Unit 6 · Standard 6.EE.2c
Evaluate Expressions
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
In 3x + 5, x can be any number — if x = 2, the expression equals 11; if x = 10, it equals 35
Variable
A letter that stands for an unknown number.
2n + 7 is an expression: the 2n means '2 times some number' and the + 7 means 'then add 7'
Expression
A math phrase with numbers and letters, but no equal sign.
Evaluate 2n + 7 when n = 4: replace n with 4 → 2(4) + 7 = 8 + 7 = 15
Evaluate
To find the value by putting numbers in for the letters.
Substitute 3 for x in 5x: replace x with 3 → 5(3) = 15
Substitute
To put a number in place of a letter.
In 7m, the coefficient 7 tells you to multiply m by 7 — if m = 3, then 7m = 21
Coefficient
The number in front of a letter, like the 3 in 3x.
4x and 2x are like terms (both x¹); 4x and 4y are NOT (different variables)
Like terms
Terms with the same letter, like 2x and 5x.
Key Ideas & Notes
- You're a music producer setting up a concert.
- The total cost of the event is given by the expression 150 + 12s, where s is the number of speakers rented.
- The venue charges $150 as a base fee, plus $12 for each speaker.
- How much will it cost for different numbers of speakers?
- Evaluate the expression 150 + 12s for each number of speakers.
Think About It
- What does the 150 represent in the expression?
- What does the 12s represent?
- What happens to the total cost as s gets bigger?
My Notes
Guided Examples
Example 1
Evaluate 3x + 7 when x = 4.
Solution: 3(4) + 7 = 12 + 7 = 19.
Answer: A. 19
Example 2
Evaluate 20 − 2n when n = 6.
Solution: 20 − 2(6) = 20 − 12 = 8.
Answer: A. 8
Example 3
Which expression means '5 less than twice a number n'?
Solution: Twice n is 2n. Five less than that is 2n − 5.
Answer: A. 2n − 5
Write About the Math The Writing Revolution
I can explain my steps using the words variable, expression, evaluate, and substitute.
1. Kernel Sentence subject + verb
Model: Expression is a math phrase with numbers and letters, but no equal sign.Expresión es una frase matemática con números y letras, pero sin signo igual.
Write a kernel sentence about expression. Use a subject and a verb.Escribe una oración base sobre expresión. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Expression matters in mathExpresión importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Expression matters in math because ___.Expresión importa en matemáticas porque ___.
Expression matters in math, but ___.Expresión importa en matemáticas, pero ___.
Expression matters in math, so ___.Expresión importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about expression.Di un hecho verdadero sobre expression.
Expression ___.
Ask a question about expression.Haz una pregunta sobre expression.
How does ___ ?¿Cómo ___ ?
Show excitement about expression.Muestra entusiasmo sobre expression.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with expression.Dile a un compañero qué hacer con expression.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
First I did ___ because ___.Primero hice ___ porque ___.
My answer is ___.Mi respuesta es ___.
Order matters when ___.El orden importa cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which expression means '5 less than twice a number n'?
- 2n − 5
- 5 − 2n
- 2(n − 5)
- 2 − 5n
2. Evaluate 4m + 1 when m = 5.
- 21
- 20
- 9
- 25
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A gym membership costs $25 per month plus a $40 signup fee. Write an expression using m for months, then evaluate it for 6 months and 12 months. Explain what each part of the expression represents.
Sentence starter: The expression is ___. For 6 months: ___ = ___. For 12 months: ___ = ___. The ___ represents the ___ and the ___ represents the ___.
Reflect — Exit Ticket
Evaluate 5(n − 3) + 2 when n = 7.
- 22
- 32
- 17
- 36
Answer Key & Teacher Guide
- Try It 1: A. 2n − 5 — Twice n is 2n. Five less than that is 2n − 5.
- Try It 2: A. 21 — 4(5) + 1 = 20 + 1 = 21.
- Exit Ticket: A. 22 — 5(7 − 3) + 2 = 5(4) + 2 = 20 + 2 = 22.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Expression is a math phrase with numbers and letters, but no equal sign.
- 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).