Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Trying Simple Chance Experiments

Active learning through chance experiments helps young students connect abstract probability concepts to tangible outcomes they can see and touch. When children physically flip coins or roll dice, they build foundational understanding that theoretical predictions and real results may not always match, fostering curiosity and critical thinking about randomness.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.1
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.2

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Pairs

Pairs Challenge: Coin Flip Marathon

Pairs predict heads or tails for 20 flips, then take turns tossing a coin and marking tallies on a shared chart. They count totals and calculate the fraction of heads, discussing if results match their one-half prediction. Pairs share class findings on the board.

What do you think will happen if you flip a coin ten times?

Facilitation Tip

During the Coin Flip Marathon, circulate and remind pairs to alternate who flips to ensure equal participation and keep the activity moving.

What to look for

Give each student a coin. Ask them to flip it 10 times and record the results using tally marks. Then, ask them to calculate the experimental probability of getting heads and write it as a fraction.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 35 min · Small Groups

Small Groups: Dice Roll Relay

Groups roll a die 30 times total, passing it relay-style, and tally even versus odd numbers. They compute relative frequency for even (theoretical three-sixths) and graph results. Groups compare graphs to spot class trends.

How can you record the results of a simple chance experiment using tally marks?

Facilitation Tip

For the Dice Roll Relay, place a timer at each station to encourage focus and transitions between turns.

What to look for

Pose the question: 'If you flip a coin 100 times, would you expect to get exactly 50 heads and 50 tails?' Facilitate a class discussion comparing their experimental results from shorter trials to this larger theoretical expectation, discussing why results might vary.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 40 min · Whole Class

Whole Class: Spinner Prediction Game

Create class spinners divided into two colors. Predict, spin 50 times as a group with a volunteer calling results, and update a large tally chart. Calculate and discuss experimental versus theoretical probabilities.

Can you compare what you expected to happen with what actually happened?

Facilitation Tip

In the Spinner Prediction Game, have students jot down their initial predictions before spinning to make their thinking visible.

What to look for

Provide students with a scenario: 'A spinner has 4 equal sections: red, blue, green, yellow. If you spin it 20 times, what is the theoretical probability of landing on red? What might be a possible experimental probability you observe?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 25 min · Individual

Individual: Bean Bag Chance Toss

Each student tosses a bean bag at a two-section target 15 times, tallies landings, and finds personal relative frequency. They add results to class data and compare individual to group outcomes.

What do you think will happen if you flip a coin ten times?

What to look for

Give each student a coin. Ask them to flip it 10 times and record the results using tally marks. Then, ask them to calculate the experimental probability of getting heads and write it as a fraction.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teachers should emphasize that probability is about patterns in the long run, not guarantees in short trials. Avoid rushing to conclusions about fairness or bias after small sets of data. Instead, encourage repeated trials and class-wide sharing to reveal how collective evidence aligns more closely with theory over time.

Students will confidently predict outcomes, conduct trials, record data with tally marks, and compare experimental results to theoretical probabilities. Their discussions will show growing awareness that chance variation is normal and that larger data sets bring results closer to expected values.

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Watch Out for These Misconceptions

• During the Coin Flip Marathon, watch for students who believe their group's 20 flips must show exactly 10 heads and 10 tails.

  After collecting all pairs’ tallies, guide students to combine their data on a class chart to show how the total results come closer to 50% heads, highlighting that variation is expected in small trials.

• During the Dice Roll Relay, watch for students who think rolling a '4' three times in a row means the die is unfair.

  Stop the relay briefly to discuss independence, using the tally sheet to show that each roll has the same chance regardless of past outcomes.

• During the Spinner Prediction Game, watch for students who claim the spinner lands on red exactly one-fourth of the time in every set of 20 spins.

  Have students compare their individual results to the theoretical 25% and then combine class data to demonstrate how experimental values fluctuate before stabilizing with more trials.

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Methods used in this brief

• Experiential Learning