6.AT.8 Lesson 8-2-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.2 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 BALANCE SCALE
    Algebraic Balance Model
    m − 14 = 32 46

    Solve: m − 14 = 32

    ✏️ Workspace & Solution Steps
  2. 2 FILL TABLE

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

    EquationInverse OperationSolutionCheck
    x + 18 = 45
    p − 22 = 19
    w + 3.5 = 10
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Unlock Card 1: Solve x + 7 = 15.

    1. Ax = 8
    2. Bx = 22
    3. Cx = 7
    4. Dx = 105
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Unlock Card 2: Solve n − 4 = 9.

    1. An = 13
    2. Bn = 5
    3. Cn = 36
    4. Dn = -5
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Unlock Card 3: A vault held some clue tokens. After the detective added 16 tokens, there were 50. The equation is t + 16 = 50. How many tokens were there before?

    1. A34
    2. B66
    3. C16
    4. D800
    My work — one step per lineWhat I did to both sides
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — Crack the Detective's Mistake

    1. 1Equation:x + 8 = 21
    2. 2Choose inverse:Undo the + 8
    3. 3Apply to both sides:x + 8 + 8 = 21 + 8
    4. 4Simplify:x = 29

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It