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

2.4 Small Group · Group 2

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

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 MULTIPLE CHOICE

    On a box plot, what does the line inside the box represent?

    1. AThe median
    2. BThe mean
    3. CThe mode
    4. DThe range
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?

    1. ATeam A's middle 50% is more consistent; Team B's is more spread out
    2. BTeam B is a better team
    3. CTeam A has a higher median
    4. DThe IQRs don't tell you about consistency
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?

    1. A13
    2. B25
    3. C10
    4. D20
    Put the data in order
    Work
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:On a box plot, what does the line inside the box represent?
    2. 2A classmate at our table answered:The range

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    The Quartile-Is-One-Value Mistake

    1. 1Data (ordered):Eagles' game scores: 4, 8, 10, 14, 18, 22, 26, 30 (8 values)
    2. 2Median:With 8 values, Median = (14 + 18) ÷ 2 = 16 ✓
    3. 3Q1:Lower half = 4, 8, 10, 14 → Q1 = 10
    4. 4Q3:Upper half = 18, 22, 26, 30 → Q3 = (22 + 26) ÷ 2 = 24

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find the Box Plot Error

    1. 1Data:3, 7, 9, 12, 15, 18, 21
    2. 2Min and Max:Min = 3, Max = 21
    3. 3Median:Middle value = 12 ✓
    4. 4Q1 and Q3:Q1 = 9, Q3 = 18

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

    ✏️ Corrected Mathematical Work & Explanation
📐 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