Mathematics · Grade 4

Active learning ideas

Probability and Likelihood

Active learning builds intuition for probability, turning abstract chance into concrete experiences. Students physically test predictions, which strengthens their grasp of likelihood terms and connects outcomes to theoretical probabilities through immediate evidence.

• Ontario Curriculum Expectations
• Ontario Curriculum, Mathematics (2020), Grade 4, Number B1.1: read, represent, compose, and decompose whole numbers up to and including 10 000, using appropriate tools and strategies
• Ontario Curriculum, Mathematics (2020), Grade 4, Number B1.2: compare and order whole numbers up to and including 10 000, in various contexts
• Ontario Curriculum, Mathematics (2020), Grade 4, Number B1: demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Small Groups: Spinner Prediction Stations

Prepare spinners with 3-4 unequal sections labeled likely or unlikely. Groups predict outcomes, spin 30 times each, tally results on charts, and compare to predictions. Rotate spinners between groups for variety.

Differentiate between an event being likely and an event being certain.

Facilitation Tip

During Spinner Prediction Stations, circulate to ensure groups record initial predictions before spinning, linking their hypothesis to the spinner's section sizes.

What to look for

Give students a spinner with 4 equal sections labeled: Red, Blue, Green, Yellow. Ask them to write: 1. The likelihood of landing on Red. 2. The theoretical probability of landing on Blue (as a fraction). 3. One reason why repeating the spin 100 times might give a different result than spinning it 10 times.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 30 min · Pairs

Pairs: Coin Flip Trials

Partners predict heads/tails ratios, flip coins 50 times together, record on shared graphs. Switch roles for prediction and flipping. Discuss why results vary from predictions.

Analyze how the number of trials affects the closeness of results to predictions.

Facilitation Tip

In Coin Flip Trials, ask pairs to first predict how many heads they expect in 30 flips before they begin, then compare their result to the prediction.

What to look for

Present students with a scenario: 'You flip a fair coin 5 times and get Heads 4 times.' Ask: 'Is this result more likely or less likely than you would expect based on theoretical probability? Explain your thinking.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 35 min · Whole Class

Whole Class: Dice Roll Challenge

Class predicts sums from two dice rolls. Everyone rolls pairs 20 times, calls out results for teacher-tallied board. Analyze total frequencies against predictions as a group.

Justify the usefulness of probability for making decisions in games or business.

Facilitation Tip

During the Dice Roll Challenge, model tallying and analyzing data on the board after each round to highlight how class totals converge toward theoretical probabilities.

What to look for

Pose the question: 'Imagine you are choosing a team for a game. One student is very good at the game, and another student is still learning. How can understanding probability help you make a fair choice or a strategic choice? Discuss the difference.'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 25 min · Individual

Individual: Probability Game Design

Students design a spinner or card game with likely/unlikely events, write rules, predict wins. Test solo 20 times, note results, then share one insight with a partner.

Differentiate between an event being likely and an event being certain.

Facilitation Tip

For Probability Game Design, provide a checklist of required elements: clear rules, a fairness statement, and a data collection plan before students begin prototyping.

What to look for

Give students a spinner with 4 equal sections labeled: Red, Blue, Green, Yellow. Ask them to write: 1. The likelihood of landing on Red. 2. The theoretical probability of landing on Blue (as a fraction). 3. One reason why repeating the spin 100 times might give a different result than spinning it 10 times.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach likelihood by starting with hands-on experiments before abstract explanations. Avoid rushing to definitions; let students discover patterns through repeated trials. Research shows that students grasp probability best when they connect visual models (like spinners) to numerical outcomes and verbal descriptions. Emphasize the language of chance early and often to build a shared vocabulary.

Students will use precise language to describe likelihood and justify predictions with evidence from trials. They will compare experimental results to theoretical probabilities and explain how repeated trials refine accuracy.

---

Watch Out for These Misconceptions

• During Spinner Prediction Stations, watch for students assuming all spinner sections have the same chance regardless of size.

  Have students measure each section's angle or area and relate it to the number of spins landing there, then recalculate their predictions based on actual data before comparing to their original guess.

• During Coin Flip Trials, watch for students believing one trial or a small set determines the likelihood of heads or tails.

  Prompt pairs to graph cumulative results after every 10 flips, then ask them to explain how the graph changes and why more trials lead to results closer to 50% heads.

• During the Dice Roll Challenge, watch for students thinking a 'likely' outcome must happen every time.

  Use the class data to point out streaks of unlikely outcomes (like rolling sixes three times in a row) and discuss how these fit within the range of expected variability.

---

Methods used in this brief

• Stations Rotation