Grade 7: Probability

Warm up with a few quick probability warm-ups on the board while the class settles, so every child starts thinking about the skill.

The sample space is the full list of possible outcomes of a chance event. This unit covers listing a sample space, finding probabilities as fractions from it, and comparing a real experiment's results with what theory predicts. Model the method clearly, thinking aloud:

• Start by listing the full sample space for a simple event (a die, a spinner), counting the total number of equally likely outcomes.
• Find a probability as a fraction: favourable outcomes divided by the total in the sample space, simplifying where possible.
• Run (or simulate) a real experiment with many trials, and calculate the relative frequency of an outcome from the actual results.
• Compare the relative frequency with the theoretical probability, discussing why they are close but not necessarily identical.
• Increase the number of trials and observe that the relative frequency usually settles closer to the theoretical probability.

Work this through step by step on the board, then have the class talk you through a second one.

• A fair 6-sided die is rolled once
• Sample space: {1, 2, 3, 4, 5, 6}, 6 equally likely outcomes
• P(rolling an even number) = 3/6 = 1/2

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Listing an incomplete sample space, missing possible outcomes.
• Assuming all listed outcomes are equally likely without checking (e.g. a weighted spinner).
• Expecting an experiment's relative frequency to exactly match the theoretical probability every time.
• Not simplifying a probability fraction to its lowest terms.

Pull the class back together. Ask one child to explain probability in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.