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Correlation and Causation *

S-ID.9, S-ID.8, S-ID.7: Explore data that highlights the difference between correlation and causation. Understand and use correlation coefficients, where appropriate. (CDE 2023, 57)

California Department of Education. 2023. Mathematics Framework Chapter 8. Sacramento, CA: California Department of Education.

Big Idea Success Criteria

The categories and their related standards below unpack the success criteria of this big idea.

Primary Standards

  • Interpret linear models. (S-ID.7–9) (CDE 2013, 94)
    • S-ID.7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data (CDE 2013, 94).
    • S-ID.8. Compute (using technology) and interpret the correlation coefficient of a linear fit (CDE 2013, 94).
    • S-ID.9. Distinguish between correlation and causation (CDE 2013, 94).

California Department of Education. 2013. California Common Core State Standards. Sacramento, CA: California Department of Education.

Alternative Means of Expression

The following options give educators and IEP teams viable alternative means of expression a student could use when showing their understanding of this big idea. Much of the initiative team’s approach to identifying options centered on developing or adopting performance tasks to show what assessment might look like for this big idea.

Remember, LEAs adopt their own policies related to how a student meets the requirements for graduation. Educators and IEP teams should explore these resources with knowledge of these local policies.

General Guidance with Selecting Options for this Big Idea

For correlation and causation, students could complete a simplified number of data points to compute and interpret the correlation and then demonstrate their knowledge of the strength of the correlation verbally, in writing, or through a presentation (e.g. google slides, powerpoint, etc.) Then they can use the same expression format, such as a presentation, to describe how two variables being related does not indicate that one variable caused the other. Students can match data sets to their correlation strengths and graphs, then verbally or in writing explain that strong correlation does not imply causation.

Sample Coursework

Project Created Performance Task

Alternate Means of Expression Option 1 is a performance task created by the project team that represents a viable alternate means of expression a school, district, teacher, or IEP team could utilize as an assessment option for this big idea.

Click the link below to download this document. Click the “comment” and the “thumb up / thumb down” buttons above to leave feedback upon completion of your review.

Integrated Mathematics I Variability and Corr/Cause (Teacher Guide)

This performance task evaluates students’ understanding of key concepts within the Integrated 1 Variability and Correlation and Causation Big Ideas. It is divided into parts, each targeting a specific component of the Big Ideas. Each part offers accessible strategies and examples of how students can demonstrate proficiency with the concepts. Various tools, mediums, and connections are provided for teachers to customize the task to the unique needs, cultures, interests, and abilities of their students, promoting an inclusive and relevant educational experience.

When preparing this performance task, distinguish between the flexible and fixed elements to ensure students have multiple ways to demonstrate their knowledge without compromising the concepts’ depth and rigor within the standards. Furthermore, educators should always consult the student’s Individualized Education Program (IEP) to ensure that all required accommodations and supplementary aids are provided during the assessment.

Variability, Correlation and Causation: PT Teacher Guide

Mathematics

Integrated Mathematics 1 *

This guide provides a sample performance task for this big idea created by the project team.

Comment

Click the link below to download this document. Click the “comment” and the “thumb up / thumb down” buttons above to leave feedback upon completion of your review.

Integrated Mathematics I Variability and Corr/Cause (Student Materials)

This document gives the companion student materials to the performance task fully described in the teacher guide. Please refer to the teacher guide linked as the option performance task for expanded details on appropriate and inappropriate supports for this task, as well as a list of potential alternate means of expression students could use when completing task items.

Variability, Correlation and Causation: PT Student Materials

Mathematics

Integrated Mathematics 1 *

These materials provide the student facing resources needed to deliver the option 1 performance task.

Comment

Performance Tasks

Alternate Means of Expression Option 2 represent either a single performance task or a set of performance tasks that have been curated from publicly available task repositories that can be used as a viable assessment option.

Click the links below to download these documents. Click the “comment” and the “thumb up / thumb down” buttons above to leave feedback upon completion of your review.

