Representing the Laws of Arithmetic

Mathematical goals

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

  • Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations.
  • Write and evaluate numerical expressions from diagrammatic representations and identify equivalent expressions.
  • Apply the distributive and commutative properties appropriately.
  • Use the method for finding areas of compound rectangles.


The lesson unit is structured in the following way:

  • Before the lesson, students work individually on an assessment task designed to reveal their current understanding and difficulties. You then review their responses and create questions for students to consider when improving their work.
  • After a whole-class introduction, students work collaboratively on a card matching activity. Towards the end of the lesson there is a whole-class discussion.
  • In a follow-up lesson, students work alone on a similar task to the introductory assessment task.

Materials required

  • Each student will need a copy of the two assessment tasks: Expressions and Areas and Expressions and Areas (revisited), a mini-whiteboard, a pen, and an eraser.
  • Each small group of students will need cut-up copies of Card Set: Expressions and Card Set: Area Diagrams, a large sheet of paper for making a poster, and a glue stick.
  • There is a projector resource to support whole-class discussions. You may also want to copy the card sets onto transparencies to be used on an overhead projector to support discussions.

Time needed

15 minutes before the lesson, an 85-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings will depend on the needs of your class.