Probability Misconceptions with Pascals Triangle
Introduction/Rationale
The following activity has the theory of “low floor high ceiling.” Where a problem can be
revisited or built upon depending on the students Mathematical maturity. In response, there are
many ways to solve this problem. At a certain point there is a “ah ha” moment, or something
happens that the student would not have thought to have happened. In this particular problem
pascals triangle emerges from the pattern. Interest can be generated in younger grades by
showing them that the older grades are working on the same problem. A possible pairing of
students in different grades can be achieved for all or for students who are working above grade
level.
NOTE: Ideas in this lesson come from the Ontario Ministry Document - Data Management and
Probability Grades 4 to 6
Activity
Low Floor
1. Students predict which of the outcomes either 2 heads, 2 tails, or 1 head and 1 tail is more
likely or if they are equally as likely to happen. Students will conduct a probability
experiment to test their predictions.
2. Students consider the effect of the number of trials on experimental probability. They describe
their reasoning in the context of typical misconceptions. The main misconception is that
“previous probability trials affect future trials” (ex. When the coin is tossed up and come up
heads 5 times in a row, the probability of getting a head on the 6th toss decreases (or the
probability of getting a tail increases)) This step students begin to think or get a feel for what
theoretical probability is.
3. Students consider all possible outcomes of flipping a coin two times (HH, HT, TH, TT) in
order to explain why the probability of getting 1 head and 1 tail is ½ while the probability of
getting 2 heads or tails is only ¼. This is the step where theoretical probability begins to really
develop. On paper anyway.
4. Students expand on finding all possible outcomes or “combinations” of flipping a coin and
extend it to flipping the coin 3, 4, and 5 times. Students also will realize that HT and TH is the
same. At this point have the students write the combinations to form a triangle.
Ex:
1H 1T
1HH 2HT 1TT
1HHH 3HHT 3HTT 1TTT
(Ask the students if they see a pattern, and to complete the triangle)
(if not have them complete another step, but there are 16 possible outcomes)
