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

Lesson 8.38.3 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can solve one-step multiplication and division equations using inverse operations — one step at a time, with support.

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 examplesolving a multiplication equation

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

A stamp album has 7 pages that each hold p stamps. It holds 91 stamps in all. Solve 7p = 91.

  1. The variable p is multiplied by 7, so the inverse operation is division.
  2. Divide BOTH sides by 7 so the equation stays balanced.
  3. Left side: 7p ÷ 7 leaves p. Right side: 91 ÷ 7 gives 13.
  4. Check: 7 × 13 makes 91, so both sides are equal.

Answer: p = 13, so each page holds 13 stamps.

Now you trySame steps, your turn

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

A choir stands in 9 equal rows and has 108 singers. Solve 9r = 108 for the singers in one row.

  1. The variable r is multiplied by , so the inverse operation is .
  2. Divide both sides by .
  3. Left side leaves . Right side: 108 ÷ 9 = .
  4. Check: 9 × = . Does it balance?
Answer:singers in one row

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 outA common mistake

A common mistake in Solve Multiplication and Division Equations is applying the SAME operation again instead of the inverse — for example, seeing 6x = 42 and multiplying both sides by 6 to get x = 252, instead of dividing by 6 to get x = 7. Before you submit, ask: did I use the OPPOSITE operation shown in the equation, and did I apply it to both sides?

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

Lesson 8.38.3 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can solve one-step multiplication and division equations using inverse operations — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    4xxxxx28
    4 equal parts make 28.

    Solve 4x = 28.

    1. 14x means 4 times x. What undoes multiplying by 4?
    2. 2Divide both sides by 4. What is x?
    3. 3Check: put 7 in for x. What is 4 × 7?
    Final answer:
  2. 2Complete each step, then write the final answer.
    x66666x
    x split into 5 equal parts gives 6 in each part.

    Solve x ÷ 5 = 6.

    1. 1Is x multiplied by 5 or divided by 5?
    2. 2Multiply both sides by 5. What is x?
    3. 3Check: put 30 in for x. What is 30 ÷ 5?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve 6x = 54.

    Show your work

    Hint 6x means 6 times x. Divide both sides by 6.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Solve n ÷ 7 = 12.

    Show your work

    Hint n is divided by 7. Do the inverse to both sides.

    Final answer:
  5. 5Complete each step, then write the final answer.
    Total c$9$9$9$9$9$9$9$9c
    The total c splits into 8 equal shares of $9.

    8 friends share the cost of a pizza party equally. Each friend pays $9. Write and solve an equation for the total cost c.

    Show your work

    Hint The total is divided by 8. Write c ÷ 8 = 9. Then undo the division.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Lia solved 3x = 45 and got x = 135. Is she right? What is x?

    Show your work

    Hint Check Lia's answer: what is 3 × 135? Then think about what undoes multiplying by 3.

    Final answer:

Explain your thinkingLia multiplied when she should have divided. How do you decide whether to multiply or divide both sides?

Sentence starter x is ___ by the number, so I ___ both sides. · I know my answer is right because ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help