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

Lesson 8.2Write and Solve Equations Using Addition or Subtraction

Start hereWords, worked example, and sentence starters

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?

Start hereWords for this lesson

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

WordWhat it meansExample
EquationSpanish: Ecuación A math sentence with an equal sign showing both sides are the same. x + 25 = 60 — both sides equal 60 when x = 35
Inverse operationSpanish: Operación inversa Two math actions that undo each other, like × and ÷. + and −
IsolateSpanish: Despejar To get the letter by itself on one side. get x by itself
SolutionSpanish: Solución A number that makes the equation or inequality true. x = 7 is the solution to x + 5 = 12 because 7 + 5 = 12 ✓
One-step equationSpanish: Ecuación de un paso An equation you can solve in a single step using one inverse operation. x + 7 = 20
BalanceSpanish: Equilibrio Keeping both sides of an equation equal by doing the same thing to each side. do the same to each side

How it worksWorked example

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

A team had some points, then scored 14 more and has 40. Solve y + 14 = 40.

  1. Subtract 14 from both sides: y + 14 − 14 = 40 − 14.
  2. Simplify: y = 26.
  3. Check: 26 + 14 = 40.

Answer: y = 26 points

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 being added or subtracted?

Answer:

Say it and write itSentence starters

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

  • The variable has added to it, so I from both sides.
  • I must do the same thing to both sides because .
  • My solution is , and my check shows .
  • Addition and subtraction are inverse operations because .

Word bank equationvariableinverse operationsubtractisolatebalanceboth sidessolutioncheckundoProperty of Equality

Watch out!A common mistake

A common mistake is applying the same operation instead of the inverse

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

Lesson 8.2Write and Solve Equations Using Addition or Subtraction

Version ASupported 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. 1Mark and label each value on the number line.

    Use the number line to solve x + 8 = 20. Start at 20 and count back 8 to find x.

    0369121518212425

    Hint Start at 20 on the number line. Since x + 8 = 20, subtract 8 to find x.

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

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

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

    Solve: n + 15 = 42

    1. An = 15
    2. Bn = 27
    3. Cn = 42
    4. Dn = 57

    Hint n is being increased by 15. To find n alone, you must undo that addition.

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

    Solve: m − 11 = 25

    1. Am = 14
    2. Bm = 25
    3. Cm = 36
    4. Dm = 275

    Hint m has 11 taken away from it. Think about which operation puts that 11 back.

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

    Spot the Common Mistake

    1. 1Equationx + 6 = 14
    2. 2Choose inverseThe inverse of + 6 is − 6.
    3. 3Subtract from one side onlyx + 6 − 6 = 14, so x = 14

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

    Hint Step 3 only subtracted 6 from the left side. What happened to the right side?

    Correct work
    Correct answer:

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

Version BCore 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. 1Decide whether each pair balances. Check Yes or No, then explain.

    Solve: m − 14 = 32

    Left sideRight sideBalanced?
    Explain your choice
  2. 2Complete the table. Show how you found each value.

    Complete the table: identify the inverse operation, solve, and check.

    EquationInverse OperationSolutionCheck
    x + 18 = 45
    p − 22 = 19
    w + 3.5 = 10
    Show your work
  3. 3Write the name of the correct group on each line.

    Sort each equation by the inverse operation needed to solve it.

    Groups: Add to both sides Subtract from both sides
    • x − 9 = 14
    • n − 20 = 35
    • y − 6 = 8
    • x + 12 = 30
    • n + 7 = 19
    • y + 15 = 40
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A shirt costs $d. After a $15 discount, it costs $38. What is d?

    1. A$23
    2. B$38
    3. C$45
    4. D$53
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Equationy − 13 = 28
    2. 2Choose inverseThe inverse of − 13 is + 13, so add 13 to both sides.
    3. 3Apply to both sidesy = 28 + 13
    4. 4Simplifyy = 31

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

Lesson 8.2Write and Solve Equations Using Addition or Subtraction

ChallengeExtension

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. 1Decide whether each pair balances. Check Yes or No, then explain.

    Solve using decimals: x + 2.7 = 9.3. Use inverse operations.

    Left sideRight sideBalanced?
    Explain your choice
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Equation Error

    1. 1Equationx − 18 = 45
    2. 2Identify inverseInverse of subtraction is subtraction
    3. 3Apply to both sidesx − 18 − 18 = 45 − 18
    4. 4Simplifyx = 27

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

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

    A detective solved x + 25 = 60 and got x = 35. Another detective solved y − 25 = 60 and got y = 35. Are both correct? Explain using inverse operations and check each answer.

    Write your 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