# Devising a Measure: Correlation

## Mathematical goals

This lesson unit is intended to help you assess how well students understand the notion of positive 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

- Before the lesson, students work individually on an assessment task 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, then work collaboratively in small groups to produce, in the form of a poster, a better solution to the task than they did individually. In a whole-class discussion students compare and evaluate the different methods they have used.
- Then, 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.
- In a follow-up lesson, students review what they have learnt.

## Materials required

- Each student will need a copy of the
*Drive-in Movie Theater*task 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 the
*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*Changing correlations.xls*. You may also need extra copies of*Scatter Graphs A*,*B*, and*C,*extra paper, and calculators.

## Time needed

20 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 10 minutes in a follow-lesson. Timings are only approximate and depend on the needs of the class.

## Lesson Type

## Mathematical Practices

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

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

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

- H.N-Q: Reason quantitatively and use units to solve problems
- H.S-ID: Summarize, represent, and interpret data on two categorical and quantitative variables