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

Lesson 8.38.1–8.3 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 8.1–8.3 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Write EquationsSpanish: Escribir ecuaciones Represent a relationship with expressions joined by an equal sign. A $5 fee plus $3 per game for g games: 5 + 3g = total.
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. n + 8 = 20 means 'some number plus 8 equals 20'
VariableSpanish: Variable A letter that stands for a number that is unknown or can change. In n + 3 = 10, the letter n stands for the unknown number (n = 7)
Equal signSpanish: Signo igual The = sign, showing both sides are the same. 7 + 3 = 10 — both sides equal 10
ExpressionSpanish: Expresión A math phrase with numbers and letters, but no equal sign. 2x + 5 is an expression; it becomes an equation when you write 2x + 5 = 15
ConstantSpanish: Constante A fixed number in an expression or equation that does not change. In x + 7 = 12, the numbers 7 and 12 are constants; only x can change.

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 8.38.1–8.3 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 8.1–8.3 by using each lesson's big idea in mixed practice.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 8.1) Which equation represents: 'A number plus 12 equals 30'?

    1. An + 12 = 30
    2. Bn − 12 = 30
    3. C12n = 30
    4. Dn / 12 = 30

    Hint Find the operation word in the sentence. What does 'plus' tell you to do with the number and 12?

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

    (Lesson 8.1) Which equation represents: 'Seven less than a number is 18'?

    1. An − 7 = 18
    2. B7 − n = 18
    3. Cn + 7 = 18
    4. Dn / 7 = 18

    Hint 'Seven less than a number' is tricky — the number comes FIRST, and then 7 is taken away from it.

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

    (Lesson 8.2) Solve: x + 9 = 15

    1. Ax = 6
    2. Bx = 9
    3. Cx = 15
    4. Dx = 24

    Hint x has 9 added to it. To get x alone, you need to UNDO that addition.

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

    (Lesson 8.2) Solve: y − 7 = 20

    1. Ay = 7
    2. By = 13
    3. Cy = 27
    4. Dy = 140

    Hint Look at what's happening to y: 7 is being SUBTRACTED. Which operation undoes subtraction?

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

    (Lesson 8.3) 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

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 ___.

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