Generate Equivalent Expressions

6.AT.7 · Unit 6 · Lesson 8

Name   Period

Objectives / Objetivos

Content Objective: I can use the commutative, associative, and identity properties to rewrite expressions.

Language Objective: I can explain my reasoning using the words commutative property, associative property, and identity property.

Key Idea / Idea clave

Properties of Operations. Formula: Commutative: a + b = b + a | Associative: (a + b) + c = a + (b + c). 1. Commutative Property: Order does not change sum or product. 2. Associative Property: Grouping does not change sum or product. 3. Identity Property: a + 0 = a; a · 1 = a

I Notice / Observo

  • Does the order you add the musicians change the total?
  • What if you group different sections together first — does the total change?

I Wonder / Me pregunto

  • Do these same rules work for subtraction or division?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Properties of Operations
Propiedades de las operaciones		Rules that let you reorder or regroup numbers without changing an expression's value.
Reglas que permiten reordenar o reagrupar números sin cambiar el valor de una expresión.
Commutative Property
Propiedad conmutativa		You can change the order and get the same answer.
Puedes cambiar el orden y obtener la misma respuesta.
Associative Property
Propiedad asociativa		You can change the grouping and get the same answer.
Puedes cambiar la agrupación y obtener la misma respuesta.
Identity Property
Propiedad de identidad		Adding 0 or multiplying by 1 keeps the same value.
Sumar 0 o multiplicar por 1 mantiene el mismo valor.
Property
Propiedad		A rule that is always true in math.
Una regla que siempre es verdadera en matemáticas.
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.

Practice Preview / Vista previa de práctica

  1. Which property is shown? 5 + 13 = 13 + 5
    1. Commutative Property
    2. Associative Property
    3. Identity Property
    4. Distributive Property
  2. Match each equation with the property it demonstrates.
  3. Match each equation to its property.
  4. Find the Property Error
    1. Step 1: Statement — 15 − 8 = 8 − 15
    2. Step 2: Student's claim — This shows the Commutative Property of Subtraction.
    3. Step 3: Reasoning — I switched the order, so it must be commutative.

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

Reflection / Reflexión

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