Unit 6 · Standard 6.EE.2a
Write Algebraic Expressions
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
In 5t + 20, t could be hours worked — if t = 3, the expression equals 35; if t = 8, it equals 60
Variable
A letter that stands for a number that is unknown or can change.
3n + 7 means 'triple a number, then add 7' — it has a variable (n), a coefficient (3), and a constant (7)
Algebraic Expression
A math phrase that has at least one letter.
In 8x, the coefficient 8 means '8 groups of x' — if x = 3, then 8x = 8 × 3 = 24
Coefficient
The number in front of a letter, like the 3 in 3x.
In 3n + 7, the 7 never changes no matter what n is — like a flat fee that stays the same
Constant
A number on its own that does not change.
4x + 2x = 6x (like terms, same variable); but 4x + 2y cannot be combined (different variables)
Like terms
Terms with the same letter, like 2x and 5x.
Key Ideas & Notes
- You're planning a concert at the music studio.
- Tickets cost $12 each, and there's a flat $50 venue fee no matter how many people attend.
- If t represents the number of tickets sold, how would you write an expression for the total revenue?
- Read each word phrase and sort it into the correct algebraic expression.
Think About It
- What value changes depending on how many people come?
- What stays the same no matter the number of tickets?
- How would you calculate the total if 10 tickets are sold?
My Notes
Guided Examples
Example 1
Which expression represents 'the product of 6 and a number n'?
Solution: 'Product' means multiplication, so the product of 6 and n is 6n.
Answer: A. 6n
Example 2
Which expression represents '9 less than a number y'?
Solution: 'Less than' means subtract from the number, so it's y − 9.
Answer: A. y − 9
Example 3
Which expression represents 'the sum of a number m and 15'?
Solution: 'Sum' means addition, so the sum of m and 15 is m + 15.
Answer: A. m + 15
Write About the Math The Writing Revolution
I can explain my expression using the words variable, coefficient, constant, and algebraic expression.
1. Kernel Sentence subject + verb
Model: Algebraic Expression is a math phrase that has at least one letter.Expresión algebraica es una frase matemática que tiene al menos una letra.
Write a kernel sentence about algebraic expression. Use a subject and a verb.Escribe una oración base sobre expresión algebraica. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Algebraic Expression matters in mathExpresión algebraica importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Algebraic Expression matters in math because ___.Expresión algebraica importa en matemáticas porque ___.
Algebraic Expression matters in math, but ___.Expresión algebraica importa en matemáticas, pero ___.
Algebraic Expression matters in math, so ___.Expresión algebraica importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about algebraic expression.Di un hecho verdadero sobre algebraic expression.
Algebraic expression ___.
Ask a question about algebraic expression.Haz una pregunta sobre algebraic expression.
How does ___ ?¿Cómo ___ ?
Show excitement about algebraic expression.Muestra entusiasmo sobre algebraic expression.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with algebraic expression.Dile a un compañero qué hacer con algebraic expression.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The words ___ mean ___.Las palabras ___ significan ___.
My expression is ___.Mi expresión es ___.
I would write one to ___.Escribiría una para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Which expression represents 'the sum of a number m and 15'?
- m + 15
- m − 15
- 15m
- m ÷ 15
2. Which key word tells you to multiply?
- Product
- Sum
- Difference
- Quotient
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Write a real-world situation that could be modeled by the expression 4n + 10. Explain what the variable n represents, what the coefficient 4 means, and what the constant 10 represents.
Sentence starter: Situation: ___. The variable n represents ___. The coefficient 4 means ___ for each ___. The constant 10 represents ___.
Reflect — Exit Ticket
Which expression represents '3 more than twice a number n'?
- 2n + 3
- 3n + 2
- 2(n + 3)
- 2 + 3n
Answer Key & Teacher Guide
- Try It 1: A. m + 15 — 'Sum' means addition, so the sum of m and 15 is m + 15.
- Try It 2: A. Product — 'Product' means multiplication. 'Sum' means addition, 'difference' means subtraction, and 'quotient' means division.
- Exit Ticket: A. 2n + 3 — 'Twice a number n' is 2n. '3 more than' means + 3. So the expression is 2n + 3.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Algebraic Expression is a math phrase that has at least one letter.
- 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).