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

Lesson 8.28.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can solve one-step addition and subtraction equations using inverse operations, explain why the method works, and use it on a problem I have not seen before.

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 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    p − 2.756.40=
    Keep both sides balanced.

    Solve p − 2.75 = 6.40.

    1. 1What is done to p? What undoes it?
    2. 2Add 2.75 to both sides. What is p?
    3. 3Check: what is 9.15 − 2.75?
    Final answer:
  2. 2Complete each step, then write the final answer.
    18.6y + 7.9=
    This time the variable is on the right side.

    Solve 18.6 = y + 7.9. Then explain why the side does not matter.

    1. 1What is done to y? What undoes it?
    2. 2Subtract 7.9 from both sides. What is y?
    3. 3Check: what is 10.7 + 7.9?
    4. 4Why can we solve it the same way when y is on the right side?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Solve m + 4.8 = 12.3.

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

    Solve 45 = k − 17.

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A pug weighs 32 pounds less than a bulldog. The pug weighs 19 pounds. Write and solve an equation to find the bulldog's weight b.

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

    Ana and Ben solve x + 9.5 = 20. Ana gets 10.5. Ben gets 29.5. What is x?

    Show your work
    Final answer:

Explain your thinkingDoes your plan change when the numbers are decimals or the variable is on the right side? Explain with 45 = k − 17.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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