The Distributive Property
I can use the distributive property to expand and factor expressions.
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🎯 Content Objective / Objetivo de contenido
I can use the distributive property to expand and factor expressions.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Each bundle is a ticket ($15) and a snack ($5). For 3 people, why does 3(15 + 5) give the same $60 as 3 × 15 + 3 × 5?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Ticket Pricing
You're selling concert bundles at the music studio. Each bundle includes a ticket ($15) and a snack ($5). If 3 people each buy a bundle, you can calculate the total as 3(15 + 5) OR as 3 × 15 + 3 × 5. Either way, the total is the same — $60! This is the distributive property.
Concept Launch
💡 What is the distributive property?
The distributive property means you can multiply a number by everything inside the parentheses, one piece at a time: a(b + c) = ab + ac.
The number outside the parentheses gets "shared" with every term inside.
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 |
|---|---|---|---|
| Distributive Property Propiedad distributiva |
Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac. Multiplicar un número por todo lo que está dentro del paréntesis: a(b + c) = ab + ac. |
3(4 + 5) = 3×4 + 3×5 = 12 + 15 = 27 — the 3 gets 'distributed' to both the 4 and the 5 | |
| Factor Factor |
A number that gets multiplied by another number. Un número que se multiplica por otro número. |
In 3(x + 2), the 3 is the factor outside the parentheses that multiplies each term inside | |
| Expand Desarrollar |
To multiply out the parentheses in an expression. Multiplicar lo que está dentro del paréntesis en una expresión. |
Expand 2(n + 6): multiply 2 × n = 2n and 2 × 6 = 12, so 2(n + 6) = 2n + 12 | |
| Equivalent Equivalente |
Expressions that always have the same value. Expresiones que siempre tienen el mismo valor. |
3(x + 4) and 3x + 12 always give the same answer: when x = 2, both = 18; when x = 10, both = 42 | |
| 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 6x + 15, the coefficient of x is 6 — it came from distributing in 3(2x + 5) | |
| Like terms Términos semejantes |
Terms with the same letter, like 2x and 5x. Términos con la misma letra, como 2x y 5x. |
4x + 2x = 6x (combine coefficients); 4x + 2y cannot be combined (different variables) |
Which Word Fits?
The rule that a(b + c) = ab + ac is the ___.
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
Each bundle is a ticket ($15) and a snack ($5). For 3 people, why does 3(15 + 5) give the same $60 as 3 × 15 + 3 × 5?
👂 Listen For
Students explain the 3 distributes to both the ticket and the snack (3 × 15 + 3 × 5 = 45 + 15 = 60), matching 3 × 20, and use the word equivalent.
Extend: If 10 people bought bundles, which form is faster to compute: 10(15 + 5) or 10 × 15 + 10 × 5? Justify your choice.
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
Expand each expression using the distributive property. Then simplify to find the value.
✍️ Explore Discourse
What pattern do you see when you expand an expression using the distributive property?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
When you expand 5(2x + 4), why must the 5 multiply BOTH terms inside the parentheses?
👂 Listen For
A strong answer expands 5(2x + 4) = 10x + 20 and explains the parentheses mean 5 copies of the whole sum, so both 2x and 4 are multiplied.
Extend: A classmate writes 5(2x + 4) = 10x + 4. Critique the error and prove the correct form is equivalent by testing x = 3.
Practice Check A
Expand 6(n + 3) using the distributive property.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Expand 4(5 − 2) using the distributive property.
✍️ 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
Expand each expression, then sort by whether the expanded form has a constant 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: "The number outside the parentheses gets "shared" with every term inside." — and it works because ___.
Because Distributive Property means ___, but a tricky part is ___, so I have to ___.
A common mistake with Distributive Property is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Factor to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
The number outside the parentheses gets "shared" with every term inside. because ___
The number outside the parentheses gets "shared" with every term inside. but ___
The number outside the parentheses gets "shared" with every term inside. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Expand each expression using the distributive property. Then simplify to find the value.
| Factored Form | Expanded Form | Value |
|---|---|---|
| 2(8 + 3) | 2 × 8 + 2 × 3 | |
| 5(10 + 4) | ||
| 3(x + 7) | ||
| 4(2n − 3) |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Expand 6(n + 3) using the distributive property.
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 is ordering supplies for 8 practice rooms. Each room needs a music stand ($12) and a stool ($9). The total cost can be written as 8(12 + 9).
✍️ Connection Reasoning
Use the distributive property to find the total cost. Which way of calculating is easier for you?
8(12 + 9) = 8 × ___ + 8 × ___ = ___ + ___ = ___. I think the ___ form is easier because ___.
Turn & Talk — Connect
For 8 practice rooms each needing a music stand ($12) and a stool ($9), the cost is 8(12 + 9). How do you use the distributive property to find the total, and which form is easier for you?
👂 Listen For
Students compute 8 × 12 + 8 × 9 = 96 + 72 = 168 (or 8 × 21 = 168) and justify which form they find easier, recognizing both are equivalent.
Extend: Working backwards, how would you factor 8x + 12 into a product? Explain how factoring undoes the distributive property.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which expression is equivalent to 7(x + 3)?
Bonus Exit Check
Expand 3(x + 4) using the distributive property.
✍️ 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 the 3 distributes to both the ticket and the snack (3 × 15 + 3 × 5 = 45 + 15 = 60), matching 3 × 20, and use the word equivalent.
• A strong answer expands 5(2x + 4) = 10x + 20 and explains the parentheses mean 5 copies of the whole sum, so both 2x and 4 are multiplied.
• Students compute 8 × 12 + 8 × 9 = 96 + 72 = 168 (or 8 × 21 = 168) and justify which form they find easier, recognizing both are equivalent.
• 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 The Distributive Property is skipping the key idea: "The number outside the parentheses gets "shared" with every term inside." — 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: 6n + 18 — 6(n + 3) = 6 × n + 6 × 3 = 6n + 18.
✓ Practice 2: 12 — 4(5 − 2) = 4 × 5 − 4 × 2 = 20 − 8 = 12.
✓ Practice 3: 3x + 12 — 3(x + 4) = 3 × x + 3 × 4 = 3x + 12.
✓ Practice 4: Both b and c — The distributive property says a(b + c) = ab + ac. You multiply the outside factor by EACH term inside the parentheses.
✓ Exit ticket: 7x + 21 — 7(x + 3) = 7 × x + 7 × 3 = 7x + 21.