The Distributive Property

6.AT.7 · Unit 6 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can use the distributive property to expand and factor expressions.

Language Objective: I can explain my steps using the words distributive property, factor, expand, and equivalent.

Key Idea / Idea clave

The number outside the parentheses gets "shared" with every term inside.

I Notice / Observo

  • Why do both methods give the same total?
  • What does the 3 represent in 3(15 + 5)?

I Wonder / Me pregunto

  • What if 10 people bought bundles — which way would be faster to calculate?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Distributive Property
Propiedad distributiva		Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.
Multiplicar un número por todo lo que está dentro del paréntesis: a(b + c) = ab + ac.
Factor
Factor		A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
Un factor de un número entero lo divide exactamente, sin dejar residuo. Por ejemplo, 3 es un factor de 12 porque 12 ÷ 3 = 4.
Expand
Desarrollar		To multiply out the parentheses in an expression.
Multiplicar lo que está dentro del paréntesis en una expresión.
Equivalent
Equivalente		Expressions that always have the same value.
Expresiones que siempre tienen el mismo valor.
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.
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.

Practice Preview / Vista previa de práctica

  1. Expand 6(n + 3) using the distributive property.
    1. 6n + 18
    2. 6n + 3
    3. n + 18
    4. 6n + 9
  2. Use the distributive property to expand each expression.
  3. Match each factored form to its expanded form.
  4. Find the Distributive Error
    1. Step 1: Expression — 5(2x + 4)
    2. Step 2: Distribute — 5 × 2x + 4
    3. Step 3: Simplify — 10x + 4

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

Reflection / Reflexión

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