Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Statistical QuestionSpanish: Pregunta estadística A question answered with data that are expected to vary. How tall is each student?
Non-statistical QuestionSpanish: Pregunta no estadística A question that does not anticipate variability in the data used to answer it. It may ask for one fact or measurement. How tall is the flagpole?
DataSpanish: Datos Facts and numbers you collect, like answers to a survey. 0, 2, 5, 1 pets
VariabilitySpanish: Variabilidad How spread out the numbers are. 0, 2, 5 pets — answers vary
SurveySpanish: Encuesta Collecting facts by asking people questions. Asking classmates one question
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A distribution is symmetric when its left and right sides have approximately matching shapes around the center.

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Which is statistical: “How many siblings does each student have?” or “How many sides does a triangle have?”

  1. Sibling counts differ: 0, 1, 3.
  2. A triangle always has 3 sides.

Answer: The sibling question is statistical; the triangle question is not.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

New question: "How many pets does each student in our class have?" Will every student give the same answer, or different answers?

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • This question statistical because .
  • I expect the answers to from person to person.
  • A non-statistical question has answer.
  • The data I would collect might look like .

Word bank statisticalnon-statisticalvariabilitydatasurveyvaryanswerscollectfixeddifferentquestiontypical

Watch out!A common mistake

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

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each question to its type.

    1. How tall is each swimmer on the team?
    2. What color is the team mascot?
    3. How many laps does each runner complete?
    4. How many players are on a soccer team?
    • AStatistical
    • BNot Statistical
    • CStatistical
    • DNot Statistical

    Hint Read each question on the left and underline the word 'each' when you see it — it's a clue that many people are being measured.

  2. 2Write the name of the correct group on each line.

    Sort each question by type.

    Groups: 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?

    Hint Statistical questions expect different answers from different people or observations.

Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    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?

    Hint Re-read each question and ask: would different people or games give different answers, or is there just one fixed answer?

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    Which question is NOT a statistical question?

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

    Hint Careful — this asks for the question that is NOT statistical: the one with a single fixed answer instead of varying data.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    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 it asks every student the same question

    Hint The question asks WHY it's statistical — focus on what happens when many students answer, not on the topic of sleep.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1QuestionHow tall is each player on the basketball team?
    2. 2Student decisionThis is NOT a statistical question.
    3. 3Student reasonHeight is just one number, so every answer will be the same.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The word "each" is a clue that you need data from many players.

    Correct work
    Correct answer:

Explain your thinkingWhat pattern do you notice about statistical questions compared to non-statistical questions?

Sentence starter Statistical questions expect ___ in the answers because ___. Non-statistical questions have only ___ answer because ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    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?
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match each question with what makes it statistical or not.

    1. How fast does each sprinter run the 100m?
    2. How long is an Olympic pool?
    3. How many goals did each player score this season?
    4. How many innings are in a baseball game?
    • AVariability — Statistical
    • BOne answer — Not Statistical
    • CVariability — Statistical
    • DOne answer — Not Statistical
  3. 3Write the name of the correct group on each line.

    Match each non-statistical question with its statistical rewrite.

    Groups: 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?'
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A coach asks: "How many hours does each athlete on the track team sleep the night before a meet?" Why is this a statistical question?

    1. ABecause it is about sports
    2. BBecause it has a numerical answer
    3. CBecause the answers will vary from athlete to athlete
    4. DBecause the whole track team is asked
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    Which of these is a statistical question?

    1. AWhat time is it right now?
    2. BWhat is my shoe size?
    3. CWhat is 7 × 8?
    4. DHow tall are the students in my class?
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1QuestionHow many points did the team score in its last completed game?
    2. 2Student decisionThis IS a statistical question.
    3. 3Student reasonIt is about basketball and the answer is a number, so it must be statistical.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhat pattern do you notice about statistical questions compared to non-statistical questions?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.1

Lesson 2.1Understand Statistical Questions

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can tell the difference between a statistical question and a non-statistical question.

Why This Matters You've just been hired as the data analyst for a youth basketball league. The head coach hands you a list of questions the staff wants to investigate about their players. Some questions will give you interesting data with variety, while others have just one fixed answer. Your job: figure out which questions are worth investigating with data. Two of the coach's questions are: "How tall is our point guard?" and "How tall is each player on the roster?"

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Rewrite each non-statistical question to make it statistical and explain the variability.

    Non-Statistical QuestionRewritten as StatisticalWhat Variability Exists?
    How many players are on the team?
    What sport does this league play?
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    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
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    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 are the resting heart rates of students in my class?
    4. DWhat is the teacher's heart rate?
    Show your work
Part 3Explain and correctreasoning
  1. 4Find the mistake. Explain it, then show the correct work.

    Find the Reasoning Error

    1. 1QuestionHow many touchdowns did the quarterback throw in each game this season?
    2. 2Student saysThis is NOT a statistical question.
    3. 3ReasonIt only asks about one player, so there is no variability.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 5Answer in complete sentences.

    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.

    Write your answer

Explain your thinkingWhat pattern do you notice about statistical questions compared to non-statistical questions?

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help