CH05-01 lesson

Statistical Questions Learning Activity

A focused Grade 6 learning session for Statistical Questions using visual models, worked examples, strategy guidance, and a short mastery check.

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15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 6 mastery of statistical questions using models, equations, and test-style reasoning.

Student goal: I can solve problems involving statistical questions.

concept

Learn the Idea

Statistical Questions means choosing a model, naming what each number means, and explaining the strategy.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.
visual model

See the Math

Visual Model 1

Question: Read the question in the box below: Is this a statistical question, and why or why not?

Visual Model 1

  • A. No, because it asks about a team that has a fixed number of players.
  • B. Yes, because it asks about many different heights.
  • C. No, because basketball teams always have the same average height.
  • D. Yes, because you must collect data from many players whose heights vary.

Why it works: This is statistical because team members have different heights and you must collect data from multiple sources. The number of people or a team's fixed size does not prevent variability—different players still have different heights.

Answer: Yes, because you must collect data from many players whose heights vary.

worked example

Follow a Worked Example

Example 1

Question: A restaurant manager asks customers: "How much time did you spend eating lunch today?" Here are responses (in minutes): What does this data show about the question?

2545305035
  • A. The question is non-statistical.
  • B. Everyone spends the same time eating lunch.
  • C. The question is statistical because responses vary.
  • D. Lunch time is always 30 minutes.
  1. The different responses (25, 45, 30, 50, 35 minutes) demonstrate that this question has variability and requires data collection, which are hallmarks of a statistical question.

Answer: The question is statistical because responses vary.

Example 2

Question: Consider these two questions: Which statement is correct?

Question AQuestion B
What is the weight of my dog?What are the weights of dogs in my neighborhood?
  • A. Both are statistical.
  • B. Question A is statistical; Question B is not.
  • C. Question A is non-statistical; Question B is statistical.
  • D. Neither is statistical.
  1. Question A asks about one dog (one answer).
  2. Question B asks about multiple dogs, whose weights vary, requiring data collection—making it statistical.

Answer: Question A is non-statistical; Question B is statistical.

real world

Connect It to a Real Situation

Problem 1

Question: A student rewrites a non-statistical question to make it statistical. Which is the BEST rewrite? Original: "How old is my teacher?"

  • A. How old are the teachers at our school?
  • B. In what year was my teacher born?
  • C. How many teachers are there?
  • D. What is the average age of all teachers in the United States?

Why it works: Rewriting "How old is my teacher?" to "How old are the teachers at our school?" introduces variability (different teachers have different ages) and requires collecting multiple data points. Options B, C, and D don't improve the statistical nature of the original question.

Answer: How old are the teachers at our school?

strategy

Avoid Mistakes and Choose a Strategy

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.
  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.
summary

Remember the Key Idea

Statistical Questions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G6-C05-T01-Q001 About 1 min

Which of these is a statistical question?

  1. A How tall am I?
  2. B What is the capital of Texas?
  3. C How many minutes do students in my class spend on homework each night?
  4. D How many days are in a year?
Check answer and explanation

Answer C: How many minutes do students in my class spend on homework each night?

A statistical question anticipates variability and is answered by collecting data. Homework time varies across students, so that question is statistical; the others have a single fixed answer.

G6-C05-T01-Q002 About 1 min

Which question is NOT statistical?

  1. A What was the temperature each day last week?
  2. B How many hours do sixth graders sleep each night?
  3. C What is the favorite sport of students in this school?
  4. D What is the boiling point of water?
Check answer and explanation

Answer D: What is the boiling point of water?

The boiling point of water has one fixed answer (100°C at sea level). The other questions all involve variability and require collecting data from multiple sources, making them statistical.

guided

1 question
G6-C05-T01-Q003 About 1 min

A student rewrites a non-statistical question to make it statistical. Which is the BEST rewrite? Original: "How old is my teacher?"

  1. A How old are the teachers at our school?
  2. B In what year was my teacher born?
  3. C How many teachers are there?
  4. D What is the average age of all teachers in the United States?
Check answer and explanation

Answer A: How old are the teachers at our school?

