Read more about the purpose of the MAP *Classroom Challenges*…

## Devising a Measure for Correlation

**Mathematical goals**

This lesson unit is intended to help you assess how well students understand the notion of correlation. In particular this unit aims to identify and help students who have difficulty in:

- Understanding correlation as the degree of fit between two variables.
- Making a mathematical model of a situation.
- Testing and improving the model.
- Communicating their reasoning clearly.
- Evaluating alternative models of the situation.

### Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task
*Drive-in Movie Theater*that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their methods. - At the start of the lesson, students work alone answering your questions about the same problem, then work collaboratively in small groups to produce, in the form of a poster, a better solution to the task
*Drive-in Movie Theater*, than they did individually. - In a whole-class discussion students compare and evaluate the different methods they have used.
- Working in the same small groups, students analyze sample responses to the task.
- In a whole-class discussion students explain and compare the alternative methods.
- Finally, students review what they have learnt.

### Materials required

- Each student will need a copy of the assessment task,
*Drive-in Movie Theater*and*Scatter Graphs A, B, and C*. - Each small group of students will need a large sheet of paper, a felt tipped pen, copies of all three
*Sample Responses to Discuss*, and a blank sheet of paper.

If possible, use a data projector and computer with spreadsheet software to demonstrate the spreadsheet *Correlation Measure Spreadsheet.xls*. You may also need extra copies of *Scatter Graphs A*, *B*, and *C,* extra sheets of paper for student work, and calculators. There are some projector resources to help with discussions.

### Time needed

20 minutes before the lesson, a 90-minute lesson (or two 45 minute lessons), and 10 minutes in the next lesson (or for homework). Timings are only approximate and depend on the needs of the class.

### Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics

### Mathematical Content

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

### Resources

#### Lesson (complete)

- devising_a_measure_for_correlation_complete.pdf ( 4234.5K PDF/Acrobat 15 Mar 2012)

#### Projector Resources

- devising_measure_correlation_slides.ppt ( 1948K MS PowerPoint 15 Mar 2012)

#### Software

- l42_correlation_measure_spreadsheet_beta_locked.xls ( 41K MS Excel 15 Mar 2012)

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP *Classroom Challenges* for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to map.info@mathshell.org.

Can you help us by sending samples of students' work on the *Classroom Challenges?*