Unit 7 · Standard 6.EE.7
Solve Multiplication and Division Equations
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Multiplication and division are inverses: 3 × 7 = 21, so 21 ÷ 3 = 7
Inverse operation
Two math actions that undo each other, like × and ÷.
3 × 7 = 21 means 3 groups of 7 equals 21
Multiply
To add equal groups again and again.
36 ÷ 4 = 9 means 36 split into 4 equal groups gives 9 per group
Divide
To split into equal groups.
3x = 21 → divide both sides by 3 → x = 7 (x is alone)
Isolate
To get the letter by itself on one side.
Key Ideas & Notes
- 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?
- Solve each equation by showing your work. Use inverse operations to isolate the variable.
Think About It
- What does the 3 represent in the equation?
- What does x represent?
- What operation connects 3 and x?
My Notes
Guided Examples
Example 1
Solve: 6x = 42
Solution: Divide both sides by 6: x = 42 ÷ 6 = 7. Check: 6 × 7 = 42 ✓
Answer: A. x = 7
Example 2
Solve: n / 3 = 8
Solution: Multiply both sides by 3: n = 8 × 3 = 24. Check: 24 / 3 = 8 ✓
Answer: A. n = 24
Example 3
Solve: 9m = 63
Solution: Divide both sides by 9: m = 63 ÷ 9 = 7. Check: 9 × 7 = 63 ✓
Answer: A. m = 7
Write About the Math The Writing Revolution
I can explain my steps using the words inverse operation, multiply, divide, and isolate.
1. Kernel Sentence subject + verb
Model: Inverse operation is two math actions that undo each other, like × and ÷.Operación inversa es dos operaciones que se deshacen entre sí, como × y ÷.
Write a kernel sentence about inverse operation. Use a subject and a verb.Escribe una oración base sobre operación inversa. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Inverse operation matters in mathOperación inversa importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Inverse operation matters in math because ___.Operación inversa importa en matemáticas porque ___.
Inverse operation matters in math, but ___.Operación inversa importa en matemáticas, pero ___.
Inverse operation matters in math, so ___.Operación inversa importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about inverse operation.Di un hecho verdadero sobre inverse operation.
Inverse operation ___.
Ask a question about inverse operation.Haz una pregunta sobre inverse operation.
How does ___ ?¿Cómo ___ ?
Show excitement about inverse operation.Muestra entusiasmo sobre inverse operation.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with inverse operation.Dile a un compañero qué hacer con inverse operation.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I divided / multiplied both sides by ___.Dividí / multipliqué ambos lados por ___.
The answer is ___ because ___.La respuesta es ___ porque ___.
I would use this to ___.Usaría esto para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Solve: y / 7 = 5
- y = 35
- y = 12
- y = 2
- y = 7
2. A detective splits 54 clues equally among 9 case files. The equation 9c = 54 represents this. What is c?
- c = 6
- c = 63
- c = 45
- c = 9
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A bakery packed muffins into boxes of 8. They made 96 muffins total. Write an equation, solve it, and explain why your answer is reasonable. Then write a different situation that uses division and has the same answer.
Sentence starter: Equation: ___. Solving: ___. The answer ___ is reasonable because ___. A division situation with the same answer: ___.
Reflect — Exit Ticket
Solve: w / 8 = 6
- w = 48
- w = 14
- w = 0.75
- w = 2
Answer Key & Teacher Guide
- Try It 1: A. y = 35 — Multiply both sides by 7: y = 5 × 7 = 35. Check: 35 / 7 = 5 ✓
- Try It 2: A. c = 6 — Divide both sides by 9: c = 54 ÷ 9 = 6 clues per file.
- Exit Ticket: A. w = 48 — Multiply both sides by 8: w = 6 × 8 = 48. Check: 48 / 8 = 6 ✓
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Inverse operation is two math actions that undo each other, like × and ÷.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).