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.

• Grade 4
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Classify simple events as impossible, unlikely, as likely as not, likely, or certain based on experimental outcomes.
2. Analyze how increasing the number of trials in a probability experiment affects the experimental probability's closeness to the theoretical probability.
3. Compare the theoretical probability of an event (e.g., rolling a 3 on a die) with the experimental probability derived from multiple trials.
4. Justify the usefulness of probability concepts for making predictions in simple games or scenarios.

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

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.

What to Expect

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

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Spinner Prediction Stations, give students a spinner with 4 unequal sections (e.g., 1/2, 1/4, 1/8, 1/8) labeled A, B, C, D. Ask: 1. Which section is most likely to land on? 2. What is the probability of landing on C as a fraction? 3. Explain why spinning this spinner 50 times might not give exactly 12 or 13 spins on C.

Quick Check

During Coin Flip Trials, present the scenario: 'You flip a fair coin 8 times and get tails 6 times.' Ask students to explain whether this result is more or less likely than expected, referencing their class data or theoretical probability.

Discussion Prompt

After Probability Game Design, ask students: 'Your game uses a spinner with two colors, red and blue. One color covers 75% of the spinner. How can understanding likelihood help you decide if the game is fair or strategic when choosing teams? Discuss the difference between fairness and strategy in your response.'

Extensions & Scaffolding

• Challenge students to design a spinner with three unequal sections where landing on red is twice as likely as landing on blue or green combined.
• Scaffolding: Provide a partially completed data table for students to fill in during Coin Flip Trials if they struggle with tallying or counting.
• Deeper exploration: Ask students to analyze why a dice roll might not match theoretical probability after 20 rolls, then test with 200 rolls to observe convergence.

Key Vocabulary

Probability	The measure of how likely an event is to occur, often expressed as a number between 0 and 1.
Likelihood	A description of how probable an event is, using words like impossible, unlikely, as likely as not, likely, or certain.
Theoretical Probability	The probability of an event occurring based on mathematical reasoning and the possible outcomes, not on actual experiments.
Experimental Probability	The probability of an event occurring based on the results of an actual experiment or a series of trials.
Trials	The number of times an experiment or activity is repeated to collect data.