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Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. ★
Standard #: MAFS.912.S-CP.1.4Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Statistics & Probability: Conditional Probability & the Rules of Probability
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand independence and conditional probability and use them to interpret data. (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
Related Resources
Educational Software / Tool
  • Two Way Frequency Excel Spreadsheet # This Excel spreadsheet allows the educator to input data into a two way frequency table and have the resulting relative frequency charts calculated automatically on the second sheet. This resource will assist the educator in checking student calculations on student-generated data quickly and easily. Steps to add data: All data is input on the first spreadsheet; all tables are calculated on the second spreadsheet
    1. Modify column and row headings to match your data.
    2. Input joint frequency data.
    3. Click the second tab at the bottom of the window to see the automatic calculations.
Lesson Plans
  • Comedy vs. Action Movies Frequency Interpretation # Using a completed survey of male and female student interest in comedy vs. action movies, the students will create a two-way frequency table using actual data results, fraction results, and percent results. The students will then act as the movie producer and interpret the data to determine if it is in their best interest to make a comedy or action movie. As the Summative Assessment, the student will take on the job/role of an actor/actress and interpret the data to support their decision.
  • Modeling Conditional Probabilities 1: Lucky Dip # This lesson unit is intended to help you assess how well students are able to understand conditional probability, represent events as a subset of a sample space using tables and tree diagrams, and communicate their reasoning clearly.
  • Modeling Conditional Probabilities 2 # This lesson unit is intended to help you assess how well students understand conditional probability, and, in particular, to help you identify and assist students who have the following difficulties representing events as a subset of a sample space using tables and tree diagrams and understanding when conditional probabilities are equal for particular and general situations.
  • Medical Testing # This lesson unit is intended to help you assess how well students are able to:
    • make sense of a real life situation and decide what math to apply to the problem
    • understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model
    • represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams
    • interpret the results and communicate their reasoning clearly
  • The Music Is On and Popping! Two-way Tables # This MEA is designed to have teams of 4 students look at data in a two-way table. Teams must discuss which categorical or quantitative factors might be the driving force of a song's popularity. Hopefully, popular songs have some common thread running through them.

    Each team must write down their thought process for creating the most popular playlist of songs for a local radio station. A major constraint for each team is explaining how they will maximize the 11 minutes available with the most popular songs.

    Students will be provided with letters from a local radio station, WMMM - where you can receive your "Daily Mix of Music and Math." WMMM has 10 songs and the researchers have collected data on each. Student teams: it is your responsibility to pick the playlist and write a letter to the station supporting why you made your selection. The winning team gets an opportunity to record a sound bite to introduce their playlist on the radio.

    Now, just when the teams believe they have addressed WMMM's request, a twist is thrown in the midst, and the student teams must return to the drawing board and write a second letter to the station which may or may not affect the team's original playlist.

    Do you have the musical swag to connect the associations? Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx.
Problem-Solving Tasks
  • How Do You Get to School? # This task requires students to use information in a two-way table to calculate a probability and a conditional probability.
  • The Titanic 2 # This task lets students explore the concepts of probability as a fraction of outcomes using two-way tables.
  • The Titanic 1 # This task asks students to calculate probabilities using information presented in a two-way frequency table.
  • The Titanic 3 # This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.
STEM Lessons - Model Eliciting Activity
  • The Music Is On and Popping! Two-way Tables # This MEA is designed to have teams of 4 students look at data in a two-way table. Teams must discuss which categorical or quantitative factors might be the driving force of a song's popularity. Hopefully, popular songs have some common thread running through them.

    Each team must write down their thought process for creating the most popular playlist of songs for a local radio station. A major constraint for each team is explaining how they will maximize the 11 minutes available with the most popular songs.

    Students will be provided with letters from a local radio station, WMMM - where you can receive your "Daily Mix of Music and Math." WMMM has 10 songs and the researchers have collected data on each. Student teams: it is your responsibility to pick the playlist and write a letter to the station supporting why you made your selection. The winning team gets an opportunity to record a sound bite to introduce their playlist on the radio.

    Now, just when the teams believe they have addressed WMMM's request, a twist is thrown in the midst, and the student teams must return to the drawing board and write a second letter to the station which may or may not affect the team's original playlist.

    Do you have the musical swag to connect the associations? Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx.
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