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

Lesson 8.2Write and Solve Equations Using Addition or Subtraction

Set B · Version ASecond form · supported practice

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

Learning target I can solve one-step addition and subtraction equations using inverse operations.

Why This Matters Detective Chen found a coded message: 'The suspect's locker number plus 23 equals 58.' She needs to figure out the locker number to crack the case. The equation is n + 23 = 58. What is n?

RememberWrite and Solve Equations Using Addition or Subtraction

Solving Addition & Subtraction Equations. Formula: x + a = b → x = b − a | x − a = b → x = b + a To solve means to find the value that makes the equation true. I use the inverse operation (the opposite) to get the variable alone, and I do the same thing to both sides.

  1. Identify operation on variable.
  2. Use inverse operation: subtract to undo addition; add to undo subtraction.
  3. Property of Equality: do same operation to both sides.

Words: Equation (Ecuación)Inverse operation (Operación inversa)Isolate (Despejar)Solution (Solución)One-step equation (Ecuación de un paso)

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

    Which equation represents: 'Three times a number equals 21'?

    1. An + 3 = 21
    2. Bn − 3 = 21
    3. C3n = 21
    4. Dn / 3 = 21
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Which equation represents: 'Seven less than a number is 18'?

    1. A7 − n = 18
    2. Bn − 7 = 18
    3. Cn + 7 = 18
    4. Dn / 7 = 18
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Which equation represents: 'A number plus 12 equals 30'?

    1. An − 12 = 30
    2. B12n = 30
    3. Cn + 12 = 30
    4. Dn / 12 = 30
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A hiker has walked some distance and still has 4.5 miles left on a 12-mile trail. The equation d + 4.5 = 12 represents her situation, where d is the distance already walked. Solve d + 4.5 = 12.

    1. Ad = 4.5
    2. Bd = 7.5
    3. Cd = 8.5
    4. Dd = 16.5
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A hiker has walked some distance and still has 4.5 miles left on a 12-mile trail. The equation d + 4.5 = 12 represents her situation, where d is the distance already walked. Which operation undoes addition?

    1. AMultiplication
    2. BDivision
    3. CSubtraction
    4. DSquaring
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A hiker has walked some distance and still has 4.5 miles left on a 12-mile trail. The equation d + 4.5 = 12 represents her situation, where d is the distance already walked. Check: does 7.5 work?

    1. AYes — 7.5 + 4.5 = 12
    2. BNo — 7.5 + 4.5 = 11
    3. CNo — 7.5 − 4.5 = 3
    4. DOnly if the trail is 11 miles
    Show your work

Explain your thinkingWhy do you have to subtract 19 from BOTH sides, not just one?

Sentence starter I subtract from both sides because an equation is like a ___ — to keep it balanced, any operation on one side must ___.

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 8.2Write and Solve Equations Using Addition or Subtraction

Set B · Version BSecond form · core practice

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

Learning target I can solve one-step addition and subtraction equations using inverse operations.

Why This Matters Detective Chen found a coded message: 'The suspect's locker number plus 23 equals 58.' She needs to figure out the locker number to crack the case. The equation is n + 23 = 58. What is n?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Unlock Card 4: Match each equation to its solution to crack the vault code.

    1. a + 6 = 13
    2. b − 5 = 8
    3. c + 11 = 20
    4. d − 9 = 6
    • Aa = 7
    • Bb = 13
    • Cc = 9
    • Dd = 15
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Unlock Card 1: Solve x + 7 = 15.

    1. Ax = 7
    2. Bx = 8
    3. Cx = 22
    4. Dx = 105
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Unlock Card 2: Solve n − 4 = 9.

    1. An = -5
    2. Bn = 5
    3. Cn = 13
    4. Dn = 36
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Unlock Card 3: A vault held some clue tokens. After the detective added 16 tokens, there were 50. The equation is t + 16 = 50. How many tokens were there before?

    1. A16
    2. B34
    3. C66
    4. D800
    My work — one step per lineWhat I did to both sides
  4. 5Circle the letter of the best answer. Show how you know.

    Solve: p + 2.8 = 9.1

    1. Ap = 3.25
    2. Bp = 6.3
    3. Cp = 7.7
    4. Dp = 11.9
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — Crack the Detective's Mistake

    1. 1Equationx + 8 = 21
    2. 2Choose inverseUndo the + 8
    3. 3Apply to both sidesx + 8 + 8 = 21 + 8
    4. 4Simplifyx = 29

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

    Correct work
    Correct answer:

Explain your thinkingWhy do you have to subtract 19 from BOTH sides, not just one?

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