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Lesson & Assessments - Equivalent Expressions

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Summary, Goals,
& Standards

Lesson
& Assessments

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Progression of Skills (outline)

Before the lesson:

  • Students should be fluent in simplifying numerical expressions. They should also have a firm grasp on variables as numbers, including exposure to (but not mastery of) equivalent expressions with positive integers. If a student can complete the pre-assessment, they are ready for this toolkit lesson.

During this toolkit lesson:

  • Focuses on identifying and generating equivalent expressions, including understanding the rules for multiplying negative numbers, distribution, factoring and combining like terms.

After the lesson:

  • Students are ready to learn to solve linear equations in one variable.

Lesson Introduction & Pre-Assessment

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Pre-assessment and answer key:

Lesson

Read the teacher's guides for directions for each session.

  1. Session 1:

  2. Session 2:

  3. Session 3:

  4. Session 4:

Anticipate Misconceptions:

  • Distributing a common factor to the first term in the parentheses only
  • Misusing operations of numbers
  • Confusing order of operations (e.g., multiplication and division are applied together)
  • Confusing integer operations, especially operations with negative numbers
  • Correctly identifying a common factor
  • Overlooking multiple equivalent expressions
  • Confusion that a number next to parentheses denotes multiplication

Optional Activities:

  1. Review of area and perimeter of rectangles
  2. Desmos for review of order of operations
  3. Review of Fractions, Decimals and Percents
  4. Tax Tip Discount practice
  5. Error Analysis for distribution and combining like terms

Progress Monitoring:

  • Listening for misconceptions during student dialogue
  • Attending to the claims initially made during each task
  • Asking questions to clarify thinking and correct misconceptions
  • Using pre and post assessments to document mastering and identify needed clarification.

Lesson Closure & Post-Assessment

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Directions for Lesson Closure:

  1. After each task is completed, revisit initial claims and make corrections so that all claims are accurate.
  2. There is a post assessment that is meant to be given after all four lessons have been completed. There are free response questions for students to type their thinking. You can give this as paper-and-pencil or as a Google form that you will need to go back and grade the free response questions.

Post-assessment and answer key:

Real-World Applications & Project Ideas

A globe with tools such as a map and measuring cup surrounding its border.

  • Area and perimeter problems: fence around a garden, painting a wall, carpeting a floor
  • Consumer applications: Amazon prime day problem, discounts, tipping on a meal.

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