6.DS.5 Lesson 2-2-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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2.2 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

    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
  2. 2 DRAG SORT

    Order the steps for making a histogram.

    Target Categories: Steps (in order)
    • Step 1: Choose equal-sized intervals that cover all the data
    • Step 2: Count how many data values fall in each interval (frequency)
    • Step 3: Draw bars for each interval — height = frequency
    • Step 4: Make sure bars touch with no gaps
  3. 3 MATCHING GAME

    Match each word to what it means on a histogram.

    1. Frequency
    2. Interval
    3. Bars touch
    • AHow many values are in an interval (the bar height)
    • BAn equal-width range like 10–19
    • CWhy a histogram has no gaps between bars
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 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
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 5 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
  3. 6 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
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE A question is statistical because it expects varied responses across different subjects rather than a single fixed value.
BUT A question might gather numbers, but it is not statistical if there is only one exact unchanging answer.
SO The researcher needed to understand group variation, so she collected data using a statistical survey question.
📐 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