Humane Education and Math: Reusable vs. Plastic Bags

by Institute for Humane Education

As part of our educator professional development, we encourage teachers to start infusing humane education into their classrooms by finding small ways to tweak their lessons.

After learning more about the impact of plastic bags, high school math teacher Tristan Bates decided to whip up a fun little activity for his students. He said:

“I have been looking at the idea of using cloth bags as opposed to plastic and how many times you would have to shop before the cloth bag paid for itself …. It would be a fantastic algebra problem and it would show the students how small changes can become large changes.”

Here’s Tristan’s activity. The answers are at the bottom.

To Bag or Not to Bag?

You shop at your local grocery store and notice that you can buy a reusable grocery bag at the checkout counter for $1.50 (let’s assume that the tax is included).

If you get back $0.06 every time you use a reusable bag instead of a plastic bag then does it make sense financially to get the reusable bag?

How many reusable bags should you get?

1.  Write a function S(t) that will show how much one bag will save each time (t) you use it (don’t forget the initial price of the bag).

2.  How many times must you use your reusable bag instead of plastic bags before you start to save money?

3.  How much total volume can one plastic bag hold if its dimensions are 6’‘x11’‘x15’’?

4.  How much total volume can one reusable bag hold if its dimensions are 14.5’‘x12.5’‘x8.5’’?

5.  If you normally need 14 plastic bags when you do your weekly shopping, how many reusable bags will you need?

6.  As well as your weekly shopping you go out twice more a week just to pick up some small things, and each time you end up using three plastic bags. How many weeks until you have saved the money you spent on the reusable bag to begin with?

7.  How many shopping trips will it take before you have saved 100 plastic bags? 1,000? Will you ever save 1,000,000 plastic bags?


1.  S(t) = 0.06t – 1.50

2.  You will have to use your reusable bag 25 times before you start to save money.

3.  The plastic bag can hold 990 cubic inches.

4.  The reusable bag can hold 1540.625 cubic inches.

5.  You will need to use nine reusable bags.

6.  It will take 18 weeks before you have saved the money you spent on the reusable bags.

7.  It will take 6 weeks to save 100 plastic bags, 56 weeks to save 1,000 plastic bags. You yourself will probably never save 1,000,000 plastic bags as it would take 1065 years at the rate of 18 bags a week.

An activity like this could then lead to exploring issues like total energy use (from production through use and disposal), as well as the comprehensive impacts of various bags on people, animals, and the Earth, and a consideration of creative, positive solutions for meeting the core need (getting products from point A to point B) in a way that does the most good and least harm for all.

Check out some of our other free activities and lesson plans in our online Resource Center.