D2. Probability
Specific Expectations
Probability
D2.1
use mathematical language, including the terms “impossible”, “possible”, and “certain”, to describe the likelihood of complementary events happening, and use that likelihood to make predictions and informed decisions
- complementary events:
- raining today and not raining today
- selecting red versus selecting any colour other than red
- The likelihood of an event can be represented along a continuum from impossible to certain.
- Complementary events are events that cannot happen at the same time. For example, if the likelihood of selecting a red marble from of a bag is certain, then its complement of not selecting a red marble from of a bag is impossible.
- Understanding likelihood can help with making predictions about future events.
Show students three clear jars, where Jar A has only blue interlocking cubes, Jar B has blue and pink interlocking cubes, and Jar C has only pink interlocking cubes. Ask them what the likelihood (impossible, possible, or certain) is of drawing a blue cube from Jar A (or Jar B or Jar C), and then ask them to describe their thinking.
Then ask students to predict the likelihood (impossible, possible, or certain) of not drawing a blue cube from Jar A (or Jar B or C) and to describe their thinking.
Repeat the questions, asking about a yellow cube or a pink cube.
Show students the weather forecast for the weekend. Ask them what decision they might make about what to do on the weekend based on the forecast. Ask them what different decisions they would make if the weather forecast was the opposite.
D2.2
make and test predictions about the likelihood that the mode(s) of a data set from one population will be the same for data collected from a different population
- prediction based on analysis of collected data:
- Most students in our class said they like the colour red. I believe that most students in other Grade 2 classes will also like red.
- In October it looks like it rained most days. It’s possible that it might rain as much in November, but I don’t think it will because it is colder, which usually means snow.
- Data can vary from one population to another.
- If two populations are similar, the modes for the two data sets will more than likely be the same.
- Data can be used to make predictions that are not based on personal feelings or opinions alone.
Note
- In order for students to do an accurate comparison in Grade 2, it is important for them to collect data from the same-sized population (e.g., the same number of days in a month, cubes in a container, or students in Grade 2).
Ask students to revisit a question that they have already asked their classmates. Have them predict the likelihood that the mode will stay the same if they ask the same question of a different population.
Have students collect the new set of data and compare the result with their prediction. When comparing the modes for two different populations, the populations do not need to be the same size.