Our team focused on the following standard for our learning cycle:
7.SP.1 Use random sampling to draw inferences about a population.

1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.


The mathematics in our learning cycle is about :
The mathematics in our learning cycle is about determining whether a statistic is valid. This will also include developing a plan to collect a representative sample.
Our goal statement is:
The goal of this learning cycle is to distinguish between a sample and a population and consider various ways to develop a sampling plan in order to make predictions about a population.
Our develop understanding task is: Is it Fair?
Students will be given the results of different surveys. They will determine whether the survey results are valid (fair) and why?
In our develop understanding task, we wish to surface ideas such as:
Are survey results valid (fair)?
What makes a survey fair/unfair?
How can we make a survey more fair?
The solidify task we chose is: Sampling Methods
Given several situations in which a sample is collected, can students determine whether a conclusion is fair.
The solidify goal is:
Students need to understand convenience sampling, voluntary response sampling and random sampling and use the appropriate vocabulary.
The practice task we chose is: Statistics on Target
Students are to develop a sample collection model to determine a statistic about a population.
The practice goal is:
Students will refine their understanding that a random sample increases the likelihood of obtaining a representative sample of a population.
Our essential idea is finishing the sentence: “A statistic is valid when...” This will also include developing a plan to collect a representative sample.
Our Goal statement is: students will be able to distinguish between valid and invalid random samples
Disclaimer: All tasks referenced do not yet exist on paper, but in the minds of teachers.
Task 1: “Is This Fair”
Objective: Develop understanding. Surface student thinking that not all surveys are going to give valid results.
-develop the ideas of fair and bias and what make a sample bias/unbiased?
-draw on students concept of fairness.
-Develop vocabulary words of: Population, survey, sample, bias, unbiased
Sample Task 1A:
Think, Pair, Share, Printable worksheet
“No More Pizza”

Lesson Opener:
Teachers decide to get rid of pizza Fridays. After a survey of all teachers, counselors, and administrators, it was overwhelmingly decided that pizza would be replaced with broccoli w/ranch sauce.

From what specific population is each of these samples taken? Write down a detailed description of the specific characteristics of the population in the second column. The first one is done for you.

We will fill in the THIRD COLUMN together during a class discussion.

Method of Sampling Description of population Type of Sample

Call every hundredth name in the phonebook / People with home phones who also have their numbers Listed.
Survey people at the bowling alley during the Wednesday night men’s bowling leagues / Convenience Sample
Survey people who come to the “Vote Now” booth at the high school Football game.
Ask every tenth student entering a high school basketball game.
Haphazardly survey students in both the first and second lunches.
Text responses to online “instant” poll.
Handout surveys to the students who are in the library before school.
Survey all students in first period English class.

CPM 8.2.1: 8-31

Students are anticipated to react and respond with reasons why the survey results aren’t valid(fair).
*Possible Questions:
-Who would be pleased with the results of the survey? Why? *Who would not like the results of the survey? Why?
-Who is the population?
-What characteristic of this survey could we change to make the situation fair?
-What could we do to make the survey more fair or accurate?
Sample Task 1B:
(Present situation and statistic first without telling students who was actually surveyed. After students interpret the statistic, tell them who the population is or discuss who might have been the sample population i.e. Girl’s P.E. classes, FACs classes, etc)
“Early lunch”

After surveying 83 students in three classes, 70% responded that girls should be allowed to go to lunch two minutes early every day and boys will go at the regular time.


-Do you think this is an accurate statistic? Why or Why not?
-What would have made this inaccurate?
-Who do you think the sample population was? Who would the statistic biased towards?
-Who is the population?
-Who would we include in our sample survey that produce a more unbiased statistic?
Task 2: Sampling Methods
Objective: Solidify understand. Explore, examine, and extend student thinking of the advantages and disadvantages of multiple sampling methods.
Sample task 2A: (include a convenience sample, voluntary response, random samples)

Mrs. Smith’s class wants to conduct this survey about hours spent sleeping and watching movies. They plan to survey students in their school. The class divides into 3 groups. Each group devises a plan for sampling the school population.
* Each member of Group 1 will survey the students who ride on his or her own bus.
* Group 3 will post a notice in the morning announcements asking for volunteers for their survey.
* Group 2 will randomly select 30 students for their survey from a list of three-digit student ID numbers. They will label the faces of a 10-sided solid with the numbers 0 through 9 and roll the die three times to generate each number.
*Students need to discuss which method(s) would best be representative of the population.
*Then teacher put up results of the surveys. Discuss which methods would lead to the most accurate predictions for students in the whole school and why.


Sample Task 2B: ( include a convenience sample, voluntary response, random samples)

There is a plan being discussed to build a skate park in a neighborhood. The city wants to have feedback to see if this is going to used and well received by the community. The city sends out a newsletter and asks for people to respond with their opinion. There is a poll taken at the mall in the community on a Saturday afternoon. Also a group is also hired to go to every third house in the surrounding neighborhood to ask their opinion of the skateboard park being built in the open field in the neighborhood.
1. What are the advantages and disadvantages of each sampling plan?
2. Which sample form do you think achieved the best representation of the population? Why?
3. Which sample form would be the least representative of the population? Why?
4. Can you think of a better way to have a true representation of the population? Why?
(Develop characteristics of a representative sample)


Debriefing discussion: The students need to realize that there are different methods of sampling that are more and less likely to be representative. Students need to understand convenience sampling, voluntary response sampling and random sampling and use the appropriate vocabulary.
Task 3: “Statistics on target”
Objective: Practice understanding.
*You are create a sample question to determine a statistic about a population.
Start as a class discussion of possible survey topics that use the student body as a target population. Make a list on the board. Assign topics to groups from the list. Each group is to develop a survey method.
-Who are you going to ask?
-What are you going to ask them?
-Look at ways of collecting samples.
-Who is the population?
-How are you going to ask people?
-How are you going to get responses?
-Who responds?
-It the sample representative of the whole population?
-Identify target population and method of sampling.
-Which types of samples lead to fair conclusions?
Explicitly write out a plan to collect the sample—include who, what, when, where, etc.
Groups will exchange plans for scrutiny of sampling method. (Could they end up with biased results?)
Class discussion will follow.