6.DS.4 Lesson 2-3-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
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2.3 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Describe the Data Using the Median · Median · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What are mean, median, and mode?
1The median is the middle value once the data is in order. With an even count, it is the mean of the two middle values — and it is the measure that an unusually high or low value cannot drag around — 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 find the median
  1. My data set: 2, 4, 4, 6, 9 — five values, already in order. Ordering first is what makes a middle exist at all.
  2. With 5 values, the middle is the 3rd one. Counting in from both ends: 2 and 9 pair off, 4 and 6 pair off, and 4 is left alone.
  3. So the median is 4. Half the values sit at or below it and half at or above it.
  4. Now an even set: 2, 4, 6, 9. There is no single middle, so I take the mean of the two middle values: (4 + 6) ÷ 2 = 5. The median is 5, even though 5 is not in the data.
3Second Model — Try it together — then prove it
  1. New data set, out of order: 13, 3, 7, 10, 7. Put it in order first.
  2. In order: 3, 7, 7, 10, 13. Five values, so the middle is the 3rd.
  3. The median is 7. Say what it means: a typical value in this set is about 7.
  4. Now change the 13 to 130. Does the median move? It does not — still 7. That resistance is exactly why the median is used.
  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
  • Describe the Data Using the Median (Describir los datos con la mediana) — Using the middle value of the ordered data to say what is typical for the whole set.
  • Median (Mediana) — The middle number when you put them in order.
  • Mode (Moda) — The number that shows up most often.
  • Outlier (Valor atípico) — A number that is much bigger or smaller than the rest.
  • 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, Median, and Mode is finding the median without ordering the data first — students pick the middle number straight from the list as given (for 9, 4, 7, 2, 6 they say the median is 7, the middle position in that original order) instead of sorting least to greatest (2, 4, 6, 7, 9) and finding the true middle value, 6. Before finalizing a median, always reorder the data smallest to largest, then count to the middle position — and if there is an even number of values, average the two middle numbers.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

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

    Data SetMeanMedianMode
    5, 8, 8, 10, 14
    20, 25, 25, 30, 25, 35
    100, 110, 90, 100, 115, 95
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each measure to its definition.

    1. Mean
    2. Median
    3. Mode
    4. Range
    • ASum ÷ Count
    • BMiddle value
    • CMost frequent
    • DMax − Min
  3. 3 MULTIPLE CHOICE

    A team scored 4, 4, 7, and 9 goals in four matches. What is the MODE?

    1. A4
    2. B7
    3. C9
    4. D6
    Put the data in order
    Work
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    A player scored 4, 8, 6, 10, and 2 points across five quarters. What is the MEAN number of points?

    1. A6
    2. B8
    3. C30
    4. D10
    Put the data in order
    Work
  2. 5 MULTIPLE CHOICE

    A goalie made 3, 7, 9, 2, and 5 saves in five games. What is the MEDIAN number of saves?

    1. A5
    2. B9
    3. C7
    4. D2
    Put the data in order
    Work
  3. 6 MULTIPLE CHOICE

    One game was a 55-point outlier. Which measure of center best shows a TYPICAL game?

    1. AThe median, because the outlier barely moves the middle value
    2. BThe mean, because it uses every score
    3. CThe mode, because it is always the typical value
    4. DThe range, because it shows the spread
    ✏️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It