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

8.1 Small Group · Group 2

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

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 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
  2. 2 BALANCE SCALE
    Algebraic Balance Model
    2n + 3 = 11 4

    Build the equation 2n + 3 = 11 on the balance scale and find n.

    ✏️ Workspace & Solution Steps
  3. 3 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. 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
  2. 5 MULTIPLE CHOICE

    A torn note reads: 'A suspect's case minutes m, after 9 fewer, leaves 24.' Which equation fits?

    1. Am − 9 = 24
    2. Bm + 9 = 24
    3. C9m = 24
    4. Dm / 9 = 24
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — Crack the Detective's Mistake

    1. 1Clue:A number of footprints divided by 4 equals 6.
    2. 2Choose a variable:Let f represent the number of footprints.
    3. 3Write the equation:4f = 6

    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