6.DS.5 Lesson 2-4-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.4 Small Group · Group 2

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

Display Data with Box Plots · Box Plot · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is a box plot?
1The box always holds the middle 50% of the data, and the line inside the box is the median — 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 build one
  1. My data, in order: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28. There are 11 numbers.
  2. The middle number is the 6th one, 14, so the median = 14.
  3. The lower half is 4, 6, 8, 10, 12. Its middle is 8, so Q1 = 8.
  4. The upper half is 15, 18, 22, 24, 28. Its middle is 22, so Q3 = 22.
  5. The lowest is 4 and the highest is 28. I draw a box from 8 to 22, a line at 14, and whiskers out to 4 and 28.
3Second Model — Try it together — then prove it
  1. New, smaller data set: 2, 5, 5, 8, 11. First, what is the median (the middle value)?
  2. The lower half is 2, 5 and the upper half is 8, 11. What is Q1? What is Q3?
  3. What are the lowest and highest values? Now picture the box stretching from Q1 to Q3 with the median line inside.
  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
  • Display Data with Box Plots (Representar datos con diagramas de caja) — Show a data set's five-number summary in a box-and-whisker display.
  • Box Plot (Diagrama de caja) — A graph that shows how data is spread using five key numbers.
  • Median (Mediana) — The middle number when you put them in order.
  • Quartile (Cuartil) — Numbers that split the data into four equal parts.
  • Interquartile Range (Rango intercuartílico) — The spread of the middle half of the data (Q3 − Q1).
  • Data distribution (Distribución de datos) — How the data looks: where it sits and how spread out it is.
5Watch out
  • A common mistake in Display Data: Box Plots is treating a quartile as just one data point instead of the median of a half — for the lower half 4, 8, 10, 14, some students pick 10 (the last value) as Q1 instead of finding the median of that half: Q1 = (8 + 10) ÷ 2 = 9. A second common slip is finding IQR by adding the quartiles instead of subtracting, writing IQR = Q3 + Q1 (like 30 + 18 = 48) instead of IQR = Q3 − Q1 (30 − 18 = 12) — always order the data first, then subtract Q1 from Q3 to find the spread of the middle 50%.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

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

    MeasureValue
    Data: 5, 8, 12, 15, 18, 20, 25, 30, 35
    Minimum
    Q1 (median of lower half: 5, 8, 12, 15)
    Median
    Q3 (median of upper half: 20, 25, 30, 35)
    Maximum
    IQR (Q3 − Q1)
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each box plot term to its meaning.

    1. Minimum
    2. Q1
    3. Median
    4. Q3
    5. IQR
    6. Maximum
    • ASmallest value in the data set
    • BMedian of the lower half
    • CMiddle value of the entire data set
    • DMedian of the upper half
    • EQ3 − Q1 (spread of middle 50%)
    • FLargest value in the data set
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    The Hawks' points per quarter are 2, 4, 5, 7, 8, 10, 12. Resting on the scoreboard, what are the minimum, median, and maximum?

    1. AMinimum 2, median 7, maximum 12
    2. BMinimum 2, median 5, maximum 12
    3. CMinimum 0, median 7, maximum 12
    4. DMinimum 2, median 8, maximum 10
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    The Comets scored 6, 10, 14, 18, 22, 26, 30, 34 across 8 games. After ordering, what are Q1 and Q3?

    1. AQ1 = 12, Q3 = 28
    2. BQ1 = 10, Q3 = 30
    3. CQ1 = 14, Q3 = 26
    4. DQ1 = 20, Q3 = 34
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A box plot for the Rockets shows Min = 8, Q1 = 15, Median = 22, Q3 = 30, Max = 38. The middle 50% of their scores falls between which two values?

    1. ABetween 15 and 30
    2. BBetween 8 and 38
    3. CBetween 8 and 22
    4. DBetween 22 and 38
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — The Skipped Ordering Mistake

    1. 1Data (as recorded):Falcons' scores: 17, 5, 21, 9, 29, 13, 25
    2. 2Minimum and maximum:Min = 5, Max = 29 ✓
    3. 3Median:The middle value of the list is 9, so Median = 9
    4. 4Q1 and Q3:Lower half = 17, 5, 21 → Q1 = 5. Upper half = 13, 25 → Q3 = 25

    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
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