Transforming 2D Figures

Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

  • Describe in words the transformation that maps an object to a transformed image.
  • Given a geometric figure and a rotation, reflection or translation, draw the transformed figure (or the original figure if the image is given.)
  • Describe transformations as algebraic functions that take points in the plane as inputs and give other points as outputs.


The lesson unit is structured in the following way:

  • Before the lesson, students work individually on a task designed to reveal their current understanding and difficulties. You then review their solutions and create questions for students to consider in order to improve their work.
  • After a whole-class introduction, students work in pairs or threes on a collaborative task, describing transformations and completing the transformed image/original figure for a given transformation. The lesson ends with a whole-class discussion of the work.
  • In a follow-up lesson, students work alone on a new assessment task, or return to the original task and try to improve their responses.

Materials required

  • Each individual student will need a copy of Figure to Figure and Figure to Figure (revisited), a mini-whiteboard, pen, and eraser.
  • Each small group of students will need the cut-up Card Set: Transformations, a glue stick, a marker pen, and a large sheet of poster paper. Tracing paper should be made available on request.
  • There is a projector resource to support whole-class discussions.

Time needed

15 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.