6.DS.4 Lesson 2-3-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.3 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • Mean, median, and mode are three ways to find the center, or "typical" value, of a data set. The mean is the average, the median is the middle, and the mode is the most common 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 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.
3Mathematical 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.
4Watch 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 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
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    Data set: 4, 6, 6, 8, 10, 12. What is the median?

    1. A7
    2. B6
    3. C8
    4. D7.67
    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. 3 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
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
  3. 4 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
    1. 1OrderSmallest to largest.
    2. 2CountHow many values?
    3. 3LocateMiddle, or add and divide.
    4. 4AnswerSay which measure it is.
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    The Mean Mistake (forgot to divide)

    1. 1Data set:A player scored 6, 8, 10, and 6 points in 4 games.
    2. 2Goal:Find the MEAN number of points.
    3. 3Add the values:6 + 8 + 10 + 6 = 30
    4. 4Answer:Mean = 30

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    The Even-Count Median Mistake

    1. 1Data set:Points per game, in order: 3, 8, 10, 14, 16, 20 (6 values)
    2. 2Goal:Find the MEDIAN number of points.
    3. 3Pick the middle:With 6 values the student grabs a single middle number and says median = 10.
    4. 4Answer:Median = 10

    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
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