Modeling Population Growth: Having Kittens
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.
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.
- 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.
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.
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