Mathematics · Grade 5

Active learning ideas

The Language of Likelihood

Let's become smart guessers! This topic explores how we can use math to predict the future, moving beyond simple luck to understand the language of likelihood.

• Ontario Curriculum Expectations
• Ontario Curriculum: Grade 5 Mathematics - Data - D2. Probability: Describe the likelihood of events happening using mathematical language.

• 30–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Four Corners
• 45 min · Pairs

Spinner Challenge

Students use paper clips and pencils to create spinners with unequal sections (e.g., 1/2 red, 1/4 blue, 1/4 yellow). They first calculate the theoretical probability of landing on each colour and then conduct 50 spins to find the experimental probability, comparing the two sets of results.

Identify an event that is impossible, unlikely, has an even chance, is likely, and is certain to happen today.

Facilitation Tip

Encourage students to pool their data with another pair to see how a larger number of trials affects the results.

What to look for

Exit Ticket: Show students a picture of a spinner with unequal sections. Ask them to identify which colour is most likely to be spun and to write the probability of landing on that colour as a fraction.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Activity 02

• Four Corners
• 30 min · Small Groups

Mystery Bag Predictions

Prepare several opaque bags with a known quantity of different coloured cubes or counters. Students calculate the theoretical probability of drawing each colour from a bag, then conduct 20 trials (replacing the cube each time) to test their prediction.

Explain why the chance of rolling a 7 on a standard six-sided die is impossible.

Facilitation Tip

After the activity, reveal the contents of a new bag and have groups predict which colour will be drawn most often in 10 trials.

What to look for

Design a Game: Students create a simple game of chance using a die or a spinner. They must write out the rules, calculate the theoretical probability of winning, and then have classmates play the game to determine the experimental probability.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

Activity 03

• Four Corners
• 40 min · Individual

Dice Roll Tally

Students predict how many times each number will be rolled if they roll a standard six-sided die 60 times. They then perform the experiment, tally the results, and write a reflection comparing their prediction to the actual outcome.

Compare the likelihood of picking a red marble from a bag with 5 red and 1 blue marble versus a bag with 1 red and 5 blue marbles.

Facilitation Tip

Use a class-wide chart to compile everyone's results, demonstrating how the distribution becomes more even with hundreds of trials.

What to look for

Confidence Checklist: Students use a checklist to rate their understanding of key vocabulary and their ability to explain the difference between theoretical and experimental probability to a friend.

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Social Awareness

A few notes on teaching this unit

Begin with concrete, hands-on activities using dice, coins, and spinners before moving to abstract calculations. Explicitly define and model the use of key vocabulary. Use a think-aloud strategy to show how you would analyze a situation, determine the theoretical probability, and then compare it to experimental results, emphasizing that differences are normal.

Students will be able to calculate the mathematical chance of an event happening and test their predictions by conducting their own fun experiments.

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Watch Out for These Misconceptions

• The gambler's fallacy: If a coin lands on heads five times in a row, it is more likely to land on tails next.

  Each coin flip is an independent event. The coin has no memory of past results, so the probability of getting heads or tails is always 1/2 for a fair coin.

• All outcomes are equally likely, regardless of the setup. For example, in a bag with 7 green and 3 blue candies, the chance of picking either colour is the same.

  Probability depends on the number of favourable outcomes compared to the total number of outcomes. Since there are more green candies, the probability of picking a green one is higher (7/10) than picking a blue one (3/10).

• Experimental results must exactly match the theoretical probability.

  Theoretical probability describes what is expected to happen over a very large number of trials. In a small experiment, results can vary significantly due to chance.

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Methods used in this brief

• Four Corners