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

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

independent variable · dependent variable · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Which quantity is doing the changing — and which is responding?
1The independent variable is subject to choice. The dependent variable changes in response to it.
  • When two quantities are related, one of them depends on the other. Naming which is which is the whole job of this lesson. 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 sort Akela's experiment
  1. The two quantities are hours of sunlight per day and average plant height after 3 weeks.
  2. Akela CHOSE where to put each tray, so she chose the sunlight. Sunlight is subject to choice — that makes it the independent variable.
  3. She did not choose how tall the plants got. Height responded. That makes height the dependent variable.
  4. Say it as a sentence: plant height depends on sunlight.
3Mathematical Word Bank
  • independent variable (variable independiente) — The quantity that is subject to choice. It does not depend on the other quantity.
  • dependent variable (variable dependiente) — The quantity that changes in response to the independent variable.
  • depends on (depende de) — One quantity depends on another when changing the first causes the second to change.
  • quantity (cantidad) — Something that can be counted or measured.
  • relationship (relación) — How two quantities change together.
4Watch out
  • Naming the variables backward — calling the responding quantity 'independent' because it is the one the question asks about.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each quantity: independent or dependent?

    Target Categories: Independent variable (input) Dependent variable (output)
    • Hours of sunlight a tray of seedlings gets
    • Months of gym membership
    • Minutes spent jogging
    • Height the seedlings grow
    • Total cost of the membership
    • Calories burned on the jog
  2. 2 FILL TABLE

    Claire burns Calories at a steady rate: 30 minutes burns 123 Calories. Complete the table.

    Minutes jogged (independent)ThinkingCalories burned (dependent)
    30
    60
    90
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    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. 4 MULTIPLE CHOICE

    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. 5 MULTIPLE CHOICE

    Claire burned 123 Calories on a 30-minute jog. Which quantity is subject to choice?

    1. AMinutes she jogs
    2. BCalories she burns
    3. CHer heart rate
    4. DThe weather
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    Which sentence is written in the correct order?

    1. ACalories burned depends on minutes jogged.
    2. BMinutes jogged depends on Calories burned.
    3. CCalories burned depends on Calories burned.
    4. DNeither quantity depends on the other.
    ✏️ Workspace & Solution Steps
✍️ 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