6.AT.8 Lesson 8-1-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Write Equations · Equation · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • 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. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
3Mathematical 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.
4Watch 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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Which equation represents: 'A number divided by 4 equals 8'?

    1. An / 4 = 8
    2. B4n = 8
    3. Cn − 4 = 8
    4. Dn + 4 = 8
    ✏️ Workspace & Solution Steps
  2. 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
  3. 4 MULTIPLE CHOICE

    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
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Detective's Mistake

    1. 1Clue:Eight fewer clues than a number n leaves 5 clues.
    2. 2Choose a variable:Let n be the starting number of clues.
    3. 3Write the equation:8 − n = 5

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 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
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It