6.DS.3 Lesson 2-5-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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2.5 Small Group · Group 1

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

Range and Interquartile Range · Range · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How spread out is the data?
1Range = greatest − least, and it covers every value. Interquartile range = Q3 − Q1, and it covers only the middle half, so one faraway value cannot stretch it.
  • A measure of center like the median tells you where the data sits. It does not tell you how far apart the values are. Two classes can share the same median and still look nothing alike. Range and interquartile range are the two numbers that describe that spread. 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 measure the spread of the test scores
  1. Here are 20 history test scores in order: 68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94. Ordering them first is what makes every step after this possible.
  2. Range: I subtract the least value from the greatest. 94 − 68 = 26. The scores span 26 points from end to end.
  3. Now the quartiles. The median splits the 20 scores into two halves of 10. The median is halfway between the 10th and 11th values: (83 + 84) ÷ 2 = 83.5.
  4. Q1 is the median of the lower 10 values: halfway between 75 and 76, so Q1 = 75.5. Q3 is the median of the upper 10: halfway between 88 and 88, so Q3 = 88.
  5. Interquartile range: IQR = Q3 − Q1 = 88 − 75.5 = 12.5. The middle half of the students' scores differed by only 12.5 points, even though the full range was 26.
3Mathematical Word Bank
  • Range and Interquartile Range (Rango y rango intercuartílico) — Two numbers that describe spread: the range covers all the data, and the interquartile range covers only the middle half.
  • Range (Rango) — The distance from the least value to the greatest value, found by subtracting: greatest − least.
  • Quartile (Cuartil) — One of the three values that cut an ordered data set into four equal-sized groups.
  • Interquartile range (Rango intercuartílico) — The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1.
  • Variability (Variabilidad) — How much the values in a data set differ from one another — whether they sit close together or far apart.
  • Measure of variation (Medida de variación) — A single number that describes the spread of a whole data set. The range and the IQR are both measures of variation.
4Watch out
  • A common mistake with Range and Interquartile Range is adding the two quartiles instead of subtracting them — writing IQR = Q3 + Q1. With Q1 = 42 and Q3 = 58 that gives 100, which is larger than the data set's entire range of 20. Every measure of variation is a DIFFERENCE, and the IQR can never exceed the range, because the middle half is part of the whole span. If your IQR comes out bigger than your range, you added when you should have subtracted.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Two classes both have a median score of 81. Class A's IQR is 13 and Class B's IQR is 8. Which statement is true?

    1. AThe middle half of Class B's scores is less spread out
    2. BClass B has a higher median
    3. CClass A has more students
    4. DClass B's highest score is greater
    ✏️ Workspace & Solution Steps
  2. 2 DRAG SORT

    Sort each fact under the measure of variation it describes.

    Target Categories: Range Interquartile range
    • Greatest value − least value
    • Q3 − Q1
    • The width of the box on a box plot
    • The distance from whisker tip to whisker tip
    • Changes a lot when one value is unusually high
    • Describes the middle 50% of the data
  3. 3 DRAG SORT

    A value far above the rest is added to a data set. Sort what happens.

    Target Categories: The range grows a lot The IQR barely changes
    • Because it uses the greatest value
    • Because it uses only Q1 and Q3
    • It measures the whole span of the data
    • It measures only the middle half
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    A data set runs from a least value of 12 to a greatest value of 30. What is the range?

    1. A18
    2. B30
    3. C12
    4. D21
    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

    On a box plot, Q1 = 20 and Q3 = 36. What is the interquartile range?

    1. A16
    2. B56
    3. C28
    4. D36
    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

    Which measure of spread uses ONLY the middle half of the data?

    1. AThe interquartile range
    2. BThe range
    3. CThe median
    4. DThe mode
    ✏️ 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
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