The Distributive Property

6.AT.7 · Unit 6 · Lesson 14

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 Distributive Property. Formula: a(b + c) = ab + ac | a(b − c) = ab − ac. 1. Expand: Multiply the outside factor by each term inside parentheses. 2. Factor: Find the GCF of terms and pull it outside: ab + ac = a(b + c). 3. Visual: Represent as the area of partitioned rectangles

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
The Distributive Property
La propiedad distributiva		Multiply a factor by every term inside parentheses.
Multiplicar un factor por cada término dentro de los paréntesis.
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.

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: