Foundations of Mathematical Thinking · 2nd Year · Data and Chance · Summer Term

Exploring Chance: Likely and Unlikely Events

Students use the language of probability to describe the likelihood of simple events.

• NCCA Curriculum Specifications
• NCCA: Primary - Data
• NCCA: Primary - Problem solving

About This Topic

Exploring Chance introduces students to probability language such as certain, likely, unlikely, and impossible to describe simple events. In this topic, students consider questions like the likelihood of snow in July in Ireland, events that will definitely happen today, or rolling a 7 on a standard die. They practice sorting events into categories and justifying their choices with reasons tied to real-world observations.

This content fits within the Data and Chance strand of the NCCA Primary curriculum, supporting problem-solving standards by encouraging students to predict outcomes and reflect on evidence. It builds foundational skills for handling uncertainty, which appear later in data handling and statistics. Students connect probability to personal experiences, such as coin tosses or weather patterns, fostering logical reasoning from grade two onwards.

Active learning suits this topic well because probability concepts feel abstract at first. When students physically spin custom spinners, roll dice repeatedly, or vote on event likelihoods in pairs, they gather their own data to test predictions. These experiences make chance visible and help students internalize language through trial and discussion.

Key Questions

1. Is it likely or unlikely that it will snow in July in Ireland?
2. Can you tell me something that will definitely happen today?
3. Is it possible to roll a 7 on a dice with numbers 1 to 6?

Learning Objectives

• Classify everyday events as certain, likely, unlikely, or impossible based on given criteria.
• Explain the reasoning behind classifying an event's likelihood using precise probability language.
• Compare the probability of two different events and justify which is more or less likely.
• Predict the outcome of a simple random event, such as a coin toss or dice roll, and describe its likelihood.

Before You Start

Sorting and Classifying Objects

Why: Students need experience grouping items based on shared characteristics to understand classifying events by likelihood.

Identifying Patterns

Why: Recognizing patterns helps students make predictions about future events, a foundational skill for understanding probability.

Key Vocabulary

Likely	An event that has a high chance of happening. For example, it is likely to rain if the sky is full of dark clouds.
Unlikely	An event that has a low chance of happening. For example, it is unlikely to see a polar bear in the Sahara Desert.
Certain	An event that is guaranteed to happen. For example, the sun is certain to rise tomorrow.
Impossible	An event that cannot happen. For example, it is impossible to jump over the moon.

Watch Out for These Misconceptions

Common Misconception

All possible events are equally likely.

What to Teach Instead

Students often assume any conceivable event has the same chance, like confusing rolling a 1 or 6 on a die. Hands-on repeated trials with dice or spinners provide data that reveals true likelihoods. Pair discussions help them articulate differences between possible and probable.

Common Misconception

Unlikely events never happen.

What to Teach Instead

Children may view unlikely as impossible, such as snow in summer. Group voting and tracking real events like lottery draws show unlikely outcomes occur sometimes. Active simulations build nuance through evidence from multiple trials.

Common Misconception

Personal luck affects chance events.

What to Teach Instead

Some believe they control outcomes with 'good luck'. Class relays with shared dice rolls demonstrate randomness persists regardless of who rolls. Collaborative tallying shifts focus to data over superstition.

Active Learning Ideas

Spinner Sorting: Event Probability Spinners

Provide spinners divided into unequal sections labeled certain, likely, unlikely, impossible. Students spin for given events like 'it rains in Ireland tomorrow' and sort cards with events into matching sections based on results. Pairs discuss and record why an event fits a category. Conclude with class sharing of surprising outcomes.

35 min·Pairs

Dice Prediction Relay: Likely Rolls

Teams line up and predict if numbers 1-6 are likely on a die, then roll 10 times per team member, tallying results on a shared chart. Rotate roles for predictor, roller, and recorder. Groups compare tallies to refine predictions about impossible rolls like 7.

45 min·Small Groups

Weather Chance Circle: Irish Events

Sit in a circle; each student shares a July event like 'snow falls' and class votes likely or unlikely with thumbs up or down. Tally votes on a board and discuss evidence from Irish weather knowledge. Extend by creating a class probability poster.

30 min·Whole Class

Coin Flip Challenges: Personal Predictions

Students predict outcomes for 20 coin flips, marking likely heads or tails on worksheets. They flip individually, then pair to compare data and adjust predictions. Share class averages to see patterns emerge from chance.

25 min·Individual

Real-World Connections

• Weather forecasters use probability to describe the likelihood of rain, sunshine, or storms, helping people plan outdoor activities or travel.
• Sports analysts discuss the likelihood of a team winning a match based on past performance and current conditions, influencing fan expectations and betting.
• Manufacturers consider the likelihood of product defects during quality control, aiming to minimize unlikely but possible flaws before items reach consumers.

Assessment Ideas

Quick Check

Present students with cards showing different scenarios (e.g., 'A cat barking', 'The next person you meet is wearing blue', 'Tomorrow's date'). Ask students to hold up a card (or point to a poster) labeled 'Certain', 'Likely', 'Unlikely', 'Impossible' that best describes each scenario and briefly explain their choice.

Discussion Prompt

Pose the question: 'Is it more likely to flip heads or tails on a fair coin?' Ask students to discuss in pairs, using the vocabulary learned. Then, facilitate a whole-class discussion, asking students to justify their answers and explain why the outcomes are equally likely.

Exit Ticket

Give each student a slip of paper. Ask them to write down one event that is 'certain' and one event that is 'impossible' in their own lives. They should then write one sentence explaining why each event fits its category.

Frequently Asked Questions

How do I introduce probability language like likely and unlikely to second years?

Start with familiar Irish contexts, such as 'snow in July is unlikely' or 'sunrise tomorrow is certain'. Use visuals like a probability line from impossible to certain. Model language by sorting event cards together, then let students practice in pairs with justifications. Reinforce through daily weather chats to build fluency over time.

What hands-on activities work best for exploring chance events?

Custom spinners, dice relays, and coin flip challenges engage students actively. These let them predict, test, and tally results, turning abstract terms into observable patterns. Group sharing refines understanding as they defend choices with data, aligning with NCCA problem-solving goals.

How can active learning help students grasp likely and unlikely events?

Active approaches like spinner stations or class voting make chance tangible by generating real data. Students predict, experiment, and discuss discrepancies, which counters misconceptions about equal likelihoods. This builds confidence in probability language through evidence, not rote memory, and supports collaborative problem-solving in the curriculum.

What are common errors in teaching chance to primary students?

Errors include equating possible with likely or seeing unlikely as impossible. Address with repeated trials and peer talks to show data patterns. Link to Irish examples like summer rain to ground concepts, ensuring students use precise terms in context.