D2. Probability
Specific Expectations
Probability
D2.1
use mathematical language, including the terms “impossible”, “possible”, and “certain”, to describe the likelihood of events happening, and use that likelihood to make predictions and informed decisions
- impossible event:
- A unicorn will come to class.
- possible event:
- You will see stars in the sky tonight.
- certain event:
- Your hand will get wet when you put it in water (if you don’t have a rubber glove on).
- The likelihood of an event happening ranges from impossible to certain.
- Understanding likelihood can help with making predictions about future events and can influence the decisions people make in daily life.
Note
- The first stage of understanding the continuum is for students to be able to identify events that happen at the two ends and understand that the likelihood of other types of events falls somewhere in between.
Provide students with three spinners – one that is all purple, one that is half purple and half white, and one that is all white. Ask them to describe the likelihood of spinning purple on Spinner A, on Spinner B, and on Spinner C. Have them explain their reasoning.
Ask students what clothes they would wear tomorrow if the weather forecast says there is a high chance of rain.
When appropriate throughout the year, highlight scenarios like these so that students can continue to develop their understanding of how probability can affect decisions and can make connections between mathematics and daily life.
D2.2
make and test predictions about the likelihood that the categories in a data set from one population will have the same frequencies in data collected from a different population of the same size
- predictions based on analysis of collected data:
- Most students in our class like kiwi. I believe that most students in the other Grade 1 class will also like kiwi.
- 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 will be colder, which usually means snow.
- Data can vary from one population to another.
- Data can be used to make predictions that are not based on personal feelings or opinions alone.
Note
- In order to do an accurate comparison between data sets in Grade 1, it is important for students to collect data from a same-sized population (e.g., same number of objects in a bin, days in a month, students in Grade 1).
Ask students to revisit a question for which they have already collected data from their classmates. Have them predict what they think the results will be if they ask the same question of students in another Grade 1 class. For example, a student might predict:
“Most students in our class have a dog as a pet. I believe that most students in the other Grade 1 class will also have a dog.”
Have students collect the new set of data and compare the result with their prediction.