## Reflection: Real World Applications Cat Island (Day 2 of 2): Cats can’t add but they do multiply! - Section 4: Improving Solutions

WARNING: This was a very time consuming assignment to 'grade.' I would definitely recommend solving the problem for yourself before trying to attempt the read students' solutions.

The first thing that I learned from analyzing my students’ work is that my students need more practice on CLEARLY demonstrating their thought process, justifying their work, and stating assumptions. It was so difficult to follow a majority of my students’ thinking and nearly all of my students did not clearly state their assumptions as they were asked to do.

These were my top 4 favorite student approaches for clearly demonstrating their thought process:

Cat Island, student work 1

Cat Island, student work 4

Cat Island, student work 5

Cat Island, student work 6

Error Analysis of a few Samples of Student Work

Many of my students (and myself) missed including one or more of the given constraints.

• Constraint not included: Kittens can get pregnant at 4 months of age.

Cat Island, student work 3

Cat Island, student work 4

Cat Island, student work 5

Cat Island, student work 9

• Constraint not included: Cats on average only have 3 litters a year. (or maybe up to 6 in the 18 months)

Cat Island, student work 3

Cat Island, student work 4

Cat Island, student work 5

Cat Island, student work 6

Cat Island, student work 9

Cat Island, student work 10

• Constraint not included: Time constraints on future generations being able to reproduce in 18 months.

Cat Island, student work 5

Many students also didn’t account for males’ line of descents, but I understand that was difficult to track.

• Constraint not included: Only factoring in that female cats can create decedents of first cat.

Cat Island, student work 7

Cat Island, student work 8

My Attempts

To help me really get a good grasp of the problem, I made a few attempts at solving before I read through my students’ work and before I read the solutions from MARS. After two attempts on my part, I somewhat sympathized with my students. This problem gets complex fast and it really was a challenge to keep my thoughts clear and organized to myself, much less another reader. Interestingly, I missed a major given assumption in both of my attempts: female cats can only carry 3 litters of kittens a year. (Note: The MARS solutions really are much more efficient and clear than either of my methods. It’s fun when I teach a lesson and get to learn something new myself!)

My first attempt:Cat Island, my first attempt

Assumptions:

• first cat got pregnant at the start of time, so first litter was born at 2 months
• high estimation, assumed 6 cats per litter with 3 boys and 3 girls
• Only counting decedents from the female cats, as male reproduction is hard to track
• Giving the females cats one month to get pregnant after giving birth

My second attempt: Cat Island, my second attempt

I failed to include the fact that cats can only have about 3 litters a year.

Assumptions:

• Mom was already pregnancy, so first litter was born at 0 months
• Cats have 6 kittens every litter
• Pregnant back-to-back (oops… missed that cats can only have 3 litters a year)
• Assuming now that males will reproduce at the same rate as a female (which is probably way too low of a rate)

Real World Applications: Analysis of Students' Final Responses

# Cat Island (Day 2 of 2): Cats can’t add but they do multiply!

Unit 4: Exponential Functions and Equations
Lesson 2 of 14

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

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6 teachers like this lesson
Subject(s):
Math, modeling, Precalculus and Calculus, PreCalculus, exponential function, function
50 minutes

### Tiffany Dawdy

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