# Modeling Population Growth: Having Kittens

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Interpret a situation and represent the constraints and variables mathematically.
- Select appropriate mathematical methods to use.
- Make sensible estimates and assumptions.
- Investigate an exponentially increasing sequence.
- Communicate their reasoning clearly.

## Introduction

This lesson is designed to help students develop strategies for modeling. Note that a video of this lesson is available in the professional development materials.

- Before the lesson, students attempt the problem individually. You then review their work and write questions to help students improve their solutions.
- At the start of the lesson, students work individually answering your questions. Then, in small groups, students work collaboratively on the task before evaluating some sample solutions. In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
- In a follow-up lesson, students review what they have learned.

## Materials required

- Each individual student will need a calculator, a copy of the
*Having Kittens*task and the*How Did You Work?*questionnaire*,*a mini-whiteboard, pen, and eraser. - Each small group will need the
*Sample Responses to Discuss,*a large sheet of poster paper, and a felt-tipped pen. Graph paper should be kept in reserve and used only when requested. - There is a projector resource to help you with whole-class discussions. Spreadsheet software might also be helpful if available.

## Time needed

20 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 15 minutes in a follow-up lesson. Timings are approximate. Exact timings will depend on the needs of your 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.F-LE: Construct and compare linear and exponential models and solve problems
- H.N-Q: Reason quantitatively and use units to solve problems