6.AT.8 Lesson 8-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.3 Small Group · Group 2

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

Solve Multiplication and Division Equations · Inverse operation · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I solve a multiplication or division equation?
1Divide to undo multiplying, and multiply to undo dividing — always on both sides — 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 3x = 21. This means 3 times x equals 21.
  2. The inverse of multiplying by 3 is dividing by 3.
  3. I divide both sides by 3: 3x ÷ 3 = 21 ÷ 3.
  4. That leaves x = 7. Check: 3 × 7 = 21. True!
3Second Model — Try it together — then prove it
  1. Solve x ÷ 4 = 9. Is x multiplied or divided?
  2. It is divided by 4, so the inverse is multiplying both sides by 4.
  3. x = 9 × 4 = 36. Check: 36 ÷ 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 Multiplication and Division Equations (Resolver ecuaciones de multiplicación y división) — Use inverse multiplication or division to isolate the variable.
  • Inverse operation (Operación inversa) — Two math actions that undo each other, like × and ÷.
  • Multiply (Multiplicar) — To add equal groups again and again.
  • Divide (Dividir) — To split into equal groups.
  • Isolate (Despejar) — To get the letter by itself on one side.
  • Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
5Watch out
  • A common mistake in Solve Multiplication and Division Equations is applying the SAME operation again instead of the inverse — for example, seeing 6x = 42 and multiplying both sides by 6 to get x = 252, instead of dividing by 6 to get x = 7. Before you submit, ask: did I use the OPPOSITE operation shown in the equation, and did I apply it to both sides?
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Solve: 6x = 42

    1. Ax = 7
    2. Bx = 48
    3. Cx = 36
    4. Dx = 252
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Solve: n / 3 = 8

    1. An = 24
    2. Bn = 11
    3. Cn = 5
    4. Dn = 3
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A detective splits 54 clues equally among 9 case files. The equation 9c = 54 represents this. What is c?

    1. Ac = 6
    2. Bc = 63
    3. Cc = 45
    4. Dc = 9
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A detective splits 54 clues equally among 9 case files. The equation 9c = 54 represents this. What is c?
    2. 2A classmate at our table answered:c = 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:n / 4 = 12
    2. 2Choose operation:n is in a fraction, so I will divide both sides by 4.
    3. 3Apply to both sides:n / 4 ÷ 4 = 12 ÷ 4
    4. 4Simplify:n = 3

    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 / 5 = 12
    2. 2Identify inverse:Inverse of division is division
    3. 3Apply to both sides:x / 5 / 5 = 12 / 5
    4. 4Simplify:x = 2.4

    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