6.AT.11 Lesson 9-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.1 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

independent variable · dependent variable · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Claire burned 123 Calories on a 30-minute jog and 246 Calories on a 60-minute jog.
  2. Which did Claire choose — the minutes, or the Calories?
  3. She chose how long to jog. So time is independent, and Calories burned is dependent.
  4. Sentence frame: ___ depends on ___ .
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 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. 2 MULTIPLE CHOICE

    A gym charges $24.95 per month. Which pair correctly names the variables?

    1. AIndependent: months; Dependent: total cost
    2. BIndependent: total cost; Dependent: months
    3. CIndependent: $24.95; Dependent: months
    4. DIndependent: months; Dependent: $24.95
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Which of these pairs is NOT a dependent relationship?

    1. ANumber of pizzas sold and number of employees the shop has
    2. BNumber of pizzas sold and weekly cost of cheese
    3. CHours jogged and Calories burned
    4. DTickets bought and total cost
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    Describe one situation where time is the independent variable, and a different situation where time is the dependent variable. For each one, say who or what does the choosing.

    ✏️ Mathematical Justification & Response
  2. 5 OPEN RESPONSE

    Here is the result of an experiment: “Water temperature depends on how long the pot has been on the stove.” Working backwards, describe the experiment. What would you choose, what would you measure, and what would the two column headings of your table be?

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Claim: “The dependent variable always has the larger values.” Is this claim always, sometimes, or never true?
    2. 2A classmate at our table answered:Only when both quantities are measured in the same unit

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 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