School Improvement in Maryland

Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.

Goal 3 Data Analysis And Probability

Expectation 3.1 The student will collect, organize, analyze, and present data.

Indicator 3.1.1 The student will design and/or conduct an investigation that uses statistical methods to analyze data and communicate results.

Assessment Limits:

  • The student will design investigations stating how data will be collected and justify the method.
  • Types of investigations may include: simple random sampling, representative sampling, and probability simulations.
  • Probability simulations may include the use of spinners, number cubes, or random number generators.
  • In simple random sampling each member of the population is equally likely to be chosen and the members of the sample are chosen independently of each other. Sample size will be given for these investigations.

Brief Constructed Response (BCR) Item - Released in 2001

The administration of Central High School has decided to add a new sport for next year's ninth-grade girls. They are considering adding either soccer, tennis, or track. The administration needs to design an investigation in which 30 ninth-grade girls are surveyed to decide which new sport next year's ninth-grade girls would prefer.

Complete the following in the answer box below:
  • Based on simple random sample principles, explain at least two of the key elements that should be part of the administration's design.

/share/clg/xml/public_release/mathematics/2001_311_alg29.xml

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Brief Constructed Response (BCR) Item - Released in 2002

Apples from an orchard need to be sampled to see if they are sweet enough for juice. The orchard has 25,000 apple trees. Each tree has at least 1,000 apples.

Alfred suggests, “Randomly choose one tree and test 500 apples from that tree.”

Betsy suggests, “Randomly choose 1,000 trees and test one apple from each tree.”

Complete the following in the answer box below:
  • Whose suggestion gives a sample that is more representative of the apples in the orchard? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2002_311_alg22.xml

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Brief Constructed Response (BCR) Item - Released in 2003

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.
Option 1:     Spend five days in the sock department of a randomly selected store and ask every person who enters what color socks they buy.
Option 2:     Spend one day in the sock departments of five randomly selected stores in randomly selected cities and ask every teenager who enters what color socks they buy.
Option 3:     Spend one day in eight randomly selected shopping centers and ask ten randomly selected teenagers at each shopping center what color socks they buy.
Complete the following in the answer box below:
  • Which option gives the company the most representative sample of sock colors that teenagers will buy?
  • Use mathematics to justify why the other two options do not give the company the most representative sample.

/share/clg/xml/public_release/mathematics/2003_311_alg06.xml

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Selected Response Item - Released in 2005

Steve is a member of the baseball team. He averages 2 hits for every 5 times at bat. Steve might get a hit his next time at bat. Which of these methods could not be used to simulate this situation?

  1. Flip a fair coin once. Let heads represent a hit and let tails represent not getting a hit.
  2. Use a random number generator. Let 1 and 5 represent a hit and let 2, 3, and 4 represent not getting a hit.
  3. Spin a spinner with 10 equally-sized sections. Let 4 sections represent getting a hit and let 6 sections represent not getting a hit.
  4. Draw a marble from a bag that contains 8 red and 12 blue marbles. Let a red marble represent getting a hit and let a blue marble represent not getting a hit.
/share/clg/xml/public_release/mathematics/2005_311_alg27.xml

Correct Answer:
A

Brief Constructed Response (BCR) Item - Released in 2005

A high school principal is meeting with the PTA to discuss the amount of time students spend doing homework each day. He asked a teacher to gather data for the parents. The teacher is going to survey 25 students from a student body of 1,000 students. Consider the methods of sampling shown below.

Method 1: randomly select 25 students from honors classes

Method 2: select 25 members of the girls' varsity softball team at random

Method 3: use a random number generator to generate 25 random numbers and use these to select 25 students from a numerical list of the students

Method 4: randomly select 25 classrooms and ask the teacher in each classroom to select a student

Complete the following in the Answer Book:

  • Which of the above methods of sampling would give the most representative random sample of the student population? Use mathematics to justify your answer. Include in your justification why you chose that method and why you did not choose each of the other three methods.

/share/clg/xml/public_release/mathematics/2005_311_alg35.xml

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Selected Response Item - Released in 2003

A teacher conducts a random survey to determine how many students use the school library on a regular basis. Which of these methods would provide the teacher with a simple random sample?

  1. Choose every 3rd student that enters the library on Monday.
  2. Select 50 students from the list of students who have perfect attendance.
  3. Choose the name of every 10th student in her grade book until 30 names are selected.
  4. Number every student in the school and then generate random numbers to select 50 students.
/share/clg/xml/public_release/mathematics/2003_311_alg23.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2006

A cereal company awards a prize to anyone who collects all 5 different game pieces. Each game piece has an equal chance of being placed in a box of cereal. Each box of cereal contains only 1 game piece.

Complete the following in the Answer Book:

  • Design a simulation of at least 30 trials that can be used to estimate how many boxes of cereal a person needs to buy to collect all 5 different game pieces. Describe how to collect and interpret the data so that you have confidence in the estimation.

/share/clg/xml/public_release/mathematics/2006_311_alg06.xml

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Selected Response Item - Released in 2006

Inés wants to conduct a survey to determine how many customers see the advertisement for her store. Which of these methods provides Inés with the most representative sample of her customers?

  1. Survey customers who live near her store.
  2. Survey customers who shop at her store on weekends.
  3. Survey customers who shop at her store early in the morning.
  4. Survey customers who shop at her store at different times throughout the week.
/share/clg/xml/public_release/mathematics/2006_311_alg30.xml

Correct Answer:
D

Brief Constructed Response (BCR) Item - Released in 2007

The principal will survey 100 students to determine which elective courses to offer next year. The principal will use one of the methods below.

Method A: Survey the first 100 students who enter the cafeteria on a randomly selected day.

Method B: Have 25 teachers each randomly select 4 eleventh-grade students to be surveyed.

Method C: Assign each student a number. Use a random number generator to generate 100 numbers. Survey those students whose numbers are generated.

Complete the following in the Answer Book:

  • Which method will provide the principal with a simple random sample of the student population? Use principles of simple random sampling to justify your answer.
  • Use principles of simple random sampling to justify why each of the other two methods does not provide a simple random sample.

/share/clg/xml/public_release/mathematics/2007_311_alg32.xml

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Selected Response Item - Released in 2007

The table below shows the number of students in a high school by grade level.

A student is selected at random. Which spinner below would best simulate the grade level of the student?





/share/clg/xml/public_release/mathematics/2007_311_alg33.xml

Correct Answer:
D
Resources for 3.1.1:
Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |