6.AT.8 Lesson 8-1-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

8.1 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 DRAG SORT

    Sort each phrase into the correct operation.

    Target Categories: Addition (+) Subtraction (−) Multiplication (×) Division (÷)
    • more than
    • increased by
    • sum of
    • less than
    • decreased by
    • fewer than
    • times
    • product of
    • twice
    • divided by
    • split equally
    • quotient of
  2. 2 FILL TABLE

    For each situation, identify what the variable represents and write the equation.

    SituationVariable RepresentsEquation
    A box holds some files. After removing 5, there are 13 left.
    A detective split 48 photos equally into folders. Each folder has 6 photos.
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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. 4 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. 5 MULTIPLE CHOICE

    Which equation represents: 'Three times a number equals 21'?

    1. A3n = 21
    2. Bn + 3 = 21
    3. Cn − 3 = 21
    4. Dn / 3 = 21
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    Is n = 3 a solution of n + 5 = 9?

    1. ANo, because 3 + 5 = 8, which does not equal 9
    2. BYes, because 3 is smaller than 9
    3. CYes, because 3 + 5 is close to 9
    4. DYou cannot tell without solving first
    ✏️ Workspace & Solution Steps
🗣️ 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
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