Skittles Graphing and Probability

 

Based on a lesson plan written by Jane Gourley, Jannea Burgess, Amy Lyon and Rachel Creasor, which was in turn based on a lesson outline written by David Reid

 

Overview:

The purpose of this lesson is to provide students with a hands-on, cooperative learning experience with respect to the process of collecting, analysing and interpreting data, and to improve decision-making skills through the use of probability. This lesson illustrates how charts and graphs are valuable instruments for communicating data quickly and simply. Data produced by students during this activity is used to stimulate discussion and promote mathematical thinking regarding probability. This lesson can be as simple as counting (Primary), or making a pictograph (1st and 2nd grades), or as involved as predicting and determining probability (3rd to 6th grades).

 

Lesson Goals:      

1.     Students will solve problems involving the collection, display and analysis of data. (GCO F)

a.      Students will collect and organize data (4-F1, 6-F1, F2)

b.     Students will create and interpret pictographs and symbolic bar graphs (4-F3, F5, 5-F2, 5-F4)

c.     Students will develop and modify predictions with respect to data collected or presented to them (4-F6)

d.     Students will describe data using the mean (4-F7)

e.      Students will make inferences from data displays (6-F7)

f.       Students will demonstrate an understanding of the differences among mean, median, and mode (6-F8)

g.     explore real-world issues of interest to students and for which data collection is necessary to determine an answer (4-F8, 5-F7, 6-F9)

 

2.     Students will represent and solve problems involving uncertainty. (GCO G)

a.      Students will demonstrate an understanding that probability predictions need not always come true

b.     Students will evaluate the reliability of sampling results (6-G2)

c.     Students will analyse simple probabilistic claims (6-G3)

d.     Students will determine theoretical probabilities (6-G4)

e.      Students will identify events that could be associated with a particular theoretical probability (6-G5)

 

Materials:     Small bags of Skittles

Graph paper

Crayons or Markers

 

 

Activities and Procedures:

  1. Divide class into groups of two. Distribute one bag of Skittles to each pair. Ask students what they think the probability is of getting a red Skittle if they were to pick a random Skittle from the bag. Also ask, if you were to take 10 Skittles from the bag, theoretically, what colours should they be? (Theoretical probability)
  2. Instruct students to open the bags, sort and classify the Skittles according to colour. Ask students to record the colour distribution on a graph. Students may use bars or pictograph symbols to represent their Skittles. (Displaying Data)
  3. Ask students to report their numbers of red Skittles to the teacher as s/he records them on a chart. Students may be allowed to nibble on their Skittles now. Ask students what they know about the concepts of mean, median, and mode. Discuss concepts and calculate each.
  4. The teacher combines all the data and shows students the big chart of Skittles distribution. Based on all of the graphs, what are the odds of getting a red Skittle? (Experimental probability) Explain to the class that as the number of Skittles increases (i.e. sample size), the experimental probability moves closer to the theoretical probability.
  5. Ask class, what is the mean number of Skittles per bag? Also ask, what are the odds of getting a red Skittle?

 

See also:

·        Ideas: Skittles® and Statistics, Teaching Children Mathematics Apr 1993, 454-462

·        http://www.skittles.com/