Write and Evaluate Numerical Expressions with Exponents

6.AT.6c · Unit 6 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.

Language Objective: I can explain my steps using the words expression, evaluate, order of operations, base, and exponent.

Key Idea / Idea clave

Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right

I Notice / Observo

  • What does the 150 represent in the expression?
  • What does the 12s represent?

I Wonder / Me pregunto

  • What if speakers cost $15 each instead?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Write and Evaluate Numerical Expressions with Exponents
Escribir y evaluar expresiones numéricas con exponentes		Turning a situation into a number sentence without an equal sign, then finding its value in the correct order.
Convertir una situación en una expresión numérica sin signo de igual y luego hallar su valor en el orden correcto.
Numerical expression
Expresión numérica		A math phrase built from numbers and operations, with no equal sign and no variable.
Una frase matemática hecha de números y operaciones, sin signo de igual y sin variable.
Evaluate
Evaluar		To find the single value an expression is worth by carrying out its operations in order.
Hallar el único valor que representa una expresión, realizando sus operaciones en orden.
Order of operations
Orden de las operaciones		The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right.
El orden acordado para evaluar: signos de agrupación, luego exponentes, luego multiplicar y dividir de izquierda a derecha, y por último sumar y restar de izquierda a derecha.
Power
Potencia		A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2.
Una forma corta de escribir la multiplicación repetida del mismo factor, como 2³ para 2 × 2 × 2.
Base
Base		In a power, the number being multiplied by itself. In 2³ the base is 2.
En una potencia, el número que se multiplica por sí mismo. En 2³ la base es 2.

Practice Preview / Vista previa de práctica

  1. Evaluate 3 + 4 × 2.
    1. 11
    2. 14
    3. 24
    4. 9
  2. Sofia buys 2 member tickets ($15), 4 non-member tickets ($20), and 8 student tickets (2³ dollars). Build the total.
  3. What is the total of 2 × 15 + 4 × 20 + 8 × 2³?
    1. 174
    2. 126
    3. 210
    4. 1,392
  4. Find the error
    1. Step 1: Expression — Evaluate 4 + 2 × (3 + 5)²
    2. Step 2: Step 1 — 3 + 5 = 8
    3. Step 3: Step 2 — 2 × 8 = 16
    4. Step 4: Step 3 — 16² = 256, so 4 + 256 = 260

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

Reflection / Reflexión

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