**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Statistics & Probability: Interpreting Categorical & Quantitative Data

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Summarize, represent, and interpret data on two categorical and quantitative variables. (Algebra 1 - Supporting Cluster) (Algebra 2 - Supporting 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

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

In data with only two categorical variables, items should require the

student to determine relative frequencies and use the frequencies

to complete the table or to answer questions**Calculator :**Neutral

**Clarification :**

Students will create or complete a two-way frequency table to

summarize categorical data.Students will determine if associations/trends are appropriate for

the data.Students will interpret data displayed in a two-way frequency table.

Students will calculate joint, marginal, and conditional relative

frequencies.**Stimulus Attributes :**

Items should use real-world data and be set in a real-world context.**Response Attributes :**

Items may require the student to apply the basic modeling cycle.Items may require the student to choose an appropriate level of

accuracy.Items may require the student to choose and interpret units.

**Test Item #:**Sample Item 1**Question:**A high school drama teacher organizes a musical production. He wants to record the number of students involved in each part of the production . He uses a two-way table to display the data.

The drama teacher knows that approximately 55% more girls participate in the production as actors than as stage crew members.

Complete the two-way table to show a possible breakdown of students.

**Difficulty:**N/A**Type:**TI: Table Item

## Related Courses

## Related Access Points

## Related Resources

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Task

## Text Resource

## Unit/Lesson Sequence

## Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

This is a model-eliciting activity where students have been asked by a new website, CollegeReview.com, to come up with a system to rank various colleges based on five categories; tuition cost, social life, athletics, education, city population and starting salary upon graduation.

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. Click here to learn more about MEAs and how they can transform your classroom.

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.**

## MFAS Formative Assessments

Students are asked to use data from a survey to create a two-way frequency table.

Students are asked to use a two-way frequency table to interpret two different conditional relative frequencies.

Students are asked to use a two-way frequency table to interpret marginal and joint relative frequencies.

Students are given a two-way frequency table and asked to determine if there is a relationship between the two variables.

## Original Student Tutorials Mathematics - Grades 9-12

Learn to define, calculate, and interpret marginal frequencies, joint frequencies, and conditional frequencies in the context of the data with this interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn to define, calculate, and interpret marginal frequencies, joint frequencies, and conditional frequencies in the context of the data with this interactive tutorial.

Type: Original Student Tutorial

## Educational Software / Tool

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

- Modify column and row headings to match your data.
- Input joint frequency data.
- Click the second tab at the bottom of the window to see the automatic calculations.

Type: Educational Software / Tool

## Problem-Solving Task

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task

## Parent Resources

## Problem-Solving Task

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task