6.DS.5 Lesson 2-2-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.2 Small Group · Group 1

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

Display Data with Histograms · Histogram · 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 histogram?
1Each bar's height shows how many data values land inside that interval.
  • A histogram is a bar graph that groups numbers into equal ranges called intervals. The height of each bar is the frequency: how many values fall in that interval. The bars touch because the intervals are continuous. 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
  1. My data: 3, 7, 12, 15, 18, 24. I will use intervals of 10: 0–9, 10–19, 20–29.
  2. Interval 0–9: the values 3 and 7 fit, so the frequency is 2.
  3. Interval 10–19: the values 12, 15, and 18 fit, so the frequency is 3.
  4. Interval 20–29: only the value 24 fits, so the frequency is 1.
  5. Now I draw three bars with heights 2, 3, and 1, touching each other. The tallest bar (10–19) is where most values are.
3Mathematical Word Bank
  • Display Data with Histograms (Representar datos con histogramas) — Group numerical data into intervals and show each interval's frequency with a bar.
  • Histogram (Histograma) — A bar graph that groups data into equal ranges. The bars touch.
  • Frequency (Frecuencia) — How many times a value shows up.
  • Interval (Intervalo) — A range of numbers used to group data.
  • Distribution (Distribución) — How the data is spread out.
  • Variability (Variabilidad) — How spread out the numbers are.
4Watch out
  • A common mistake in Display Data: Histograms is counting a boundary value in two intervals at once — for example, putting the value 10 in both the '0–9' bin and the '10–19' bin. Each data value belongs to exactly ONE interval. Before you submit, add up all your frequencies and check that the total matches the number of data values you started with.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    A histogram bar for the interval 20–29 reaches a height of 7. What does the 7 tell you?

    1. AThe largest value is 7
    2. BThere are 7 intervals
    3. CThe interval is 7 wide
    4. D7 data values fall between 20 and 29
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    A histogram of test scores shows: 50–59: 2, 60–69: 5, 70–79: 10, 80–89: 8, 90–99: 3. Which interval has the most students?

    1. A90–99 with 3 students
    2. B70–79 with 10 students
    3. C80–89 with 8 students
    4. D60–69 with 5 students
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    A histogram of goals-per-game shows: 0–1: 9 players, 2–3: 6, 4–5: 3, 6–7: 1. What shape is this distribution?

    1. APerfectly symmetric
    2. BFlat / uniform (all bars equal)
    3. CSkewed right (most players low, tail toward high values)
    4. DSkewed left (most players high, tail toward low values)
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE

    Data: 4, 8, 9, 12, 14, 15, 17, 18, 19, 22, 24, 27, 31, 33. How many values fall in the 10–19 interval?

    1. A9
    2. B5
    3. C6
    4. D3
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Counting Mistake

    1. 1Data (points per game):3, 7, 11, 13, 16, 22
    2. 2Intervals:0–9, 10–19, 20–29
    3. 3Frequency count:0–9: 2, 10–19: 2, 20–29: 1
    4. 4Conclusion:So the histogram bars have heights 2, 2, and 1.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Spot the Interval Mistake

    1. 1Data (assists per game):1, 4, 6, 9, 12, 15, 18
    2. 2Intervals the student chose:0–5, 6–10, 12–18
    3. 3Frequency count:0–5: 2, 6–10: 2, 12–18: 3
    4. 4Conclusion:The student drew three bars and said the histogram was complete.

    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