Rewriting "How old is my teacher?" to "How old are the teachers at our school?" introduces variability (different teachers have different ages) and requires collecting multiple data points. Options B, C, and D don't improve the statistical nature of the original question.

practice

5 questions
G6-C05-T01-Q004 About 1 min

Which statement BEST describes a statistical question?

  1. A It has a single, definite answer.
  2. B It involves a very large number of people.
  3. C It is asked only once per year.
  4. D It anticipates variability and is answered by collecting data.
Check answer and explanation

Answer D: It anticipates variability and is answered by collecting data.

By definition, a statistical question expects different answers from different sources and requires collecting and analyzing data. The size of the number or frequency of asking does not define a statistical question.

G6-C05-T01-Q005 About 1 min

A survey asks: "How many hours did you spend reading last week?" What is the population for this question?

  1. A All the people whose reading time is being studied
  2. B Hours of the day
  3. C Books in the library
  4. D The number 7
Check answer and explanation

Answer A: All the people whose reading time is being studied

The population is the entire group of people you want to learn about. In this survey, that group consists of all people whose reading hours the question targets (which could be all students in a class, all sixth graders, etc.).

G6-C05-T01-Q006 About 1 min

A student asks: "How many hours per week do students in my grade spend exercising?" Why is this a statistical question?

  1. A Because exercise is healthy.
  2. B Because it involves numbers and hours.
  3. C Because different students exercise different amounts, requiring data from many people.
  4. D Because the question is asked in science class.
Check answer and explanation

Answer C: Because different students exercise different amounts, requiring data from many people.

Variability (different exercise times) and multiple data sources (many students) are what make it statistical. Context (class, subject) and topic alone do not define a statistical question.

G6-C05-T01-Q007 About 1 min

A researcher asks students: "How many minutes did you exercise yesterday?" Which describes the population being sampled?

  1. A All students in the school
  2. B The number of minutes in a day
  3. C The students who answered the survey
  4. D All sixth graders in the state
Check answer and explanation

Answer A: All students in the school

If this survey asks all students in the school, that is the population. The sample would be the subset of students who actually answered the survey. Option C describes the sample, not the population.

G6-C05-T01-Q008 About 1 min

Which question would produce the MOST variability in answers?

  1. A What time does lunch start at your school?
  2. B How many legs do dogs have?
  3. C What year was the Statue of Liberty built?
  4. D How many siblings do you have?
Check answer and explanation

Answer D: How many siblings do you have?

This question would produce the most variability: different students have different numbers of siblings (0, 1, 2, 3, etc.). The other questions have fixed or nearly-fixed answers across a group.

exit

3 questions
G6-C05-T01-Q009 About 1 min

Consider: "What is the average age of people in my city?" Why is this a statistical question?

  1. A Because it asks about a large group of people.
  2. B Because people have different ages and data must be collected.
  3. C Because it uses the word "average."
  4. D Because age is a number.
Check answer and explanation

Answer B: Because people have different ages and data must be collected.

The key feature of a statistical question is that it expects variability in the data. Since people in a city have different ages, you must collect data from many people and calculate. Using "average" or "large group" alone does not make it statistical.

G6-C05-T01-Q010 About 1 min

A teacher asks: "How many books did each student read last month?" What is the sample in this scenario?

  1. A All students in the entire state
  2. B The students in the class who answered the question
  3. C The number of books
  4. D All books in the library
Check answer and explanation

Answer B: The students in the class who answered the question

A sample is a subset of the population. The students who answered are the sample; the full population would be all students you want to study (e.g., all sixth graders).

G6-C05-T01-Q011 About 1 min

Read the question in the box below: \tcbox[colback=lightyellow, colframe=midnight, boxrule=1pt]{% "How tall are the players on the basketball team?" } Is this a statistical question, and why or why not?

  1. A No, because it asks about a team that has a fixed number of players.
  2. B Yes, because it asks about many different heights.
  3. C No, because basketball teams always have the same average height.
  4. D Yes, because you must collect data from many players whose heights vary.
Check answer and explanation

Answer D: Yes, because you must collect data from many players whose heights vary.

This is statistical because team members have different heights and you must collect data from multiple sources. The number of people or a team's fixed size does not prevent variability—different players still have different heights.

Keep the learning path connected
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