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

6.5 Small Group · Group 2

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

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 MULTIPLE CHOICE

    Which expression represents 'the product of 6 and a number n'?

    1. A6n
    2. B6 + n
    3. Cn − 6
    4. Dn ÷ 6
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    The expression 8n + 15 gives the cost of n tickets plus a fee. What is the cost for 6 tickets?

    1. A$63
    2. B$138
    3. C$29
    4. D$48
    My work — one step per lineWhat I did to both sides
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Level 2 Extension — Remix the Translation Error

    1. 1Lyric:5 less than a number of streams x
    2. 2Producer's expression:5 − x
    3. 3Reasoning:I see 'less than' so I subtract, and 5 comes first in the lyric.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Line 2: The chorus says '5 less than a number of tracks x.' Which expression matches?
    2. 2A classmate at our table answered:x + 5

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Phrase:8 divided by a number m
    2. 2Student's expression:m ÷ 8
    3. 3Reasoning:I saw 'divided by' so I wrote the variable first and then 8.

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 ERROR ANALYSIS

    Find the Translation Error

    1. 1Phrase:12 less than a number g
    2. 2Student's expression:12 − g
    3. 3Reasoning:I see 'less than' so I subtract, and 12 comes first in the phrase.

    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