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

2.2 Small Group · Group 2

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

Display Data with Histograms · Histogram · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is a histogram?
1Each bar's height shows how many data values land inside that interval — 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
  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.
3Second Model — Try it together — then prove it
  1. New data: 2, 4, 8, 11, 13, 16, 21. We will use intervals of 10 again: 0–9, 10–19, 20–29.
  2. How many values fall in 0–9? Count them. How many fall in 10–19?
  3. How many fall in 20–29? Which interval would have the tallest bar?
  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 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.
5Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Frequencies: 0–9: 3, 10–19: 9, 20–29: 5, 30–39: 2. Which interval has the tallest bar?

    1. A20–29 with 5 players
    2. B0–9 with 3 players
    3. C30–39 with 2 players
    4. D10–19 with 9 players
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Read this histogram of assists per game — 0–4: 2 players, 5–9: 8 players, 10–14: 5 players, 15–19: 1 player. About how many players are on the team?

    1. A15
    2. B16
    3. C8
    4. D4
    per 1
  3. 3 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
  4. 4 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Two histograms show the SAME 40 test scores — one uses intervals of 5, the other intervals of 20. Which statement is true?
    2. 2A classmate at our table answered:The interval-of-20 histogram has more bars

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    Two histograms show the SAME 40 test scores — one uses intervals of 5, the other intervals of 20. A classmate says the interval-of-20 histogram is simply wrong because it hides the shape of the data. Is a wider interval WRONG, or just different? Give one question the interval-of-20 display answers BETTER, and one it answers worse.

    ✏️ Mathematical Justification & Response
📐 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