# MAFS.8.SP.1.4Archived Standard

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
General Information
Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Statistics & Probability
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Investigate patterns of association in bivariate data. (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
Test Item Specifications

• Assessment Limits :
Numbers in items must be rational numbers. Data given should include the grand total of the survey. Tables must not include more than two columns (plus category and total) and two rows (plus category and total).
• Calculator :

Yes

• Context :

Required

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question: Two hundred sixty students were surveyed on whether they prefer apple juice or orange juice. A table of relative frequencies is shown.

How many more girls prefer apple juice than boys?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 2
• Question:

Five hundred students were asked whether they prefer apple juice or orange juice. The table shown displays the results.

How many more girls were surveyed than boys?

• Difficulty: N/A
• Type: EE: Equation Editor

• Test Item #: Sample Item 3
• Question:

The manager of an ice cream shop is considering which ice cream flavor to offer as the special flavor next month. She asks 175 people whether they like mint or strawberry ice cream.

The manager wants to increase sales, so she is deciding whether to offer mint or strawberry ice cream.

Complete the sentence to support the best decision based on the relative frequencies in the table.

The manager should offer _____ ice cream because _____ of the customers surveyed like mint and _____ of the customers like strawberry.

• Difficulty: N/A
• Type: ETC: Editing Task Choice

## Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002080: M/J Comprehensive Science 2, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002110: M/J Comprehensive Science 3, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1508400: M/J Extreme/Alternative Sports - Grade 8 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
1508500: M/J Individual/Dual Sports - Grade 8 (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
2002055: M/J Comprehensive Science 1 Accelerated Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
2002085: M/J Comprehensive Science 2 Accelerated Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1508040: M/J Extreme/Alternative Sports - Grade 8 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
1508050: M/J Individual/Dual Sports - Grade 8 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Two-Way Relative Frequency Table:

Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

Type: Formative Assessment

School Start Time:

Students are asked to describe an association between two variables given a table of relative frequencies by column.

Type: Formative Assessment

Music and Sports:

Students are asked to construct a two-way frequency table given a set of raw data.

Type: Formative Assessment

Siblings and Pets:

Students are asked to describe an association between two variables given a table of relative frequencies by row.

Type: Formative Assessment

## Lesson Plans

Where Should We Move? STEM Lesson Plan:

Students will collect data to identify planet composition, average temperature, and the distance of some planets within the Milky Way Galaxy from the Sun. Students will complete two-way tables to make comparisons. Students will then analyze and interpret their data. Students will make inferences and justify their reasoning.

Type: Lesson Plan

Height Arm Juxtaposition:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and arm length. Using technology the students will explore in-depth how to perform a least square regression as a procedure for determining the line of best fit.

Type: Lesson Plan

Two-Way Math Survey:

In this lesson, students will construct a two-way table based on data given. They will interpret the data to find if there is a correlation between the two variables from the same subject. As the lesson progresses, students will create their own testable questions that they will collect data on using the survey method. Students will show their mastery of this math concept with the presentation of the data in a two-way table and interpretation of the data to draw inferences.

Type: Lesson Plan

Tackling 2 Way Tables:

This highly engaging and interactive lesson will have students constructing 2 way tables, calculating relative frequency and analyzing the bivariate data to determine a possible association between the two variable categories.

Type: Lesson Plan

## Problem-Solving Tasks

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Type: Problem-Solving Task

What's Your Favorite Subject?:

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

Type: Problem-Solving Task

## Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Virtual Manipulatives

Univariate and Bivariate Data:

This lesson is designed to introduce students to the difference between univariate and bivariate data, and how the two can be represented graphically. This lesson provides links to model discussions and online graphing applets, as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

## MFAS Formative Assessments

Music and Sports:

Students are asked to construct a two-way frequency table given a set of raw data.

School Start Time:

Students are asked to describe an association between two variables given a table of relative frequencies by column.

Siblings and Pets:

Students are asked to describe an association between two variables given a table of relative frequencies by row.

Two-Way Relative Frequency Table:

Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Problem-Solving Tasks

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Type: Problem-Solving Task

What's Your Favorite Subject?:

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

Type: Problem-Solving Task

## Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Problem-Solving Tasks

Music and Sports:

This task asks the student to gather data on whether classmates play an instrument and/or participate in a sport, summarize the data in a table and decide whether there is an association between playing a sport and playing an instrument. Finally, the student is asked to create a graph to display any association between the variables.

Type: Problem-Solving Task

What's Your Favorite Subject?:

Students are asked to examine data given in table format and then calculate either row percentages or column percentages and state a conclusion about the meaning of the data. Either calculation is appropriate for the solution since there is no clear relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and demonstrates understanding that an association means the distribution of favorite subject is different for 7th graders and 8th graders.

Type: Problem-Solving Task