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

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

Statistical Questions and Data · Statistical Question · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What makes a question a statistical question?
1If you expect the answers to vary, it is a statistical question.
  • A statistical question is one you answer by collecting data, and the answers are different for different people or cases. A non-statistical question has just one fixed answer. 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. Question 1: "How many points did our top player score last night?" There is one player and one game, so there is one fixed answer, like 18 points.
  2. One answer, no variety, so this is NOT a statistical question.
  3. Question 2: "How many points does each player score per game?" The answers vary: 8, 12, 12, 15, 18, 20, 22.
  4. Because the answers are different for different players, I must collect data. This IS a statistical question.
3Mathematical Word Bank
  • Statistical Questions and Data (Preguntas estadísticas y datos) — A statistical question expects varied answers that can be collected as data.
  • Statistical Question (Pregunta estadística) — A question where the answers will be different for different people.
  • Non-statistical Question (Pregunta no estadística) — A question that has just one fixed answer that is the same no matter who you ask, so there is no data to collect.
  • Data (Datos) — Facts and numbers you collect, like answers to a survey.
  • Variability (Variabilidad) — How spread out the numbers are.
  • Survey (Encuesta) — Collecting facts by asking people questions.
4Watch out
  • A common mistake in Statistical Questions and Data is judging a question by its topic or its numbers instead of its variability. Students see a question about ONE player, ONE game, or ONE fixed fact — like "How many points does the team need to win a game?" — and call it statistical just because it has a number or is about sports. Or they see a question about a single player's whole season, like "How many touchdowns did the quarterback throw this season?", and call it NOT statistical because only one player is named, forgetting that a season covers many games with a different result each time. Both errors skip the real test: will the answers actually differ from case to case (game to game, player to player)? If yes, it is a statistical question; if there is one fixed answer, it is not.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each question by type.

    Target Categories: Statistical Question Not a Statistical Question
    • How many books did each student read this month?
    • What grade did each student earn on the test?
    • How many days are in a week?
    • What is the school mascot?
  2. 2 FILL TABLE

    Decide if each question is statistical and explain why.

    QuestionStatistical?Why?
    How many push-ups can each student do in one minute?
    How many sides does a basketball court have?
    How far does each player kick the ball?
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Which of the following is a statistical question?

    1. AHow many points did each player score this season?
    2. BHow many points are scored for a free throw?
    3. CWhat sport does this team play?
    4. DHow many halves are in a soccer game?
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Which question is NOT a statistical question?

    1. AHow many innings are in a baseball game?
    2. BHow many home runs did each player hit this year?
    3. CHow many miles does each runner train per week?
    4. DHow tall is each player on the basketball team?
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Why is 'How many hours of sleep did each student get last night?' a statistical question?

    1. ABecause different students got different amounts of sleep
    2. BBecause it asks about sleep
    3. CBecause hours are numbers
    4. DBecause the answer is always 8 hours
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Question:How tall is each player on the basketball team?
    2. 2Student decision:This is NOT a statistical question.
    3. 3Student reason:Height is just one number, so every answer will be the same.

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ 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