Performance Tasks Scoring Materials
Performance Task Materials
Performance Task Primary Source Documents

These performance tasks were gathered from publicly available performance task repositories, including theMathematics Assessment Project (partnership with UC Berkeley, University of Nottingham, and the Shell Center for Mathematical Education), tied to the Common Core State Standards. According to the Mathematics Assessment Project, these “[performance] tasks are substantial, often involving several aspect of mathematics, and structured so as to ensure that all students have access to the problem. Students are guided through a “ramp” of increasing challenge to enable them to show the levels of performance they have achieved. While any of the mathematical practices may be required, these tasks especially feature MP2, MP6 and two others (MP3 – construct viable arguments and critique the reasoning of others; MP7 – look for and make use of structure).” These tasks exemplify different ways to assess a student’s understanding of the Big Ideas tied to Algebra 1. Educators should feel free to either use these tasks directly to assess students’ learning through alternate means of expression or to use these tasks as a model of different ways to assess student learning. These tasks are especially powerful when making real world connections to the Big Ideas and their related standards.

Overview Statement: This performance task is intended to help you assess how well students are able to use a scatter graph to investigate patterns of association in bivariate data and Modeling with Mathematics.

Correlation and Causation: Public Performance Task

Mathematics

Integrated Mathematics 1 *

Task assesses using scatter graphs to model and analyze bivariate data.

Comment

Performance Task

Alternate Means of Expression Option 3 represent either a single performance tasks or a set of performance tasks that have been curated from publically avaible task repositories that can be used as a viable assessment option.

Click the links below to download these documents. Click the “comment” and the “thumb up / thumb down” buttons above to leave feedback upon completion of your review.

Performance Tasks Scoring Materials
Performance Task Materials
Performance Task Primary Source Documents

These performance tasks were gathered from publicly available performance task repositories, including theMathematics Assessment Project (partnership with UC Berkeley, University of Nottingham, and the Shell Center for Mathematical Education), tied to the Common Core State Standards. According to the Mathematics Assessment Project, these “[performance] tasks are substantial, often involving several aspect of mathematics, and structured so as to ensure that all students have access to the problem. Students are guided through a “ramp” of increasing challenge to enable them to show the levels of performance they have achieved. While any of the mathematical practices may be required, these tasks especially feature MP2, MP6 and two others (MP3 – construct viable arguments and critique the reasoning of others; MP7 – look for and make use of structure).” These tasks exemplify different ways to assess a student’s understanding of the Big Ideas tied to Algebra 1. Educators should feel free to either use these tasks directly to assess students’ learning through alternate means of expression or to use these tasks as a model of different ways to assess student learning. These tasks are especially powerful when making real world connections to the Big Ideas and their related standards.

Overview Statement: This activity is intended to help you assess how well students are able to:

  • select and use mathematical ideas to solve a problem and then compare and critique alternative approaches.
  • investigate patterns of association in bivariate data.

Variability: Taxi Fares PT

Mathematics

Integrated Mathematics 1 *

This task assesses solving problems, critiquing methods, and analyzing bivariate data.

Comment

Bring Your Own Task (BYOT)

A Call to IEP Teams

We want students’ IEP team members to share their ideas regarding viable alternative means of expression pertaining to this big idea for students with disabilities, including those eligible for the CAA, these teams serve. IEP teams can define viable alternative means of expression for an individual student with an IEP, as long as these mediums meet the local requirements of the coursework.

A Call to Content-based Educators

In addition to IEP teams, we know secondary teachers and district curriculum leads have a wealth of experience and ideas related to innovative ways to assess students’ understanding of this content. We are interested in sample alternative means of expression this community sees as viable assessments of this big idea.

Please use the entry boxes below to share these ideas.

Important Note —These assessment tools will not be shared outside the review of the initiative team and will remain the intellectual property of the users who have made this submission. Furthermore, feedback or comments from the initiative team will not be given to uploaded content, nor does uploading materials imply that the alternative means of expression strategy is a viable option for this big idea.

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