Trashcan probability (lesson)

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      (See attachment or link at bottom for full lesson with handouts)

      Teacher Directions


      By attempting to make baskets from differing distances and analyzing data on results, students will begin to understand the concept of chance and quantify the likelihood of an event using a value from 0 to 1.


      Prior Knowledge

      • Students should be able to represent a part of a whole or a part of a set using fractions.
      • Student should be able to place 1/4, 1/2, and 3/4 correctly on a number line.
      • Students should have had experience using a metric ruler.


      Materials and Equipment

      Ø  Sheets of scrap paper or recycled paper – all the same size

      Ø  Trashcans or other large containers (buckets work well)

      Ø  Metric tape measures or meter sticks

      Ø  Masking tape

      Ø  Sidewalk chalk if outdoors – post-it notes if indoors



      Ask students if they have ever crumpled up a piece of paper and aimed it at a trashcan.  Did their tosses go in?  Ask, “Can we predict whether or not a toss will go in the trash can?”  Ask, “Do tosses go in every time?  Why not?”  Introduce the idea that it is NEVER certain that a toss will go in, but it may be likely to go in.  Continue by stating that other tosses may or may not go in, while there are tosses that are unlikely to land in the trashcan or that cannot possibly land in it (for example, the if ball is larger than the can or the can has no opening). 


      Write the terms on the board and ask students what each word means to them. 

      Certain, likely, equally likely, unlikely, impossible.


      Explain to students that students will be experimenting to determine the likelihood of a paper toss landing in a container, and we will be using these terms to analyze our tosses.



      Divide students into equal groups of 3 (if possible) and give each group their materials and equipment.  Students will make tosses from the following distances to the trashcan:  3 cm, 150 cm, 250 cm, and 6 m.  Tell students that on the 6-meter toss, they will close their eyes while tossing!   


      Students will first measure and mark the distances before tossing. Before tossing, students will predict the likelihood of their tosses on their paper.  After they have made their predictions, students can begin tossing and recording.  Each student will toss a crumpled piece of paper three times from each distance and record the number of tosses that land in the basket.  The final toss is with eyes closed.




      Once tossing is completed, combine the class data on a chart.  Discuss the data.  The goal is to help students agree on descriptors for each likelihood and to notice the relationship between attempts and successes from each distance.

      Click to access Trash%20Can%20Probability.pdf

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