6.DS.6d Lesson 2-10-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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2.10 Small Group · Group 1

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

Appropriate Measures of Center · Mean · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Should I use the mean or the median?
1Use the mean for data with no outliers; use the median when an outlier or a skewed shape would pull the mean away from typical.
  • The mean and the median both describe the center of a data set, but one fits better depending on the shape. When the data has an outlier (a value far from the rest), the median is usually the better choice. 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, the top scorer's points: 22, 24, 20, 25, 23, 21, 58. I notice 58 is much bigger than the rest, so it is an outlier.
  2. Mean: 22 + 24 + 20 + 25 + 23 + 21 + 58 = 193, then 193 ÷ 7 ≈ 27.6.
  3. Median: in order they are 20, 21, 22, 23, 24, 25, 58. The middle (4th) value is 23.
  4. The mean (27.6) is higher than 6 of the 7 games because 58 pulled it up. So the median (23) better shows a typical game.
3Mathematical Word Bank
  • Appropriate Measures of Center (Medidas de centro apropiadas) — A mean, median, or mode chosen because it describes a data set fairly.
  • Mean (Media) — The average. Add all the numbers, then divide by how many there are.
  • Median (Mediana) — The middle number when you put them in order.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • Skewed (Sesgado) — When most data sits on one side with a tail on the other.
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
4Watch out
  • A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each feature by which measure of center it supports.

    Target Categories: Use Mean Use Median
    • No outliers in the data
    • Data is symmetric
    • All values are close together
    • Data has one or more outliers
    • Data is skewed to one side
    • One extreme value pulls the average
  2. 2 FILL TABLE

    Solve the mathematical problem. Show all of your work and reasoning.

    Data SetMeanMedianOutlier?Best Measure
    15, 18, 16, 17, 15
    15, 18, 16, 17, 72
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?

    1. AMean
    2. BMedian
    3. CNeither — the data is too small
    4. DBoth are equally bad
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    A runner's mile times are: 7:10, 7:15, 7:12, 7:20, 12:00. The 12:00 was due to a cramp. Which measure best represents a typical mile?

    1. AMedian — the outlier 12:00 pulls the mean too high
    2. BMean — it uses all the data
    3. CMode — it shows the most common time
    4. DNeither measure works
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Data set: 5, 6, 7, 7, 8, 50. The mean is about 13.8 and the median is 7. Which better represents the typical value?

    1. AMedian (7) — the outlier 50 inflates the mean
    2. BMean (13.8) — it includes all values
    3. CBoth are equally good
    4. DNeither works for this data
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Mistake — Forgetting to Order the Data

    1. 1Data:A swimmer's lap counts: 9, 12, 8, 11, 10 (no outliers).
    2. 2Find the median:The student keeps the numbers as written (9, 12, 8, 11, 10) and picks the middle one: median = 8.
    3. 3Choose a measure:The student reports the median (8) as the typical lap count.

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ 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