Generate Equivalent Expressions
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 / Término | Definition / 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
Read each task. Show your work in the spaces provided and explain how you know.
1. Which property is shown? 5 + 13 = 13 + 5
- A Commutative Property
- B Associative Property
- C Identity Property
- D Distributive Property
Answer:
2. Match each equation with the property it demonstrates.
Write each item in its correct group.
3. Match each equation to its property.
Write the letter of the matching item in the blank.
| 1. | 7 + 9 = 9 + 7 | A. | Associative (Mult) | |
| 2. | (2 × 5) × 3 = 2 × (5 × 3) | B. | Commutative (Mult) | |
| 3. | 15 × 1 = 15 | C. | Identity (Add) | |
| 4. | 0 + 23 = 23 | D. | Commutative (Add) | |
| 5. | 6 × 4 = 4 × 6 | E. | Identity (Mult) | |
| 6. | (8 + 3) + 7 = 8 + (3 + 7) | F. | Associative (Add) |
4. Find the Property Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: