Neft Teacher · Notes Packet

Unit 6 · Standard 6.EE.1

Powers and Exponents Flagship

Lesson 6-1-flagship

Name:Date:Class:

Sound Studio Mission

The Doubling Mixboard

You are the lead sound engineer at Amplitude Studios. Every time you flip a switch on the new mixboard, the volume doubles — that is the power of exponents. The headline act goes on in one hour, and you must master powers before the speakers can be safely dialed in.

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Exponent: A small number that tells how many times to multiply the number by itself.

In 2³, the small 3 means multiply 2 by itself 3 times: 2 × 2 × 2 = 8

Exponent

A small number that tells how many times to multiply the number by itself.

Illustration of Base: The number that gets multiplied by itself.

In 5², the base is 5 — it is the number being multiplied: 5 × 5 = 25

Base

The number that gets multiplied by itself.

Illustration of Power: A number written with a base and an exponent, like 2³.

10³ = 10 × 10 × 10 = 1,000 — read as '10 to the third power' or '10 cubed'

Power

A number written with a base and an exponent, like 2³.

Illustration of Evaluate: To find the value of an expression.

Evaluate 3⁴: write 3 × 3 × 3 × 3, then multiply step by step: 9 × 9 = 81

Evaluate

To find the value of an expression.

Illustration of Coefficient: The number in front of a letter, like the 3 in 3x.

In 3x, the 3 is the coefficient — if x = 4, then 3x = 3 × 4 = 12

Coefficient

The number in front of a letter, like the 3 in 3x.

Illustration of Like terms: Terms with the same letter, like 2x and 5x.

4x and 2x are like terms (both have x); 4x and 4x² are NOT like terms (different powers)

Like terms

Terms with the same letter, like 2x and 5x.

Key Ideas & Notes

Think About It

  • What happens to the volume each time you flip a switch?
  • Why is 2³ equal to 8, not 6?
  • How is repeated multiplication different from repeated addition?

My Notes

Guided Examples

Example 1

What is the value of 4³?

Solution: 4³ = 4 × 4 × 4 = 64.

Answer: A. 64

Example 2

What is the value of 6²?

Solution: 6² = 6 × 6 = 36.

Answer: A. 36

Example 3

Which expression shows 5³ as repeated multiplication?

Solution: 5³ means use 5 as a factor 3 times: 5 × 5 × 5. The exponent tells how many times to multiply, not what to multiply by.

Answer: A. 5 × 5 × 5

Write About the Math The Writing Revolution

I can explain my work using the words exponent, base, power, and evaluate.

1. Kernel Sentence subject + verb

Model: Exponent is a small number that tells how many times to multiply the number by itself.Exponente es un número pequeño que dice cuántas veces multiplicar el número por sí mismo.

Write a kernel sentence about exponent. Use a subject and a verb.Escribe una oración base sobre exponente. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Exponent matters in mathExponente importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Exponent matters in math because ___.Exponente importa en matemáticas porque ___.

butpero

Exponent matters in math, but ___.Exponente importa en matemáticas, pero ___.

soentonces

Exponent matters in math, so ___.Exponente importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about exponent.Di un hecho verdadero sobre exponent.

Exponent ___.

QuestionPregunta

Ask a question about exponent.Haz una pregunta sobre exponent.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about exponent.Muestra entusiasmo sobre exponent.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with exponent.Dile a un compañero qué hacer con exponent.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I know ___ because ___.Sé que ___ porque ___.

First I ___, then I ___.Primero ___, luego ___.

This is important because ___.Esto es importante porque ___.

Try It

Solve on your own. Check the answer key when you are done.

1. Which expression shows 5³ as repeated multiplication?

  1. 5 × 5 × 5
  2. 5 × 3
  3. 5 + 5 + 5
  4. 3 × 3 × 3 × 3 × 3
Show your work:

2. Evaluate: 3 × (4 + 2)²

  1. 108
  2. 54
  3. 36
  4. 144
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A bacteria colony doubles every hour. Starting with 1 bacterium, write a power expression for the number after 6 hours. Explain why exponential growth is so much faster than adding the same number each hour.

Sentence starter: After 6 hours there are ___ bacteria because 2⁶ = ___. If it grew by adding 2 each hour instead, there would only be ___ bacteria. Exponential growth is faster because ___.

Show your work:

Reflect — Exit Ticket

What is the value of 3⁴?

  1. 81
  2. 12
  3. 34
  4. 64
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 5 × 5 × 5 — 5³ means use 5 as a factor 3 times: 5 × 5 × 5. The exponent tells how many times to multiply, not what to multiply by.
  2. Try It 2: A. 108 — 4 + 2 = 6. 6² = 36. 3 × 36 = 108.
  3. Exit Ticket: A. 81 — 3⁴ = 3 × 3 × 3 × 3 = 81.

Writing (TWR) — what to look for