Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Write and Solve Equations Using Multiplication or Division

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

Why This Matters 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?

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Inverse operationSpanish: Operación inversa Two math actions that undo each other, like × and ÷. × and ÷
MultiplySpanish: Multiplicar To add equal groups again and again. 3 × 7 = 21 means 3 groups of 7 equals 21
DivideSpanish: Dividir To split into equal groups. 20 ÷ 4 = 5
IsolateSpanish: Despejar To get the letter by itself on one side. get p by itself
CoefficientSpanish: Coeficiente The number in front of a letter, like the 3 in 3x. the 3 in 3x
SolutionSpanish: Solución A number that makes the equation or inequality true. x = 3 is the solution of 6x = 18 because 6 × 3 = 18.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

5 boxes each hold the same number of pencils, 45 in all. Solve 5b = 45.

  1. Divide both sides by 5: 5b ÷ 5 = 45 ÷ 5.
  2. Simplify: b = 9.
  3. Check: 5 × 9 = 45.

Answer: Each box holds 9 pencils.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Solve x ÷ 4 = 9. Is x multiplied or divided?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The variable is multiplied by , so I both sides by it.
  • My equation is because each group holds .
  • The solution means in this problem.
  • I checked my answer by multiplying and .

Word bank equationcoefficientmultiplydivideinverse operationisolateboth sidesequal groupssolutioncheckundobalance

Watch out!A common mistake

A common mistake in Solve Multiplication and Division Equations is applying the SAME operation again instead of the inverse

Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Write and Solve Equations Using Multiplication or Division

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

Why This Matters 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?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Sort each equation by the inverse operation needed.

    Groups: Divide both sides Multiply both sides
    • 4x = 32
    • 7n = 56
    • 10p = 80
    • x / 6 = 3
    • m / 2 = 15
    • y / 9 = 4

    Hint If the variable is being multiplied (like 4x), divide to undo it.

Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Solve: 6x = 42

    1. Ax = 7
    2. Bx = 36
    3. Cx = 48
    4. Dx = 252

    Hint 6x means 6 TIMES x — the variable is being multiplied by 6.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Solve: n / 3 = 8

    1. An = 3
    2. Bn = 5
    3. Cn = 11
    4. Dn = 24

    Hint n is being DIVIDED by 3. Which operation undoes division?

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Solve: 9m = 63

    1. Am = 7
    2. Bm = 54
    3. Cm = 72
    4. Dm = 567

    Hint 9m means 9 times m — that's multiplication, even with no × symbol written.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Solve: y / 7 = 5

    1. Ay = 2
    2. By = 7
    3. Cy = 12
    4. Dy = 35

    Hint y is split into 7 equal parts. To rebuild y, you need the opposite of dividing.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Equation6x = 42
    2. 2Choose operationTo undo it, I will multiply both sides by 6.
    3. 3Apply to both sides6x × 6 = 42 × 6
    4. 4Simplifyx = 252

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The student multiplied again instead of dividing. Does multiplying by 6 get x alone?

    Correct work
    Correct answer:

Explain your thinkingHow do you decide whether to multiply or divide to solve an equation?

Sentence starter When I see ___ in the equation, I know to ___ both sides because the inverse of ___ is ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Write and Solve Equations Using Multiplication or Division

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

Why This Matters 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?

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Solve each equation, show your work, and check.

    EquationWorkSolutionCheck
    8m = 56
    y / 6 = 11
    12k = 96
    Show your work
  2. 2Decide whether each pair balances. Check Yes or No, then explain.

    Solve 5x = 40 using the balance scale.

    Left sideRight sideBalanced?
    Explain your choice
  3. 3Use the model to solve. Show your work.
    Total121212121212

    A detective found 72 pieces of evidence and divided them equally into 6 bags. Use the bar model to show how many are in each bag.

    Show your work
    Answer:
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A detective splits 54 clues equally among 9 case files. The equation 9c = 54 represents this. What is c?

    1. Ac = 6
    2. Bc = 9
    3. Cc = 45
    4. Dc = 63
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Equationn / 4 = 12
    2. 2Choose operationn is in a fraction, so I will divide both sides by 4.
    3. 3Apply to both sidesn / 4 ÷ 4 = 12 ÷ 4
    4. 4Simplifyn = 3

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow do you decide whether to multiply or divide to solve an equation?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 8: Equations & InequalitiesStandard 6.AT.8

Lesson 8.3Write and Solve Equations Using Multiplication or Division

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can solve one-step multiplication and division equations using inverse operations.

Why This Matters 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?

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Solve each equation, then write and solve a related equation that uses the inverse operation.

    EquationSolutionRelated EquationRelated Solution
    4x = 36
    x / 7 = 8
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Equation Error

    1. 1Equationx / 5 = 12
    2. 2Identify inverseInverse of division is division
    3. 3Apply to both sidesx / 5 / 5 = 12 / 5
    4. 4Simplifyx = 2.4

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete 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.

    Write your answer

Explain your thinkingHow do you decide whether to multiply or divide to solve an equation?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help