Identify Equivalent Algebraic Expressions

6.AT.7 · Unit 6 · Lesson 6

Name   Period

Objectives / Objetivos

Content Objective: I can show that two expressions are equivalent by simplifying and combining like terms.

Language Objective: I can explain my work using the words equivalent, simplify, like terms, and combine.

Key Idea / Idea clave

Equivalent Algebraic Expressions. 1. Equivalent expressions produce the same value for any substitution of the variable. 2. Simplify expressions using algebraic properties (Distributive, Commutative, Associative). 3. Test equivalence by substituting two different test numbers

I Notice / Observo

  • Why did both formulas give the same answer?
  • What did Producer B do differently from Producer A?

I Wonder / Me pregunto

  • Can two expressions look completely different but always give the same answer?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Equivalent Expressions
Expresiones equivalentes		Expressions that look different but have the same value for every allowed variable value.
Expresiones que se ven diferentes pero tienen el mismo valor para cada valor permitido de la variable.
Equivalent
Equivalente		Expressions that always have the same value.
Expresiones que siempre tienen el mismo valor.
Simplify
Simplificar		To rewrite an expression in a shorter form that is still equal to the original.
Reescribir una expresión en una forma más corta que sigue siendo igual a la original.
Like Terms
Términos semejantes		Terms with the same letter raised to the same power, like 2x and 5x.
Términos con la misma letra elevada a la misma potencia, como 2x y 5x.
Combine
Combinar		To add or subtract terms with the same letter into one.
Sumar o restar términos con la misma letra en uno solo.
Coefficient
Coeficiente		The number in front of a letter, like the 3 in 3x.
El número frente a una letra, como el 3 en 3x.

Practice Preview / Vista previa de práctica

  1. Which expression is equivalent to 4x + 3x?
    1. 7x
    2. 12x
    3. 7x²
    4. 43x
  2. Match each expression with its simplified form.
  3. Match each expression to its simplified equivalent.
  4. Find the Simplification Error
    1. Step 1: Expression — 3x + 5 + 2x + 1
    2. Step 2: Combine — 3x + 2x + 5 + 1
    3. Step 3: Simplify — 5x² + 6

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: