##
* *Reflection: Staircase of Complexity
Modeling Population Growth - Section 1: Opening

Students really struggled with the Warm Up activity in this lesson. In hindsight, I would have spent more time at the start of class reviewing arithmetic and geometric means prior to giving them the next task. We ended up taking a majority of class time for the warm up, but I still think it is time well spent. The task that follows, Growing, Growing, Gone, is a more complicated problem because the intervals between the population data is set at 20 years. I think that with a fuller understanding of the warm up problem, students will experience greater success on the main task.

*Opportunity to Spiral Content*

*Staircase of Complexity: Opportunity to Spiral Content*

# Modeling Population Growth

Lesson 10 of 11

## Objective: SWBAT use their understanding of linear and exponential growth patterns to model the growth of a population.

#### Opening

*10 min*

I start today's class by asking students to make a prediction about population growth. I want them to draw a rough sketch of a graph that they think would represent the world's population growth from 1800 to today. The purpose of this task is to get students thinking about population growth and for them to generate their own starting point with the problem. Even if there graph is way off, I think starting with their own ideas helps them to buy in to the problem and later have something to compare the actual growth to.

Next, I show students the National Geographic video 7 Billion . We pause the video when it shows the graph and I tell students that we'll use these numbers and a linear and exponential model to look at how population might grow.

I hand out the Population Growth Warm Up for today's class which requires students to use arithmetic and geometric means to figure out the rates of change. This work is designed to prepare them for today's primary task, where they get two data points about US population over time and they are asked to generate l**inear and exponential models**. Students will work individually on the Warm Up, before we quickly go over the work together.

Source URL for National Geographic Video:

http://video.nationalgeographic.com/video/news/7-billion/ngm-7billion%20%20

*expand content*

#### Investigation

*40 min*

Next, we will read through Growing, Growing, Gone together and then students will get to work. There is a lot here for students to chew on and they have been working on many representations to model situations (tables, equations and graphs). One issue that is confusing for this task is the intervals of the years that pass and what scale students will want to use. For clarity's sake, I think it is easier to mark each 20 year interval by ones, so students can find arithmetic and geometric means using only 4 missing intervals, rather than 80. This will also make working with the tables much easier.

Things I will be looking for:

- Students in my class sometimes struggle working with big numbers. I will remind them that in real life, numbers are not always neat and friendly and they can use technology to work with numbers of this size.
- I anticipate students having a fairly easy time with the linear model but struggling more with the exponential model. I may ask students to guess and check different growth rates if they are having trouble finding a common factor. I might ask students, "What would your table look like if the population was growing at 5% rate every 20 years/each interval?"

When students are ready to look at the graph of their models, they will use desmos.com on Chromebooks to construct their graphs. Students often have difficulty selecting an appropriate viewing window, so I might pause class and conduct a brief discussion about this issue.

I anticipate that students will need the full 40 minutes to work on this task. If students finish early, I will be asking them to write an argument about which model provides a better forecast for the U.S. population in the year 2030 and why.

#### Resources

*expand content*

#### Discussion + Reflection

*10 min*

We will likely discuss this task at the start of the following lesson as students will use the full class period to work on the task.

At the end of class, I check in at each table and see where students are with their work. In the last five minutes of class, I ask students to reflect on today's work in light of our discussion in the next class. I ask them to complete an exit ticket that addresses the following prompt: "Which representation (table, graph, equation) do you this is most effective to show exponential or linear growth. Why? Which representation do you find least useful? Why?

*expand content*

Growing, Growing, Gone is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

http://www.mathematicsvisionproject.org/secondary-1-mathematics.html

*expand content*

##### Similar Lessons

###### Higher Degree Polynomials, Day 2 of 2

*Favorites(2)*

*Resources(14)*

Environment: Suburban

###### Parking and Pencils: Step Functions and Piecewise Functions

*Favorites(4)*

*Resources(14)*

Environment: Suburban

###### Leap of Faith!

*Favorites(6)*

*Resources(14)*

Environment: Urban

- UNIT 1: Introduction to Algebra: Focus on Problem Solving
- UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
- UNIT 3: Systems of Equations and Inequalities
- UNIT 4: Quadratics!
- UNIT 5: Data and Statistics
- UNIT 6: Arithmetic & Geometric Sequences
- UNIT 7: Functions

- LESSON 1: A Re- Introduction to Functions
- LESSON 2: Fun with Functions
- LESSON 3: How Many Diagonals Does a Polygon Have?
- LESSON 4: Building Functions
- LESSON 5: Discrete and Continuous Functions
- LESSON 6: Equal Differences, Equal Factors
- LESSON 7: Linear and Exponential Functions Project
- LESSON 8: Comparing Rates of Growth
- LESSON 9: Functions Applications: Money grows and the rainforest disappears
- LESSON 10: Modeling Population Growth
- LESSON 11: Exponential Growth and Decay