# Modeling: Hot and Cold

## Mathematical goals

- This lesson unit is intended to help students judge the accuracy of two different approximations to a particular linear relationship. Students will compare two linear functions as approximations to the relationship between Celsius and Fahrenheit temperature and consider under what circumstances each of the approximations may be reasonable.

## Introduction

The lesson is structured in the following way:

- Before the lesson, students tackle the problem individually. You review their solutions and write questions to help students improve their work.
- At the beginning of the lesson, students respond to your questions. Students are then grouped into pairs or threes and work collaboratively to produce a better solution to the same task.
- There is a whole-class discussion to compare and evaluate different approaches.
- This is followed by a second collaborative activity in which students work in small groups to evaluate and comment on sample solutions, followed by a second whole-class discussion about the work.
- Finally, in a follow-up lesson, students review and evaluate their work on the problem.

## Materials required

- Each student will need a copy of the assessment task
*Hot and Cold*,*How Did You Work?*questionnaire, and a mini-whiteboard, pen, and eraser. - Each small group of students will need a large sheet of paper for making a poster, a felt-tipped pen, and copies of the
*Sample Responses to Discuss.* - You will need a supply of graph paper and rules available on request.

## Time needed

Approximately 15 minutes before the lesson, a 90-minute lesson (or two 45-minute lessons), and 10 minutes in a follow-up lesson. Exact timings will depend on the needs of your students.

## 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:*