6.DS.5 Lesson 2-4-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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2.4 Small Group · Group 1

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is a box plot?
1The box always holds the middle 50% of the data, and the line inside the box is the median.
  • A box plot is a simple picture that shows how a set of data is spread out, using just five key numbers: the lowest value, the first quartile (Q1), the median (middle), the third quartile (Q3), and the highest value. 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 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.
3Mathematical 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.
4Watch 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 DRAG SORT

    Order the steps for making a box plot.

    Target Categories: Steps (in order)
    • Step 1: Order the data from least to greatest
    • Step 2: Find the median (middle value)
    • Step 3: Find Q1 (median of the lower half)
    • Step 4: Find Q3 (median of the upper half)
    • Step 5: Draw the box from Q1 to Q3 with a line at the median, and whiskers to min and max
  3. 3 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
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 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
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  2. 5 MULTIPLE CHOICE

    What percentage of data falls between Q1 and Q3 on a box plot?

    1. A50%
    2. B25%
    3. C75%
    4. D100%
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 6 MULTIPLE CHOICE

    Find the range of: 14, 22, 8, 31, 17

    1. A23
    2. B31
    3. C8
    4. D18
    Put the data in order
    Work
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
🗣️ 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