Equivalent 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 expressions give the same answer for every value of the variable.

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
Equivalente		Expressions that always have the same value.
Expresiones que siempre tienen el mismo valor.
Simplify
Simplificar		To write an expression in a shorter, simpler way.
Escribir una expresión de forma más corta y simple.
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: