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

Lesson 8.28.2 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 addition and subtraction 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
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 examplesolving an addition equation

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

A shop had x hats. After 17 hats were delivered, the shop had 45 hats. Solve x + 17 = 45.

  1. Look at the variable side: 17 is added to x, so the inverse move is subtraction.
  2. Subtract 17 from BOTH sides so the equation stays balanced.
  3. Left side: x + 17 − 17 leaves x. Right side: 45 − 17 gives 28.
  4. Check by substituting: 28 + 17 makes 45, so both sides agree.

Answer: x = 28, so the shop had 28 hats before the delivery.

Now you trySame steps, your turn

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

Lin had n trading cards. After a swap brought 24 more, she had 51. Solve n + 24 = 51.

  1. What is done to n? is added, so the inverse operation is .
  2. Do the same to each side: subtract from both sides.
  3. Left side leaves . Right side: 51 − 24 = .
  4. Check: + 24 = . Does it balance?
Answer:n = the cards Lin had before the swap

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 outA common mistake

A common mistake is applying the same operation instead of the inverse — for example, solving x − 7 = 15 by subtracting 7 from both sides (getting the wrong x = 8) instead of adding 7 to both sides (the correct x = 22). Another common mistake is doing the inverse operation to only one side, like solving x + 6 = 14 by subtracting 6 from the left but forgetting the right side. Before you submit, name the operation shown in the equation, choose its inverse, apply it to BOTH sides, and check by substituting your answer back into the original equation.

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

Lesson 8.28.2 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 addition and subtraction equations using inverse operations — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    n + 1431=
    Take 14 from both sides to keep it balanced.

    Solve n + 14 = 31.

    1. 1What number is added to n?
    2. 2Subtract 14 from both sides. What is 31 − 14?
    3. 3Check: put 17 in for n. What is 17 + 14?
    Final answer:
  2. 2Complete each step, then write the final answer.
    x − 815=
    Keep both sides balanced.

    Solve x − 8 = 15.

    1. 1Is 8 added to x or subtracted from x? What undoes it?
    2. 2Add 8 to both sides. What is x?
    3. 3Check: put 23 in for x. What is 23 − 8?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve x + 6 = 20.

    Show your work

    Hint 6 is added to x. Subtract 6 from both sides.

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

    Solve n − 27 = 46.

    Show your work

    Hint 27 is subtracted from n. Do the inverse to both sides.

    Final answer:
  5. 5Complete each step, then write the final answer.
    w + 926=
    The old weight plus 9 pounds is 26 pounds.

    A puppy gained 9 pounds this year. Now it weighs 26 pounds. Write and solve an equation. How much did it weigh before?

    Show your work

    Hint Let w be the weight before. Write w + 9 = 26. Undo the + 9.

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

    Kai solved x − 12 = 30 and got x = 18. Is he right? What is x?

    Show your work

    Hint Check Kai's answer first: what is 18 − 12? Then think about which operation undoes − 12.

    Final answer:

Explain your thinkingKai subtracted when he should have added. How do you know which inverse operation to use?

Sentence starter The equation ___ the number, so I ___ to undo it. · I check my answer by ___.

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