Write and Evaluate Numerical Expressions with Exponents
I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.
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🎯 Content Objective / Objetivo de contenido
I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers.
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
The studio's booking sheet lists a price for each kind of seat. Writing one numerical expression for the whole order — and evaluating it in the right order — is faster and easier to check than adding costs one at a time. Some counts are written as powers, so the exponent has to be handled before any multiplying.
Concept Launch
💡 Write the expression, then evaluate it in order
A numerical expression is a math phrase made of numbers and operations, with no equal sign. Writing one for a whole situation keeps every part visible; evaluating it means finding its single value, following the order of operations.
Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Write and Evaluate Numerical Expressions with Exponents Escribir y evaluar expresiones numéricas con exponentes |
Turning a situation into a number sentence without an equal sign, then finding its value in the correct order. Convertir una situación en una expresión numérica sin signo de igual y luego hallar su valor en el orden correcto. |
2 × 15 + 4 × 20 + 8 × 2³ = 174 | |
| Numerical expression Expresión numérica |
A math phrase built from numbers and operations, with no equal sign and no variable. Una frase matemática hecha de números y operaciones, sin signo de igual y sin variable. |
4 × 20 is an expression; 4 × 20 = 80 is an equation | |
| Evaluate Evaluar |
To find the single value an expression is worth by carrying out its operations in order. Hallar el único valor que representa una expresión, realizando sus operaciones en orden. |
Evaluate 3 + 2 × 4 → 3 + 8 = 11 | |
| Order of operations Orden de las operaciones |
The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right. El orden acordado para evaluar: signos de agrupación, luego exponentes, luego multiplicar y dividir de izquierda a derecha, y por último sumar y restar de izquierda a derecha. |
3 + 4 × 2² → 3 + 4 × 4 → 3 + 16 = 19 | |
| Power Potencia |
A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2. Una forma corta de escribir la multiplicación repetida del mismo factor, como 2³ para 2 × 2 × 2. |
2³ = 2 × 2 × 2 = 8 | |
| Base Base |
In a power, the number being multiplied by itself. In 2³ the base is 2. En una potencia, el número que se multiplica por sí mismo. En 2³ la base es 2. |
2³ — the 2 is the base |
Which Word Fits?
Write the situation as an expression, then follow the ___ ___ ___ to value 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
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
You are evaluating 3 + 4 × 2² − 6. Sort each step into the order it must be done.
✍️ Explore Discourse
Two students evaluate 3 + 4 × 2 and get 14 and 11. Which one followed the order of operations, and why does the order have to be agreed on at all?
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
What is the total of 2 × 15 + 4 × 20 + 8 × 2³?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Miguel evaluates 12 − 2 × 3 and gets 30. Margaret gets 6. Who is right?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Equivalent Ratio Sort
Complete the interactive activity using today's strategy.
✍️ Justify Your Thinking
Sort each label into the correct box.
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: "Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right" — and it works because ___.
Because Write and Evaluate Numerical Expressions with Exponents means ___, but a tricky part is ___, so I have to ___.
A common mistake with Write and Evaluate Numerical Expressions with Exponents is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Numerical expression to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right because ___
Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right but ___
Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Evaluate 3 + 4 × 2.
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.
Summarize: Write and Evaluate Numerical Expressions with Exponents
Order of Operations (PEMDAS). 1. Grouping Symbols: Parentheses, brackets, fraction bars inner to outer. 2. Exponents: Evaluate all powers. 3. Multiply & Divide left to right; Add & Subtract left to right
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Evaluate 2 × 15 + 8 × 2³.
Bonus Exit Check
Evaluate 3 + 4 × 2.
✍️ 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.AT.6c — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9. A second is evaluating strictly left to right, so 3 + 4 × 2 becomes 14 instead of 11. The order of operations exists so one expression has exactly one value: grouping symbols, then powers, then × and ÷ left to right, then + and − left to right.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 174 — Power first: 2³ = 8. Multiply: 30, 80, 64. Add: 30 + 80 + 64 = 174.
✓ Practice 2: Margaret, because multiplication comes before subtraction — Multiplying first gives 2 × 3 = 6, then 12 − 6 = 6. Miguel subtracted first, getting 10 × 3 = 30.
✓ Practice 3: 11 — Multiplication comes before addition: 4 × 2 = 8, then 3 + 8 = 11.
✓ Practice 4: 2 × 2 × 2 — The exponent says how many times the base is used as a factor, so 2³ = 2 × 2 × 2 = 8.
✓ Exit ticket: 94 — Powers first: 2³ = 8. Then multiply left to right: 2 × 15 = 30 and 8 × 8 = 64. Then add: 30 + 64 = 94.