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Fair samples: 7th grade math

Random sampling; inference about populations; comparing two populations. A free 7th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: random sampling; inference about populations; comparing two populations.

Teach (10 min)

  • The population is the whole group you want to know about. A sample is a part of it.
  • A random sample gives everyone the same chance, so it is fair. Asking only friends or only one group is biased.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/chance.sampling?lesson=7-chance-sampling-1&at=7

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. A random sample of 50 students from a school of 500 found that 10 walk to school. About how many of the 500 students walk?
  • 2. Which is a random sample of 30 students from a class of 90?
  • 3. A city wants to know how many residents ride the bus. Which sample is most likely to represent all the residents?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. A random sample of 50 students from a school of 500 found that 10 walk to school. About how many of the 500 students walk?
  2. Which is a random sample of 30 students from a class of 90?
  3. A city wants to know how many residents ride the bus. Which sample is most likely to represent all the residents?
  4. Which is a random sample of 30 students from a class of 90?
  5. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
  6. A random sample of 50 students from a school of 500 found that 10 walk to school. About how many of the 500 students walk?
  7. A student asks 10 friends at lunch and 8 say they like soccer. The student says, "80% of the school likes soccer." What is the problem?
  8. Two random samples are taken from the same town to estimate how many people own a bike. One has 20 people and one has 400. Which gives the better estimate?
  9. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
  10. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
Answers
  1. about 100 students
  2. Put every name in a hat and draw 30
  3. 200 residents chosen by a computer from a list of everyone
  4. Put every name in a hat and draw 30
  5. Only people who already visit the park were asked, so they may like it more than others do
  6. about 100 students
  7. The sample is small and made of friends, so it may not represent the school
  8. the sample of 400 people
  9. Only people who already visit the park were asked, so they may like it more than others do
  10. Only people who already visit the park were asked, so they may like it more than others do

Printable sheet

Name: ____________________   Date: ____________

Fair samples (7th grade)

  1. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
  2. A principal wants to know the favorite lunch of all 600 students. Which sample is most likely to represent the whole school?
  3. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
  4. Which is a random sample of 30 students from a class of 90?
  5. To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
  6. To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
  7. To learn whether people in a city like a new park, a surveyor asks 100 people as they leave the park. Why might this sample be a poor one?
  8. Which is a random sample of 30 students from a class of 90?
  9. To find the average height of all 7th graders in a district, a researcher measures 80 of them. What is the population?
  10. Two random samples are taken from the same town to estimate how many people own a bike. One has 20 people and one has 400. Which gives the better estimate?
  11. Which is a random sample of 30 students from a class of 90?
  12. A teacher wants to estimate how many of 1,000 students own a pet. Which sample is best?
Key
  1. Only people who already visit the park were asked, so they may like it more than others do
  2. 40 students chosen at random from the school's list
  3. Only people who already visit the park were asked, so they may like it more than others do
  4. Put every name in a hat and draw 30
  5. all 7th graders in the district
  6. all 7th graders in the district
  7. Only people who already visit the park were asked, so they may like it more than others do
  8. Put every name in a hat and draw 30
  9. all 7th graders in the district
  10. the sample of 400 people
  11. Put every name in a hat and draw 30
  12. 100 students chosen at random from the roster

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.