collection

Big Idea
Use mathematics to analyze our past waste generation behaviour and based on that understand the waste problem that we are facing in Metro Vancouver. Realize that when we throw something away, there is no such place as “away”, and that we all have a responsibility when it comes to managing our waste.

Math Topics

1. Linear functions: graphing lines, independent and dependent variables, slope, extrapolation, finding output given input, finding input given output (graphically and algebraically), finding equation of a line (given two points; given a point and the slope), vertical and horizontal intercepts
2. Arithmetic series
3. Quadratic functions

Introduction
What do students already know about waste disposal in Metro Vancouver?
Watch and discuss video about waste disposal (2007, Episode 27, Zero-Waste-Challenge):
http://www.metrovancouver.org/region/tsr_tv/Pages/default.aspx

Total Waste Generation
Waste generation in our region has been increasing approximately linearly from 3 million tonnes in 2004 to 3.625 million tonnes in 2007. Represent this information graphically. Assuming this trend has been continuing,

• How much waste are we generating now in 2010? How much will we generate in 2030?
• When will we generate 4 million tonnes? 6 million tonnes?
• Find the equation of a line that describes the amount of waste we generate. Use this equation to verify your answers for the above questions
• What does the slope of this line mean?
• What does this mean for us in Metro Vancouver?

Waste Generation and Population:
More people mean more waste. Metro Vancouver’s population increased from 2,147,273 in 2004 to 2,237,220 in 2007. Is the increase in waste only due to an increase in the population in the region?
Graph the per capita waste generation and find an algebraic description. What does the slope of this line represent?

Waste Diversion and the Cache Creek Landfill:
Thanks to recycling programs, yard waste collection, and other efforts, 50% of the waste generated has been diverted from disposal in 2007. The rest ends up in a landfill (some of it is first incinerated), we will call this “landfill waste”. In particular, about 30% of landfill waste ends up in the Cache Creek landfill. How many tonnes of waste went to Cache Creek in 2007?

The Cache Creek landfill was scheduled to close in 2009. However, in 2009 it was extended by 7 hectares. One hectare can hold about 225,000 tonnes of waste. When will the extra 7 hectares be filled up, based on how much waste went to Cache Creek in 2007? What does this mean for us as residents of Metro Vancouver?

In January 2010 another 42 hectare expansion of Cache Creek was approved. How many years will it take for this site to fill up

1. based on the amount of waste that went to Cache Creek in 2007?
2. keeping in mind that the amount of total waste generated has been increasing every year?

Green Waste Video: http://www.metrovancouver.org/region/tsr_tv/Pages/default.aspx (2009, Episode 41, Food Compost)

Metro Vancouver is hoping to achieve a 75% diversion rate. This means that 75% of the total waste generated would be recycled or composted. Suppose we already had a 75% diversion rate today (and from now on), and assume that the amount of total waste generated is still increasing every year.

1. Find the equation of a function that models the number of tonnes of waste that the Cache Creek expansion can receive (currently it can receive the equivalent of 42 hectares).
2. What does the vertical intercept of this function represent? What about the horizontal intercept?
3. How many years would it take for the 42 hectare expansion of Cache Creek to fill up?
4. What else can we do in addition to recycling and composting to better manage our waste?

Landfills and CO2:
One kg of garbage can emit up to 1.7 kg of CO2 in a landfill. Let’s look at the amount of CO2 emitted from the 42 hectare Cache Creek expansion site. Given that garbage is just starting to accumulate there (i.e. it is currently empty) and assuming that every kilogram of garbage emits exactly 1.7 kg of CO2,

1. How much CO2 will this site emit one year from now? Two years from now? Three?
2. How much CO2 will it emit n years from now?
3. Represent the amount of CO2 emitted n years from now graphically

Other Ideas:

• Design a survey about waste habits to be given out to students at the school. Collect and analyze this data to talk about statistics, bias, representative samples, etc.
• Track the amount of waste that students produce throughout the year (either in school, or students can track their family’s waste). You can introduce your own zero-waste-challenge. The idea is to get students to reduce their waste by keeping them accountable.