D2. Probability
Specific Expectations
Probability
D2.1
use mathematical language, including the terms “impossible”, “unlikely”, “equally likely”, “likely”, and “certain”, to describe the likelihood of events happening, represent this likelihood on a probability line, and use it to make predictions and informed decisions
- probability line:
- Probability has a continuum from impossible to certain with the following benchmarks between: unlikely, equally likely, and likely.
Note
- Sometimes equally likely is thought of as an equal chance of events happening (e.g., rolling a 4 or rolling a 6 on a single die). However, on a probability line, equally likely is the probability that an event will happen half of the time (e.g., rolling an even number with a single die).
Provide students with a range of events, as shown below, and have them place the events at the appropriate spots on the probability line according to the five terms (impossible, unlikely, equally likely, likely, and certain). Have students identify other events to add to their probability line as well.
- the probability that you will get a 7 when you roll a standard die
- the probability that heads will come up when you toss a coin
- the probability that someone else in the room has the same birthday as you
- the probability that someone else in the room was born in the same month as you
- the probability that someone else in the room was born in the same year as you
- the probability that the Moon will be visible tonight
It is important for students to understand that probability is based not on absolute thinking but on proportional thinking.
To this end, show students five spinners, where Spinner A is all red, Spinner B is mostly red with a little bit of blue, Spinner C has an equal amount of red and blue, Spinner D has more blue than red, and Spinner E is all blue.
Ask students the likelihood of spinning blue for each of the spinners, using the mathematical language “impossible”, “unlikely”, “equally likely”, “likely”, and “certain”. Ask students to explain their thinking. Then discuss what would happen if the spinners came in different sizes. Would it affect the probability?
D2.2
make and test predictions about the likelihood that the mean, median, and mode(s) of a data set will be the same for data collected from different populations
- predictions based on analysis of collected data:
- Most students in our class do not have reptiles as pets. I believe that most students in the other Grade 4 class will also not have reptiles as pets.
- The median distance that Grade 4 students can jump is 1 metre. I believe that it is unlikely that the median will be the same for Grade 2 students because they are shorter.
- The mean or average amount that Grade 4 students read each day during the Read-A-Thon was 20 minutes. I believe that it is likely that the mean for Grade 5 students is higher because they have a later bedtime.
Tell students that they will be collecting data from another Grade 4 class for a question for which they already have data from their classmates. Have them predict the likelihood that the data from the other class will have the same mean, mode, or median. Then have them collect the data. Finally, have them compare the result with their prediction.
