6.AT.11 Lesson 9-3-part2 Apply Day · Set B
MASTERY CHECK
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9.3 · Part II

Second Practice Form · Independent Application and Spiral Review

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

    In the equation c = 24.95m for the gym membership, what does m represent?

    1. AThe number of months of membership
    2. BThe total cost in dollars
    3. CThe monthly fee of $24.95
    4. DThe name of the gym
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    (Lesson 9.1) Akela chooses how many hours of sunlight each tray gets. Which is the INDEPENDENT variable?

    1. AHours of sunlight
    2. BPlant height
    3. CNumber of trays
    4. DNumber of seeds
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    (Lesson 9.1) In Akela's experiment, which is the DEPENDENT variable?

    1. APlant height
    2. BHours of sunlight
    3. CThe kind of seed
    4. DThe size of the tray
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    On the canoe graph with hours on the horizontal axis and cost on the vertical axis, which point lies on the graph?

    1. A(4, 60)
    2. B(60, 4)
    3. C(4, 19)
    4. D(4, 55)
    ✏️ Workspace & Solution Steps
  4. 5 MULTIPLE CHOICE

    The friends have $90 to spend. Using c = 15h, for how many hours can they rent the canoe?

    1. A6 hours
    2. B5 hours
    3. C75 hours
    4. D1,350 hours
    My work — one step per lineWhat I did to both sides
  5. 6 MULTIPLE CHOICE

    What is the benefit of an equation over a table for the membership costs?

    1. AThe equation gives the total cost for ANY number of months, not just the rows listed
    2. BThe equation lists more rows than the table
    3. CThe equation is the only representation that shows the cost increasing
    4. DThe table is always wrong and the equation is always right
    ✏️ Workspace & Solution Steps
  6. 7 MULTIPLE CHOICE

    The friends spent exactly $120 on the canoe. Solve 15h = 120. How long was the rental?

    1. A8 hours
    2. B105 hours
    3. C9 hours
    4. D1,800 hours
    My work — one step per lineWhat I did to both sides
  7. 8 MULTIPLE CHOICE

    Recreation World charges $24.95 per month. What is the total cost of 2 months of membership?

    1. A$49.90
    2. B$26.95
    3. C$24.95
    4. D$74.85
    per 1
  8. 9 MULTIPLE CHOICE

    A canoe rents for $15 per hour. Let h = hours and c = total cost. Which equation represents the relationship?

    1. Ac = 15h
    2. Bc = 15 + h
    3. Ch = 15c
    4. Dc = h − 15
    ✏️ 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