SWBAT investigate an exponentially increasing sequence and make sensible estimates and assumptions based on this sequence.

Looking at the life cycle of cats, students use exponential models to see how quickly populations can grow in the real world.

Today's lesson is adapted from the lesson *Modeling: Having Kittens* from the Mathematics Assessment Resource Service website. You can find the original lesson here. (last accessed 10/22/2013) The original lesson and materials can also be seen in this pdf: having_kittens_complete.

The lesson will begin with a quick introduction about Cat Island: Cat Island Day 1, video narrative, introduction

Use the Flipchart - Having Kittens Day 1 to present the details of cat island and really get students hooked.

*Please note: This lesson can also be taught in a single 50-minute class period. I ended up having to do this due to time constraints. This is how I broke down that class period:

- 5 minutes: Introduce Cat Island
- 10 minutes: Students Solve Independently (quiet work time)
- 10 minutes: Present 3 students’ work (provided in this lesson) and talk about the assumptions each student made and what we liked or didn’t like about their work
- 25 minutes: Revise/finalize answers in teams

See my reflection in day 2 of this lesson for more details.

20 minutes

**Preparation:** I am going to copy page 11 of the PDF file from the *Having Kittens *lesson for every student.

**Narrative:** During this part of the lesson, students should work independently to explore this claim. They should document all work and write up a final answer. Do they support the claim yes? No? and why? Students should be encouraged to work as far as they can and then make a conclusion with an emphasis on documenting all work. I plan to let students know we will revisit this problem in teams later, but right now I want to know what they think as an individual. Students will have an opportunity to view one another's work in the next lesson.

I am specifically going to let students struggle over this claim and trying to justify their answer one way or another. I will answer clarifying questions if they are unsure about the facts given, but will not be providing any scaffolding toward reaching a conclusion. Mainly, I want to see what students come up with, right or wrong. While engaging in this complex task, students will be improving their ability to make sense of a problem and persevere to solve it (**MP1**). Students will also be reasoning quantitatively (**MP2**) and should be using tools strategically (**MP5**). Students will also have to decide whether or not an estimation will be sufficient or whether they need an exact answer. Students should also be encouraged to attend to precision (**MP6**) as they document their thoughts and answers including any assumptions they make on the problem.

All materials for this lesson have been adapted from the Mathematics Assessment Resource Services website: accessed 10/21/2013

2 minutes

To close out today’s lesson, have students submit their responses for feedback (not grading!). Let students know that we will be coming back to this problem the next time we see them. We just want to see what they have so far. I am going to reassure my students that I am not GRADING this at this point.

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