Simplify Algebraic Expressions
I can simplify algebraic expressions by combining like terms.
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🎯 Content Objective / Objetivo de contenido
I can simplify algebraic expressions by 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
Three rooms need microphones and stands. Why can you add all the microphones together (4 + 2 + 6) but not mix microphones with stands?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Equipment Order
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. Instead of ordering separately, you can combine: (4 + 2 + 6) microphones and (3 + 5 + 1) stands = 12 microphones and 9 stands. That's simplifying by combining like items!
Concept Launch
💡 How do we simplify by combining like terms?
Like terms are terms with the same variable, like 2x and 5x. To simplify an expression, you add or subtract the like terms to make it shorter.
Only combine terms that have the same variable part; numbers without a variable combine with each other.
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 |
|---|---|---|---|
| Like Terms Términos semejantes |
Terms with the same letter, like 2x and 5x. Términos con la misma letra, como 2x y 5x. |
5x and 3x are like terms (both x); 5x and 5y are NOT (different variables); 2x and 2x² are NOT (different powers) | |
| Combine Combinar |
To add or subtract terms with the same letter into one. Sumar o restar términos con la misma letra en uno solo. |
8m + 3m = 11m — add the coefficients (8 + 3 = 11) and keep the variable (m) | |
| Simplify Simplificar |
To write an expression in its shortest form. Escribir una expresión en su forma más corta. |
2a + 5a + 3 simplifies to 7a + 3 — the two a-terms combine, the constant stays | |
| 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 9x, the coefficient is 9 — it tells you 'nine groups of x'; if x = 2, then 9x = 18 | |
| Term Término |
A single number, variable, or product of them, separated by + or − signs. Un solo número, variable o producto de ellos, separado por signos + o −. |
In 3x + 5 − 2x, the terms are 3x, 5, and 2x. | |
| Distributive property Propiedad distributiva |
Multiplying a sum by a number means multiplying each part by that number. Multiplicar una suma por un número significa multiplicar cada parte por ese número. |
3(x + 4) = 3·x + 3·4 = 3x + 12. |
Which Word Fits?
Terms with the same variable part, like 3y and 8y, are ___.
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
Three rooms need microphones and stands. Why can you add all the microphones together (4 + 2 + 6) but not mix microphones with stands?
👂 Listen For
Students explain microphones combine with microphones (4 + 2 + 6 = 12) but not with stands, connecting this to combining like terms in algebra.
Extend: How is mixing microphones and stands like trying to add 3x and 5? Generalize the rule for which terms can combine.
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
Identify the like terms in each expression. Group the terms that can be combined.
✍️ Explore Discourse
What rule determines whether two terms are 'like terms'? Why can't you combine unlike terms?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
To simplify 6x + 4 + 2x + 7, which are the like terms, and how do you combine them?
👂 Listen For
A strong answer combines 6x + 2x = 8x and 4 + 7 = 11 to get 8x + 11, adding coefficients of like terms and keeping the variable.
Extend: A classmate simplifies 5x + 3 + 2y + 4x as 11xy + 3. Critique the error and give the correct simplified form.
Practice Check A
Simplify 7x + 3x.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Simplify 9n + 4 + 2n.
✍️ 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
Simplify each expression, then sort by whether the simplified coefficient of the variable is greater than 6 or not.
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: "Only combine terms that have the same variable part; numbers without a variable combine with each other." — and it works because ___.
Because Like Terms means ___, but a tricky part is ___, so I have to ___.
A common mistake with Like Terms is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Combine to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Only combine terms that have the same variable part; numbers without a variable combine with each other. because ___
Only combine terms that have the same variable part; numbers without a variable combine with each other. but ___
Only combine terms that have the same variable part; numbers without a variable combine with each other. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Identify the like terms in each expression. Group the terms that can be combined.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Simplify 7x + 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 festival needs supplies for 3 stages. Stage 1 needs 8m + 5 cables, Stage 2 needs 3m + 7 cables, and Stage 3 needs 4m + 2 cables, where m represents the number of microphones per stage. The total order is (8m + 5) + (3m + 7) + (4m + 2).
✍️ Connection Reasoning
Simplify the total order expression. What does each part of the simplified expression tell you?
The total order simplifies to ___m + ___. The ___ tells us ___ and the ___ tells us ___.
Turn & Talk — Connect
The festival order is (8m + 5) + (3m + 7) + (4m + 2), where m is microphones per stage. What does the simplified expression tell you?
👂 Listen For
Students simplify to 15m + 14, explaining 15m is the total cables tied to microphones and 14 is the extra fixed cables across stages.
Extend: Why is 15m + 14 easier to use for ordering than the original three grouped expressions? Justify how simplifying makes the real problem clearer.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Simplify 6x + 3 + 2x + 5.
Bonus Exit Check
Which pair are like terms?
✍️ 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 microphones combine with microphones (4 + 2 + 6 = 12) but not with stands, connecting this to combining like terms in algebra.
• A strong answer combines 6x + 2x = 8x and 4 + 7 = 11 to get 8x + 11, adding coefficients of like terms and keeping the variable.
• Students simplify to 15m + 14, explaining 15m is the total cables tied to microphones and 14 is the extra fixed cables across stages.
• Listen for students naming a specific strategy tied to 6.EE.3 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Simplify Algebraic Expressions is skipping the key idea: "Only combine terms that have the same variable part; numbers without a variable combine with each other." — 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: 10x — 7x + 3x = 10x. Add the coefficients: 7 + 3 = 10.
✓ Practice 2: 11n + 4 — 9n + 2n = 11n. The constant 4 has no like term, so it stays. Result: 11n + 4.
✓ Practice 3: 6x and 2x — 6x and 2x are like terms because they both have the same variable (x) raised to the same power (1).
✓ Practice 4: 7a + 3 — 5a + 2a = 7a. The constant 3 stays. Result: 7a + 3.
✓ Exit ticket: 8x + 8 — 6x + 2x = 8x and 3 + 5 = 8, so the simplified expression is 8x + 8.