6.7.C

Math6th Grade

The Standard

determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations

Texas Essential Knowledge and Skills for Mathematics

Teacher's field guide

What This Standard Means

What Students Need to Do

Students build and draw expressions with algebra tiles, then write matching algebraic forms. They rewrite each expression using properties and decide whether both forms have the same value for every variable value.

What Mastery Looks Like

A student can build or draw both expressions and show that the same quantities result. They can use distribution and combining like terms to justify equivalence for every variable value.

Common Misconceptions

Students may think different-looking expressions cannot be equivalent. They may distribute incorrectly, combine unlike terms, or treat the equal sign as a command to calculate. Some believe checking one variable value proves equivalence.

How to Assess It

Exit ticket: Use algebra tiles or a drawing to decide whether 3(x + 2) and 3x + 6 are equivalent, then verify algebraically.

Lesson moves

Ways to Teach It

  1. Give students algebra tiles to build 2(x + 3) and 2x + 6, then match and label corresponding pieces.

  2. Have students write why checking one value can suggest equivalence but does not prove two expressions are always equivalent.

  3. Play an expression matching game with cards showing tile models, drawings, expanded expressions, and factored expressions.

  4. Compare 4 bags holding x apples plus 2 extras each with 4x apples plus 8 extras, then explain why the totals match.

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