Equivalent Expressions
I can show that two expressions are equivalent by simplifying and combining like terms.
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🎯 Content Objective / Objetivo de contenido
I can show that two expressions are equivalent by simplifying and combining like terms.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Producer A wrote 3x + 2x + 10 and Producer B wrote 5x + 10. They look different but both give 30 when x = 4. Why are they equivalent?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Remix Studio
At the music studio, two producers wrote formulas for the cost of renting equipment. Producer A wrote 3x + 2x + 10, and Producer B wrote 5x + 10. They look different, but are they really? Let's check: if x = 4, Producer A gets 3(4) + 2(4) + 10 = 30, and Producer B gets 5(4) + 10 = 30. Same result — they're equivalent expressions!
Concept Launch
💡 When are two expressions equivalent?
Two expressions are equivalent when they always give the same value, no matter what number you put in for the variable. They can look different but mean the same thing.
Equivalent expressions give the same answer for every value of the variable.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Equivalent Equivalente |
Expressions that always have the same value. Expresiones que siempre tienen el mismo valor. |
2x + 4 and 2(x + 2): when x = 3, both = 10; when x = 7, both = 18 — always the same | |
| Simplify Simplificar |
To write an expression in a shorter, simpler way. Escribir una expresión de forma más corta y simple. |
3x + 2x + 5 simplifies to 5x + 5 — fewer terms, same value | |
| Like Terms Términos semejantes |
Terms with the same letter raised to the same power, like 2x and 5x. Términos con la misma letra elevada a la misma potencia, como 2x y 5x. |
3x and 7x are like terms (both x); 3x and 3y are NOT (x vs y); 3x and 3x² are NOT (x vs x²) | |
| Combine Combinar |
To add or subtract terms with the same letter. Sumar o restar términos con la misma letra. |
4n + 3n = 7n — add the coefficients (4 + 3 = 7) and keep the variable (n) | |
| Coefficient Coeficiente |
The number in front of a letter, like the 3 in 3x. El número frente a una letra, como el 3 en 3x. |
In 5x + 3, the coefficient of x is 5 — when x = 2, the 5x part equals 10 |
Vocabulary — True or False?
Which statements correctly use Equivalent?
Fix the False One
Which Word Fits?
To write an expression in its shortest equal form is to ___ it.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Producer A wrote 3x + 2x + 10 and Producer B wrote 5x + 10. They look different but both give 30 when x = 4. Why are they equivalent?
👂 Listen For
Students explain 3x + 2x = 5x (combining like terms), so both equal 5x + 10, and verify by substituting a value like x = 4 to get 30 both ways.
Extend: Is testing only x = 4 enough to be sure two expressions are equivalent? Justify why or why not.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Sort each expression into the group with its equivalent expression.
✍️ Explore Discourse
How did you decide which expressions belong in the same group? What strategies did you use?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How can you prove 2(n + 4) and 2n + 8 are equivalent? What two strategies could you use?
👂 Listen For
A strong answer uses the distributive property (2(n + 4) = 2n + 8) and/or substitutes a value into both to confirm equal results.
Extend: Are 2x + 3 and 5x equivalent? Find a value of x that proves your answer and explain why one test value showing equality is not enough.
Practice Check A
Which expression is equivalent to 4x + 3x?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Which expression is equivalent to 2(m + 5)?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Expression Simplify
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Match each expression with its simplified form.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Equivalent expressions give the same answer for every value of the variable." — and it works because ___.
Because Equivalent means ___, but a tricky part is ___, so I have to ___.
A common mistake with Equivalent is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Simplify to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Equivalent expressions give the same answer for every value of the variable. because ___
Equivalent expressions give the same answer for every value of the variable. but ___
Equivalent expressions give the same answer for every value of the variable. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Sort each expression into the group with its equivalent expression.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Which expression is equivalent to 4x + 3x?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A music studio charges different clients using different formulas. Client A pays 4h + 2h + 30 for h hours. Client B pays 6h + 30. A new client asks if the pricing is fair.
✍️ Connection Reasoning
Are these expressions equivalent? How can you prove it?
The expressions ___ equivalent because when I simplify 4h + 2h + 30, I get ___. I can prove it by substituting h = ___: both expressions equal ___.
Turn & Talk — Connect
Client A pays 4h + 2h + 30 and Client B pays 6h + 30. Is the pricing fair (equivalent)? How can you prove it?
👂 Listen For
Students simplify 4h + 2h + 30 to 6h + 30, conclude the pricing is fair/equivalent, and verify by substituting a value of h.
Extend: A third client pays 5h + 30. Critique whether that is the same deal, and explain for which client it is cheaper as hours grow.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which expression is equivalent to 6n + 4 + 3n − 1?
Bonus Exit Check
Which property is shown: 3(x + 7) = 3x + 21?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students explain 3x + 2x = 5x (combining like terms), so both equal 5x + 10, and verify by substituting a value like x = 4 to get 30 both ways.
• A strong answer uses the distributive property (2(n + 4) = 2n + 8) and/or substitutes a value into both to confirm equal results.
• Students simplify 4h + 2h + 30 to 6h + 30, conclude the pricing is fair/equivalent, and verify by substituting a value of h.
• Listen for students naming a specific strategy tied to 6.EE.4 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Equivalent Expressions is skipping the key idea: "Equivalent expressions give the same answer for every value of the variable." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 7x — 4x + 3x = 7x. Combine the coefficients: 4 + 3 = 7.
✓ Practice 2: 2m + 10 — 2(m + 5) = 2m + 10 using the distributive property.
✓ Practice 3: Distributive — Multiplying 3 by each term inside the parentheses is the distributive property.
✓ Practice 4: 7n — 5n + 2n = 7n. Add the coefficients: 5 + 2 = 7. The variable stays as n.
✓ Exit ticket: 9n + 3 — 6n + 3n = 9n and 4 − 1 = 3, so the simplified expression is 9n + 3.