6.DS.1 Lesson 2-1-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

2.1 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

Statistical Questions and Data · Statistical Question · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What makes a question a statistical question?
1If you expect the answers to vary, it is a statistical question — 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. 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.
3Second Model — Try it together — then prove it
  1. New question: "How many pets does each student in our class have?" Will every student give the same answer, or different answers?
  2. Some students have 0 pets and others have 2 or 3, so the answers vary. Is this statistical or not statistical?
  3. Now a different question: "How many days are in one week?" Does this have one fixed answer or many?
  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
  • 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.
5Watch 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 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
  2. 2 DRAG SORT

    Match each non-statistical question with its statistical rewrite.

    Target Categories: Original: 'How many students are in 6th grade?' Original: 'What time does school start?'
    • Rewritten: 'How many hours does each 6th grader study per week?'
    • Rewritten: 'What time does each student arrive at school?'
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A survey asks 30 students how many books they read last month, collecting 30 answers. What makes this a statistical question?

    1. AIt is about books
    2. BEveryone reads the same number
    3. CThe answers vary from student to student
    4. DIt has exactly one correct answer
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    Which rewrite turns 'What is my resting heart rate?' into a statistical question?

    1. AIs my heart rate high?
    2. BWhat is a heart rate?
    3. CWhat is the teacher's heart rate?
    4. DWhat are the resting heart rates of students in my class?
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Find the Reasoning Error

    1. 1Question:How many touchdowns did the quarterback throw this season?
    2. 2Student says:This is NOT a statistical question.
    3. 3Reason:It only asks about one player, so there is no variability.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    Write one statistical question and one non-statistical question about your school's cafeteria. Explain why each question is or is not statistical, and describe what the data would look like for the statistical question.

    ✏️ Mathematical Justification & Response
🗣️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It