6.AT.11 Lesson 9-3-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.3 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

equation · variable · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — From a pattern in the table to an equation
1When the total is the rate times the amount, write it as an equation: dependent variable = rate × independent variable.
  • A table can only list some values. An equation captures the whole pattern at once, so it works for any number of months or hours. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me write Miguel's equation
  1. The quantities are the number of months of membership and the total cost. The total cost depends on the number of months.
  2. In the table, each month adds $24.95: 1 month is $24.95, 2 months are $49.90, 3 months are $74.85.
  3. The pattern in words: the total cost is $24.95 times the number of months.
  4. Define the variables — let m = number of months and c = total cost in dollars — and write the equation: c = 24.95m.
  5. Now ANY number of months works: for 10 months, c = 24.95 × 10 = 249.50.
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

    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
  2. 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
  3. 4 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
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  4. 5 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
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  5. 6 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
📐 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