Mathematics · Junior Infants

Active learning ideas

Compound Events: Independent Events

Active learning transforms abstract probability concepts into tangible experiences. Children need repeated, hands-on trials to see how independent events behave over time. Concrete materials like coins, spinners, and dice make these ideas visible and memorable for young learners.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - P.1.5

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Simulation Game
• 30 min · Pairs

Simulation Game: Double Coin Flip Races

Pairs flip two coins 20 times, tally heads-heads, heads-tails, and so on. Predict the most common outcome first, then compare class tallies on a shared board. Discuss why heads-heads is rarest.

Differentiate between independent and dependent events.

Facilitation Tip

During Double Coin Flip Races, circulate and ask pairs to explain why the second flip does not depend on the first before they start each round.

What to look for

Present students with two scenarios: (1) Rolling a die and then flipping a coin. (2) Drawing two marbles from a bag without putting the first one back. Ask students to circle 'Independent' or 'Dependent' for each scenario and explain their choice in one sentence.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Stations Rotation
• 35 min · Small Groups

Stations Rotation: Color Spinner Duos

Set up stations with two spinners (red/blue). Small groups spin both, record outcomes on sticky notes, and rotate. Tally class data to find two-reds probability.

Explain how to calculate the probability of two independent events both occurring.

Facilitation Tip

At Color Spinner Duos, model how to mark tally marks on the chart before students begin spinning to avoid confusion.

What to look for

Give each student two blank spinners, each with 4 equal sections labeled Red, Blue, Green, Yellow. Ask them to: 1. Write the probability of spinning Red on the first spinner. 2. Write the probability of spinning Red on both spinners. 3. Explain how they found the answer for the second question.

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

Activity 03

• Outdoor Investigation Session
• 25 min · Whole Class

Whole Class: Dice Roll Chains

Teacher rolls two dice repeatedly; class predicts and shouts outcomes like two 3s. Record on floor chart, count trials for 1/36 chance. Children take turns rolling.

Construct a scenario involving two independent events and calculate their combined probability.

Facilitation Tip

During Dice Roll Chains, demonstrate how to hold the die steady so the roll is fair and the results trustworthy.

What to look for

Pose the question: 'Imagine you have two separate bags of colored blocks, one with red and blue, and another with yellow and green. If you pick one block from each bag, are the events independent? How would you figure out the chance of picking a red block and then a yellow block?' Facilitate a class discussion to guide students toward multiplying probabilities.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 20 min · Pairs

Pairs: Bag Draw Doubles

Each pair has a bag with 3 red, 3 blue beads; draw one with replacement, record twice. Repeat 15 times, discuss why probabilities stay the same each draw.

Differentiate between independent and dependent events.

Facilitation Tip

With Bag Draw Doubles, remind students to replace the first block before the second draw to keep events independent.

What to look for

Present students with two scenarios: (1) Rolling a die and then flipping a coin. (2) Drawing two marbles from a bag without putting the first one back. Ask students to circle 'Independent' or 'Dependent' for each scenario and explain their choice in one sentence.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teachers should focus on repetition and discussion rather than rushing to formal rules. Young children learn probability through pattern recognition in small group trials, not abstract formulas. Avoid correcting too early—instead, let students notice discrepancies between predictions and results themselves. Research shows that concrete, repeated experiences build lasting understanding of independence better than verbal explanations alone.

Students will confidently identify independent events, predict simple probabilities, and explain why outcomes remain unchanged across trials. They will use tally charts to record results and compare predictions to actual outcomes during group work.

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Watch Out for These Misconceptions

• During Double Coin Flip Races, watch for students who think a tails flip makes heads 'due' next. Have them record the next flip result on a fresh chart to show chances stay 50/50 each time.

  During Double Coin Flip Races, pause the game after two flips and ask, 'Was the second flip affected by the first? How do you know?' Use the tally chart to point out equal totals of heads and tails in the group.

• During Color Spinner Duos, watch for students who assume every color pair is equally likely. Have them spin until they see a rare outcome like two reds to challenge this idea.

  During Color Spinner Duos, ask students to predict the probability of two reds before they start and compare it to their tally results after 10 spins. Highlight when their prediction matches or differs from the actual count.

• During Bag Draw Doubles, watch for students who treat two draws as one combined event with four total blocks. Ask them to recount the original numbers in each bag to clarify independence.

  During Bag Draw Doubles, have students draw twice and tally each outcome separately before discussing probability. Ask, 'Does the first draw change how many blocks are left in the bag for the second draw?'

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Methods used in this brief

• Simulation Game
• Stations Rotation
• Outdoor Investigation Session