6.AT.11 Lesson 9-3-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.3 · Part II

Supported Application · Guided Entry to Today's Problem

equation · variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 9.3 · Part II
1Writing Two-Variable Equations
2Strategy Model — step by step
  1. Identify the independent variable (x) and dependent variable (y)
  2. Find the constant unit rate (k = y ÷ x)
  3. Write the equation relating the two variables: y = kx (or y = x + c)
3Mathematical Word Bank
  • equation (ecuación) — A mathematical sentence with an equals sign that shows two amounts are the same.
  • variable (variable) — A letter that represents a quantity that can change, or vary.
  • rate (tasa) — A fixed amount of one quantity for every one unit of the other quantity.
  • represent (representar) — To show a relationship using a tool such as a table, a graph, or an equation.
  • define the variables (definir las variables) — To state exactly what quantity each letter in an equation stands for.
4Watch out
  • Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.
  1. 1 MULTIPLE CHOICE

    Using c = 15h, what is the total cost of a 3-hour canoe rental?

    1. A$45
    2. B$18
    3. C$15
    4. D$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

    In the gym membership situation, which quantity is the DEPENDENT variable?

    1. AThe total cost
    2. BThe number of months
    3. CThe monthly fee of $24.95
    4. DThe number of gyms in town
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The membership table shows: 1 month, $24.95; 2 months, $49.90; 3 months, $74.85. By how much does the total cost increase each month?

    1. A$24.95
    2. B$49.90
    3. C$25.00
    4. D$24.05
    ✏️ 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.11 Lesson 9-3-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.3 · Part II

On-Level Application · Standard Rigor

equation · variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 9.3 · Part II
1Writing Two-Variable Equations
2The Structural Procedure
  1. Identify the independent variable (x) and dependent variable (y)
  2. Find the constant unit rate (k = y ÷ x)
  3. Write the equation relating the two variables: y = kx (or y = x + c)
3Mathematical Word Bank
  • equation (ecuación) — A mathematical sentence with an equals sign that shows two amounts are the same.
  • variable (variable) — A letter that represents a quantity that can change, or vary.
  • rate (tasa) — A fixed amount of one quantity for every one unit of the other quantity.
  • represent (representar) — To show a relationship using a tool such as a table, a graph, or an equation.
  • define the variables (definir las variables) — To state exactly what quantity each letter in an equation stands for.
4Watch out
  • Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    A table pairs months with total cost: (1, 24.95), (2, 49.90), (4, 99.80). Which equation matches the table, with m = months and c = cost?

    1. Ac = 24.95m
    2. Bc = m + 24.95
    3. Cc = 49.90m
    4. Dm = 24.95 + c
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Using c = 24.95m, what is the total cost of 10 months of membership?

    1. A$249.50
    2. B$34.95
    3. C$224.55
    4. D$2,495.00
    My work — one step per lineWhat I did to both sides
  2. 3 MULTIPLE CHOICE

    Using c = 15h, what is the total cost of a 5-hour canoe rental?

    1. A$75
    2. B$20
    3. C$60
    4. D$80
    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.11 Lesson 9-3-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.3 · Part II

Extension & Non-Routine Application

equation · variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 9.3 · Part II
1Writing Two-Variable Equations
2The Structural Procedure
  1. Identify the independent variable (x) and dependent variable (y)
  2. Find the constant unit rate (k = y ÷ x)
  3. Write the equation relating the two variables: y = kx (or y = x + c)
3Mathematical Word Bank
  • equation (ecuación) — A mathematical sentence with an equals sign that shows two amounts are the same.
  • variable (variable) — A letter that represents a quantity that can change, or vary.
  • rate (tasa) — A fixed amount of one quantity for every one unit of the other quantity.
  • represent (representar) — To show a relationship using a tool such as a table, a graph, or an equation.
  • define the variables (definir las variables) — To state exactly what quantity each letter in an equation stands for.
4Watch out
  • Writing the equation with addition — c = 24.95 + m — instead of multiplication. The fee is charged EVERY month, so the total is the rate times the number of months; always test the equation against a row of the table.
  1. 1 MULTIPLE CHOICE

    A spin studio charges $7.50 for each class. Let n be the number of classes a member takes and let c be the total cost in dollars. Which equation represents the relationship?

    1. Ac = 7.5 + n
    2. Bn = 7.5c
    3. Cc = n ÷ 7.5
    4. Dc = 7.5n
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Miguel wants the cost of a full year (12 months) at Recreation World. Using c = 24.95m, what is the total?

    1. A$299.40
    2. B$249.50
    3. C$36.95
    4. D$300.00
    My work — one step per lineWhat I did to both sides
  3. 3 MULTIPLE CHOICE

    A different gym charges $19.95 per month. How does Miguel's equation change for this gym?

    1. AThe rate changes: c = 19.95m instead of c = 24.95m
    2. BThe variable changes: c = 24.95x instead of c = 24.95m
    3. CThe operation changes: c = 19.95 + m
    4. DNothing changes — all gyms have the same equation
    ✏️ 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
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