6.AT.8 Lesson 8-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 Small Group · Group 2

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

Write Equations · Equation · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do I turn a word clue into an equation?
1An equation says two amounts are equal. A value is a SOLUTION when substituting it makes that statement true — so any guess can be checked, not just solved for — 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. Clue: 'A number of stolen gems plus 8 more equals 20 total.'
  2. The unknown is the number of gems. I let n stand for it.
  3. 'Plus 8 more' means + 8. 'Equals 20 total' means = 20.
  4. So my equation is n + 8 = 20.
3Second Model — Try it together — then prove it
  1. New clue: 'A number plus 5 equals 9.' What is the unknown?
  2. We let n be the unknown. What does 'plus 5' tell us to write?
  3. What does 'equals 9' tell us? Put it together: n + 5 = 9.
  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
  • Write Equations (Escribir ecuaciones) — Represent a relationship with expressions joined by an equal sign.
  • Equation (Ecuación) — A math sentence with an equal sign showing both sides are the same.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
  • Equal sign (Signo igual) — The = sign, showing both sides are the same.
  • Expression (Expresión) — A math phrase with numbers and letters, but no equal sign.
  • Constant (Constante) — A fixed number in an expression or equation that does not change.
5Watch out
  • A common mistake in Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first. For 'a number decreased by 8 equals 5,' students often write 8 − n = 5 instead of the correct n − 8 = 5; for 'a number divided by 4 equals 6,' they write 4 ÷ n (or 4n) instead of n / 4 = 6. Always start with the variable, then attach the operation in the order the words describe it, and check by substituting your answer back in.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Which equation represents: 'A number plus 12 equals 30'?

    1. An + 12 = 30
    2. Bn − 12 = 30
    3. C12n = 30
    4. Dn / 12 = 30
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which equation represents: 'Seven less than a number is 18'?

    1. An − 7 = 18
    2. B7 − n = 18
    3. Cn + 7 = 18
    4. Dn / 7 = 18
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A detective found some fingerprints on Monday and 14 more on Tuesday, for a total of 30. Which equation represents this?

    1. Af + 14 = 30
    2. Bf − 14 = 30
    3. C14f = 30
    4. Df / 14 = 30
    ✏️ 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 found some fingerprints on Monday and 14 more on Tuesday, for a total of 30. Which equation represents this?
    2. 2A classmate at our table answered:14f = 30

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Crack the Equation Error

    1. 1Clue:A number of case files divided by 3 equals 6.
    2. 2Choose a variable:Let n be the number of case files.
    3. 3Write the equation:3n = 6

    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. 1Situation:Twice a number is 16
    2. 2Identify operation:Twice means addition
    3. 3Write equation:n + 2 = 16

    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