Unit 7 · Standard 6.EE.6
Write Equations
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
x + 5 = 12 means 'some number plus 5 equals 12'
Equation
A math sentence with an equal sign showing both sides are the same.
In n + 3 = 10, the letter n stands for the unknown number (n = 7)
Variable
A letter that stands for an unknown number.
7 + 3 = 10 — both sides equal 10
Equal sign
The = sign, showing both sides are the same.
2x + 5 is an expression; it becomes an equation when you write 2x + 5 = 15
Expression
A math phrase with numbers and letters, but no equal sign.
Key Ideas & Notes
- Detective Ruiz received a tip: 'A number of stolen gems plus 8 more equals 20 total gems.' She needs to write an equation to represent this clue before she can solve the case.
- How would you write this situation as an equation?
- Use the balance scale to see how each word problem translates into an equation. Drag the correct expression to each side of the scale to make it balance.
Think About It
- What quantity is unknown in this situation?
- What does 'plus 8 more' tell you about the operation?
- What does 'equals 20 total' tell you?
My Notes
Guided Examples
Example 1
Which equation represents: 'A number plus 12 equals 30'?
Solution: 'Plus' means addition, so the equation is n + 12 = 30.
Answer: A. n + 12 = 30
Example 2
Which equation represents: 'Seven less than a number is 18'?
Solution: 'Seven less than a number' means start with the number and subtract 7: n − 7 = 18.
Answer: A. n − 7 = 18
Example 3
Which equation represents: 'Three times a number equals 21'?
Solution: 'Three times' means multiply by 3, so the equation is 3n = 21.
Answer: A. 3n = 21
Write About the Math The Writing Revolution
I can explain my equation using the words equation, variable, equal sign, and expression.
1. Kernel Sentence subject + verb
Model: Equation is a math sentence with an equal sign showing both sides are the same.Ecuación es una oración matemática con un signo igual que muestra que ambos lados son iguales.
Write a kernel sentence about equation. Use a subject and a verb.Escribe una oración base sobre ecuación. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Equation matters in mathEcuación importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Equation matters in math because ___.Ecuación importa en matemáticas porque ___.
Equation matters in math, but ___.Ecuación importa en matemáticas, pero ___.
Equation matters in math, so ___.Ecuación importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about equation.Di un hecho verdadero sobre equation.
Equation ___.
Ask a question about equation.Haz una pregunta sobre equation.
How does ___ ?¿Cómo ___ ?
Show excitement about equation.Muestra entusiasmo sobre equation.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with equation.Dile a un compañero qué hacer con equation.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The unknown is ___.La incógnita es ___.
My equation is ___.Mi ecuación 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 equation represents: 'A number divided by 4 equals 8'?
- n / 4 = 8
- 4n = 8
- n − 4 = 8
- n + 4 = 8
2. A detective found some fingerprints on Monday and 14 more on Tuesday, for a total of 30. Which equation represents this?
- f + 14 = 30
- f − 14 = 30
- 14f = 30
- f / 14 = 30
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Write a real-world situation that can be modeled by the equation n / 5 = 9. Explain what n represents and verify your equation makes sense.
Sentence starter: Situation: ___. In this problem, n represents ___. Check: n = ___ because ___ ÷ 5 = 9.
Reflect — Exit Ticket
Which equation represents: 'A number divided by 6 equals 9'?
- n / 6 = 9
- 6n = 9
- n − 6 = 9
- n + 6 = 9
Answer Key & Teacher Guide
- Try It 1: A. n / 4 = 8 — 'Divided by 4' means division: n / 4 = 8.
- Try It 2: A. f + 14 = 30 — The detective's Monday fingerprints (f) plus 14 more equals 30: f + 14 = 30.
- Exit Ticket: A. n / 6 = 9 — 'Divided by 6' means division: n / 6 = 9. Check: 54 / 6 = 9 ✓
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Equation is a math sentence with an equal sign showing both sides are the same.
- 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).