately 60° with the first leg, and then swing the fourth “knot” down to the same position as the beginning “knot”. Pull the rope as taut as possible at the second and third “knots” to insure a nicely formed equilateral triangle.
- For the second equilateral triangle, from the joined “knot 1/4”, swing “knot 5” out away from the first equilateral triangle to form an angle of roughly 60° with segment 3–4. Once “knot 5” is in position, move “knot 6” to the same position as “knot 3”. At this stage, “knot 5” should be pulled taut and the second of our three equilateral triangles formed.
- Next move “knot 7” up at an angle from “knot 3/6” until it is roughly in line with “knots 1/4”, forming another roughly 60° angle with segment 3–5. Then swing “knot 8” down to occupy the same position as “knot 5”, forming the last leg of the third and final equilateral triangle. Pull all the vertices taut to get the best formation of the triangles.
- With rope or string of another color, form one leg of a right angle by starting at “knot 1/4” and passing through “knot 2”; for the other leg, start at “knot 1/4” and pass through “knot 7”. This angle is a right angle because it is the sum of a 60 degree angle from the original equilateral triangle and a perfectly bisected 60 degree angle from the second and third equilateral triangles, for a sum of 60° + 30° = 90°.