Evaluate Expressions
I can evaluate algebraic expressions by substituting values for the variables.
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🎯 Content Objective / Objetivo de contenido
I can evaluate algebraic expressions by substituting values for the variables.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The concert cost is 150 + 12s, where s is the number of speakers. How do you find the cost for 5 speakers, and why does this one expression work for any number of speakers?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Mix the Track
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?
Concept Launch
💡 How do we find the value of an expression?
To evaluate an expression means to put a number in place of the variable and then do the math to get one answer.
Replace the variable with its number, then follow the order of operations to find the total.
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 |
|---|---|---|---|
| Variable Variable |
A letter that stands for an unknown number. Una letra que representa un número desconocido. |
In 3x + 5, x can be any number — if x = 2, the expression equals 11; if x = 10, it equals 35 | |
| Expression Expresión |
A math phrase with numbers and letters, but no equal sign. Una frase matemática con números y letras, pero sin signo igual. |
2n + 7 is an expression: the 2n means '2 times some number' and the + 7 means 'then add 7' | |
| Evaluate Evaluar |
To find the value by putting numbers in for the letters. Encontrar el valor poniendo números en lugar de las letras. |
Evaluate 2n + 7 when n = 4: replace n with 4 → 2(4) + 7 = 8 + 7 = 15 | |
| Substitute Sustituir |
To put a number in place of a letter. Poner un número en lugar de una letra. |
Substitute 3 for x in 5x: replace x with 3 → 5(3) = 15 | |
| 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 7m, the coefficient 7 tells you to multiply m by 7 — if m = 3, then 7m = 21 | |
| Like terms Términos semejantes |
Terms with the same letter, like 2x and 5x. Términos con la misma letra, como 2x y 5x. |
4x and 2x are like terms (both x¹); 4x and 4y are NOT (different variables) |
Which Word Fits?
A letter that stands for an unknown number, like x, is a ___.
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
The concert cost is 150 + 12s, where s is the number of speakers. How do you find the cost for 5 speakers, and why does this one expression work for any number of speakers?
👂 Listen For
Students substitute s = 5 (150 + 12 × 5 = 210), explain 150 is the fixed venue fee and 12 is the cost per speaker, and note s can be any number.
Extend: Predict whether doubling the speakers from 5 to 10 doubles the total cost. Justify using the $150 base fee.
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
Evaluate the expression 150 + 12s for each number of speakers.
✍️ Explore Discourse
What happens to the total cost each time you add one more speaker? Why?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
When you evaluate an expression like 4x² + 3, what order do you follow, and why must you square before you multiply?
👂 Listen For
A strong answer substitutes the value first, then applies the exponent before multiplying (e.g., 4 × 2² = 4 × 4 = 16, not (4 × 2)² ), citing order of operations.
Extend: A classmate evaluates 4x² + 3 at x = 2 as (4 × 2)² + 3 = 67. Critique the error and give the correct value.
Practice Check A
Evaluate 3x + 7 when x = 4.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Evaluate 20 − 2n when n = 6.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Power Matching
Match each expression to its value. Click pairs that belong together.
✍️ Justify Your Thinking
Evaluate each expression when a = 3. Sort by whether the result is greater than 15 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: "Replace the variable with its number, then follow the order of operations to find the total." — and it works because ___.
Because Variable means ___, but a tricky part is ___, so I have to ___.
A common mistake with Variable is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Expression to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Replace the variable with its number, then follow the order of operations to find the total. because ___
Replace the variable with its number, then follow the order of operations to find the total. but ___
Replace the variable with its number, then follow the order of operations to find the total. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Evaluate the expression 150 + 12s for each number of speakers.
| Speakers (s) | Expression | Total Cost ($) |
|---|---|---|
| 2 | 150 + 12(2) | |
| 5 | 150 + 12(5) | |
| 8 | 150 + 12(8) | |
| 10 | 150 + 12(10) |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Evaluate 3x + 7 when x = 4.
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 rideshare app charges $2.50 plus $1.75 per mile. The expression for the fare is 2.50 + 1.75m, where m is miles traveled. Your friend lives 8 miles away.
✍️ Connection Reasoning
How much will the ride cost? How does the expression model this situation?
The ride costs $___ because 2.50 + 1.75(___) = ___. The 2.50 is the ___ and 1.75 is the ___.
Turn & Talk — Connect
The rideshare fare is 2.50 + 1.75m for m miles. How much is an 8-mile ride, and what does each part of the expression represent?
👂 Listen For
Students evaluate 2.50 + 1.75 × 8 = 16.50 and identify 2.50 as the base fee and 1.75 as the per-mile rate.
Extend: Two riders pay the same fare, but one traveled fewer miles. How is that possible with 2.50 + 1.75m? Justify what would have to differ.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Evaluate 5(n − 3) + 2 when n = 7.
Bonus Exit Check
Which expression means '5 less than twice a number n'?
✍️ 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 substitute s = 5 (150 + 12 × 5 = 210), explain 150 is the fixed venue fee and 12 is the cost per speaker, and note s can be any number.
• A strong answer substitutes the value first, then applies the exponent before multiplying (e.g., 4 × 2² = 4 × 4 = 16, not (4 × 2)² ), citing order of operations.
• Students evaluate 2.50 + 1.75 × 8 = 16.50 and identify 2.50 as the base fee and 1.75 as the per-mile rate.
• Listen for students naming a specific strategy tied to 6.EE.2c — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Evaluate Expressions is skipping the key idea: "Replace the variable with its number, then follow the order of operations to find the total." — 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: 19 — 3(4) + 7 = 12 + 7 = 19.
✓ Practice 2: 8 — 20 − 2(6) = 20 − 12 = 8.
✓ Practice 3: 2n − 5 — Twice n is 2n. Five less than that is 2n − 5.
✓ Practice 4: 21 — 4(5) + 1 = 20 + 1 = 21.
✓ Exit ticket: 22 — 5(7 − 3) + 2 = 5(4) + 2 = 20 + 2 = 22.