Want students to problem solve? Check. Want to challenge their reasoning skills? Check. Need to focus on reading and writing in math? Then check out the Shaded Rectangle task. I found it in the Sept. 2012 issue of Mathematics Teaching in the Middle School and couldn’t be more delighted.

It’s the only geometry task I have ever given where a geometric shape, or visual, is not provided. Students must construct a specific rectangle and 11 triangles within it, shade the alternating triangles, then determine the area of the shaded region–all from written directions. Way cool!!!

Draw a rectangle based on the following information

• Divide the height into 3 congruent line segments by placing points on the line segment.
• Divide the base into 4 congruent line segments by placing points on the base.

Construct triangles and determine the area

• From the point just below the top-left corner, draw a line segment to each point on the rectangle.
• Shade the triangle at the upper-left corner and then shade every other triangular region.
• What is the total area of the shaded region?

Before I gave the task, I wanted my department chair’s opinion. “Hmm. I’m visual. Will the kids have a hard time with this?” For me that was exactly the point. Would they think to, at a minimum, just sketch a rectangle as a starting point. Then place points somewhere on the base and height; think about what congruent means; think about a unit of measure and, as one student said, “The points need to be evenly spaced.”

As with writing, beginning from a blank page is the most difficult part. I wanted the students to struggle but not feel defeated, so I tweaked  the original lesson to include three resource cards. If students were stuck they received a hint.