Solve Multiplication and Division Equations
I can solve one-step multiplication and division equations using inverse operations.
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🎯 Content Objective / Objetivo de contenido
I can solve one-step multiplication and division equations using inverse operations.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Detective Park has 3 identical boxes holding 21 pieces of evidence total, written as 3x = 21. What does each part of the equation mean, and how is solving this different from solving x + 3 = 21?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Case File: The Multiplied Evidence
Detective Park discovered that 3 identical locked boxes contain a total of 21 pieces of evidence. She writes the equation 3x = 21 to find how many pieces are in each box. How can she solve for x?
Concept Launch
💡 How do I solve a multiplication or division equation?
When a variable is multiplied or divided by a number, I use the inverse operation to get it alone. Division undoes multiplication, and multiplication undoes division.
Divide to undo multiplying, and multiply to undo dividing — always on both sides.
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 |
|---|---|---|---|
| Inverse operation Operación inversa |
Two math actions that undo each other, like × and ÷. Dos operaciones que se deshacen entre sí, como × y ÷. |
Multiplication and division are inverses: 3 × 7 = 21, so 21 ÷ 3 = 7 | |
| Multiply Multiplicar |
To add equal groups again and again. Sumar grupos iguales una y otra vez. |
3 × 7 = 21 means 3 groups of 7 equals 21 | |
| Divide Dividir |
To split into equal groups. Repartir en grupos iguales. |
36 ÷ 4 = 9 means 36 split into 4 equal groups gives 9 per group | |
| Isolate Despejar |
To get the letter by itself on one side. Dejar la letra sola en un lado. |
3x = 21 → divide both sides by 3 → x = 7 (x is alone) | |
| Coefficient Coeficiente |
The number multiplied by a variable. El número que multiplica a una variable. |
In 6x = 18, the coefficient is 6; divide both sides by 6 to get x = 3. | |
| Solution Solución |
The value of the variable that makes the equation true. El valor de la variable que hace verdadera la ecuación. |
x = 3 is the solution of 6x = 18 because 6 × 3 = 18. |
Which Word Fits?
An operation that undoes another, like division undoing multiplication, is an ___.
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
Detective Park has 3 identical boxes holding 21 pieces of evidence total, written as 3x = 21. What does each part of the equation mean, and how is solving this different from solving x + 3 = 21?
👂 Listen For
Students read 3x as 3 groups of x, recognize multiplication, and contrast it with addition, knowing they will divide (not subtract) to solve.
Extend: Predict: would x in 3x = 21 be larger or smaller than in 5x = 21? Justify before solving.
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
Solve each equation by showing your work. Use inverse operations to isolate the variable.
✍️ Explore Discourse
How do you decide whether to multiply or divide to solve an equation?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How did you undo the multiplication in 3x = 21 (or the division in x / 4 = 9) to isolate the variable?
👂 Listen For
Students divide both sides by 3 to get x = 7 (or multiply by 4 to get x = 36) and name division/multiplication as inverse operations.
Extend: Why does dividing only one side of 3x = 21 give the wrong answer? Compare doing it to one side versus both sides.
Practice Check A
A detective splits 54 clues equally among 9 case files. The equation 9c = 54 represents this. What is c?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Solve: 6x = 42
✍️ 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
Detective, decide which key opens each vault: do you MULTIPLY or DIVIDE to unlock the variable?
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: "Divide to undo multiplying, and multiply to undo dividing — always on both sides." — and it works because ___.
Because Inverse operation means ___, but a tricky part is ___, so I have to ___.
A common mistake with Inverse operation is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Multiply to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Divide to undo multiplying, and multiply to undo dividing — always on both sides. because ___
Divide to undo multiplying, and multiply to undo dividing — always on both sides. but ___
Divide to undo multiplying, and multiply to undo dividing — always on both sides. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Solve each equation by showing your work. Use inverse operations to isolate the variable.
| Column A | Column B |
|---|---|
| [object Object] | |
| [object Object] | |
| [object Object] |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Solve: 6x = 42
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 detective ordered fingerprint kits for her team. Each kit costs $7, and the total bill was $63. The equation 7k = 63 represents this situation, where k is the number of kits.
✍️ Connection Reasoning
How many kits did the detective order? How did inverse operations help you solve this?
The detective ordered ___ kits because 7k = 63 means k = 63 ÷ ___ = ___.
Turn & Talk — Connect
When would you solve a multiplication or division equation in real life?
👂 Listen For
Students name a real context (equal price per item, sharing equally, total from groups) and choose the correct inverse operation to isolate the variable.
Extend: Critique: 'To solve x / 5 = 12 you divide both sides by 5.' Explain the error and the correct inverse operation.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Solve: w / 8 = 6
Bonus Exit Check
Solve: n / 3 = 8
✍️ 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 read 3x as 3 groups of x, recognize multiplication, and contrast it with addition, knowing they will divide (not subtract) to solve.
• Students divide both sides by 3 to get x = 7 (or multiply by 4 to get x = 36) and name division/multiplication as inverse operations.
• Students name a real context (equal price per item, sharing equally, total from groups) and choose the correct inverse operation to isolate the variable.
• Listen for students naming a specific strategy tied to 6.EE.7 — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Solve Multiplication and Division Equations is skipping the key idea: "Divide to undo multiplying, and multiply to undo dividing — always on both sides." — 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: c = 6 — Divide both sides by 9: c = 54 ÷ 9 = 6 clues per file.
✓ Practice 2: x = 7 — Divide both sides by 6: x = 42 ÷ 6 = 7. Check: 6 × 7 = 42 ✓
✓ Practice 3: n = 24 — Multiply both sides by 3: n = 8 × 3 = 24. Check: 24 / 3 = 8 ✓
✓ Practice 4: m = 7 — Divide both sides by 9: m = 63 ÷ 9 = 7. Check: 9 × 7 = 63 ✓
✓ Exit ticket: w = 48 — Multiply both sides by 8: w = 6 × 8 = 48. Check: 48 / 8 = 6 ✓