Unit 6 · Standard 6.EE.1
Powers and Exponents
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
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.
In 5², the base is 5 — it is the number being multiplied: 5 × 5 = 25
Base
The number that gets multiplied by itself.
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.
Evaluate 3⁴: write 3 × 3 × 3 × 3, then multiply step by step: 9 × 9 = 81
Evaluate
To find the value of an expression.
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.
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
- You're a sound engineer at a music studio.
- Each time you flip a switch, the volume doubles.
- The starting volume is 1 unit.
- After flipping the switch 3 times, the volume is 2³ = 2 × 2 × 2 = 8 units — that's 8 times louder!
- Evaluate each exponential expression. Write the repeated multiplication and find the value.
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.
Exponent matters in math because ___.Exponente importa en matemáticas porque ___.
Exponent matters in math, but ___.Exponente importa en matemáticas, pero ___.
Exponent matters in math, so ___.Exponente importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about exponent.Di un hecho verdadero sobre exponent.
Exponent ___.
Ask a question about exponent.Haz una pregunta sobre exponent.
How does ___ ?¿Cómo ___ ?
Show excitement about exponent.Muestra entusiasmo sobre exponent.
Wow, ___ !¡Guau, ___ !
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
The exponent means multiply ___ by itself ___ times.El exponente significa multiplicar ___ por sí mismo ___ veces.
So ___ equals ___.Entonces ___ es igual a ___.
I see exponents when ___.Veo exponentes cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which expression shows 5³ as repeated multiplication?
- 5 × 5 × 5
- 5 × 3
- 5 + 5 + 5
- 3 × 3 × 3 × 3 × 3
2. Evaluate: 3 × (4 + 2)²
- 108
- 54
- 36
- 144
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 ___.
Reflect — Exit Ticket
What is the value of 3⁴?
- 81
- 12
- 34
- 64
Answer Key & Teacher Guide
- 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.
- Try It 2: A. 108 — 4 + 2 = 6. 6² = 36. 3 × 36 = 108.
- Exit Ticket: A. 81 — 3⁴ = 3 × 3 × 3 × 3 = 81.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Exponent is a small number that tells how many times to multiply the number by itself.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).