6.DS.5 Lesson 2-2-part2 Apply Day · Set B
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2.2 · Part II

Second Practice Form · Independent Application and Spiral Review

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Two histograms show the SAME 40 test scores — one uses intervals of 5, the other intervals of 20. Which statement is true?

    1. AThe interval-of-5 histogram leaves some scores out
    2. BThe interval-of-5 histogram has more bars and shows more detail about the shape
    3. CThe interval-of-20 histogram has more bars
    4. DBoth histograms must look exactly the same
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    In a histogram, what does the height of each bar represent?

    1. AThe average of the data in that interval
    2. BThe range of the interval
    3. CThe median of the data
    4. DThe frequency (count) of data in that interval
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 GUIDED FILL

    A histogram has interval counts 3, 5, 4. How many data values are represented?

    1. 1Add the bar frequencies: ___.
    2. 2Total data values: ___.
    Final answer:
  2. 4 GUIDED FILL

    A histogram has interval counts 4, 6, 3. How many data values are represented?

    1. 1Add the bar frequencies: ___.
    2. 2Total data values: ___.
    Final answer:
  3. 5 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
  4. 6 MULTIPLE CHOICE

    A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?

    1. A20
    2. B15
    3. C28
    4. D12
    per 1
  5. 7 MULTIPLE CHOICE

    How is a histogram different from a regular bar graph?

    1. AThere is no difference
    2. BHistogram bars touch (no gaps) because the intervals are continuous ranges
    3. CHistograms use colors and bar graphs don't
    4. DBar graphs show numbers and histograms show words
    ✏️ 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