6.AT.11 Lesson 9-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.1 · Part II

Supported Application · Guided Entry to Today's Problem

independent variable · dependent variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 9.1 · Part II
1Independent & Dependent Variables
2Strategy Model — step by step
  1. Independent Variable (x): The input / cause that is chosen or changes freely
  2. Dependent Variable (y): The output / effect that depends on the independent variable
  3. Sentence check: 'The (dependent) depends on the (independent)'
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.
  1. 1 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
  2. 2 MULTIPLE CHOICE

    A tray that got 2 hours of sun grew to 4 cm. A tray that got 6 hours grew to 12 cm. As sunlight increases, plant height…

    1. Aincreases
    2. Bdecreases
    3. Cstays the same
    4. Dcannot be determined
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    You buy tickets at $45 each. Which quantity depends on the other?

    1. ATotal cost depends on number of tickets
    2. BNumber of tickets depends on total cost
    3. CThe price per ticket depends on the total cost
    4. DNothing depends on anything here
    ✏️ 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
6.AT.11 Lesson 9-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.1 · Part II

On-Level Application · Standard Rigor

independent variable · dependent variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 9.1 · Part II
1Independent & Dependent Variables
2The Structural Procedure
  1. Independent Variable (x): The input / cause that is chosen or changes freely
  2. Dependent Variable (y): The output / effect that depends on the independent variable
  3. Sentence check: 'The (dependent) depends on the (independent)'
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.
  1. 1 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. 2 MULTIPLE CHOICE

    Claire jogs 30 minutes and burns 123 Calories. At the same rate, how many Calories would a 90-minute jog burn?

    1. A369
    2. B246
    3. C410
    4. D300
    ✏️ Workspace & Solution Steps
  3. 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
📐 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
6.AT.11 Lesson 9-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.1 · Part II

Extension & Non-Routine Application

independent variable · dependent variable

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 9.1 · Part II
1Independent & Dependent Variables
2The Structural Procedure
  1. Independent Variable (x): The input / cause that is chosen or changes freely
  2. Dependent Variable (y): The output / effect that depends on the independent variable
  3. Sentence check: 'The (dependent) depends on the (independent)'
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 MULTIPLE CHOICE

    Two quantities are related. Which statement is ALWAYS true?

    1. AThe independent variable is subject to choice
    2. BThe independent variable is always the larger number
    3. CThe dependent variable is always measured in dollars
    4. DThe independent variable is always listed first in a table
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Devon adds a different number of scoops of plant food to each tray of seedlings. Two weeks later he counts the new leaves on every tray. Which pair correctly names the variables?

    1. AIndependent: new leaves counted; Dependent: scoops of plant food
    2. BIndependent: the number of trays; Dependent: scoops of plant food
    3. CIndependent: scoops of plant food; Dependent: new leaves counted
    4. DIndependent: new leaves counted; Dependent: the two weeks of growing time
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    Give an example where the SAME quantity can be independent in one problem and dependent in another.

    1. ATime: chosen when you pick how long to jog, but measured as a result when you run a set distance
    2. BTime is always independent
    3. CTime is always dependent
    4. DA quantity can never switch roles
    ✏️ 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