6.AT.6a Lesson 6-5-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.5 Small Group · Group 2

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

Write Algebraic Expressions · Variable · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we turn words into an expression?
1Words like “each” or “per” mean multiply and attach to the variable; a one-time amount is a constant. Once the variable has a number, substitute it in and evaluate using the order of operations — 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. Tickets cost $12 each, plus a flat $50 venue fee. Let t be the number of tickets.
  2. "$12 each ticket" means 12 times t, which I write as 12t.
  3. The flat fee $50 is added once, so I add 50.
  4. I put them together: total revenue = 12t + 50.
3Second Model — Try it together — then prove it
  1. The field day committee orders one $4.25 item for each student, plus a one-time $23.50 shipping fee. The number of students is unknown.
  2. Let s stand for the number of students. “$4.25 for each student” means 4.25 times s, written 4.25s.
  3. The shipping fee does not depend on how many students there are, so it is a constant that is added once: 4.25s + 23.50.
  4. The expression 4.25s + 23.50 has two terms: 4.25s, whose coefficient is 4.25, and the constant 23.50.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Write Algebraic Expressions (Escribir expresiones algebraicas) — Translate words or a situation into numbers, variables, and operation symbols.
  • Variable (Variable) — A letter that stands for a number that is unknown or can change.
  • Algebraic Expression (Expresión algebraica) — A math phrase that has at least one letter.
  • Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
  • Constant (Constante) — A fixed number in an expression or equation that does not change.
  • Like terms (Términos semejantes) — Terms with the same letter raised to the same power, like 2x and 5x.
5Watch out
  • A common mistake in Write Algebraic Expressions is treating 'each' or 'per' as if it means add instead of multiply, and attaching the variable to the wrong number. For 'a $25 setup fee plus $8 per hour, h,' students often write 25 + 8 + h (adding all three numbers) or 25h + 8 (multiplying the flat fee by h) instead of the correct 8h + 25. Since $8 applies per hour, it must multiply the variable (8h), and the flat $25 fee is a constant added only once — check that the per-unit rate, not the flat fee, is the number multiplied by the variable.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Match each word phrase to its correct algebraic expression.

    Target Categories: Correctly Matched
    • 2 MATCHING GAME

      Match each word phrase to its algebraic expression.

      1. the product of 5 and n
      2. 8 less than a number w
      3. a number p increased by 12
      4. twice a number x, plus 3
      5. a number y divided by 4
      6. 7 more than a number z
      • A5n
      • Bw − 8
      • Cp + 12
      • D2x + 3
      • Ey ÷ 4
      • Fz + 7
    • 3 MULTIPLE CHOICE

      Line 1: A lyric says '7 more than a number of beats n.' Which expression matches?

      1. An + 7
      2. B7n
      3. Cn − 7
      4. D7 − n
      ✏️ Workspace & Solution Steps
    • 4 MULTIPLE CHOICE

      Line 2: The chorus says '5 less than a number of tracks x.' Which expression matches?

      1. Ax − 5
      2. B5 − x
      3. C5x
      4. Dx + 5
      ✏️ Workspace & Solution Steps
    • 5 MULTIPLE CHOICE

      Line 3: A verse says 'twice a number of speakers' (use s). Which expression matches?

      1. A2s
      2. Bs + 2
      3. Cs − 2
      4. Ds ÷ 2
      ✏️ Workspace & Solution Steps
    SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
    1. 6 OPEN RESPONSE

      Write a real-world situation that could be modeled by the expression 4n + 10. Explain what the variable n represents, what the coefficient 4 means, and what the constant 10 represents.

      ✏️ Mathematical Justification & Response
    🗣️ 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