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

2.9 Small Group · Group 2

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

Mean Absolute Deviation · Deviation · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is the mean absolute deviation (MAD)?
1MAD = the average of how far each number is from the mean (always a positive distance) — 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
  1. My data set: 6, 8, 10, 12. First I find the mean: 6 + 8 + 10 + 12 = 36, then 36 ÷ 4 = 9. The mean is 9.
  2. Next I find each deviation (value − mean): 6−9 = −3, 8−9 = −1, 10−9 = 1, 12−9 = 3.
  3. Then I take the absolute value of each (the distance, always positive): 3, 1, 1, 3.
  4. Finally I average those distances: 3 + 1 + 1 + 3 = 8, then 8 ÷ 4 = 2. So the MAD = 2 points.
3Second Model — Try it together — then prove it
  1. New data set: 9, 10, 11. First, what is the mean? Add the three numbers and divide by 3.
  2. Now find how far each number is from the mean. What is the distance for 9? For 10? For 11?
  3. Add those distances and divide by 3. Is this MAD small or large? What does that tell us about the spread?
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Mean Absolute Deviation (Desviación media absoluta) — The average distance of data values from the mean; it describes spread.
  • Deviation (Desviación) — How far a number is from the mean.
  • Absolute Value (Valor absoluto) — How far a number is from zero. It is never negative.
  • Spread (Dispersión) — How far apart the numbers are.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
  • Variability (Variabilidad) — How spread out the numbers are.
5Watch out
  • A common mistake in Mean Absolute Deviation is adding the signed deviations (value − mean) instead of their absolute values, so the positives and negatives cancel out to 0. For 6, 8, 10, 12 (mean = 9), the deviations are −3, −1, 1, 3 — they sum to 0, but that is NOT the MAD. Before averaging, take the absolute value of every deviation so each becomes a positive distance: |−3| = 3, |−1| = 1, |1| = 1, |3| = 3. Sum = 8, so MAD = 8 ÷ 4 = 2. A MAD of exactly 0 is a warning sign — it only happens if every value in the data set equals the mean.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Two runners have the same average time of 60 seconds. Runner A's MAD is 1.2 seconds. Runner B's MAD is 5.8 seconds. Which runner is the coach more likely to pick for a relay race that needs a reliable time?

    1. ARunner A — lower MAD means more consistent times
    2. BRunner B — higher MAD means faster potential
    3. CEither — they have the same average
    4. DNeither — MAD doesn't matter for relay races
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A guard scored 2, 4, 6, 8 points in four scrimmages, so the mean is 5 points. The distances from the mean are 3, 1, 1, 3. What is the mean absolute deviation (MAD)?
    2. 2A classmate at our table answered:1

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 3 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Data set:A swimmer's lap times: 2, 5, 8, 9. Mean = (2 + 5 + 8 + 9) ÷ 4 = 24 ÷ 4 = 6.
    2. 2Find each absolute deviation:|2 − 6| = 4, |5 − 6| = 1, |8 − 6| = 2, |9 − 6| = 3
    3. 3Find the MAD:Sum of absolute deviations = 4 + 1 + 2 + 3 = 10. MAD = 10 ÷ 3 ≈ 3.33

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 4 ERROR ANALYSIS

    Find the MAD Error

    1. 1Data set:5, 10, 15, 20, 25
    2. 2Find mean:Sum = 75, Count = 5, Mean = 15
    3. 3Find deviations:−10, −5, 0, 5, 10
    4. 4Find MAD:MAD = (−10 + −5 + 0 + 5 + 10) ÷ 5 = 0

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 5 OPEN RESPONSE

    Two basketball teams both average 75 points per game. Team A's last 5 scores: 73, 76, 74, 77, 75. Team B's last 5 scores: 60, 90, 65, 85, 75. Calculate the MAD for each team and explain which team a coach would prefer if they need predictable scoring.

    ✏️ Mathematical Justification & Response
📐 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