6.DS.5 Lesson 2-2-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.2 · Part II

Supported Application · Guided Entry to Today's Problem

Display Data with Histograms · Histogram

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 2.2 · Part II
1Histograms & Frequency Distributions
2Strategy Model — step by step
  1. Set equal intervals along the horizontal axis with no gaps
  2. Count the frequency (how many data values fall into each interval)
  3. Draw adjacent bars with heights equal to frequency
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 has intervals: 0–4, 5–9, 10–14, 15–19. What is the width of each interval?

    1. A10
    2. B19
    3. C5
    4. D4
    ✏️ Workspace & Solution Steps
  2. 3 GUIDED FILL

    A histogram has interval counts 2, 4, 3. How many data values are represented?

    1. 1Add the bar frequencies: ___.
    2. 2Total data values: ___.
    Final answer:
📐 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
6.DS.5 Lesson 2-2-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.2 · Part II

On-Level Application · Standard Rigor

Display Data with Histograms · Histogram

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.2 · Part II
1Histograms & Frequency Distributions
2The Structural Procedure
  1. Set equal intervals along the horizontal axis with no gaps
  2. Count the frequency (how many data values fall into each interval)
  3. Draw adjacent bars with heights equal to frequency
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.
  1. 1 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. 2 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. 3 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
📐 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
6.DS.5 Lesson 2-2-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.2 · Part II

Extension & Non-Routine Application

Display Data with Histograms · Histogram

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 2.2 · Part II
1Histograms & Frequency Distributions
2The Structural Procedure
  1. Set equal intervals along the horizontal axis with no gaps
  2. Count the frequency (how many data values fall into each interval)
  3. Draw adjacent bars with heights equal to frequency
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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A histogram uses intervals 0–9, 10–19, 20–29, and 30–39. A data value of 19 belongs in which interval?

    1. A10–19
    2. B0–9
    3. C20–29
    4. DIt belongs in two intervals.
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A histogram of points-per-game has its tallest bars on the LEFT (low scores) and a long tail stretching RIGHT toward a few high scorers. How is this distribution described?

    1. ASkewed left
    2. BSymmetric
    3. CBimodal (two equal peaks)
    4. DSkewed right
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A teacher collected test scores and made two different histograms — one with intervals of 5 (50–54, 55–59, etc.) and one with intervals of 20 (50–69, 70–89, 90–109). Both use the same data. How might the two histograms look different? Which interval size gives you more detail about the distribution? When might the larger interval be better?

    ✏️ 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