6.DS.6c Lesson 2-9-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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2.9 Small Group · Group 1

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

Visual Models · Mean Absolute Deviation · Deviation · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the mean absolute deviation (MAD)?
1MAD = the average of how far each number is from the mean (always a positive distance).
  • The mean absolute deviation, or MAD, is the average distance of each value from the mean. It tells you how spread out the data is: a small MAD means the data is close together, and a large MAD means it is spread out. 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
  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.
3Mathematical 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.
4Watch 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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 NUMBER LINE

    The mean is 10. Place each data value on the number line, then find how far each is from the mean: Data: 7, 10, 13.

    ✏️ Workspace & Solution Steps
  2. 2 FILL TABLE

    Deviation Detective: the quiz scores are 12, 8, 10, 14, 6 and the mean is 10. Complete each deviation and absolute deviation, then compute the MAD.

    ScoreDeviation (Score − Mean)Absolute Deviation
    12
    8
    10
    14
    6
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

    1. A4
    2. B−4
    3. C26
    4. D11
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

    1. A3
    2. B5
    3. C15
    4. D1
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    The mean of a data set is 20. A value is 26. What is the absolute deviation?

    1. A6
    2. B−6
    3. C46
    4. D26
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    Team A has MAD = 2.1 points. Team B has MAD = 6.8 points. Which team is more consistent?

    1. ATeam A — lower MAD means scores are closer to the mean
    2. BTeam B — higher MAD means better performance
    3. CBoth are equally consistent
    4. DCannot tell from MAD alone
    ✏️ Workspace & Solution Steps
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE A question is statistical because it expects varied responses across different subjects rather than a single fixed value.
BUT A question might gather numbers, but it is not statistical if there is only one exact unchanging answer.
SO The researcher needed to understand group variation, so she collected data using a statistical survey question.
📐 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