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

Lesson 8.1Understand Equations and Their Solutions

Set B · Version ASecond form · supported practice

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

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

Why This Matters Detective Ruiz received a tip: 'A number of stolen gems plus 8 more equals 20 total gems.' She needs to write an equation to represent this clue before she can solve the case. How would you write this situation as an equation?

RememberUnderstand Equations and Their Solutions

Equations & Solutions. Formula: Left Expression = Right Expression An equation is a math sentence with an equal sign (=). To write one, I pick a letter (a variable) for the unknown number and match the words to math symbols.

  1. An equation is a mathematical sentence stating two expressions are equal.
  2. A solution is a value for the variable that makes the equation true.
  3. Check: Substitute the value into the equation and verify that both sides balance

Words: Equation (Ecuación)Variable (Variable)Equal sign (Signo igual)Expression (Expresión)Constant (Constante)

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

    Reflect the point (4, 3) across the x-axis. What are the new coordinates?

    1. A(3, 4)
    2. B(4, −3)
    3. C(−4, 3)
    4. D(−4, −3)
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Reflect the point (−2, 5) across the y-axis.

    1. A(2, 5)
    2. B(−2, −5)
    3. C(2, −5)
    4. D(5, −2)
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    When you reflect a point across the x-axis, which coordinate changes sign?

    1. AThe y-coordinate
    2. BThe x-coordinate
    3. CBoth of them
    4. DNeither of them
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    The point (−6, −1) is reflected across the y-axis. In which quadrant does the image land?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant IV
    4. DQuadrant III
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A detective is tracking stolen paintings. She knows that the number of paintings recovered plus 14 paintings still missing equals the 37 total stolen. The equation p + 14 = 37 represents this situation. Solve p + 14 = 37.

    1. Ap = 14
    2. Bp = 23
    3. Cp = 37
    4. Dp = 51
    Show your work
Part 2Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Detective's Mistake

    1. 1ClueEight fewer clues than a number n leaves 5 clues.
    2. 2Choose a variableLet n be the starting number of clues.
    3. 3Write the equation8 − n = 5

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

    Hint Does 'eight fewer than a number' start with the 8 or with the number n?

    Correct work
    Correct answer:

Explain your thinkingHow did you decide what expression to put on each side of the balance?

Sentence starter I put ___ on the left side because ___, and ___ on the right side because ___. The equal sign means ___.

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 8.1Understand Equations and Their Solutions

Set B · Version BSecond form · core practice

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

Learning target I can write an equation for a real situation and check whether a given value is a solution by substituting it.

Why This Matters Detective Ruiz received a tip: 'A number of stolen gems plus 8 more equals 20 total gems.' She needs to write an equation to represent this clue before she can solve the case. How would you write this situation as an equation?

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    A witness statement reads: 'A number c of security cameras plus 6 more equals 19.' Which equation matches?

    1. Ac + 6 = 19
    2. B6c = 19
    3. Cc − 6 = 19
    4. Dc / 6 = 19
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each detective clue to the equation that cracks it.

    1. A number d of door codes plus 4 equals 17.
    2. 6 times the number of tips t equals 42.
    3. A pile of files f, after losing 11, equals 20.
    4. A number of suspects s split into 5 vans equals 8 per van.
    • Ad + 4 = 17
    • B6t = 42
    • Cf − 11 = 20
    • Ds / 5 = 8
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A detective is tracking stolen paintings. She knows that the number of paintings recovered plus 14 paintings still missing equals the 37 total stolen. The equation p + 14 = 37 represents this situation. Why subtract 14 from BOTH sides?

    1. ATo keep the equation balanced while isolating p
    2. BBecause subtraction is easier than addition
    3. CBecause 14 is the smaller number
    4. DTo make the answer a whole number
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A detective is tracking stolen paintings. She knows that the number of paintings recovered plus 14 paintings still missing equals the 37 total stolen. The equation p + 14 = 37 represents this situation. Check your answer: does 23 work?

    1. AYes — 23 + 14 = 37
    2. BNo — 23 + 14 = 47
    3. CNo — 23 − 14 = 9
    4. DYou cannot check an equation
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The lab tech says: '5 times the number of evidence bags b equals 35.' Which equation represents this clue?

    1. A5b = 35
    2. Bb + 5 = 35
    3. Cb − 5 = 35
    4. Db / 5 = 35
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A torn note reads: 'A suspect's case minutes m, after 9 fewer, leaves 24.' Which equation fits?

    1. Am − 9 = 24
    2. Bm + 9 = 24
    3. C9m = 24
    4. Dm / 9 = 24
    Show your work

Explain your thinkingHow did you decide what expression to put on each side of the balance?

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