Unit 6 · Standard 6.EE.3
Simplify Algebraic Expressions
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
5x and 3x are like terms (both x); 5x and 5y are NOT (different variables); 2x and 2x² are NOT (different powers)
Like Terms
Terms with the same letter, like 2x and 5x.
8m + 3m = 11m — add the coefficients (8 + 3 = 11) and keep the variable (m)
Combine
To add or subtract terms with the same letter into one.
2a + 5a + 3 simplifies to 7a + 3 — the two a-terms combine, the constant stays
Simplify
To write an expression in its shortest form.
In 9x, the coefficient is 9 — it tells you 'nine groups of x'; if x = 2, then 9x = 18
Coefficient
The number in front of a letter, like the 3 in 3x.
Key Ideas & Notes
- The music studio is placing supply orders for three rehearsal rooms.
- Room A needs 4 microphones and 3 stands.
- Room B needs 2 microphones and 5 stands.
- Room C needs 6 microphones and 1 stand.
- Identify the like terms in each expression. Group the terms that can be combined.
Think About It
- Why can you add the microphones together but not mix microphones with stands?
- What makes microphones and stands 'different types' of items?
- How is this like combining like terms in algebra?
My Notes
Guided Examples
Example 1
Simplify 7x + 3x.
Solution: 7x + 3x = 10x. Add the coefficients: 7 + 3 = 10.
Answer: A. 10x
Example 2
Simplify 9n + 4 + 2n.
Solution: 9n + 2n = 11n. The constant 4 has no like term, so it stays. Result: 11n + 4.
Answer: A. 11n + 4
Example 3
Which pair are like terms?
Solution: 6x and 2x are like terms because they both have the same variable (x) raised to the same power (1).
Answer: A. 6x and 2x
Write About the Math The Writing Revolution
I can explain my steps using the words like terms, combine, simplify, and coefficient.
1. Kernel Sentence subject + verb
Model: Simplify is to write an expression in its shortest form.Simplificar es escribir una expresión en su forma más corta.
Write a kernel sentence about simplify. Use a subject and a verb.Escribe una oración base sobre simplificar. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Simplify matters in mathSimplificar importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Simplify matters in math because ___.Simplificar importa en matemáticas porque ___.
Simplify matters in math, but ___.Simplificar importa en matemáticas, pero ___.
Simplify matters in math, so ___.Simplificar importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about simplify.Di un hecho verdadero sobre simplify.
Simplify ___.
Ask a question about simplify.Haz una pregunta sobre simplify.
How does ___ ?¿Cómo ___ ?
Show excitement about simplify.Muestra entusiasmo sobre simplify.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with simplify.Dile a un compañero qué hacer con simplify.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The like terms are ___.Los términos semejantes son ___.
I combined them to get ___.Los combiné para obtener ___.
This makes it clearer when ___.Esto lo aclara cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which pair are like terms?
- 6x and 2x
- 6x and 6y
- 6x and 6
- 6x and 2x²
2. Simplify 5a + 3 + 2a.
- 7a + 3
- 10a
- 7a² + 3
- 52a + 3
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Three students simplified 4x + 3 + 2x + 5 + x differently. Student A got 7x + 8. Student B got 7x² + 8. Student C got 6x + 9. Who is correct? Explain the mistakes the other two students made.
Sentence starter: Student ___ is correct because 4x + 2x + x = ___x and 3 + 5 = ___. Student ___'s error was ___. Student ___'s error was ___.
Reflect — Exit Ticket
Simplify 6x + 3 + 2x + 5.
- 8x + 8
- 8x² + 8
- 62x + 35
- 16x
Answer Key & Teacher Guide
- Try It 1: A. 6x and 2x — 6x and 2x are like terms because they both have the same variable (x) raised to the same power (1).
- Try It 2: A. 7a + 3 — 5a + 2a = 7a. The constant 3 stays. Result: 7a + 3.
- Exit Ticket: A. 8x + 8 — 6x + 2x = 8x and 3 + 5 = 8, so the simplified expression is 8x + 8.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Simplify is to write an expression in its shortest form.
- 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).