6.AT.11 Lesson 9-3-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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9.3 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

    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
  2. 2 DRAG SORT

    Sort each equation by what it really says.

    Target Categories: Says 'y is 4 times x' Says something different
    • y = 4x
    • y = x × 4
    • x = y ÷ 4
    • y = x + 4
    • x = 4y
    • y = 4 ÷ x
  3. 3 FILL TABLE

    A canoe rents for $15 per hour: c = 15h. Complete the table.

    Hours (h)SubstituteCost in dollars (c)
    2
    5
    8
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 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
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 5 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
  3. 6 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.
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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