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Lesson Review

Author:Michael Bautista
ETP Title:A Mathmatical Analysis of Paper Usage
Organization:Synopsys, Inc.
ETP Type:Enhance Existing Curriculum
Grade Level(s):10,11,12
Subject Area(s):Mathematics

Lesson Abstract:

In this ETP, math students will collect data on their paper usage over a two week period. They will first analyze current global paper consumption trends and learn about the environmental impacts of paper production.  Students will then create a spreadsheet in Google Docs that will allow them to see the environmental effects of their own paper consumption, such as C02 emissions, H20 used, and trees cut down. Upon completing their data matrix, students will create graphs of the various data sets used and find linear modeling equations. Each student will use the graphs to make estimations of their yearly environmental impact caused by paper consumption.  Students will use their data to make conclusions and predictions for the average student, a typical classroom, and the entire school.

Focal Standards

Common Core Standard Mathematics - 

Build a function that models a relationship between two quantities

1. Write a function that describes a relationship between two quantities.

  • Determine an explicit expression, a recursive process, or steps for calculation from a context.
  • Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decayingexponential, and relate these functions to the model 

from page 59 of the Common Core Standards, found at the following site: 


Measurable Objectives:

  • Students will create a Google Spreadsheet that calculates the environmental impact of their individual paper consumption. 
  • Students will create graphs and modeling equations to predict their yearly environmental impact based on current trends of paper useage. Their final work will be a Google Presentation or PowerPoint.  



Students will submit a completed Google Spreadsheet (or Excel doc) and a Google Presentation (or PowerPoint) that contains a written analysis with charts, modeling equations, and conclusions. See ETP Doc - 0 for Rubric. 

Additional Standards

Algebra II 12.0 - Students know the laws of fractional exponents, understand exponential func­tions, and use these functions in problems involving exponential growth and decay

21st Century Skill(s)

  • Information, Media and Technology Skills
  • Information Literacy
  • Media Literacy
  • Critical Thinking and Problem Solving


21st Century Skill(s) Application

  • Analyzing indivual paper usage and using that information to form modeling equations
  • Creating Excel sheets with cell formulas based on analysis of data from web sources
  • Creating functions from data that model real-world scenarios
  • Compiling final sets of information into a convincing presentation
  • Directly connecting math to a relevant environmental issue
  • Collaborating online via Google Docs

Fellowship Description

1) I am working at Synopsys this summer and doing the following:

  • Updating and migrating an IT matrix webpage to SharePoint 2007
  • Updating all info and docs on the Synopsys New Employee site
  • Creating a PowerPoint to propose changes for an internal company website
  • Collaborating online with other employees on the same SharePoint site

2) Skills used: 

  • Website updating 
  • Data organization in spreadsheets
  • Digital presentation of information
  • Proofreading and technical writing

3) Types of careers

  • IT support
  • Technical writing

4) IT support and managment

The connection between the ETP and Fellowship. :

I plan to:

  • Explain how web-editing and document sharing is used in the workplace, which emphasizes team collaboration and limits paper printing 
  • Explain the how spreadsheet tools, online collaboration, and an environmentally-responsible mindset will be useful in future work experiences for students


Instructional Plan:

Instructional Plan
Time Required:  

  • Two 55 minute periods 
  • One week of outside of class for students to collect data
  • One week of outside-of-class time finalize graphs/charts and final report

Math Level 
Algebra II or Precalculus

Prerequisites for students

  • Knowledge of linear and exponential functions -- how to find trend equations from two points on a graph
  • Basic knowledge of Excel
  • Basic knowledge of Google Docs - a tutorial can be found here:  http://www.youtube.com/watch?v=lMqdex3KDQM

Day 1

1. Place students into pairs and have them discuss the following questions:  

  • Estimate how much paper do you use throughout the school year?
  • Estimate how much paper does the school use throughout the year?
  • How much paper do you think entire countries use in a year? Do you think this amount is increasing or decreasing?
  • What are some of the environmental impacts caused by this paper use?

2. Students will then work with their partners to analyze current worldwide paper consumption trends. They will form exponential and linear models based on graphs.

  • Distribute "ETP Doc 1"  and have students study the graphs 
  • Have students work together to find equations that model the US and China's paper cosumption
  • For HW, students will individual find modeling equations based on the graph on page 3

Formulas to review if necessary

  • slope-intercept: y = mx + b
  • point-slope: y-y1 = m(x-x1)
  • Exponential: y = a(b^x)

Concepts to review if necessary

  • Finding a trendline by plugging in two points to a linear equation
  • Find an exponential curve of best fit by plugging in two points to a general exponential function equation

Day 2 (computer lab required)



  • Review modeling equations that students produced. Choose one or two examples that the class can check for accuracy by plugging in data points.


  • Distribute (or give students digital access)  "ETP Doc 2."  Have students perform a webquest to gather data about environmental  impacts of paper useage.


Day 3

  • Explain the instructions for the Individual Project and discuss how students will accomplish this outside of class.  

Individual Project Instructions

  • Students will analyze the impact of their own paper consumption by collecting paper usage data for a week (The teacher should check in with students about their data on a daily basis)
  • Students will enter the data into the Excel spreadsheet (ETP Doc 3).
  • Students will then analyze the data in terms of daily totals and daily averages. Students will complete the Excel chart using formulas that can be derived from the information found in their webquest.
  • Students will then make charts that represents the averages various data sets over time. They will make charts in Google Spreadsheets with "time" on the x-axis and "amount" on the y-axis (see ETP Doc - Making Google Charts from Data).  
  • Students will inserts their final charts into the Google Presentation template 
  • Students will find and interpret the equation of the trend lines.  

Assessment (what students will turn in)

Students will turn in a final PowerPoint report (electronically) that contains:

  • Charts and modeling graphs for each data set to extrapolate yearly environmental impact
  • Written analysis that explains the environmental impact caused by the student's current paper-use trends and the reductions that would occure if paper use is reduced 
  • Links to their other ETP documents (Paper Consumption Trends, Webquest, and Spreadsheet)


  • ETP Doc 0
  • ETP Doc 1
  • ETP Doc 2
  • ETP Doc 2a
  • ETP Doc 3
  • ETP Doc 3a
  • ETP Doc 4

Bibliographic or other resources you used in creating this curriculum:

  1. Johnson, Ben. "Paper and Pencil Curriculum: How Much Do You Rely on It?." Edutopia. N.p., 23 02 2011. Web. 2 Jul 2012.
  2. "Paper Cut." Carbon Rally. N.p., 30 05 2008. Web. 2 Jul 2012. 
  3. "Paperless Guide." stopwaste.org. N.p., 2009. Web. 2 Jul 2012. .
  4. Thayer School of Engineering at Dartmouth, Forest and paper industry. N.p., n.d. Web. 2 Jul 2012. .




environment, precalculus, carbon, global warming