Creating Rich Mathematical Tasks

If you are a teacher preparing to teach mathematics, or are currently doing so, and you have not read Jo Boaler's book Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching, be sure to find a copy and start reading. 

Boaler indicates that she believes there are 5 C's of mathematics engagement: curiosity, connection making, challenge, creativity, and collaboration. The chapters of this book dive into a variety of topics related to mathematics teaching and learning but the fifth chapter specifically talks about what are known as rich mathematical tasks. This chapter describes six different cases, all of which are scenarios she has personally witnessed, that demonstrate the importance of the nature of teaching mathematics. 

Boaler indicates that rich mathematical tasks give students the opportunities to learn in a way that is essential to developing their mathematical mindsets. When designing math tasks for your students, their richness can be enhanced by considering the following six questions: 

1. Can you open the task to encourage multiple methods, pathways, and representations?

2. Can you make it an inquiry task?

3. Can you ask the problem before teaching the method?

4. Can you add a visual component?

5. Can you make it low floor and high ceiling?

6. Can you add the requirement to convince and reason?

I have proposed a rich mathematical task for you to try within your Grade 8 classroom. It specifically goes with Strand E of the Ontario curriculum (E2.3 solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas)

Task: Create a composite shape that has an area of 125 square units using each of these shapes at least once: Triangle, Square, Trapezoid, and parallelogram. Once you have developed a solution, describe how you arrived at your answer. Draw your final shape on grid paper for accurate measurements. 

Resource: Boaler, J. (2015). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.