Several days ago, I was reminded of an interactive pattern block puzzle that I designed during the pandemic in collaboration with Toni Cameron of Reimagined. It provides an engaging opportunity to promote proportional reasoning in the context of geometry.

On page 1 of the websketch below (and here), students are given the numerical values of four pattern blocks and asked to create one or more designs whose shapes sum to 20.Students drag shapes from the well in the top-left corner and rotate them by dragging the vertex points. Below are several designs students might build.

After the class has shared their work, the teacher asks what they notice about the numerical values of the shapes. Why, for example, does the hexagon have a value of 6? Students might explain that the hexagon is composed of six triangles, each with a value of 1. Similarly, they can explain the numerical significance of the rhombus and trapezoid values.

Students continue to page 2 by using the page control in the lower-right corner. This page presents four puzzles. In each one, the numerical value of just one pattern block is given. Students reason about the values of the other three shapes and then build one or more designs with the desired sum.

Finally on page 3, students create puzzles of their own. They assign values to the four pattern block shapes (making sure the values make mathematical sense), pick a value for the sum of the shapes, and then hide the values of all but one of the shapes. They can now challenge a friend to solve their puzzle.