6.AT.8 Lesson 8-2-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.2 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Solve One-Step Addition and Subtraction Equations · Equation · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I solve an addition or subtraction equation?
1Undo the operation with its inverse, and do it to both sides to keep the equation balanced — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me
  1. Solve n + 23 = 58. The 23 is added to n.
  2. The inverse of adding 23 is subtracting 23.
  3. I subtract 23 from both sides: n + 23 − 23 = 58 − 23.
  4. That leaves n = 35. Check: 35 + 23 = 58. True!
3Second Model — Try it together — then prove it
  1. Solve x − 4 = 9. Is x being added or subtracted?
  2. It is subtracted, so the inverse is adding 4 to both sides.
  3. x = 9 + 4 = 13. Check together: 13 − 4 = 9. True?
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Solve One-Step Addition and Subtraction Equations (Resolver ecuaciones de suma y resta de un paso) — Use one inverse addition or subtraction operation to isolate the variable.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Inverse operation (Operación inversa) — Two math actions that undo each other, like × and ÷.
  • Isolate (Despejar) — To get the letter by itself on one side.
  • Solution (Solución) — A number that makes the equation or inequality true.
  • One-step equation (Ecuación de un paso) — An equation you can solve in a single step using one inverse operation.
5Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Solve: x + 9 = 15

    1. Ax = 6
    2. Bx = 24
    3. Cx = 9
    4. Dx = 15
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Solve: y − 7 = 20

    1. Ay = 27
    2. By = 13
    3. Cy = 7
    4. Dy = 140
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

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

    1. A$53
    2. B$23
    3. C$38
    4. D$45
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Solve: x + 9 = 15
    2. 2A classmate at our table answered:x = 9

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Equation:y − 13 = 28
    2. 2Choose inverse:The inverse of − 13 is + 13, so add 13 to both sides.
    3. 3Apply to both sides:y = 28 + 13
    4. 4Simplify:y = 31

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Equation Error

    1. 1Equation:x − 18 = 45
    2. 2Identify inverse:Inverse of subtraction is subtraction
    3. 3Apply to both sides:x − 18 − 18 = 45 − 18
    4. 4Simplify:x = 27

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It