Interpreting Algebraic Expressions

Mathematical goals

This lesson unit is intended to help you assess how well students are able to translate between words, symbols, tables, and area representations of algebraic expressions. It will help you to identify and support students who have difficulty:

  • Recognizing the order of algebraic operations.
  • Recognizing equivalent expressions.
  • Understanding the distributive laws of multiplication and division over addition (expansion of parentheses).


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 work and formulate questions for students to answer, to help them improve their solutions.
  • During the lesson, students work in pairs or threes to translate between word, symbol, table of values, and area representations of expressions.
  • In a whole-class discussion, students find different representations of expressions and explain their answers.
  • Finally, students return to their original assessment task and try to improve their own responses.

Materials required

  • Each student will need two copies of Interpreting Expressions, a mini-whiteboard, pen, and eraser.
  • Each pair of students will need glue, a felt-tipped pen, a large sheet of poster paper, and cut-up copies of Card Set A: Expressions, Card Set B: Words, Card Set C: Tables, and Card Set D: Areas. Note that the blank cards are part of the activity.
  • If you think you will need to continue with the activities into a second lesson, provide envelopes and paper clips for storing matched cards between lessons.

Time needed

10 minutes for the assessment task, a 90-minute lesson (or two 50-minute lessons), and 10 minutes in a follow-up lesson. All timings are approximate and will depend on the needs of the class.

Lesson Type

Mathematical Practices

This lesson involves a range of mathematical practices from the standards, with emphasis on:

Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the content standards: