6.AT.6a Lesson 6-5-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.5 · Part II

Supported Application · Guided Entry to Today's Problem

Write Algebraic Expressions · Variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.5 · Part II
1Writing & Evaluating Algebraic Expressions
2Strategy Model — step by step
  1. Define the variable to represent the unknown quantity
  2. Translate mathematical phrases into operations, coefficients, and constants
  3. Evaluate by substituting given numerical values for the variable
3Mathematical 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.
4Watch 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.
  1. 1 MULTIPLE CHOICE

    Evaluate 4.25s + 23.50 when s = 10.

    1. A$66.00
    2. B$277.50
    3. C$47.75
    4. D$66.75
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  2. 2 MULTIPLE CHOICE

    Which key word tells you to multiply?

    1. AProduct
    2. BSum
    3. CDifference
    4. DQuotient
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 6.3) What is the value of 4³?

    1. A64
    2. B12
    3. C43
    4. D7
    ✏️ Workspace & Solution Steps
📐 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
6.AT.6a Lesson 6-5-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.5 · Part II

On-Level Application · Standard Rigor

Write Algebraic Expressions · Variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.5 · Part II
1Writing & Evaluating Algebraic Expressions
2The Structural Procedure
  1. Define the variable to represent the unknown quantity
  2. Translate mathematical phrases into operations, coefficients, and constants
  3. Evaluate by substituting given numerical values for the variable
3Mathematical 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.
4Watch 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

    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
  2. 2 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
📐 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
6.AT.6a Lesson 6-5-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.5 · Part II

Extension & Non-Routine Application

Write Algebraic Expressions · Variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.5 · Part II
1Writing & Evaluating Algebraic Expressions
2The Structural Procedure
  1. Define the variable to represent the unknown quantity
  2. Translate mathematical phrases into operations, coefficients, and constants
  3. Evaluate by substituting given numerical values for the variable
3Mathematical 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.
4Watch 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

    A concert ticket costs 8 dollars. The website also charges one 5 dollar service fee for the whole order. Let t represent the number of tickets bought in one order. Which expression gives the total cost in dollars?

    1. A8t + 5
    2. B8 + 5t
    3. C8(t + 5)
    4. D13t
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    Field day needs one $4.25 item per student plus a one-time $23.50 shipping fee. Write the expression, then find the cost for 30 students AND for 60 students. Does doubling the students double the cost? Explain.

    ✏️ Mathematical Justification & Response
  2. 3 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
📐 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